REAL ESTATE FINANCE AND INVESTMENTS 17TH INTERNATIONAL EDITION BY JEFFREY FISHER, WILLIAM B BRUEGGEMAN (CHAPTER 1_23) SOLUTIONS MANUAL Solutions to Questions—Chapter 1 An Introduction to Real estate Investment: Legal Concepts Question 1-1 What is the difference between real property and personal property? Real property refers to the ownership rights associated with realty. Realty refers to land and all things permanently attached. Personal property refers to ownership rights associated with personalty. Personalty are all things, tangible, intangible that are movable. This includes all things that are not realty. Question 1-2 What is meant by an estate? Estate is used to denote a possessory or potentially possessory interest in real estate. However, not all interests in real property are estates. Ownership can be quite different from possession and a variety of legal factors affect the ownership rights associated with real estate. The economic benefits expected by lenders, investors, and other parties in a real estate transaction are affected by these legal factors. Question 1-3 How can a leased fee estate have a value that could be transferred to another party? The original fee owner can give up some property rights to a lessee. The value of the leased fee estate will depend on the amount of lease payments expected during the term of the lease plus the value of the property when the lease terminates, and the original owner receives the reversionary interest. Question 1-4 What are title records? What is an abstract of title? Title records (sometimes referred to as deeds and conveyances records and/or real property records) are created and maintained usually at the county level. These records identify all properties in a county, including location, present ownership and any liens or encumbrances affecting each property. These records are critical to investors who want to identify the owner of specific tracts or land, existing buildings, etc. These records are also important because they contain evidence of encumbrances such as mortgage liens, tax liens (to be covered in later chapters), etc. Example: a prospective investor sees a vacant tract of land that he is interested in purchasing. Because there is no signage or any improvements on the land, how can the land owner be identified and contacted? By going to the county records office (deeds and conveyancers department) the investor can use the address to locate a property (usually in plat books), then the current owner. These records are used to link a precise property to its owner. At some point, if this investor continues to be interested in purchasing the land, he will likely retain an attorney or abstractor to do a title search and abstract of title. The latter is done to not only 18-1
identify the current owner but to trace all previous owners with commentary on the likelihood of other parties who may ownership rights and /or interests in the tract of land. Question 1-5 What is a deed? How is it different from the title? The deed is a document usually created by the owner of a property containing the property legal I.D. and location in addition to any improvements that exist on the property. It also describes the extent to which the seller warrants that he is the owner of the property and has the right to convey ownership. A deed is used to convey the title from one person (the grantor) to another (the regrantee) by means of a written instrument. The term ―title‖ is an abstract term frequently used to link an individual or entity who owns property to the property itself. When a person has ―title,‖ he is said to have all the elements, including the documents, records, and acts, that prove ownership. Title establishes the quantity of rights in real estate being conveyed from seller to It differs from title because title provides evidence of ownership based on the collective records that exist pertaining to a property. Question 1-6 What is meant by a title record? Why are these records so important? The title record refers to records on file, usually at the county level, that help to specify tracts of real estate and determine if a seller has the right to convey ownership of such real property. These records are the most important sources of events affecting real estate ownership over time and are usually reviewed when trying to identify the ―quality‖ of title that investors will receive if they purchase. After a review of these records (usually by an attorney), if in his opinion, they are complete, he will indicate that the seller has ownership and title to the property. Most of the instruments that affect title to real estate are recorded, in accordance with the recording acts of the various states, at what is typically called the county recorder’s office.
Question 1-7 What is a future estate? Give an example? We think of most real estate transactions as acquiring ownership at the present time. However, ownership can also occur at a later time, say after the current owner dies. The person who becomes the owner at that time is said to be a ―remainder‖ estate. Future estates include a reversion and remainder. A reversion results in the state reverting back to the original possessor whereas the remainder results in a third-party obtaining possession at some point in the future.
Question 1-8 Name the three general methods of title assurance and briefly describe each. Which would you recommend to a friend purchasing real estate? Why? General Warranty Deed - the grantor warrants that the title he/she conveys to the property is free and clear of all encumbrances, other than those that are specifically listed in the deed. Special Warranty Deed - makes the same warranties as a general warranty deed except that it limits their application to defects and encumbrances which occurred only while the grantor held title to the property. Quitclaim Deed - offers the grantee the least protection in that it imply conveys to the grantee whatever rights,, interests,, and title that the grantor may have in the property. No warranties are made about the nature of these rights and interests or of the quality of the grantor’s title to the property. 18-2
Would recommend the General Warranty Deed, because it offers the most comprehensive warranties about the quality of the title. Question 1-9 Would it be legal for you to give a quitclaim deed for the Statue of Liberty to your friend? Yes, the quitclaim deed simply says that the grantor ―quits‖ whatever claim he has in the property (which may well be none) in favor of the grantee.
Solutions to Questions—Chapter 2 Financing: Notes and Mortgages Question 2-1 Distinguish between a mortgage and a note. A note admits the debt and generally makes the borrower personally liable for the obligation. A mortgage is usually a separate document which pledges the designated property as security for the debt. Question 2-2 What does it mean when a lender accelerates on a note? What is meant by forbearance? The acceleration clause gives the lender the right or option to demand the loan balance owed if a default occurs. Forbearance by the lender allows the borrower time to cure a deficiency without the lender giving up the right to foreclose at a future time. Question 2-3 Can borrowers pay off, part or all, of loans anytime that they desire? No. In general, prepayment is a privilege not a right. In cases of residential/consumer loans made by federally related lenders, this option is usually provided to borrowers. In commercial real estate loans it is not. Question 2-4 What does non-recourse financing mean? The borrower is not personally liable on the note. The lender may look only to the property (security) to satisfy the loan in the event of default. Question 2-5 What does assignment mean and why would a lender want to assign a mortgage loan? Assignment gives the lender the right to sell or exchange a mortgage loan to another party without the approval of the borrower. Question 2-6 What is meant by a “purchase money“ mortgage loan? When could a loan not be a purchase money mortgage? Purchase money means funds from the loan will be used to purchase a property. It will not provide funds for other uses such as could be the case with a refinancing. 18-3
Question 2-7 What does default mean? Does it occur only when borrowers fail to make scheduled loan payments? Default means that the borrower has failed to (1) make scheduled loan payments or (2) violated on a provision in the note or mortgage. Question 2-8 When might a borrower want to have another party assume his liability under mortgage loan? If the loan was made with a favorable interest rate, the seller of the property may want to include this low rate loan as an additional incentive to sell the property. Question 2-9 What does deficiency judgment mean? If default occurs and the property is sold, if the dollars from the sale is not enough to pay off the loan balance, the borrower is liable for the difference. Question 2-10 What is a land contract? An agreement between a buyer and seller to purchase and sell real estate. However, passage of title is usually deferred until some future date or deferred until some event or condition occurs (e.g., Payment of money, rent, etc.).
18-4
Question 2-11 How can mechanics‟ liens achieve priority over first mortgages that were recorded prior to the mechanics‟ lien? Mechanics’ liens are permitted to be recorded after the fact. State laws generally give contractors, laborers, or suppliers of materials a certain period of time following the completion of work or delivery of materials during which to file their lien. When the lien is filed it relates back and takes priority over all liens filed after the time when materials were first delivered or work was first performed on real estate. Question 2-12 Name possible mortgageable interests in real estate and comment on their risk as collateral to lenders. Fee simple estates, life estates, estates for years, remainders, reversions, leasehold interests, and options. Fee Simple estate - represents the most complete form of ownership of real estate. The holder is free to divide, sell, lease, or borrow against them as he/she wishes. Little risk to lenders because the owner completely owns all rights to the real estate. Life estate - is a freehold estate that lasts only as long as the life of the owner of the estate or the life of some other person. Because of the uncertainty surrounding the duration of the life estate, its marketability and value as collateral are severely limited. Remainder - exists when the grantor of a present estate with less ownership rights than his/her own conveys to a third person the reversionary interest he/she or his/hers heirs would otherwise have in the property upon termination of the grantee’s estate. Reversion - exists when the holder of an estate in land (the grantor) conveys to another person (a grantee) a present estate in the property that has less ownership rights than his/her own estate and retains for himself/herself or his/her heirs the right to take back, at some time in the future, the full estate which he/she enjoyed before the conveyance. A reversionary interest can be sold or mortgaged because it is an actual interest in the property. Question 2-13 What is meant by mortgage foreclosure, and what alternatives are there to such action? Foreclosure involves the sale of property by the courts to satisfy the unpaid debt. Alternatives: 1. Restructuring the mortgage loan 2. Transfer of the mortgage to a new owner 3. Voluntary conveyance of the title to the mortgagee 4. A ―friendly‖ foreclosure 5. A prepackaged bankruptcy Question 2-14 Explain the difference between a buyer assuming the mortgage and taking title “subject to” the mortgage. If the purchaser acquires the property ―subject to‖ the existing debt, he does not acquire any personal liability for the debt. When a mortgage is assumed the original borrower may be released from any obligations to the lender. Question 2-15 What dangers are encountered by mortgagees and unreleased mortgagors when property is sold “subject to” a mortgage? 18-5
The mortgagor will be responsible if the person acquiring the property subject to the mortgage defaults. In turn, if the original mortgagor then defaults, the bank will have to foreclose on the property which may not be worth what is left to pay on the mortgage. Question 2-16 What is the difference between the equity of redemption and statutory redemption? The equity of redemption is the right of a mortgagor to redeem his/her property from default during the period from the time of default until foreclosure proceedings are begun. Statutory redemption is the right to redeem after foreclosure.
18-6
Question 2-17 What special advantages does a mortgagee have in bidding at the foreclosure sale where the mortgagee is the foreclosing party? How much will the mortgagee normally bid at the sale? The mortgagee can use his/her claims as a medium of exchange in the purchase, except for costs, which must be paid in cash. Others must pay cash for their purchases or by obtaining a new loan. Lenders will normally bid the full amount of their claim only where it is less than or equal to the market value of the security less foreclosure, resale, and holding costs. Question 2-18 Is a foreclosure sale sometimes desirable or even necessary when the mortgagor is willing to give a voluntary deed? The mortgagee may find it necessary to foreclose instead of taking a voluntary conveyance, because the title conveyed is subject to junior liens. Foreclosure provides the mortgagee with a lawful method of becoming free from the liens of junior claimants.
Question 2-19 What are the risks to the lender if a borrower declares bankruptcy? The probability of default or bankruptcy by a borrower and the legal alternatives available to each party affect the expected return to lender from the loan. Lenders may find that their security is tied up for years during the reorganization of the debtor’s financial affairs and that they are unable to foreclose on their liens where such a foreclosure would interfere with the debtor’s plan of reorganization. Lastly, lenders may not be able to accelerate balances or raise interest rates because borrowers have the right to cure default in bankruptcy and reinstate the mortgage.
Question 2-20 What is a deficiency judgment and how is its value to a lender affected by the Bankruptcy Code? A deficiency judgment is any deficit remaining after a foreclosure and subsequent sale of a property. Unless the mortgagor owns other real estate, deficiency judgments are unsecured claims and take their place alongside other debts of the mortgagor. Unlike the mortgage from which such judgment springs, the latter gives the holder no right of preference against any of the non-real estate assets of the debtor. Therefore, a holder of a deficiency judgment has the same rights to a debtor’s nonexempt assets and is affected by the Bankruptcy Code in the same manner as any holder of an unsecured loan.
Solutions to Problems—Chapter 2 Financing: Notes and Mortgages Problem 2-1 Jones only has the right to prepay the loan if there is a prepayment clause in the loan agreement that provides for early payment. Otherwise the lender has the right to collect the full amount of interest specified in the original loan agreement. Furthermore, if there is a prepayment clause, it may provide for a penalty if some or all of the loan is prepaid. Problem 2-2 Generally, in addition to the $80,000 first lien, the lender also has first lien on any improvements made on land serving as security for the mortgage loan under the initial mortgage terms (see: after acquired 18-7
property clause). In other words, depending provisions contained in the existing mortgage document, ABC Bank also probably has a first lien on the new building constructed by Mr. Smith, even though Mr. Smith built the building with his own funds. Whether Duce Bank is willing to provide $16,000 in new financing may be problematic at this point. Mr. Smith should have approached Duce Bank before constructing a new building on land serving as security for the initial mortgage loan. Problem 2-3 Mrs. Brown has probably violated a covenant in the mortgage agreement (see: preservation and maintenance of the property) with ABC Bank by destroying part of the security held by ABC Bank. In other words, the land and building are part of the realty serving as security for the mortgage loan. By tearing down the building, she has, in essence, destroyed some of the security. The lender may give her notice that she has violated this covenant and is in default and call the remaining loan balance due immediately. Mrs. Brown should have notified the lender prior to the tear down. Let’s hope that (1) the total value of the proposed new project far exceeds the outstanding loan balance, plus the cost of any new improvements and (2) that ABC Bank can be persuaded to finance the new project. Problem 2-4 (a) In the case of a land contract (contract for future deed) essentially Mr. Investor is contracting to deliver title to buyer of the property at the end of 5 years. Under a purchase money mortgage, however, the buyer takes title at the time of sale. Holding all else constant, Mr. Investor must evaluate the risk of the buyer defaulting, during the next 5 years under each alternative. Under the land contract, since the seller retains title, upon default, the buyer may have to vacate the property and because the seller has title, the seller may be free to sell the property again. Under a purchase money mortgage, depending on the state where the property is located, the seller will have to reacquire title through some type of foreclosure procedure. In many states, since a land contract does not convey title, Mr. Investor may not have to expend as much time and money to reacquire possession of the property as would be the case with a purchase money mortgage. (b) In this case, since the property value has increased by $10,000 at the time of default, things may be more complicated. In some states, even under a contract for deed, the buyer may now have an ―equitable interest‖ which must be satisfied before the seller can re-sell or even refinance a property. Things may become even more complicated, if under the land contract, the buyer has made improvements to the property prior to default. In this case, the buyer has expended funds to make improvements to a property that he does not yet own. Clearly, when contracting for future deed, both the buyer and seller should undertake a careful review of relevant state law. Solutions to Questions—Chapter 3 The Interest Factor in Financing Question 3-1 What is the essential concept in understanding compound interest? The concept of earning interest on interest is the essential idea that must be understood in the compounding process and is the cornerstone of all financial tables and concepts in the mathematics of finance. Question 3-2 How are the interest factors (IFs) Exhibit 3-3 developed? How may financial calculators be used to calculate IFs in Exhibit 3-3? 18-8
Computed from the general formula for compounding for monthly compounding for various combinations of ―i‖ and years. FV = PV × (1+i)n. Calculators can be used by entering $ 1 for PV, the desired values for n and i and solving for FV. Question 3-3 What general rule can be developed concerning maximum values and compounding intervals within a year? What is an equivalent annual yield? Whenever the nominal annual interest rates offered on two investments are equal, the investment with the more frequent compounding interval within the year will always result in a higher effective annual yield. An equivalent annual yield is a single, annualized discount rate that captures the effects of compounding (and if applicable, interest rate changes). Question 3-4 What does the time value of money (TVM) mean? Time value simply means that if an investor is offered the choice between receiving $1 today or receiving $1 in the future, the proper choice will always be to receive the $1 today, because that $1 can be invested in some opportunity that will earn interest. Present value introduces the problem of knowing the future cash receipts for an investment and trying to determine how much should be paid for the investment at present. When determining how much should be paid today for an investment that is expected to produce income in the future, we must apply an adjustment called discounting to income received in the future to reflect the time value of money. Question 3-5 How does discounting, as used in determining present value, relate to compounding, as used in determining future value? How would present value ever be used? The discounting process is a process that is the opposite of compounding. To find the present value of any investment is simply to compound in a ―reverse‖ sense. This is done by taking the reciprocal of the interest factor for the compound value of $1 at the interest rate, multiplying it by the future value of the investment to find its present value. Present value is used to find how much should be paid for a particular investment with a certain future value at a given interest rate. Question 3-6 What are the interest factors (IFs) in Exhibit 3-9? How are they developed? How may financial calculators be used to calculate IFs in Exhibit 3-9? Compound interest factors for the accumulation of $1 per period, e.g., $1 × [1 + (1+i) + (1+i)2 …] etc. Calculators may be used by entering $ 1 values for PMT, entering the desired values for n and i then solving for FV.
18-9
Question 3-7 What is an annuity? How is it defined? What is the difference between an ordinary annuity and an annuity due? An annuity is a series of equal deposits or payments. An ordinary annuity assumes payments or receipts occur at the end of a period. An annuity due assumes deposits or payments are made at the beginning of the period. Question 3-8 How must one discount a series of uneven receipts to find PV? Each periodic cash receipt or payment must be discounted individually then summed to obtain present value. That is: PV= CF1 (1/1 + i)1 + CF2 (1/1+ i)2 ….+ CFn (1/1 + i)n where CF is cash inflow and i equals the discount rate. Question 3-9 What is the sinking-fund factor? How and why is it used? A sinking-fund factor is the reciprocal of interest factors for compounding annuities. These factors are used to determine the amount of each payment in a series needed to accumulate a specified sum at a given time. To this end, the specified sum is multiplied by the sinking-fund factor. Question 3-10 What is an internal rate of return? How is it used? How does it relate to the concept of compound interest? The internal rate of return integrates the concepts of compounding and present value. It represents a way of measuring a return on investment over the entire investment period, expressed as a compound rate of interest. It tells the investor what compound interest rate the return on an investment being considered is equivalent to.
18-10
Solutions to Problems—Chapter 3 The Interest Factor in Financing Problem 3-1 a) Future Value = = = b)
FV(n,i,PV,PMT) FV (7yrs, 6%, $12,000, 0) $18,044 (annual compounding)
Future Value = = =
FV(n,i,PV,PMT) FV (28 quarters, 9% ÷ 4, $12,000, 0) $22,375 (quarterly compounding)
c) Equivalent annual yield: (consider one year only) Future Value of (a) = FV(n,i,PV,PMT) = FV (1yr, 6%, $12,000, 0) = $12,720 ($12,720 - $12,000) / $12,000 = 6.00% effective annual yield Future Value of (b) = = ($13,117 - $12,000) / $12,000 =
= FV(n,i,PV,PMT) FV (1yr, 9%, $12,000, 0) $13,117 9.31% effective annual yield
Alternative (b) is better because of its higher effective annual yield. Problem 3-2 Investment A: 6% compounded monthly Future Value of A = =
= FV(n,i,PV,PMT) FV (12 mos., 6% ÷ 12, $25,000, 0) $26,542 (monthly compounding)
Investment B: 7% compounded annually Future Value of B = =
= FV(n,i,PV,PMT) FV (1yr, 7%, $25,000, 0) $26,750 (annual compounding)
Investment B should be chosen over A. Investment B pays 7% compounded annually and is the better choice because it provides the greater future value. Problem 3-3 Find the future value of 24 deposits of $5,000 made at the end of each 6 months. Deposits will earn an annual rate of 8.0%, compounded semi-annually. Future Value
= = =
FV(n,i,PV,PMT) FV (24 periods, 8% ÷ 2, 0, $5,000) $195,413 18-11
Note: Total cash deposits are $5,000 × 24 = $120,000. Total interest equals $75,413 or ($195,413 $120,000). The $120,000 represents the return of capital (initial principal) while the $75,413 represents the interest earned on the capital contributions.
Find the future value of 24 beginning-of-period payments of $5,000 at an annual rate of 8.0%, compounded semi-annually based on an annuity due. Future Value
=
$195,413 × (1.04) = $203,230
Note: If the payments are made at the beginning of each period, each payment has earned an additional 4% interest (8% / 12). Therefore, we can multiply the answer above for the payments at the end of each period by 1.04 to get the future value if payments are at the beginning of each period.
Problem 3-4 Find the future value of quarterly payments of $1,250 for four years, each earning an interest rate of 10 percent annually, compounded quarterly. Future Value
= =
FV(n,i,PV,PMT) FV (16 periods, 10% ÷ 4, 0, $1,250)
=
$24,225
Problem 3-5 End of Year 1
Amount Deposited $2,500
2 3
$0 $750
4
$1,300
5
$0
FV(n,i,PV,PMT) FV(4 yrs, 15%,$2,500, 0) FV(3 yrs, 15%,0, 0) FV(2 yrs, 15%, $750, 0) FV(1 yr, 15%, $1,300, 0)
Future Value $4,373 $0 $992 $1,495
Total Future Value =
$0 $6,860
The investor will have $6,860 on deposit at the end of the 5th year. *Each deposit is made at the end of the year. Problem 3-6 a) Find the present value of 96 monthly payments, of $750 (end-of-month) discounted at an interest rate of 15 percent compounded monthly. 18-12
Present Value
= = =
PV (n,i,PMT,FV) PV(96 periods, 15% ÷ 12, $750, 0) $41,793 should be paid today
b) The total sum of cash received over the next 8 years will be: 8 years × 12 payments per year × $750 per month = c)
$72,000
Total cash received by the investor Initial price paid by the investor
$72,000 $41,793
Difference: Interest Earned
$30,207
The difference represents the total interest earned by the investor on the initial investment of $41,793 if each $750 payment is discounted at 15 percent compounded monthly.
Problem 3-7 Find the present value of 10 end-of-year payments of $2,150 discounted at an annual interest rate of 12 percent. Present Value
= = =
PV (n,i,PMT,FV) - ordinary annuity PV (10 yrs, 12%, $2,150, 0) $12,148 should be paid today
Find the present value of 10 beginning-of-year payments of $2,150 discounted at an annual interest rate of 12 percent. Present Value
= = =
PV (n,i,PMT,FV) PV (9 yrs,12%, $2,150, 0) + $2,150 $13,606 should be paid today
Note: 1st payment of $2,150 is not discounted because it is received immediately or at the beginning of year 1. The remaining 9 payments are discounted at 12% annually. This problem illustrates an annuity due.
Problem 3-8 Find the present value of $45,000 received at the end of 6 years, discounted at a 9% annual rate, compounded quarterly. Present Value
= = =
PV (n,i,PMT,FV) PV (24 quarters, 9% ÷ 4, $0, $45,000) $26,381 should be paid today 18-13
Note that a quarterly interest factor is used in this problem because the investor indicates that an annual rate of 9% compounded quarterly is desired. Problem 3-9 Year 1 2
Amount Received $12,500 $10,000
3 4 5 6 7
$7,500 $5,000 $2,500 $0 $12,500
PV (n,i,PMT,FV) PV (1 yr, 12%, 0, $12,500) PV (2 yrs, 12%, 0, $10,000) PV (3 yrs, 12%, 0, $7,500) PV (4 yrs, 12%, 0, $5,000) PV (5 yrs, 12%, 0, $2,500) PV (6 yrs, 12%, 0, $0) PV (7 yrs, 12%, 0, $12,500)
Present Value $11,161 $7,972 $5,338 $3,178 $1,419 $0 $5,654
Total Present Value =
$34,
722 * Each deposit is made at the end of the year The investor should pay no more than $34,722 for the investment in order to earn the 12% annual interest rate compounded annually.
18-14
Problem 3-9 Part B using Monthly PV Factors Year 1 2 3 4 5 6 7
Amount Received $12,500 $10,000 $7,500 $5,000 $2,500 $0 $12,500
PV (n,i,PMT,FV) PV (12 mo, 9%/12, 0, $12,500) PV (24 mo, 9%/12, 0, $10,000) PV (36 mo, 9%/12, 0, $7,500) PV (48 mo, 9%/12, 0, $5,000) PV (60 mo, 9%/12, 0, $2,500) PV (72 mo, 9%/12, 0, $0) PV (84 mo, 9%/12, 0, $12,500)
Present Value $11,428 $8,358 $5,731 $3,493 $1,597 $0 $6,673
Total Present Value =
$37,
280 * Each deposit is made at the end of the year The investor should pay no more than $37,280 for the investment in order to earn the 9% annual interest rate compounded monthly.
Problem 3-10 Find the present value of $15,000 discounted at an annual rate of 8% for 10 years. Present Value
= = =
PV (n,i,PMT,FV) PV (10 yrs, 8%, 0, $15,000) $6,948 (annual compounding)
The investor should not purchase the lot because the present value of the lot (discounted at the appropriate interest rate) is less than the current asking price of $7,000. If the investor does pay $7,000 the IRR is i (n,PV,PMT,FV) = i (10, $7,000, 0, $15,000) = 7.92%. This also indicates that the investor should not purchase the lot if he wants an 8% IRR since the 7.92% return is less than the 8% desired return.
Problem 3-11 What will be the rate of return (yield) on a project that initially costs $100,000 and is expected to pay out $15,000 per year for the next ten years?
Interest/IRR Interest/IRR Interest/IRR
= = =
i (n,PV,PMT,FV) i(10 yrs, -$100,000, $15,000, 0) 8.14%
18-15
It is a good investment for DDC because the IRR of 8.14% exceeds DDC’s desired return of 8%.
18-16
Problem 3-12 What will be the rate of return (yield) on a project that initially costs $75,000 and is expected to pay out $1,000 per month for the next 25 years?
Interest/IRR Interest/IRR Interest/IRR
= = =
i (n,PV,PMT,FV) i (300 months, -$75,000, $1,000, 0) 15.67%
The total cash received will be: $1,000 × 25 years × 12 months = $300,000 How much is profit and how much is return on capital? Total Amount Received Total Capital Invested (returned) Total Profit (interest earned)
$300,000 $75,000 $225,000
The total cost of the investment, $75,000, is capital recovery. The difference between the total amount received and the capital recovery is total profit earned. Problem 3-13 (a) Year 1 2 3 4
Amount Received* $5,500 $7,500 $9,500 $12,500
PV (n,i,PMT,FV) PV (1 yr, 12%, 0, $5,500) PV (2 yrs, 12%, 0, $7,500) PV (3 yrs, 12%, 0, $9,500) PV (4 yrs, 12%, 0, $12,500) Total Present Value =
Present Value $4,911 $5,979 $6,762 $7,944
$25,596
The investor should pay not more than $25,596 for investment in order to earn the 12 percent annual interest rate compounded annually. (b) End of Month 12
Amount Received*
24
$7,500
36
$9,500
48
$12,500
$5,500
PV (n,i,PMT,FV) PV (12 mos., 12% ÷ 12, 0, $5,500) PV (24 mos., 12% ÷ 12, 0, $7,500) PV (36 mos., 12% ÷ 12, 0, $9,500) PV (48 mos., 12% ÷ 12, 0, $12,500) 18-17
Present Value $4,881 $5,907 $6,639 $7,753
Total Present Value =
$25,180
The investor should pay not more than $25,180 for investment in order to earn the 12 percent annual interest rate compounded monthly. (Note: the periods (n) above should be calculated using a monthly number i.e., 1 year = 12 periods) (c) These two amounts are different because the return demanded in part (b) is compounded monthly. The greater compounding frequency results in a lower present value. Problem 3-14 What will be the internal rate of return (yield) on a project that initially costs $100,000 and is expected to receive $1,600 per month for the next 5 years and, at the end of the five years, return the initial investment of $100,000?
Interest/IRR Interest/IRR Interest/IRR
= = =
19.2%
i(n,PV,PMT,FV) i(60 months, -$100,000, $1,600, $100,000) 1.6% --and 1.6% × 12= 19.2% (internal rate of return of compounded monthly)
Problem 3-15 a) Annual sinking fund payments required to accumulate $60,000 after ten years Payment Payment
= = =
Payment(n,i,PV, FV) Payment(10 yrs, 10%, 0, $60,000) $3,764.72 per year
b) Monthly sinking fund payments required to accumulate $60,000 after ten years. Payment Payment
= = =
Payment(n,i,PV, FV) Payment(120 periods, 10%/12, 0, $60,000) $292.90 per month
c) The monthly payment in part b would add to 12 × $292.90 or $3,114.80 per year. Thus, by making monthly payments with monthly compounding, the total needed each year would be $649.92 per year less or $6,499 over the ten years. Problem 3-16 a) Find the ENAR for 12% EAY given Monthly Compounding. ENAR
= = = =
[( 1 + EAY) ^ (1/m) - 1] × m [( 1 + .12) ^ (1/12) -1] × 12 [ 1.0094888 - 1] × 12 [.0094888] × 12 18-18
=
.1138655 or 11.39%
b) Find the ENAR for 12% EAY given Quarterly Compounding ENAR
= = = = =
[( 1 + EAY) ^ (1/m)] × m [( 1 + .12) ^ (1/4) -1] × 4 [ 1.0287373 - 1] × 4 [.02887373] × 4 .1149494 or 11.49%
18-19
Problem 3-17 Part 1, calculate annual returns compounded annually: (Note: calculator should be set for one payment per period) The Annual Rate compounded Monthly: Solution : N = PMT = PV = FV = Solve for the yield: i =
28 $1,200 -24,000 0 2.486% (×12) = 29.83%
The monthly rate can now be used to calculate the equivalent annual rate as follows: The Annual Rate compounded annually: Solution: PV = -1 i = 29.83% ÷ 12 PMT = 0 N = 12 Solve for the future value: FV = 1.34266 The annual rate of interest (compounded annually) needed to provide a return equivalent to that of an annual rate compounded monthly is: FV - PV = 1.34266 - 1.0 = 34.2660% This return is far greater than the annual rate compounded monthly or 29.830% This tells us that an investor would have to find an investment yielding 34.3% if compounding occurred on an annual basis (once per year) for it to be equivalent to an investment that provides an annual rate of 29.8% compounded monthly. Problem 3-18 Goa1: To show the relationship between IRRs, compound interest, recovery of capital and cash flows. a) Note: The sum of all cash flows is $17,863.65. The investment is $13,000, therefore $4,863.64 must be interest (profit). The goal is (1) to determine the annual breakdown between interest (profit), recovery of capital (principal) from the cash flows and (2) show that compound interest is being earned on the investment balance at an interest rate equal to the IRR. This exercise should prove that the IRR is equivalent to an interest rate of 10% compounded annually. It should also demonstrate the equivalence between an IRR and compound interest. (b) IRR = 10% (annual rate, compounded annually) (c) Proof: Recovery of 18-20
Beginning Investment of Year 1 13,000.00 2 9,300.00 3 9,230.00 4 10,153.00 5 6,168.30 6 785.13
10% Interest
Cash Flow
$1,300.00 $ 5,000.00 930.00 1,000.00 923.00 -01,015.30 5,000.00 616.83 6,000.00 78.51 863.65 $4,863.64 $17,863.76
Capital (ROC) $ 3,700.00 70.00 -03,984.70 5,383.17 785.14 $13,000.00
End of Year (Balance) $ 9,300.00 9,230.00 10,153.00* 6,168.30 785.13 -0-
* Note: Because the cash flow in year 3 is zero, interest must be accrued on the balance of $9,230 during year 3 and added to the investment balance. Solutions to Questions—Chapter 4 Fixed Rate Mortgage Loans Question 4-1 What are the major differences between the CAM, and CPM loans? What are the advantages to borrowers and risks to lenders for each? What elements do each of the loans have in common? CAM - Constant Amortization Mortgage - Payments on constant amortization mortgages are determined first by computing a constant amount of each monthly payment to be applied to principal. Interest is then computed on the monthly loan balance and added to the monthly amount of amortization to determine the total monthly payment. CPM - Constant Payment Mortgage - This payment pattern simply means that a level, or constant, monthly payment is calculated on an original loan amount at a fixed rate of interest for a given term. CAM - lenders recognized that in a growing economy, borrowers could partially repay the loan over time, as opposed to reducing the loan balance in fixed monthly amounts. CPM - At the end of the term of the mortgage loan, the original loan amount or principal is completely repaid and the lender has earned a fixed rate of interest on the monthly loan balance. However, the amount of amortization varies each month. When both loans are originated at the same rate of interest, the yield to the lender will be the same regardless of when the loans are repaid (i.e., early or at maturity). Question 4-2 Define amortization. List the five types discussed in this chapter. Amortization is rate at which the process of loan repayment occurs over the loan term. Types of amortization are fully, partially, zero, negative and constant rates of amortization. Question 4-3 Why do the monthly payments in the beginning months of a CPM loan contain a higher proportion of interest than principal repayment? The reason for such a high interest component in each monthly payment is that the lender earns an annual percentage return on the outstanding monthly loan balance. Because the loan is being repaid over a long period of time, the loan balance is reduced only very slightly at first and monthly interest charges are correspondingly high. 18-21
Question 4-4 What are loan closing costs? How can they be categorized? Closing costs are incurred in many types of real estate financing, including residential property, income property, construction, and land development loans. Categories include statutory costs, third party charges, and additional finance charges. Closing costs that do affect the cost of borrowing are additional finance charges levied by the lender. These charges constitute additional income to the lender and as a result must be included as a part of the cost of borrowing. Lenders refer to these additional charges as loan fees. Question 4-5 In the absence of loan fees, does repaying a loan early ever affect the actual or true interest cost to the borrower? No, the true interest rate always equals the contract rate of interest. Question 4-6 Why do lenders charge origination fees, especially loan discount fees? Lenders usually charge these costs to borrowers when the loan is made, or ―closed‖, rather than charging higher interest rates. They do this because if the loan is repaid soon after closing, the additional interest earned by the lender as of the repayment date may not be enough to offset the fixed costs of loan origination. Question 4-7 What is the connection between the Truth-in-Lending Act and the annual percentage rate (APR)? Truth-in-Lending Act - the lender must disclose to the borrower the annual percentage rate being charged on the loan. The APR reflects origination fees and discount points and treats them as additional income or yield to the lender regardless of what costs the fees are intended to cover. The APR is always calculated assuming that the loan is repaid at maturity. Question 4-8 What is the effective borrowing cost? This differs from the contract rate because it includes financing fees (points, origination). It differs from the APR because the latter is calculated assuming that the loan is repaid at maturity. When calculating the effective cost, the expected repayment or payoff date must be used. The latter is usually sooner than the maturity date. Question 4-9 What is meant by the “nominal rate” on a mortgage loan? This rate is usually quoted as an annual rate, however the time intervals used to accrue interest is generally not quoted explicitly. Further, the rate generally does not specify the extent of any origination fees and/or discount points. Question 4-10 What is the accrual rate and payment rate on a mortgage loan? What happens when the two are equal? What happens when the accrual rate exceeds the payment rate? What if the payment rate exceeds the accrual rate? The accrual rate is usually the nominal rate divided by the number of periods within a year that will be used to calculate interest. For example, if interest is to be accrued monthly, the nominal 18-22
rate is divided by 12; if daily, the nominal rate is divided by 365. The payment rate, or ―pay rate‖, is the % of the loan to be paid at time intervals specified in the loan agreement. This rate is used to calculate payments which are usually made monthly (but could be quarterly, semiannual, etc.) If the pay rate exceeds the accrual rate, this indicates that some loan repayment (amortization) is occurring. When it is equal to the accrual rate, amortization is not occurring. If the accrual rate is lower than the interest rate there will be negative amortization. Question 4-11 An expected inflation premium is said to be part of the interest rate, what does this mean? In general, the nominal interest rates for a specified period (say 10 years) is said to be a composite of three things; (a) real return-such as the growth rate in real GDP (underlying economic growth in the economy, (b) expected inflation , and (c) premium for risk. For example, if a lender quotes a 6% rate on a mortgage loan at a time when 10 year U.S. government bonds are yielding 3.6%, then the risk premium would be 2.4%. If at that same time growth in real GDP is 2.0% and is expected to continue at that rate for 10 years, then expected inflation can be estimated to be 1.6% (or 6%-2.4%-2.0% = 1.6%). Alternatively, if 10 year U.S. Government Bonds that are indexed for inflation (TIPs) are currently yielding 2.0% and 10 year Treasuries not indexed for inflation are yielding 3.6%, the difference, or 3.6%-2.0%, or 1.6% is an estimate of expected inflation. Question 4-12 A mortgage loan is made to Mr. Jones for $30,000 at 10 percent interest for 20 years. If Mr. Jones has a choice between a CPM and a CAM, which one would result in his paying a greater amount of total interest over the life of the mortgage? Would one of these mortgages be likely to have a higher interest rate than the other? Explain your answer. A CPM loan reduces the principal balance more slowly, as a result, if Mr. Jones chooses a CPM, he will pay a greater amount of interest over the life of the loan. As to the contract rate of interest, the borrower’s income constant, initial payments with the CAM will be higher and default risk will be greater. The initial monthly payments for a CPM are considerably less than those of a CAM. Because of lower initial payments with a CPM, this would reduce borrower default risk associated with a CPM loan. Additionally, lenders receive a greater portion of their return (interest earned) early with a CPM. By decreasing default risk a CPM may have lower rate of interest than a CAM. Question 4-13 What is negative amortization? Negative amortization means that the loan balance owed increases over time because payments are less than interest due. Question 4-14 What is partial amortization? Partial amortization occurs when payments exceed interest due but not by enough to reduce the amount owed to zero at maturity.
18-23
Solutions to Problems—Chapter 4 Fixed Rate Mortgage Loans Problem 4-1 A borrower makes a fully amortizing CPM mortgage loan. Principal = $125,000 Interest = 6.00% Term = 10 years CPM Payment: The monthly payment for a CPM is found using the following formula: Monthly payment Monthly payment Payment =
= PMT (n,i,PV, FV) = PMT (10 yrs, 6%,$125,000 , $0) $1,387.76
If the loan maturity is increased to 30 years the payment would be: Monthly payment Monthly payment Payment =
= PMT (n,i,PV, FV) = PMT (30 yrs, 6%,$125,000 , $0) $749.44
Problem 4-2 (a) Monthly payment (PMT (n,i,PV, FV) = $515.44 Solution: n = 25×12 or 300 i = 6%/12 or .50 PV = $80,000 FV = 0 Solve for payment: PMT =
-$515.44
(b) Month 1: interest payment: $80,000 × (6%/12) = $400 principal payment: $515.44 - $400 = $115.44 (c) Entire 25 Year Period: total payments: $515.44 × 300 = $154,632 total principal payment: $80,000 total interest payments: $154,632 - $80,000= $74,632 (d) Outstanding loan balance if repaid at end of ten years = $61,081.77 Solution: 18-24
n = i = PMT = PV = Solve for FV: FV =
120 (pay off period) 6%/12 or 0.50 $515.44 $80,000 $61,081.77
(e) Through ten years: total payments: $515.44 × 120 = $61,852.80 total principal payment (principal reduction): $80,000 – 61,081.77* = $18,918.23 *PV of loan at the end of year 10 total interest payment: $61,852.80 - $18,918.23 = $42,934.57 (f) Step 1, Solve for loan balance at the end of month 49: n = 49 i = 6%/12 or 0.50 PMT = $515.44 PV = - $80,000 Solve for loan balance: PV = $73,608.28 Step 2, Solve for the interest payment at month 50: interest payment: $73,608.28 × (.06/12)= $368.04 principal payment: $515.44 - $368.04 = $147.40 Problem 4-3 (a) Monthly payment PMT (n,i,PV, FV) = $599.55 Solution: n = 30×12 or 360 i = 6%/12 or 0.50 PV = -$100,000 FV = 0 Solve for payment: PMT = $599.55
(b) Quarterly Payment PMT (n,i,PV, FV) = $1,801.85 Solution: n = 30×4 or 120 i = 6%/4 or 1.50 PV = -$100,000 FV = 0 18-25
Solve for payment: PMT =
$1,801.85
(c) Annual Payment PMT (n,i,PV, FV) = $7,264.89 Solution: n = 30 i = 6% PV = -$100,000 FV = 0 Solve for payment: PMT = $7,264.89
(d) Weekly Payment (n,i,PV, FV) = $138.26 Solution: n = 52×30 or 1,560 i = 6%/52 or 0.12 PV = -$100,000 FV = 0 Solve for payment: PMT = $138.26
Problem 4-4 Monthly: total principal payment: total interest: ($599.55 × 360) - $100,000 = Quarterly: total principal payment: total interest: ($1,801.85 × 120) - $100,000 = Annually: total principal payment: total interest: ($7,264.89 × 30) - $100,000 = Weekly: total principal payment: total interest: ($138.26 × 1560) - $100,000 =
$100,000 $115,838 $100,000 $116,222 $100,000 $117,946.70 $100,000 $115,685.60
The greatest amount of interest payable is with the Annual Payment Plan because you are making payments less frequently. Therefore, the balance is reduced slower and interest is paid on a larger loan balance each period. 18-26
Problem 4-5 (a) Monthly Payment PMT (n,i,PV,FV): Solution: n = 20×12 or 240 i = 6%/12 or 0.50 PV = -$100,000 FV = 0 Solve for payment: PMT = $716.43
(b) Entire Period: Monthly Payment PMT (n,i,PV,FV): total payment: $716.43 × 240 = $171,943.45 total principal payment: $100,000 total interest: $171,943.45- 100,000 = $71,943.45
(c) Outstanding loan balance if repaid at end of year eight = $73,415.98 Solution: n = 96 i = 6%/12 or 0.50 PMT = -$716.43 PV = $100,000 Solve for mortgage balance: FV = $73,416.22 Total interest collected: total payment + mortgage balance - principal $716.43 × (8×12) + $73,416.22 - 100,000 total interest collected = $42,193.50 (d) Step 1, Solve for the loan balance at the end of year 8: n = 96 i = 6%/12 or 0.50 PMT = -$716.43 PV = $100,000 Solve for loan balance: FV = $73,416.22 18-27
After reducing the loan by $5,000, the balance is: $73,416.22 - 5,000 = $68,416.22 (e) The new loan maturity will be 131 months after the loan is reduced at the end of year 8. Solution: i = 6%/12 or 0.50 PMT = -$716.43 PV = $68,416.22 FV = 0 Solve for maturity: n = 131 (months)
(f) The new payment would be $667.64 Solution: i = 6%/12 or 0.50 n = 12×12 or 144 PV = $68,416.22 FV = 0 Solve for payment: PMT = -$667.64
Problem 4-6 Step 1, Solve for the original monthly payment: i = 6%/12 or 0.50 n = 30×12 or 360 PV = -$75,000 FV = 0 Solve for payment: PMT = $449.66
Step 2, Solve for current balance: i = 6%/12 or 0.50 n = 10×12 or 120 PV = -$75,000 PMT = $449.66 Solve for mortgage balance: FV = $62,764.29
(a) New Monthly Payment = $378.02 Solution: i = 6%/12 or 0.50 n = 12×20 or 240 PV = $52,764.29* 18-28
FV = Solve for payment: PMT =
0 $378.02
(b) New Loan Maturity = 161 months Solution: i = 6%/12 or 0.50 PMT = -$449.66 PV = $52,764.29* FV = 0 Solve for maturity: n = 178 *$62,764.29 - 10,000
Problem 4-7 The loan will be repaid in 145 months. Solution: n (PMT,i,PV,FV) i = 6.5%/12 or 0.54 PMT = $1,000 PV = $100,000 FV = 0 Solve for maturity: n = 145
Problem 4-8 The interest rate on the loan is 12.96%. Solution: n = 25×12 or 300 PMT = -$900 PV = $80,000 FV = 0 Solve for the annual interest rate: i = 1.08 (×12) or 12.96%
Problem 4-9 (a) Monthly Payments = $656.70 Solution: n = 10×12 or 120 i = 7%/12 or 0.58 18-29
PV = -$60,000 FV = $20,000 Solve for monthly payment: PMT = $581.10
(b) Loan balance at the end of year five = $43,454.81 Solution: n = 5×12 or 60 i = 7%/12 or 0.58 PMT = $581.10 FV = $20,000 Solve for the loan balance: PV = -$43,454.81
Problem 4-10 (a) Monthly Payments = $400.00 Solution: n = 10×12 or 120 i = 6%/12 or 0.00500 PV = -$80,000 FV = $80,000 Solve for monthly payments: PMT = $400.00
(b) Loan balance = $80,000 Solution: n = 12×5 or 60 i = 6%/12 or 0.0050 PV = -$80,000 PMT = $400.00 Solve for loan balance: FV = $80,000
The solution does not have to be calculated because the loan balance will be the same as initial loan amount. This is because it is an interest only loan and there is no loan amortization or reduction of principal. (c) Yield to the lender i(n,PV,PMT,FV) =6% Solution: n = 12×5 or 60 PMT = $400.00 PV = -$80,000 FV = $80,000 Solve for the annual yield: i = 0.0050 (×12) or 6% 18-30
(d) Yield to the lender i(n,PV,PMT,FV) = 8% Solution: n = 12×10 or 120 PMT = $400.00 PV = -$80,000 FV = $80,000 Solve for the annual yield: i = 0.0050 (×12) or 6%
Problem 4-11 Monthly Payments PMT (n,i,PV,FV) = $877.14 Solution: n = 10×12 or 120 i = 6%/12 or 0.50 PV = $90,000 FV = -$20,000 Solve for monthly payments: PMT = $877.14
Yield to the lender i(n,PV,PMT,FV) = 6.39% Solution: n = 12×10 or 120 PMT = $877.14 PV = -$88,200* FV = $20,000 Solve for the annual yield: i = 6.39% *-$90,000 × (100-2)% =
-$88,200 (amount disbursed)
Step 1, Solve the loan balance if repaid in four years: Solution: n = 4×12 or 48 i = 6%/12 or 0.50 PV = - $90,000 PMT = $877.14 Solve for the loan balance: FV = $66,892.65
Step 2, Solve for the yield: 18-31
Solution: n = 12×4 or 48 PMT = $877.14 PV = -$88,200* FV = $66,892.65 Solve for the annual yield: i = i(n,PV,PMT,FV) i = 6.64% *-$90,000 × (100-2)% =
-$88,200
Problem 4-12 (a) At the end of year ten $94,622.86 will be due: Solution: n = 12×10 or 120 i = 8%/12 or 0.67 PV = -$50,000 PMT = 0 Solve for loan balance: FV = $110,982.01 (b) Step 1, the loan yield remains 8%, this can be ―proved‖ by solving for loan balance at end of year eight. Solution: n = 8×12 or 96 i = 8%/12 or 0.67 PV = -$50,000 PMT = 0 Solve for loan balance: FV = $94,622.86
Step 2, Solve for the yield: Solution: n = 8×12 or 96 PMT = 0 PV = -$50,000 FV = $94,622.86 Solve for the annual yield: i = .67 (×12) or 8% Note: because there were no points, the yield must be the same as the initial interest rate of 8% so no calculations were really necessary. (c) Yield to lender with one point charged = 8.13% 18-32
Solution: n = 8×12 or 96 PMT = 0 PV = -$49,500* FV = $94,622.86 Solve for the annual yield: i = .68 (×12) or 8.13% (annual rate, compounded monthly) *-$50,000 × (100-1)% =
-$49,500
Problem 4-13 (a) Property value = Principal = Interest rate = Maturity = Loan origination fee
$105,000 $84,000 6.00% 30 years = $3,500
Lender will disburse $84,000.00 less the loan origination fee of $3,500.00 or $80,500.00
(b) Monthly payments are based on the loan amount of $84,000 and would be PMT (n,i,PV,FV): Monthly Payment n = i = FV = PV =
=
PMT (n,i,PV,FV)
=
$503.62
Effective Interest rate n = 360 PMT = $503.62 FV = 0 PV = $80,500
=
i(n,PV,PMT,FV)
Effective Interest rate
=
.533472 × 12=6.40%
360 6% 12 0 -$84,000
Monthly Payment The effective interest rate would be:
(c) Assuming the loan payoff occurs after 5 years, determine the mortgage balance: Mortgage balance = PV of 300 monthly payments of $503.62 discounted at 6.00% PV =
PV (n,i,PMT,FV) 18-33
n PMT FV i
= = = =
PV =
60 $503.62 0 6 12 $78,165.66
The effective interest rate would be: n PMT PV FV i i
= = = = = =
60 $503.62 -$80,500 $78,165.66 i(n,PV,PMT,FV) 7.02%
The effective interest rate in this part is different from the APR because the loan origination fee is amortized over a much shorter period (5 years instead of 30 years). (d) With a prepayment penalty of 2% on the outstanding loan balance of $78,165.66, the penalty would be $1,563.30. The effective interest cost would be: n PMT PV FV i i
= = = = = =
60 $503.62 -$80,500 $79,728.96 ($78,165.66+$1,563.30) i(n,PV,PMT,FV) 7.35%
This rate is different from the APR because penalty points are not used in the calculation of the APR. Note: Penalty equals $78,165.66 × .02 = $1,563.30 Problem 4-14 Solution: Loan fees are now being loaned by adding $3,500 to $84,000. Amount borrowed is now $87,500. (a) Lender will now disburse $87,500 less the loan fees of $3,500 or $84,000 (b) Payment calculation is based on new loan amount $87,500 and new PMT: PV = $-87,500 n = 360 FV = $0 6% 12 i = Solve: PMT = $524.61 (vs $503.62 in problem 13) APR is now: 18-34
PV = $-84,000 PMT = $524.61 N = 360 FV = 0 Solve: i = 6.39% APR This can be compared to 6.40% in 13(b). (c) If the loan is repaid after 5 years, the effective interest rate can be calculated as follows: Solve for mortgage balance: Part I: PMT = $524.61 6% 12 i = N = 60 PV = $87,500 FV Part
=
$81,422.56 at end of month 60
II: Solve for i or effective interest rate. PV = $-84,000 n = 60 FV = $81,422.56 PMT = $524.61
Solve for (i)
=
6.98%
(d) Include prepayment penalty of 2% of $81,422.56 or $1,628.45 Solution i: PV = $-84,000 PMT = $524.61 n = 60 FV = $83,051.01 i
=
7.31% effective rate
Problem 4-15 Points required to achieve a yield to 10% for the 25 year loan. Fv is now $83,186.41 = $1,663.73 = $84,850.14 Monthly payments PMT (n,i,PV,FV): n = 300 9% 12 i = PV = $95,000 FV = $0 Solve for monthly payments: PMT = $797.24
PV (n,i,PMT,FV) of 300 payments of $797.24 discounted at 10% = $87,733.67 18-35
Subtracting $87,733.67 from $95,000.00, we get $7,266.33 The loan origination fee should be $7,266.33 if the loan is to be repaid after 25 years and the lender requires a 10% yield. If the loan is expected to be repaid after 10 years, the loan balance at the end of 10 years must be determined: n = i = PMT = PV = Solve for FV: FV =
120 9% $797.24 $95,000 $78,601.60
Loan balance after 10 years = $78,601.60
Discounting $797.24 monthly for 120 months and $78,601.60 at the end of the 120th month by the desired yield of 10% gives: Present value = $89,364.06 Subtracting $89,364.06 from $95,000.00, we get $5,635.94. The loan origination fee should be $5,635.94if the loan is to be repaid after 10 years, and the lender requires a yield of 10%. Problem 4-16 (a) In order to find which loan is the better choice after 20 years, the effective interest rate for each loan must be calculated.
Principal Nominal interest rate Term (years) Points Payment Loan Balance after 20 years Loan Balance after 5 years
Loan A $75,000 6.00% 30 6 $449.66 $40,502.43 $69,790.32
Loan A n = PMT = PV =
240 $449.66 -$70,500 18-36
Loan B $75,000 7.00% 30 2 $498.98 $42,975.33 $70,599.14
FV i i
= = =
$40,502.43 i(n,PV,PMT,FV) .5525% × 12 = 6.63%
n PMT PV FV i i
= = = = = =
240 $498.98 -$73,500 $42,975.33 i(n,PV,PMT,FV) .6008% × 12 = 7.21%
Loan B
Loan A is the better alternative if the loan is repaid after 20 years. (b) This part is solved the same as (a) except using the assumption that the loan is repaid after 5 years.
Loan A
Note: Balance at the end of 60 months = $69,790.32
n PMT PV FV i i
= = = = = =
60 $449.66 -$70,500 $69,790.32 i(n,PV,PMT,FV) .623917% × 12 = 7.49% Note: Balance at the end of 60 months = $70,599.14
Loan B n PMT PV FV i i
= = = = = =
60 $498.98 -$73,500 $70,599.14 i(n,PV,PMT,FV) .624417 × 12 = 7.49%
The borrower would be indifferent between the two loans if the repayment period is 5 years. Problem 4-17 (a) Monthly Payments = $1,830.61 to be made to the borrower Solution: n = 10×12 or 120 i = 6%/12 or 0.005 PV = 0 FV = -$300,000 Solve for monthly payments: PMT = $1,830.61 18-37
(b) The borrower will have received monthly payments of $1,830.61 during months 1 to 36 Solve for loan balance at the end of month 36 Solution: n = 36 i = 6%/12 or 0.005 PV = 0 PMT = $1,830.61 Solve for loan balance*: FV = -$72009.27 *Note that this is equivalent to finding the Future Value of a $1,830.61 monthly ordinary annuity at an annual rate of 6%, compounded monthly. (c) The borrower will receive $2,000 per month for 50 months and then will receive monthly payments of $626.22 during months 51 to 120. This is calculated as follows: Step 1, Solve for loan balance at the end of month 50 Solution: n = 50 i = 6%/12 or 0.005 PV = 0 PMT = $2,000 Solve for loan balance at the end of month 50: FV = -$113,290.33
Step 2, Solve for payments during months 51 to 120 Solution: n = 120-50 or 70 i = 6%/12 or 0.005 PV = $113,290.33 FV = -$300,000 Solve for monthly payments beginning in month 51 through 120 or for the next 70 months: PMT = $1,667.82
Problem 4-18 Find the balance at the end of 5 years for a fully amortizing $200,000, 5% mortgage with a 25 year amortization schedule: PV i n
= -200,000 = 5% 12 = 300
FV Solve PMT
=0 = $1,169.18
PMT FV Solve PV
= $1,169.18 =0 = -$177,160.38
Solve for balance at end of 5 years:
i n
= 5% =240
18-38
Problem 4- 19 CAM loan: (a) Calculate constant monthly amortization: $125,000 240 months = $520.83 per month Calculate Monthly Interest: Beg. Month Balance Rate 1 125,000 *6%/12 2 124,479.17 *6%/12 3 123,958.34 *6%/12 4 123,437.51 *6%/12 5 122,916.68 *6%/12 6 122,395.85 *6%/12
Interest 625.00 622.40 619.79 617.18 614.58 611.98
Amortization 520.83 520.83 520.83 520.83 520.83 520.83
Total Payment 1145.83 1143.23 1140.62 1138.01 1135.41 1132.80
End Balance 124,479.17 123,958.34 123,437.51 122,916.68 122,395.85 121,875.02
(b) For a constant payment loan (CPM) we have: PV = -$125,000 n = 240 i = 6% 12 FV = 0 Solve PMT = $895.54
(c) In the absence of point and origination fees, the effective interest rates on both loans will be an annual rate of 6%, compounded monthly. This is true regardless of when either of the loans are repaid. Monthly payments are different, however i is the same for both loans.
18-39
Problem 4-20 (a) Determine monthly payments based on interest being accrued daily. Solve for interest due at the end of month one: PV i n Solve for FV FV
= = =
$50,000 6% 360 360 / 12 = 30*
=
$50,250.61 Thus the interest that accrues each month is $250.61
*Assumes a 360 day year to have an even number of months. Answer will be slightly different if you use a 365 day year. Because this is an ―interest only‖ loan, payments of $250.61 will be due at the end of each month for 360 months. (b) The loan balance will be $50,000 at the end of each month for the life of the loan. At the end of 30 years it also will be $50,000. (c) The equivalent annual rate will be: FV n PV PMT
= = = =
$50,000 360 -$50,000 250.61
Solve for i = .5012 × 12 = 6.01% (annual rate, compounded monthly) Or
($50,250.61 - $50,000) / $50,000 = 5012 × 12= 6.01%
Problem 4- 21 Comprehensive Review Problem Loan = 100,000, 6% interest, 20 years A. Monthly payments if (1) Fully amortizing: PV = -100,000 n i = 6% Solve PMTs FV = 0
= 240 = $716.43
(2) Partial amortizing: PV = -100,000 i = 6% FV = $50,000
n Solve PMTs
= 240 = $608.22
(3) Interest only PV = 100,000 i = 6% FV = 100,000
n Solve PMTs
= 240 = $500.00
18-40
(4) Negative amortization: PV = -100,000 i = 6% FV = 150,000 B.
C.
= 240 = $391.78
Loan Balances for A.1. – A.4 after 5 years A.1
PMTs = $716.43 i = 6% n = 240
FV Solve PV
=0 = $84,899.60
A.2
PMTs = $608.22 i = 6% n = 180
FV Solve PV
= 50,000 = $92,450.33
A.3
PMTs = $500.00 i = 6% n = 180
FV Solve PV
= 100,000 = $100,000.00
A.4
PMTs = $391.78 i = 6% n = 180
FV Solve PV
= 150,000 = $107,549.67
Interest at the end of month 61 for A.1 – A.4 A.1 A.2 A.3 A.4
D.
n Solve PMTs
$84,899.60 * .005 $92,450.33 * .005 $100,000.00 * .005 $107,549.67 * .005
= $424.50 = $479.36 = $500.00 = $537.75
APR* for loans in A.1 – A.4 A.1 PV = -97,000, PMT = $716.43, FV = 0, n = 240 Solve i = 6.38% A.2 PV = -97,000, PMT = $608.22, FV = 50,000, n = 240 Solve i = 6.31% A.3 PV = -97,000, PMT = $500.00, FV = 100,000, n = 240 Solve i = 6.26% A.4 PV = -97,000, PMT = $391.78, FV = 150,000, n = 240 Solve i = 6.23% *Solution shown based on calculation – final answers may be rounded to nearest 1/4%
E.
Effective yield if loan prepaid EOY5. Balances must be calculated at EOY5 for each loan (not shown see solution 4-21B). A.1 A.2 A.3 A.4
PV = -97,000, PMT = $716.43, FV = 84,899.60 n = 60 Solve i = 6.76% PV = -97,000, PMT = $608.22, FV = 92,450.33 n = 60 Solve i = 6.73% PV = -97,000, PMT = $500.00, FV = 100,000.00 n = 60 Solve i = 6.70% PV = -97,000, PMT = $391.78, FV = 107,549.67 n = 60 Solve i = 6.68%
18-41
F.
―Interest only‖ monthly payments in A.1 = $100,000 × (6% 12) or $500 per month for 36 mos. What must payments be from yr. 4-17 to fully amortize the loan at the end of 240 mos.? Part 1: PV = -100,000 i = 6% n = 36 PMT = $500.00 Solve FV = $100,000 Part 2: PV = -100,000 i = 6% 12 n = 204 FV = 0 Solve PMT = $783.10
G.
(1) Total PMTs = (391.78 × 240) + 150,000 = $244,027.20 Interest = 144,027.20 Amortization (Principal) = 100,000
(2) n = 204 FV = 150,000 PMTs = $391.78 i = 6% Solve PV = $104,256.20 balance (3) 12% because there are no points (4) 4 points charged, loan payoff 36 months, what is effective interest rate? PV = -96,000 n = 36 FV = 107,550
PMT = 783.10 Solve i
Problem 4-22 The effective cost is now 12.64% versus 12.82%.
Problem 4-23 The loan balance is now $61,680 versus $63,793.
Chapter 4 Appendix Questions 18-42
= .621989% × 12 = 7.46%
Question 4-A1 Why do monthly mortgage payments increase so sharply during periods of inflation? What does the tilt effect have to do with this? In order to receive the full interest necessary to leave enough for a real return and risk premium over the life of the loan, more ―real dollars‖ must be collected in the early years of the loan (payments collected toward the end of the life of the mortgage will be worth much less in purchasing power.) Tilting - the real payment stream in the early years have to make up for the loss in purchasing power in later years. Question 4-A2 As inflation increases, the impact of the tilt effect is said to become even more burdensome on borrowers. Why is this so? With the general rate of inflation and growth in the economy, borrower incomes will grow gradually or on a year-by-year basis. However, as expected inflation increases, lenders must build estimates of the full increase into current interest rates ―up front‖ or when the loan is made. This causes a dramatic increase in required real monthly payments relative to the borrower’s current real income. Problems Problem 4A-1 (a)
Year 2 3 4 5
Payment $498.57 × 1.075 = $535.96 $535.96 × 1.075 = $576.16 $576.16 × 1.075 = $619.37 $619.37 × 1.075 = $665.82
(b) Loan payment with a CPM Monthly payment: $63,000.00 × (MLC, 12%, 30 years) = monthly payment $63,000.00 × 0.010286 = $648.03 (c) Effective yield of the GPM is the loan is originated with 2 discount points CF0 = 61,740 CFj = 498.57 nj = 12 CFj = 535.96 nj = 12 CFj = 576.16 nj = 12 CFj = 619.76 nj = 12 CFj = 665.82 nj = 12 CFj = 715.76 18-43
nj = 11* CFj = 66,982.97 +715.76 nj = 1* * Note the last scheduled payment and the loan balance are received by the lender at the same time or at the end of month 84. Therefore they must be added. The effective yield is the internal rate of return that equates the payment stream with the initial loan amount. Effective Yield = 12.41%
18-44
Problem 4A-2 Excel template Ch4 GPM from course website modified to solve this problem. Chapter 4 Loan Balance on GPM Spreadsheet Limitations: Projections for 5 years Input Assumptions Loan Amount $100,000 Interest Rate 9.00% Loan Term 25 years Pmt Increase 7.50% Inc. Years 3 Points 4 Lender's Yield (after 7 yrs)
10.02%
INITIAL PAYMENT CALCULATION:
(1) (2) (3) Payment Period Payment MPVIFA 1 1.00000 11.43491 2 1.07500 11.43491 3 1.15563 11.43491 4 1.24230 11.43491 5 1.24230 11.43491 6-25 1.24230 111.14495
(4)
(5)
MPVIF (2x3x4) 1.00000 11.43491 0.91424 11.23830 0.83583 11.04507 0.76415 10.85516 0.69861 9.92420 0.63870 88.18848 Pmt factor = 142.68613
Initial Payment : $700.84 <====
$100,000 142.68613 Loan Amt / Pmt Factor
a. Calculation of initial payment is shown above. Payments for years 2 through 5 are shown in the exhibit below. b. The loan balance at the end of year 3 is shown in the exhibit below.
18-45
LOAN AMORTIZATION SCHEDULE: Month 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
Payment Interest Principle ($96,000) <==Amount Dispersed $700.84 $750.00 ($49.16) $700.84 $750.37 ($49.53) $700.84 $750.74 ($49.90) $700.84 $751.11 ($50.28) $700.84 $751.49 ($50.65) $700.84 $751.87 ($51.03) $700.84 $752.25 ($51.42) $700.84 $752.64 ($51.80) $700.84 $753.03 ($52.19) $700.84 $753.42 ($52.58) $700.84 $753.81 ($52.98) $700.84 $754.21 ($53.37) $753.40 $754.61 ($1.21) $753.40 $754.62 ($1.22) $753.40 $754.63 ($1.23) $753.40 $754.64 ($1.24) $753.40 $754.65 ($1.25) $753.40 $754.66 ($1.26) $753.40 $754.67 ($1.27) $753.40 $754.68 ($1.27) $753.40 $754.69 ($1.28) $753.40 $754.70 ($1.29) $753.40 $754.71 ($1.30) $753.40 $754.72 ($1.31) $809.91 $754.73 $55.18 $809.91 $754.31 $55.60 $809.91 $753.89 $56.01 $809.91 $753.47 $56.43 $809.91 $753.05 $56.86 $809.91 $752.62 $57.28 $809.91 $752.19 $57.71 $809.91 $751.76 $58.14 $809.91 $751.33 $58.58 $809.91 $750.89 $59.02 $809.91 $750.44 $59.46 $809.91 $750.00 $59.91 $870.65 $749.55 $121.10 $870.65 $748.64 $122.01 $870.65 $747.73 $122.92 $870.65 $746.80 $123.85 $870.65 $745.87 $124.78 $870.65 $744.94 $125.71 $870.65 $744.00 $126.65 $870.65 $743.05 $127.60 $870.65 $742.09 $128.56 $870.65 $741.12 $129.53 $870.65 $740.15 $130.50 $870.65 $739.17 $131.48 $870.65 $738.19 $132.46 $870.65 $737.20 $133.46 $870.65 $736.19 $134.46 $870.65 $735.19 $135.46 $870.65 $734.17 $136.48 $870.65 $733.15 $137.50 $870.65 $732.11 $138.54 $870.65 $731.08 $139.57 $870.65 $730.03 $140.62 $870.65 $728.97 $141.68 $870.65 $727.91 $142.74 $97,639.01 $726.84 $143.81
18-46
Balance CPM Payment $100,000 $100,049 $839.20 $100,099 $839.20 $100,149 $839.20 $100,199 $839.20 $100,250 $839.20 $100,301 $839.20 $100,352 $839.20 $100,404 $839.20 $100,456 $839.20 $100,509 $839.20 $100,562 $839.20 $100,615 $839.20 $100,616 $839.20 $100,617 $839.20 $100,619 $839.20 $100,620 $839.20 $100,621 $839.20 $100,622 $839.20 $100,624 $839.20 $100,625 $839.20 $100,626 $839.20 $100,627 $839.20 $100,629 $839.20 $100,630 $839.20 $100,575 $839.20 $100,519 $839.20 $100,463 $839.20 $100,407 $839.20 $100,350 $839.20 $100,293 $839.20 $100,235 $839.20 $100,177 $839.20 $100,118 $839.20 $100,059 $839.20 $100,000 $839.20 $99,940 $839.20 $99,819 $839.20 $99,697 $839.20 $99,574 $839.20 $99,450 $839.20 $99,325 $839.20 $99,199 $839.20 $99,073 $839.20 $98,945 $839.20 $98,817 $839.20 $98,687 $839.20 $98,557 $839.20 $98,425 $839.20 $98,293 $839.20 $98,159 $839.20 $98,025 $839.20 $97,889 $839.20 $97,753 $839.20 $97,615 $839.20 $97,477 $839.20 $97,337 $839.20 $97,197 $839.20 $97,055 $839.20 $96,912 $839.20 $96,768 $839.20
EOY 1
EOY 2
EOY 3
EOY 4
EOY 5
c. Input Assumptions Loan Amount $100,000 Interest Rate 9.00% Loan Term 25 years Pmt Increase 7.50% Inc. Years 3 Points 4 Lender's Yield (after 7 yrs)
10.02%
Problem 4A-3 The initial payment would now be $518.09 as shown below. Chapter 4 Loan Balance on GPM Spreadsheet Limitations: Projections for 7 years Input Assumptions Loan Amount $60,000 Interest Rate 12.00% Loan Term 30 years Pmt Increase 5.00% Inc. Years 5 Points 0 Lender's Yield (after 7 yrs)
12.00% INITIAL PAYMENT CALCULATION:
(1) Payment Period 1 2 3 4 5 6-25
(2)
(3)
(4)
(5)
Payment 1.00000 1.05000 1.10250 1.15763 1.21551 1.27628
MPVIFA 11.25508 11.25508 11.25508 11.25508 11.25508 94.94655
MPVIF 1.00000 0.88745 0.78757 0.69892 0.62026 0.55045 Pmt factor =
(2x3x4) 11.25508 10.48773 9.77269 9.10640 8.48555 66.70268 115.81012
$60,000
115.81012
Initial Payment: $518.09 <====
18-47
Loan Amt
/ Pmt Factor
Solutions to Questions—Chapter 5 Adjustable Rate and Variable Payment Mortgages Question 5-1 In the previous chapter, significant problems regarding the ability of borrowers to meet mortgage payments and the evolution of fixed interest rate mortgages with various payment patterns were discussed. Why didn‟t this evolution address problems faced by lenders? What have lenders done in recent years to overcome these problems? These inadequacies stem from the fact that although payment patterns can be altered to suit borrowers as expectations change, the CAM, CPM, and GPM are all originated in fixed interest rates and all have predetermined payment patterns. Neither the interest rate nor the payment patterns will change, regardless of economic conditions. A variety of mortgages are now made with either adjustable interest rates or with variable payment provisions that change with economic conditions. Question 5-2 How do inflationary expectations influence interest rates on mortgage loans? Most savings institutions had been making constant payment mortgage loans with relatively long maturities, and the yields on those mortgages did not keep pace with the cost of deposits. These problems prompted savings institutions (lenders) to change the mortgage instruments to now make more mortgages with adjustable interest rate features that will allow adjustments in both interest rates and payments so that the yields on mortgage assets will change in relation to the cost of deposits. Question 5-3 How does the price level adjusted mortgage (PLAM) address the problem of uncertainty in inflationary expectations? What are some of the practical limitations in implementing a PLAM program? One concept that has been discussed as a remedy to the imbalance problems for savings institutions is the price level adjusted mortgage (PLAM). To help reduce interest rate risk, or the uncertainty of inflation and its effect on interest rates, it has been suggested that lenders should originate mortgages at interest rates that reflect expectations of the real interest rate plus a risk premium for the likelihood of loss due to default on a given mortgage loan. Should prices of other goods, represented in the CPI increase faster than housing prices, indexing loan balances to the CPI could result in loan balances increasing faster than property values. If this occurred, borrowers would have an incentive to default. A second problem with PLAMs has to do with the relationship between mortgage payments and borrower incomes. Should inflation increase sharply, it is not likely that borrower incomes would increase at the same rate in the short run. During short periods, the payment burden may increase and households may find it more difficult to make mortgage payments. A third problem with PLAMs is that the price level chosen for indexation is usually measured on a historical basis. In other words, the index is based on data collected in the previous period but published currently. Question 5-4 18-48
Why do adjustable rate mortgages (ARMs) seem to be a more suitable alternative for mortgage lending than PLAMs? An ARM provides for adjustments that are more timely for lenders than a PLAM because values for r, p, and f are revised at specific time intervals to reflect market expectations of future values for each component of i between adjustments dates. Question 5-5 List each of the main terms likely to be negotiated in an ARM. What does pricing an ARM using these terms mean? Initial interest rate, index, adjustment interval, margin, composite rate, limitations or caps, negative amortization, floors, assumability, discount points, prepayment privilege. Anytime the process of risk bearing is analyzed, individual borrowers and lenders differ in the degree to which they are willing to assume risk. Consequently, the market for ARMs contains a large set of mortgage instruments that differ with respect to how risk is to be shared between borrowers and lenders. The terms listed above are features that might be used in pricing an ARM and establishing the bearing of risk.
18-49
Question 5-6 What is the difference between interest rate risk and default risk? How do combinations of terms in ARMs affect the allocation of risk between borrowers and lenders? Interest rate risk is the risk that the interest rate will change at some time during the life of the loan. Default risk is the risk to the lender that the borrower will not carry out the full terms of the loan agreement. The fact that ARMs shift all or part of the interest rate risk to the borrower, the risk of default will generally increase to the lender, thereby reducing some of the benefits gained from shifting interest rate risk to borrowers. Question 5-7 Which of the following two ARMs is likely to be priced higher, that is, offered with a higher initial interest rate? ARM A has a margin of 3 percent and is tied to a three-year index with payments adjustable every two years; payments cannot increase by more than 10 percent from the preceding period; the term is 30 years and no assumption or points will be allowed. ARM B has a margin of 3 percent and is tied to a one-year index with payments to be adjusted each year; payments cannot increase by more than 10 percent from the preceding period; the term is 30 years and no assumption or points are allowed. ARM A is likely to be priced higher because it has a longer-term index and adjustment period. Subsequently, the lender bears more risk and can expect a higher return. Question 5-8 What are forward rates of interest? How are they determined? What do they have to do with indexes used to adjust ARM payments? Forward rates are based on future interest rate expectations that are implicit in the yield curve and reveal investor expectations of interest rates between any two maturity periods on the yield curve. For example, the yield for a security maturing one year from now is 8 percent, and the yield for a security that matures two years from now is 9 percent. Based on these two yields, we can compute a forward rate, or rate that an investor who invests in a one-year security can expect to reinvest funds for one additional year. This forward rate will be 10 percent because if investors have the opportunity to invest today in either the one- or the two-year security and are indifferent between the two choices, the investor buying a one-year security must be able to earn 10 percent on funds available for reinvestment at the end of year 1. This information is important and represents a reference point that may help lenders and borrowers when pricing ARMs and calculating expected yields at the time ARMs are made. Additionally, interest rate series, which may include forward rates of interest, comprise the indexes used to adjust ARMs. This is especially true if an index is long term in nature. Question 5-9 Distinguish between the initial rate of interest and expected yield on an ARM. What is the general relationship between the two? How do they generally reflect ARM terms? One important issue in ARMs is the yield to lenders, or cost to borrowers, for each category of loan. Given the changes in interest rates, payments, and loan balances, it is not obvious what these yields (costs) will be. This means that the costs of each category of loan will be added to the initial interest rate, thus producing an expected yield. Question 5-10 If an ARM is priced with an initial interest rate of 8 percent and a margin of 2 percent (when the ARM index is also 8 percent at origination) and a fixed rate mortgage (FRM) with constant payment is available at 11 percent, what does this imply about inflation and the forward rates in 18-50
the yield curve at the time of origination? What is implied if a FRM were available at 10 percent? 12 percent? The initial interest rate and expected yield for all ARMs should be lower than that of a FRM on the day of origination. The extent which the initial rate and expected yield on an ARM will be lower than that on a FRM or another ARM, depends on the terms relative to payments, caps, etc. One would expect the difference between interest rates at the point if origination to reflect expectations of inflation and forward rates as well. As a FRM’s interest rate increases from 11 percent to 10 percent and 12 percent, greater inflation and/or greater uncertainty with respect to inflation is implied.
18-51
Solutions to Problems—Chapter 5 Adjustable Rate and Variable Payment Mortgages Problem 5-1 (a) Compute the payments at the beginning of each year of the PLAM. Principal 6.00% Term 6.00% Interest Rate
=
$95,000
Inflation Adjustment =
=
30 years
Points
=
4.0%
(1)
(2)
Year
BOY Balance
Annual Interest Rate
(3) Monthly Interest Rate (2)/12
0
$95,000
4.00%
0.33%
1 3 4 5
98,927 102,906 106,922 110,956
4.00% 4.00% 4.00% 4.00%
0.33% 0.33% 0.33% 0.33%
(4)
=
(5)
(6)
(7)
(8)
(9)
Monthly Interest (3) × (1)
Monthly Amort (4) - (5)
Annual Amort
EOY Balance (1) -(7)
Inflation Adjusted EOY Balance
$453.54
$316.67
$136.88
$93,327
$98,927
480.76 509.60 540.18 572.59
329.76 343.02 356.41 369.85
151.00 166.58 183.77 202.73
$1,672.9 8 1,845.61 2,036.05 2,246.15 2,477.92
97,081 100,870 104,676 108,479
102,906 106,922 110,956 114,987
(8) EOY Balance (1) - (7)
Payment s
(b) The loan balance at the end of the fifth year = $$108,479. (c) IRR(CF1, CF2, ….CFn) CFj nj -$89,300 453.54 n = 12 480.76 n = 12 509.60 n = 12 540.18 n = 12 572.59 n = 11 572.59 + 114,987 n = 1 Solve for the annual IRR: = 0.85% × 12 = 11.11% Problem 5-2 (1)
(2)
(3)
(4)
(5)
(6)
(7)
BOY Balance
Annual Interest Rate
Monthly Interest Rate (2)/12
Payments
Monthly Interest (3) × (1)
Monthly Amort
Annual Amort.
18-52
Year 0 1 2
(4) -(5) $200,000 $197,544
6.00% 7.00%
0.50% 0.58%
$1,199.10 $1,000.00 $1,327.75 $1,152.34
$199.10 $2,456.02 $197,544 $175.41 $2,173.82 $195,370
(a) Monthly Payment = $1,199.10 (b) Loan balance at EOY 1 = $197,544 (c) Monthly Payment = $1,327.75 (d)
Loan balance at EOY 2 = $195,370 (e)
Monthly Payment for year 1= $1,000
Problem 5-3 (1)
(2)
(3)
Annual Interest Rate
Monthly Interest Rate (2)/12
(4)
(5)
(6)
(7)
Monthl y Interest (3) × (1)
Monthl y Amort
Annual Amort.
(8) EOY Balance (1) - (7)
$1,523.7 1 $1,633.8 6
$148,4 76 $146,8 42
BOY Balance
(4) (5)
Year
Paymen ts
0 1
$150,000
7.00%
0.58%
$997.95
2
148,525
7.00%
0.58%
$997.95 18-53
$875.0 0 $866.1 1
$122.9 5 $131.8 4
3
146,942
7.00%
0.58%
$997.95
$856.5 8 $725.4 5
$141.3 7 $179.8 9
4
145,244
6.00%
0.50%
$905.34
$1,751.9 8 $2,219.0 6
$145,0 90 $142,8 71
(5)
(6)
(7)
Monthly Amort
Annual Amort.
(8) EOY Balance (1) - (7)
Monthly Interest
(a) Monthly Payment = $997.95 Loan Balance EOY 3 = $145,090 (b) New Monthly Payment = $906.30 (c) Interest only monthly payment = $875 Monthly payments in year 4 = $935.98 Problem 5-4 (1)
(2)
(3)
Annual Interest Rate
Monthly Interest Rate (2)/12
(4)
BOY Balance Year 0 1 2
(4) -(5) Payments
$100,000 96,885
2.00% 6.00%
0.17% 0.50%
$423.85 $635.55
(a) Monthly payment during 1 year = $423.85 (b) Monthly payment in 2 year = $635.55 (c) Percentage increase in monthly payment = 50% (d) 18-54
$166.67 $484.43
$257.19 $3,114.70 $96,885 $151.12 $1,864.15 $95,021
(1)
(2)
(3)
Annual Interest Rate
Monthly Interest Rate (2)/12
(4)
(5)
(6)
(7)
Monthly Interest (3) × (1)
Monthl y Amort
Annual Amort.
(8) EOY Balance (1) - (7)
$3,114.7 0 $3,177.5 7 $3,241.7 1 $2,043.0 2
$96,88 5 $93,70 8 $90,46 6 $88,42 3
BOY Balance
(4) (5)
Year
Paymen ts
0 1
$100,000
2.00%
0.17%
2
96,885
2.00%
0.17%
3
93,708
2.00%
0.17%
4
90,466
6.00%
0.50%
$423.8 5 $423.8 5 $423.8 5 $617.9 5
$166.67 $161.48 $156.18 $452.33
$257.1 9 $262.3 8 $267.6 7 $165.6 2
Monthly payments at beginning of year 4 = $ 617.95
Problem 5-5 (a) Interest only payments for the 1 year = $833.33 (b) The loan balance is $200,000. To reset the interest rate at 6% and to amortize the loan over the remaining 27 years (or 324 months) we have: PV i FV n
= = = =
-$200,000 6 12 0 324 18-55
Solve PMT =
$1,247.97
Problem 5-6 Compute the payments, loan balance, and yield for an unrestricted ARM Principal Points Term Initial Rate (1)
= = = =
$150,000 2.00% 30 years 6.0%
(2)
(3)
Annua l Interes t Rate
Monthly Interest Rate (2)/12
(4)
(5)
(6)
(7)
Monthly Interest (3) × (1)
Month ly Amort
Annual Amort.
BOY Balance
(4) (5)
Year 0 1
(8) EOY Balance (1) - (7)
Payment s 6.00%
0.50%
$899.33
$750.00
2
$150,00 0 148,158
9.00%
0.75%
3
147,043
0.88%
4
146,126
5
145,282
10.50 % 11.50 % 13.00 %
$1,200.3 1 $1,359.4 2 $1,467.1 2 $1,630.4 2
$1,111.1 8 $1,286.6 $72.79 3 $1,400.3 $66.74 8 $1,573.8 $56.53 9
0.96% 1.08%
$149.3 3 $89.13
$1,842.0 2 $1,114.7 8 $916.79 $844.50 $720.27
$148,15 8 $147,04 3 $146,12 6 $145,28 2 $144,56 2
IRR(CF1, CF2, ….CFn) CFj
nj
-$147,000 899.33 n = 12 1200.31 n = 12 1359.42 n = 12 1467.12 n = 12 1630.42 n = 11 1630.42 + 144,562 n = 1 Solve for the IRR: = 0.85% × 12 = 10.16% (annual rate, compounded monthly)
18-56
Problem 5-7 Compute the payments, loan balances, and yield for an ARM that has a maximum 5% annual payment cap and allows negative amortization. Principal Term Points Initial Rate
= = = =
$150,000 30 years 2.00% 7.0%
(1)
(2)
(3)
(4)
(5)
BOY
Uncapped Rate
Payment
Payment
EOY
Uncapped
Capped
Balance
$997.95 $1,202.89 $1,380.27 $1,525.03 $1,747.28
$997.95 $1,047.85 $1,100.24 $1,155.26 $1,213.02
$148,476 $149,298 $151,894 $155,695 $161,731
Year
Balance
1 2 3 4 5 6
$150,000 $148,476 $149,298 $151,894 $155,695 $161,731
7.00% 9.00% 10.50% 11.50% 13.00%
Note: EOY Balance is calculated by using: FV(n,i,pv,pmt) PV = Loan amount n = 12 months i = Uncapped rate PMT = Capped payment FV = Calculator: IRR(CF1, CF2, ….CFn) CFj
nj
-$147,000 997.95 n = 12 1047.85 n = 12 1100.24 n = 12 1155.26 n = 12 1213.02 n = 11 1213.02 + 161,731 n = 1 Solve for the IRR: = 0.8706% × 12 = 10.45% (annual rate, compounded monthly)
18-57
Problem 5-8 Compute the payments, loan balances, and yield for an ARM that has a 1% annual and 3% lifetime interest rate cap and does not accumulate negative amortization. Principal Points Term Initial Rate
= = = =
$150,000 2.00% 30 years 7.5%
(1)
(2)
(3)
Uncapped Interest Rate
7.50% 9.00% 10.50% 11.50% 13.00%
Capped Interest Rate
(4) Monthly Interest Rate (3) /12
(5) Payment (@ Capped Rate)
(6) (7) Monthly Interest Monthly Amort (1) × (5) - (6) (3)/12
(8) Annual Amort
7.50% 8.50% 9.50% 10.50% 10.50%
0.63% 0.71% 0.79% 0.88% 0.88%
$1,048.82 $1,151.44 $1,255.55 $1,360.78 $1,360.78
$937.50 $1,052.71 $1,166.80 $1,279.88 $1,270.97
$1,382.75 $1,232.11 $1,112.59 $1,018.84 $1,131.12
(9) EOY Balance (1) - (8)
BOY Balance Year 0 1 2 3 4 5
$150,000 148,617 147,385 146,273 145,254 144,123
$111.32 $98.74 $88.75 $80.89 $89.81
Calculator: IRR(CF1, CF2, ….CFn) CFj
nj
-$147,000 1048.82 n = 12 1151.44 n = 12 1255.55 n = 12 1360.78 n = 12 1360.78 n = 11 1360.78 + 144,123 n = 1 Solve for the IRR: = 0.80% × 12 = 9.65% (annual rate, compounded monthly) 18-58
$148,617 $147,385 $146,273 $145,254 $144,123
Problem 5-9 (a) Compute the payments, loan balances, and yield for a Stable Home Mortgage which is comprised of a fixed and adjustable rate component. Loan Amount = Points = Fixed Rate Portion:
$95,000 2.00% 75.00% of the loan balance 10.50% annual interest rate 30 year term
(1)
(2)
(3)
Year
BOY Balance
Annual Interest Rate
Monthly Interest Rate (2)/12
0 1 2 3 4 5
$71,250 70,893 70,497 70,058 69,570
10.50% 10.50% 10.50% 10.50% 10.50%
0.88% 0.88% 0.88% 0.88% 0.88%
Adjustable Rate Portion:
(4)
(5)
(6)
(7)
(8)
Monthly Amort (4) -(5)
Annual Amort.
Payments
Monthly Interest (3) × (1)
EOY Balance (1) - (7)
$651.75 651.75 651.75 651.75 651.75
$623.44 620.32 616.85 613.01 608.74
$28.31 31.43 34.90 38.74 43.01
$356.61 395.91 439.54 487.98 541.75
$70.893 70.497 70,058 69,570 69,028
25.00% of the loan balance 9.00% initial interest rate 2.00% margin
(1)
(2)
(3)
BOY Balance
Annual Interest Rate
Monthly Interest Rate (2)/12
$23,750
9.00%
0.75%
(4)
(5)
(6)
(7)
(8)
Monthly Amort (4) -(5)
Annual Amort
Payments
Monthly Interest (3) × (1)
EOY Balance (1) - (7)
$191.10
$178.13
$12.97
$162.26
$23,588
Year
0 1
18-59
2 3 4 5
23,588 23,491 23,402 23,223
12.00% 13.00% 10.00% 14.00%
1.00% 1.08% 0.83% 1.17%
243.51 261.49 209.23 278.40
235.88 254.49 195.01 270.94
7.63 7.00 14.22 7.46
96.80 89.19 178.68 95.55
23,491 23,402 23,223 23,128
MORTGAGE SUMMARY: YEAR 0 1 2 3 4 5
BOY Balance
Payments
EOY Balance
$95,000.00 94,481.13 93,988.42 93,459.69 82,793.03
$842.85 895.26 913.24 860.99 930.15
$94,481.13 93,988.42 93,459.69 92,793.03 92,155.73
Calculator: Calculator: IRR(CF1, CF2, ….CFn) CFj nj -$93,100 842.85 n = 12 895.26 n = 12 913.24 n = 12 860.99 n = 12 930.15 n = 11 930.15 + 92,155.73 n = 1 Solve for the IRR: =
0.94% × 12 = 11.26% (annual rate, compounded monthly)
(b) Adjustable rate portion now has an initial rate of 9.5% and an annual interest rate cap of 1% Loan Amount = Points = Fixed Rate Portion:
$95,000 2.00% 75.00% of the loan balance 10.50% annual interest rate 30 year term
(1)
(2)
(3)
Year
BOY Balance
Annual Interest Rate
Monthly Interest Rate (2)/12
0 1 2 3 4 5
$71,250 70,893 70,497 70,058 69,570
10.50% 10.50% 10.50% 10.50% 10.50%
0.88% 0.88% 0.88% 0.88% 0.88%
(4)
(5)
(6)
(7)
(8)
Monthly Amort (4) -(5)
Annual Amort.
Payments
Monthly Interest (3) × (1)
EOY Balance (1) - (7)
$651.75 651.75 651.75 651.75 651.75
$623.44 620.32 616.85 613.01 608.74
$28.31 31.43 34.90 38.74 43.01
$356.61 395.91 439.54 487.98 541.75
$70.893 70.497 70,058 69,570 69,028
18-60
Adjustable Rate Portion:
25.00% of the loan balance 9.00% initial interest rate 2.00% margin
(1)
(2)
(3)
BOY Balance
Capped Interest Rate
Monthly Interest Rate (2)/12
$23,750 23,604 23,472 23,351 23,173
9.50% 10.50% 11.50% 10.00% 11.00%
0.791% 0.875% 0.958% 0.833% 0.917%
(4)
(5)
(6)
(7)
(8)
Monthly Amort (4) -(5)
Annual Amort
Payments
Monthly Interest (3) × (1)
EOY Balance (1) - (7)
See note.
See note.
See note.
$23,604 23,472 23,351 23,173 23,008
Year
0 1 2 3 4 5
$199.70 217.00 234.45 208.78 225.50
Note: Although shown above, these columns are not necessary if a financial calculator are used to get the ending loan balance as was done here. To get the EOY balance, simply enter the BOY Balance as PV, the monthly interest rate in effect during that year as i, the monthly payment as PMT, 12 (for 12 months) as n, and solve for the FV. For example, in year 1 we have: PV = -$23,750, i = 9.50%/12, PMT = $199.70, n=12, solve for FV. Answer is $23,604. MORTGAGE SUMMARY: YEAR 0 1 2 3 4 5
BOY Balance
Payments
EOY Balance
$95,000. 94,497. 93,969. 93,409. 92,473.
$851.45 868.75 886.20 860.53 877.25
$94,497. 93,969. 93,409. 92,743. 92,036.
Yield: Using a financial calculator, the yield is now 11.01%.
Problem 5-10 (a) Loan Balance at the end of year five is $102,536.50 Solution: n = 1x12 or 12 i = 12% /12 or 1% PV = -$100,000 PMT = $800 Solve for the loan balance: FV = $102,536.50 (b) Loan balance at the end of year 2 will be $106,496.70 18-61
n = 1x12 or 12 i = 13/12 or 1 PV = -$102,536.50 (balance at the end of year 1) PMT = $800 Solve for the loan balance: FV = $106,496.70 Negative amortization during year 2 is $106,496.70 - $102,536.50 = $3,960.20 Total interest in year 2 will be all the mortgage payments plus the negative amortization or ($800 × 12) + $3,960.20 = $13,560.
Year 5: n = 4 x12 or 48 i = 13/12 or 1 PV = -$102,536.50 (balance at the end of year 1) PMT = $800 Solve for the loan balance: FV = $121,969.35 Negative amortization during year 2 to 5 is $121,969.35- $102,536.50 = $19,432.85 Total interest in year 2 to 5 (4 years) will be all the mortgage payments plus the negative amortization or ($800 × 48) + $19,432.85 = $57,832.85.
Problem 5-11 The effective cost increases to 14.13% Problem 5-12 The effective cost increase to 13.96%. The interest rate is limited to the lifetime cap of 5% which is why the rate is the same as the prior year. Problem 5-13 The yield increases to 17.84%. The payment cap limits the payment increase but not the effective cost because interest is still paid at the market interest rate. The unpaid interest accrues (negative amortization) and is reflected in the higher loan balance. Solutions to Questions—Chapter 6 Residential Financial Analysis Question 6-1 What are the primary considerations that should be made when refinancing? 18-62
The borrower must determine whether to present value of the savings in monthly payments is greater than the refinancing costs (points, origination fees, costs of (1) appraisal, (2) credit reports, (3) survey, (4) title insurance, (5) closing fees, etc. Question 6-2 What factors must be considered when deciding whether to refinance a loan after interest rates have declined? The payment savings resulting from the lower interest rate must be weighed against the costs associated with refinancing such as points on the new loan or prepayment penalties on the loan being refinanced. Question 6-3 Why might the market value of a loan differ from its outstanding balance? The balance of a loan depends on the original contract rate, whereas the market value of the loan depends on the current market interest rate. Question 6-4 Why might a borrower be willing to pay a higher price for a home with an assumable loan? An assumable loan allows the borrower to save interest costs if the interest rate is lower than the current market interest rate. The investor may be willing to pay a higher price for the home if the additional price paid is less than the present value of the expected interest savings from the assumable loan. Question 6-5 What is a buydown loan? What parties are usually involved in this kind of loan? A buydown loan is a loan that has lower payments than a loan that would be made at the current interest rate. The payments are usually lowered for the first one or two years of the loan term. The payments are ―bought down‖ by giving the lender funds in advance that equal the present value of the amount by which the payments have been reduced. Question 6-6 Why might a wraparound lender provide a wraparound loan at a lower rate than a new first mortgage? Although the wraparound loan is technically a ―second mortgage,‖ the wraparound lender is only required to make payments on the existing mortgage if the borrower makes payments on the wraparound loan. Furthermore, the wraparound lender is typically taking over an existing mortgage that has a below market interest rate. Thus, the wraparound lender is benefiting from the spread between the rate being earned on the wraparound loan and that being paid on the existing loan. This allows the wraparound lender to earn a higher return on the incremental funds being advanced even if the rate on the wraparound loan is less than the rate on a new first mortgage. Question 6-7 Assuming the borrower is in no danger of default, under what conditions might a lender be willing to accept a lesser amount from a borrower than the outstanding balance of a loan and still consider the loan paid in full? If interest rates have risen significantly, the market value of the loan will be less. Thus, the lender may be willing to accept less than the outstanding balance of the loan, especially if the lender still 18-63
receives more than the market higher market interest rate.
value of the loan. The lender can then make a new loan at the
Question 6-8 Under what conditions might a home with an assumable loan sell for more than comparable homes with no assumable loans available? The home with an assumable loan might be expected to sell for more than comparable homes with no assumable loans available when the contract interest rate on the assumable loan is significantly less than the current market rate on a loan with similar maturity and similar loan-tovalue ratio. Note that if the dollar amount of the assumable loan is significantly less than that which could be obtained with a market rate loan, the benefit of the assumable loan is diminished because the borrower may need to make up the difference with a second mortgage.
18-64
Question 6-9 What is meant by the incremental cost of borrowing additional funds? The incremental cost of borrowing funds is a measure of what it really costs to obtain additional funds by getting a loan with a higher loan-to-value ratio that has a higher interest rate. This measure is important because the contract rate on the loan with the higher loan-to-value ratio does not take into consideration the fact that this higher rate must be paid on the entire loan - not just the additional funds borrowed. Thus, the borrower should consider the incremental cost of the additional funds to know what it is really costing to borrow the additional funds. Question 6-10 Is the incremental cost of borrowing additional funds affected significantly by early repayment of the loan? The incremental cost of borrowing additional funds can be affected significantly by early repayment of the loan, especially if additional points were paid to obtain the additional funds. Thus, the borrower should consider how long he or she expects to have the loan when calculating the incremental cost of the additional funds.
18-65
Solutions to Problems—Chapter 6 Residential Financial Analysis INTRODUCTION The following solutions were obtained using an HP 12C financial calculator. Answers may differ slightly due to rounding or use of the financial tables to approximate the answers. As pointed out in the chapter, there is often more than one way of approaching the solution to the problems in this chapter. Thus ―alternative solutions‖ are shown were appropriate. Problem 6-1 (a) Because the amount of the loan does not matter in this case, it is easiest to assume some arbitrary dollar amount that is easy to work with. Therefore we will assume that the purchase price of the home is $100,000. Thus the choice is between an 80 percent loan for $80,000 or a 90 percent loan for $90,000. The loan information and calculated payments are as follows: Alternative 90% Loan 80% Loan Difference
Interest Rate 8.5% 8.0%
Loan Term 25 yrs. 25 yrs.
Loan Amount $90,000 80,000 $10,000
Monthly Payments $724.70 617.45 $107.25
i(n,PV,PMT,FV) n = 25×12 or 300 PMT = $107.25 PV = -$10,000 FV = 0 Solve for the annual interest rate: i = 12.26%
Solving for the interest rate with a financial calculator we obtain an incremental borrowing cost of 12.3 percent. (Note: Be sure to solve for the interest rate assuming monthly payments. With an HP12C you will first solve for the monthly interest rate, then multiply the monthly rate by 12 to obtain the nominal annual rate.) (b) Alternative 90% Loan 80% Loan Difference
Loan Amount $90,000 80,000
Points $1,800 0
Net Proceeds $88,200 80,000 $8,200
$107.25 × (MPVIFA, ?%, 25 yrs..) = $8,200 i(n,PV,PMT,FV) n = PMT =
25×12 or 300 $107.25 18-66
Monthly Payments $724.70 617.45 $107.25
PV = -$8,200 FV = 0 Solve for the annual interest rate: i = 15.35%
Solving for the interest rate with a financial calculator we now obtain an incremental borrowing cost of 15.35 percent.
(c) We now need the loan balance after 5 years. Alternative 90% Loan 80% Loan Difference
Loan Amount $90,000 80,000 $10,000
Monthly PaymentsLoan Balance $724.70 $83,508.62 617.45 73,819.37 $107.25 $9,689.37
Note that the net proceeds of the loan is still $8,200 as in Part b. Thus we have: i(n,PV,PMT,FV) n = 25×12 or 300 PMT = $107.25 PV = -$8,200 FV = $9,689.37 Solve for the annual interest rate: i = 17.96%
Solving for the interest rate with a financial calculator we now obtain an incremental borrowing cost of 17.96 percent. Problem 6-2 (a) For this problem we need to know the effective cost of the $180,000 loan at 9% combined with the $40,000 loan at 13%
Combined
Loan Amount $180,000 40,000 $220,000
Interest Rate 9% 13%
i(n,PV,PMT,FV) 18-67
Loan Term 20 yrs.. 20 yrs..
Monthly Payments $1619.51 468.63 $2,088.14
n = 240 PMT = $2,088.14 PV = -$220,000 FV = $0 Solve for the annual interest rate: i = 9.76%
Solving for the effective cost of the combined loans we obtain 9.76%. This is greater than the 9.5% rate on the single $220,000 loan. Thus, the $220,000 loan is preferable.
(b) REV We now need the loan balance after 5 years
Combined
Loan Amount $180,000 40,000 $220,000
Interest Rate Loan Term 9% 20 yrs.. 13% 20 yrs..
Monthly Payments Loan Balance $1619.51 $159,672.44 468.63 37,038.81 $2,088.14 $196,711.25
i(n,PV,PMT,FV) n = 60 PMT = $2,088.14 PV = -$220,000 FV = $196,711.25 Solve for the annual interest rate: i = 9.74%
Solving for the interest rate, which represents the combined cost, we obtain 9.74%. The effective cost of the single $220,000 would still be 9.5% even if it is repaid after 5 years because there were no points or prepayment penalties. Thus the $220,000 loan is still better. (c) 18-68
Assuming the loan is held for the full term (to compare with Part a:)
Combined
Loan Amount $180,000 40,000 $220,000
Interest Rate 9% 13%
Loan Term 20 yrs.. 10 yrs..
Monthly Payments $1619.51 597.24 $2,216.75
The combined payments are made for the first 10 years only. After that, only the payment on the $180,000 loan is made. (c) IRR(CF1, CF2, ….CFn) CFj -$220,000.00 2,216.75 2,216.75 2,216.75 2,216.75 2,216.75 2,216.75 2,216.75 2,216.75 2,216.75 2,216.75 1,619.51 1,619.51 1,619.51 1,619.51 1,619.51 1,619.51 1,619.51 1,619.51 1,619.51 1,619.51 Solve for the IRR: =
nj n = 12 n = 12 n = 12 n = 12 n = 12 n = 12 n = 12 n = 12 n = 12 n = 12 n = 12 n = 12 n = 12 n = 12 n = 12 n = 12 n = 12 n = 12 n = 12 n = 12 0.79% × 12 = 9.49% (annual rate, compounded monthly)
Note that the payment of $1,619.51 is first discounted as a 10 year annuity (years 11 to 20) and further discounted as a lump sum for 10 years to recognized the fact that the annuity does not start until year 10. When calculating the IRR in Excel, input the monthly payment (annuity) in each cell for each period as opposed to one lump annual payment amount. Solving for the cost we obtain 9.49%. This is less than 9.5% rate for the single $220,000 loan. Thus, the combined loans are preferred. Assuming the loan is held for 5 years (to compare with Part b): We now need the loan balance after 5 years. 18-69
Loan Amount $180,000 40,000 $220,000
Combined
Interest Rate Loan Term 9% 20 yrs.. 13% 10 yrs..
Monthly Payments Loan Balance $1619.51 $159,672.68 597.24 26,248.89 $2,216.75 $185,921.57
i(n,PV,PMT,FV) n = 60 PMT = $2,216.75 PV = -$220,000 FV = $185,921.57 Solve for the annual interest rate: i = 9.67%
We now obtain 9.67%. This is greater than the 9.5% rate for a single loan. Problem 6-3 Preliminary calculation: The existing loan is for $95,000 at a 11% interest rate for 30 years (monthly payments). The monthly payment is $904.71. The balance of the loan after 5 years is $92,306.41. Payment on a new loan for $92,306.41 at a 10% rate with a 25 year term are $838.79. (a) Alternative Old loan New loan Savings
Interest Rate Loan Term 11% 30 yrs.. 10% 25 yrs..
Loan Amount $95,000 92,306
Monthly Payments $904.71 838.79 $65.92
Cost of refinancing are $2,000 + (.03 × $92,306.41) = $4,769.19. Considering the $4,769.19 as an ―investment‖ necessary to take advantage of the lower payments resulting from refinancing i(n,PV,PMT,FV) n = 300 PMT = $65.92 PV = -$4,769.19 FV = $0 Solve for the annual interest rate: i = 16.30%
Solving for the rate we obtain 16.30%. It is desirable to refinance if the investor can not get a higher yield than 16.30% on alternative investments. Alternate solution: 18-70
Amount of new loan Cost of refinancing Net proceeds
$92,306.00 $4,769.19 $87,536.81
The net proceeds can be compared with the payment on the new loan to obtain an effective cost of the new loan. We have: i(n,PV,PMT,FV) n = 300 PMT = $838.79 PV = -$87,536.81 FV = $0 Solve for the annual interest rate: i = 10.70%
Solving for the effective cost we obtain 10.70%. Because the effective cost is less than the cost of the existing loan (11%) the conclusion is to refinance. (b) For a 5-year holding period we must also consider the balance of the old and new loan after 5 years. We have: Alternative
Loan Amount
Interest Rate
Loan Term
Old loan New loan
$95,000 92,306
11% 10%
30 yrs.. 25 yrs..
Monthly Payments $904.71 838.79 65.92
Loan Balance $87,648.82* 86,918.44 $730.38
* Balance after 5 additional years or 10 years total. Looking at the refinancing cash outflows as an investment we have: i(n,PV,PMT,FV) n = 60 PMT = $65.92 PV = -$4,769.19 FV = $730.38 Solve for the annual interest rate: i = -0.60%
Solving for the IRR we obtain -0.60%. The negative return tells you this is a bad investment if the new loan is paid off so quickly. The reason for the negative return, is that you pay for the refinancing up-front, but do not benefit from the lower 18-71
monthly payments on the new financing for a period of time long enough to cover and/or justify the cost of refinancing.
Alternative solution: The effective cost is now as follows: i(n,PV,PMT,FV) n = 60 PMT = $838.79 PV = -$87,536.81 FV = $86,918.44 Solve for the annual interest rate: i = 11.39% Solving for the effective cost we obtain 11.39%. The effective cost is now higher than the rate of return on the old loan (11%) so refinancing is not desirable. Problem 6-4 Payments on the $140,000 loan at 10%, 30 years are $1,228.60 per month. (a) Note that there are 25 years remaining. The balance after 5 years can be found by discounting the remaining payments as follows: PV (n,i,PMT,FV) n = 300 PMT = $1,228.60 i = 10% FV = $0 Solve for the annual interest rate: PV = $135,204.03
The market value of the loan can be found by discounting the payments of $1,228.60 for 25 years (monthly) using the required rate of 11%. We have: PV (n,i,PMT,FV) n = PMT = i = FV =
300 $1,228.60 11%/12 $0 18-72
Solve for the annual interest rate: PV = $125,352.88
This is lower than the balance of the loan because payments are discounted at a higher rate than the contract rate on the loan. (b) The balance of the original loan after five additional years (10 years from origination) is $127,313.21. To calculate the market value assuming the loan is repaid after 5 additional years, we have: PV (n,i,PMT,FV) n = 300 PMT = $1,228.60 i = 11% FV = $127,313.21 Solve for present value: PV = $130,144.64 Problem 6-5 (a) Alternative 1: Purchase of $150,000 home:
First mortgage
Interest Rate 10.5%
Loan Term 20 yrs..
Loan Amount $120,000
Monthly Payments $1,198.06
Loan Term 20 yrs.. 20 yrs..
Loan Amount $100,000 20,000 $120,000
Monthly Payments $899.73 234.32 $1,134.05
or Alternative 2: Purchase of $160,000 home:
Assumption Second mortgage
Interest Rate 9% 13%
The loan amounts are the same under the two alternatives. The second alternative has lower total payments resulting in savings of $64.01 per month ($1,198.06 - $1,134.05), but requires an additional $10,000 cash outflow as an additional down payment. i(n,PV,PMT,FV) n = 240 PMT = $64.01 PV = -$10,000 FV = $0 Solve for the annual interest rate: i = 4.64% 18-73
The IRR is 4.64%. This does not make sense if the investor can earn more than this on the $10,000. This appears to be too low to justify the additional $10,000 equity - especially with mortgage interest rates at 10.5%. Note that the borrower could take the $150,000 home and use the extra $10,000 to borrow less money, e.g., $110,000 instead of $120,000 which results in interest savings of 10.5% (the rate on the loan). The point is that the investor’s opportunity cost is 10.5%, which is higher than the 4.64% that would be earned by taking the second alternative.
Note to instructors: It is informative to calculate exactly how much more the borrower could pay for alternative 2. This is found by discounting the payment savings at 10.5%. We have: PV (n,i,PMT,FV) n = 240 PMT = $64.01 i = 10.50%/12 FV = $0 Solve for the annual interest rate: PV = $6,411.39 Thus, the borrower would be indifferent between alternative 1 and 2 if the price of the home for alternative 2 was $156,411. (b) With the homeowner providing the second mortgage for the additional $20,000 at 9% (purchase money mortgage) we have: Alternative 2: Purchase of $160,000 home:
Assumption Second mortgage
Interest Rate 9% 9%
Loan Term 20 yrs.. 20 yrs..
Loan Amount $100,000 20,000 $120,000
Monthly Payments $899.73 179.95 $1,079.68
Savings are now $1,198.06 - $1,079.68 = $118.38 per month. An additional down payment of $10,000 is still required. The IRR is now 13.17% (c) Alternative 2: Purchase of $160,000 home:
Assumption Second mortgage
Interest Rate 9% 9%
Loan Term 20 yrs.. 20 yrs..
18-74
Loan Amount $100,000 30,000 $130,000
Monthly Payments $899.73 269.92 $1,169.65
The savings are now $1,198.06 - $1,169.65 or $28.41 per month. Because of the additional amount of the second mortgage, there is no additional down payment even though $10,000 more is paid for the home. Thus, the borrower saves $28.41 under alternative 2 with no additional cash outlay- which is clearly desirable. Problem 6-6 Loan Wraparound Existing Difference
Amount $150,000 100,000 $50,000
Payment $1,800.25 1,100.25 $700.25
Term 15 yrs. 15 yrs. (remaining)
$700.25 × (MPVIFA, ?%, 15 yrs..) = $50,000 i(n,PV,PMT,FV) n = 180 PMT = $700.25 PV = -$50,000 FV = $0 Solve for the annual interest rate: i = 15.01% Solving for the IRR we obtain 15.01%. This is the incremental return on the wraparound. Because this is greater than the 14% rate on a second mortgage, the second mortgage is better. Alternative solution: Loan Second mortgage Existing loan Total
Amount $50,000 100,000 $150,000
Payment $665.87 1,100.00 $1765.87
Term 15 yrs. 15 yrs. (remaining)
The total payments on the existing loan plus a second mortgage is $1,765.87, which is less than the payments on the wraparound. Furthermore, the effective cost of the combined loans is as follows: i(n,PV,PMT,FV) n = 180 PMT = $1,765.87 PV = -$150,000 FV = $0 Solve for the annual interest rate: i = 11.64%
The IRR is 11.64%. Thus, the effective cost of the combined loans is less than the wraparound. Thus, the combined loans are better. Note: we can only compare payments when the loan terms are the same. However, we can compare effective costs when they differ. As a result, the effective cost is more general than simply comparing payments. 18-75
Problem 6-7 (a) Payments on a $100,000 loan at 9% for 25 years is $839.20. The present value of $839.20 at 9.5% for 25 years is $96,051.64. The difference between the contract loan amount ($100,000) and the value of the loan ($96,051.64) is $3,948. This must be added on to the home price. Thus, the home would have to be sold for $110,000 + $3,948 or $113,948. Alternative solution: Payments on a loan for $100,000 at 9.5%: $873.70 Payments on a loan for $100,000 at 9%: 839.20 Savings by getting the loan at 9%: $34.50 Present value of the saving discounted at 9.5%: PV (n,i,PMT,FV) n = 300 PMT = $34.50 i = 9.50% FV = $0 Solve for the annual interest rate: PV = $3,948
This is the amount that has to be added to the home as before. (b) The balance of the $100,000 loan (9%, 25 yrs.) after 10 years is $82,739.23. We now discount the payments on the $100,000 loan which are $839.20 and the balance after 10 years which is 82,739.23. Both are discounted at the market rate of 9.5%. We have: PV (n,i,PMT,FV) n = 300 PMT = $839.20 i = 9.50% FV = $82,739.23 Solve for the annual interest rate: PV = $96,973 Subtracting this from the loan amount of $100,000 we have $100,000 - $96,973.69 or $3,027. This is the amount that must be added to the home price. Thus, the home price must be $110,000 + $3,027 or $113, 027. Not as much has to be added relative to (a) because the borrower would not have to be given the interest savings for as many years. Alternative solution: The difference in payments for a $100,000 loan at 9% and $100,000 at 9.5% is $34.50 (same as alternative solution to part a.) We must also consider the difference in loan balances after 10 years. 18-76
Balance of $100,000 loan at 9.5% after 10 years:$83,668.75 Balance of $100,000 loan at 9% after 10 years: 82,739.23 Savings $929.52 We now discount the payment savings and the savings after 10 years. PV (n,i,PMT,FV) n = 120 PMT = $34.50 i = 9.50% FV = $929.52 Solve for the annual interest rate: PV = $3,027
Thus $3,027 must be added to the home price as above. Problem 6-8 (a)
Amount of Reduction Payment will be
Months Monthly payment reduction during the first year (50% of $726.96): $363.48 Monthly payment reduction during the second year (25% of $726.96): $181.74 Discounting the payment reduction at 10% per annum (10%/12 per month) $726.96 276
$363.48 $545.22 -
12 12
Solve for PV of all future monthly payments: PV (i,PMT,n,FV) CFj = 363.48 nj = 12 CFj = 181.74 nj = 12 Discount at i = 10% ÷ 12 And find PV = $6005.66
Note that the second year payment reduction is an annuity that starts after one year i.e., period 13. Thus, the builder would have to give the bank $6,005.66 up front. (b) Based on the results from (a), the buydown loan is worth $6,005.66 in present value terms. We would expect the home to sell for $6,005.66 more than a comparable home that did not have this loan available. Thus, if the home could be purchased for $5,000 more, the borrower would gain in present value terms by $6,006 - $5,000 or $1,006. Problem 6-9 (a) Step 1, Calculate the dollar monthly difference between the two financing options. Original loan payment: 18-77
PV = -$140,000 i = 7/12 or 0.58 n = 15×12 or 180 FV = 0 Solve for the payment: PMT = $1,258.36 Find present value of the payments at the market rate of 8% i = n = FV = PMT = Solve for PV: PV =
8%/12 15×12 or 180 0 $1,258.36 $131,675.49
This is the market (cash equivalent) value of the loan. The buyer made a cash down payment of $60,000. Cash equivalent value of loan $131,675.49 Cash down payment 60,000.00 Cash equivalent value of property $191,675.49 (b) If it is assumed that the buyer only expected to benefit from the favorable financing for five years: Loan balance after 5 years is $108,378 Find present value of payments for 5 years and loan balance at the end of the 5th year. i = n = FV = PMT = Solve for PV: PV =
8%/12 5×12 or 60 $108,378 $1,258.36 $134,804.72
Cash equivalent value of loan $134,804.72 Cash down payment 60,000.00 Cash equivalent value of property $194,804.72 The cash equivalent value is higher because the buyer was not assumed to have discounted the loan by as much. Problem 6-10 Question: A borrower is making a choice between a mortgage with monthly payment or bi-weekly payments; the loan will be $200,000@6% interest for 20 years. 18-78
A) How would you analyze these alternatives? B) What if the bi-weekly loan was available for 5.75%? How would your answer change? A. Calculate Monthly Payments: PV = <$200,000> FV = 0 n = 240 (12×20) i = 6% /12 Solve: PMT = $1,432.86 B. Calculate Bi-Weekly Payments: $1432.86 ÷ 2 = $716.43. Remember: bi-weekly payments total 26 per year C. Calculate maturity period: PV = <$200,000> FV = 0 i = 6% ÷ 26 PMT = $716.43 (1432.86/2) Solve: n = 17.3 years (449 payments / 26 payments per year) D. Compare Total Payments: $1,432.86 × 240 = $343,866.40 $716.43 × 449 = $321,677.07 Bi-weekly payments would be less costly by $22,209.33 (343,886.40 - 321,977.07). E. Recalculate the above based on 5.75% interest: Calculate Monthly Payments: PV = <$200,000> FV = 0 n = 240 (12×20) i = 5.75% /12 Solve: PMT = $1,404.17 Calculate Bi-Weekly Payments: $1,404.17 ÷ 2 = $702.08. PV = <$200,000> FV = 0 i = 5.75% /26 PMT = $702.08. Solve: n = 17.35 years (451 payments / 26 payments per year) The total number of payments is about the same as above but the payments are lower and less interest is being paid. 18-79
Total payments $702.08 × 451 = $316.638 This is even lower than the $321,677 with the rate at 6%. The difference is $5,039 over the loan term.
18-80
Chapter 6 Appendix Problem 6A-1 (a) Loan Monthly payment
$100,000, 10% interest, 15 yrs (monthly payments) $1,074.61
Before-tax
Month
After-tax Value Payment Interest Principal Balance AT of Deduction Payment 0 -100000 -100000 1 1074.61 833.33 241.27 99,759 250.00 824.61 2 1074.61 831.32 243.28 99,515 249.40 825.21 3 1074.61 829.30 245.31 99,270 248.79 825.82 4 1074.61 827.25 247.35 99,023 248.18 826.43 5 1074.61 825.19 249.42 98,773 247.56 827.05 6 1074.61 823.11 251.49 98,522 246.93 827.67 7 1074.61 821.02 253.59 98,268 246.30 828.30 8 1074.61 818.90 255.70 98,013 245.67 828.93 9 1074.61 816.77 257.83 97,755 245.03 829.57 10 1074.61 814.62 259.98 97,495 244.39 830.22 11 1074.61 812.46 262.15 97,233 243.74 830.87 12 1074.61 810.27 264.33 96,968 243.08 831.52 13 1074.61 808.07 266.54 96,702 242.42 832.18 14 1074.61 805.85 268.76 96,433 241.75 832.85 15 1074.61 803.61 271.00 96,162 241.08 833.52 16 1074.61 801.35 273.26 95,889 240.40 834.20 17 1074.61 799.07 275.53 95,613 239.72 834.88 18 1074.61 796.78 277.83 95,335 239.03 835.57 19 1074.61 794.46 280.14 95,055 238.34 836.27 20 1074.61 792.13 282.48 94,773 237.64 836.97 21 1074.61 789.77 284.83 94,488 236.93 837.67 22 1074.61 787.40 287.21 94,201 236.22 838.39 23 1074.61 785.01 289.60 93,911 235.50 839.10 24 1074.61 782.59 292.01 93,619 234.78 839.83 25 1074.61 780.16 294.45 93,325 234.05 840.56 26 1074.61 777.71 296.90 93,028 233.31 841.29 27 1074.61 775.23 299.37 92,728 232.57 842.04 28 1074.61 772.74 301.87 92,427 231.82 842.78 29 1074.61 770.22 304.38 92,122 231.07 843.54 30 1074.61 767.68 306.92 91,815 230.31 844.30 31 1074.61 765.13 309.48 91,506 229.54 845.07 32 1074.61 762.55 312.06 91,194 228.76 845.84 33 1074.61 759.95 314.66 90,879 227.98 846.62 34 1074.61 757.33 317.28 90,562 227.20 847.41 35 1074.61 754.68 319.92 90,242 226.40 848.20 Balance 90993.83 752.02 322.59 89,919 225.60 90768.23 18-81
36
The before-tax effective cost is 10 percent, the same as the interest rate on the loan. The after tax effective cost is 7 percent. This can be verified by computing the IRR using the after-tax payment column above. Because there are no points, the answer is also exactly equal to the before-tax effective cost times the complement of the tax rate, i.e. 10% (1 - .3) = 7% (b) Before-tax Month
After-tax Value Principal Balance AT Paymen Interest of t Deduction Payment 0 -95000 -96500 1 1074.61 833.33 241.27 94,759 250.00 824.61 2 1074.61 789.66 284.95 94,474 236.90 837.71 3 1074.61 787.28 287.32 94,186 236.18 838.42 4 1074.61 784.89 289.72 93,897 235.47 839.14 5 1074.61 782.47 292.13 93,605 234.74 839.86 6 1074.61 780.04 294.57 93,310 234.01 840.59 7 1074.61 777.58 297.02 93,013 233.28 841.33 8 1074.61 775.11 299.50 92,714 232.53 842.07 9 1074.61 772.61 301.99 92,412 231.78 842.82 10 1074.61 770.10 304.51 92,107 231.03 843.58 11 1074.61 767.56 307.05 91,800 230.27 844.34 12 1074.61 765.00 309.61 91,490 229.50 845.11 13 1074.61 762.42 312.19 91,178 228.73 845.88 14 1074.61 759.82 314.79 90,863 227.95 846.66 15 1074.61 757.19 317.41 90,546 227.16 847.45 16 1074.61 754.55 320.06 90,226 226.36 848.24 17 1074.61 751.88 322.72 89,903 225.56 849.04 18 1074.61 749.19 325.41 89,578 224.76 849.85 19 1074.61 746.48 328.12 89,250 223.94 850.66 20 1074.61 743.75 330.86 88,919 223.12 851.48 21 1074.61 740.99 333.62 88,585 222.30 852.31 22 1074.61 738.21 336.40 88,249 221.46 853.14 23 1074.61 735.41 339.20 87,910 220.62 853.98 24 1074.61 732.58 342.03 87,568 219.77 854.83 25 1074.61 729.73 344.88 87,223 218.92 855.69 26 1074.61 726.86 347.75 86,875 218.06 856.55 27 1074.61 723.96 350.65 86,524 217.19 857.42 28 1074.61 721.04 353.57 86,171 216.31 858.29 29 1074.61 718.09 356.52 85,814 215.43 859.18 30 1074.61 715.12 359.49 85,455 214.54 860.07 31 1074.61 712.12 362.48 85,092 213.64 860.97 32 1074.61 709.10 365.50 84,727 212.73 861.87 33 1074.61 706.06 368.55 84,358 211.82 862.79 34 1074.61 702.99 371.62 83,987 210.90 863.71 18-82
Balance 36
35 1074.61 90993.8 3
699.89 696.77
374.72 377.84
83,612 83,234
209.97 209.03
864.64 90784.80
The after-tax effective cost is 8.56%, found by the IRR of the ATCF column above (c) The before-tax effective cost is not 12.09%. It is higher than (a) due to the effect of the 5 points. The after-tax effective cost is still approximately the same as the answer that would be found by multiplying the before-tax cost times the complement of the tax rate which is 12.09 × (1 -.3) = 8.46%.
18-83
Problem 6A -2 Initial loan amount Monthly payment
$100,000 $839.20
Monthly loan schedule Cumulat ive Ending Intere Cumulat Cumulat Deferr Beginn ing st ive ive ed Mont Balanc Payme Inter Princi Balanc Deduct Deducti Interes Intere h e nt est pal e ion on t st - 100,25 500.00 500.00 750.00 250.00 1 100,00 500.0 750.0 0 0 0 250.00 0 2 100,25 500.0 751.8 - 100,50 500.00 1000.0 1501.8 501.88 0 0 8 251.88 2 0 8 3 100,50 500.0 753.7 - 100,75 500.00 1500.0 2255.6 755.64 2 0 6 253.76 6 0 4 100,75 500.0 755.6 101,01 2000.0 3011.3 1011.3 4 500.00 6 0 7 255.67 1 0 1 1 5 101,01 500.0 757.5 - 101,26 500.00 2500.0 3768.8 1268.8 1 0 8 257.58 9 0 9 9 - 101,52 500.00 3000.0 4528.4 1528.4 6 101,26 500.0 759.5 9 0 2 259.52 8 0 1 1 7 101,52 500.0 761.4 - 101,79 500.00 3500.0 5289.8 1789.8 8 0 6 261.46 0 0 7 7 - 102,05 500.00 4000.0 6053.2 2053.2 8 101,79 500.0 763.4 0 0 2 263.42 3 0 9 9 9 102,05 500.0 765.4 - 102,31 500.00 4500.0 6818.6 2318.6 3 0 0 265.40 9 0 9 9 10 102,31 500.0 767.3 - 102,58 500.00 5000.0 7586.0 2586.0 9 0 9 267.39 6 0 8 8 - 102,85 500.00 5500.0 8355.4 2855.4 11 102,58 500.0 769.4 6 0 0 269.40 5 0 8 8 12 102,85 500.0 771.4 - 103,12 500.00 6000.0 9126.9 3126.9 5 0 2 271.42 7 0 0 0 13 103,12 875.2 773.4 101.75 103,02 875.20 6875.2 9900.3 3025.1 7 0 5 5 0 5 5 14 103,02 875.2 772.6 102.51 102,92 875.20 7750.4 10673. 2922.6 5 0 9 3 0 04 3 15 102,92 875.2 771.9 103.28 102,81 875.20 8625.6 11444. 2819.3 3 0 2 9 0 96 5 16 102,81 875.2 771.1 104.06 102,71 875.20 9500.8 12216. 2715.3 9 0 5 5 0 10 0 17 102,71 875.2 770.3 104.84 102,61 875.20 10376. 12986. 2610.4 5 0 6 0 01 47 6 18 102,61 875.2 769.5 105.62 102,50 875.20 11251. 13756. 2504.8 0 0 8 5 21 05 4 18-84
19 102,50 875.2 768.7 106.41 102,39 875.20 12126. 14524. 2398.4 5 0 9 8 41 83 2 20 102,39 875.2 767.9 107.21 102,29 875.20 13001. 15292. 2291.2 8 0 9 1 61 82 1 21 102,29 875.2 767.1 108.02 102,18 875.20 13876. 16060. 2183.1 1 0 8 3 81 00 9 22 102,18 875.2 766.3 108.83 102,07 875.20 14752. 16826. 2074.3 3 0 7 4 01 38 7 23 102,07 875.2 765.5 109.64 101,96 875.20 15627. 17591. 1964.7 4 0 6 5 21 94 2 24 101,96 875.2 764.7 110.47 101,85 875.20 16502. 18356. 1854.2 5 0 4 4 41 67 6 a) For the first 12 months the payments are $500 and the actual interest incurred is higher than $500. However, the maximum interest deduction allowed is the amount of cash paid. Thus, the interest deduction in the first year is for the first 12 months the payments are $500 and the actual interest incurred is higher than $500. However, the maximum interest deduction allowed is the amount of cash paid. Thus, the interest deduction in the first year is 12 × $500.00 = 6,000 b) Because only the amount of the cash payment could be deducted and the actual amount of interest paid exceeded the cash paid, the excess interest must be carried forward into year 2. The deferred interest for a given month is defined as the excess of interest on the loan less the actual cash payment made. As seen above the deferred interest at the end of year 1 is $3,127. c) Interest deducted in year 2 is $875.20 × 12 = $10,502 Solutions to Questions—Chapter 7 Single Family Housing: Pricing, Investment and Tax Considerations Question 7-1 Why is the income approach to value often difficult to use on a single-family residential appraisal? Typically, the income approach is difficult to use because the sale of single family, rental properties are rare in the area. Question 7-2 What are the differences between the cost and sales comparison approaches to appraising property? When using the market approach, the appraiser estimates the value of a property by comparing the selling prices of properties similar to, and near, the property being appraised. Because no two properties are exactly alike, the values of similar properties are adjusted by the appraiser for dissimilarities. When using the cost approach, the appraiser establishes a value for the site on which the improvement is located, then determines the cost of reproducing the improvements and adds the two. After the costs of the improvement and land value are added, the appraiser deducts an amount for any depreciation that improvements have suffered since they were constructed. Question 7-3 What are the capital gains rules as applied to residential property owners? 18-85
For sales of personal residence a homeowner may exclude from income $250,000 of gain, and a married couple may exclude up to $500,000 of gain realized on the sale. (1) Individual must have owned and used the home as a principal residence for at least two of the five years prior to the sale (the two years do not have to be consecutive). (2) Exclusion applies to only one sale every two years. Question 7-4 List four important drivers of housing demand and price appreciation. Population growth, income, households, price of rental housing Question 7-5 What are public goods? How may they be reflected in house prices? Public goods include education, police, fire, health and other services provided by the local public sector. To the extent the quality/value of these services provided to homeowners exceed the cost (taxes, fees), paid, a net benefit is thought to exist. This net benefit is generally reflected in land/property prices. Question 7-6 When considering an investment in “distressed” properties, what are the most important areas of research that should be considered? (1) Market research to determine an expected future price when the investor plans to sell. (2) Title search to determine any defects in the title and/or liens as well as the cost to clear the title.
18-86
Solutions to Problems—Chapter 7 Single Family Housing: Pricing, Investment and Tax Considerations Problem 7-1 (a)
18-87
Tax deductions from owning
Property taxes Interest
$4,000
$4,080
$4,162
$4,245
6,349
6,234
6,114
5,990
5,861
Total tax deductions
$10,349 2,484
$10,314 2,475
$10,276 2,466
$10,235 2,456
$10,190 2,446
16,166
16,336
16,511
16,689
16,873
2,484
2,475
2,466
2,456
2,446
13,683
13,861
14,044
14,233
14,427
$24,480
$24,970
$25,469
$25,978
$25,978
Tax savings
$4,330
Net cost of owning
Cash Outflows before taxes Tax savings After tax cost
Net cost of renting
$24,000
Rents
Net Cash Flow from Owning Before Sale Cost of renting Cost of owning After Tax Cash Flow Own vs Rent
$24,000
$24,480
$24,970
$25,469
13,683
13,861
14,044
14,233
14,427
$10,317
$10,619
$10,925
$11,236
$11,551
1 204,000 14,280
2 208,080 14,566
3 212,242 14,857
4 5 216,486 220,816 15,154 15,457
157,182
154,250
151,198
148,022
144,716
32,538
39,265
46,187
53,311
60,643
$204,000 14,280
$208,080 14,566
$212,242 14,857
$216,486 $220,816 15,154 15,457
200,000
200,000
200,000
200,000
200,000
(10,280) 0 0 0 32,538
(6,486) 0 0 0 39,265
(2,615) 0 0 0 46,187
1,332 1,332 0 0 53,311
5,359 5,359 0 0 60,643
3
4
5
BT Cash Flow - Sale
Sales price Selling Costs Mortgage balance Benefit from sale (own - rent)
AT Cash Flow - Sale
Sales price Less selling costs Less purchase price Gain on sale Exclusion Taxable gain Tax After tax cash flow
Cash savings and IRR summary Cash flows
Year Sold 1 2 3 4 5
0 -40,000 -40,000 -40,000 -40,000 -40,000
1 $42,855 10,317 10,317 10,317 10,317
ATIRR
2 49,883 10,619 10,619 10,619
57,112 10,925 10,925
64,547 11,236
72,194
7.14% 25.31% 30.29% 31.91% 32.36%
The IRR from the cash flow savings from owning vs leasing is only 7.14% if the property is only held for one year but it increases significantly after that. So if the holding period is 2 years or more, owning is better than leasing. In fact, the 10% return would be achieved somewhere during the 2nd year of ownership.
18-88
Problem 7-1 (b) As noted above, the IRR from holding versus leasing is significantly in excess of 10% beyond a 1 year holding period. The longer the holding period, the more favorable the benefits of owning in this case.
Problem 7-1 (c) The initial rent would have to be $12,492 to get an after tax IRR of 5% in year 4 as shown in the following exhibit. Goal seek was used to find this answer in Excel. Trial and error could also be used. Chapter 7 Rent versus Own Analysis of a Personal Residence Property information
Loan Information:
Loan-to-value ratio Purchase price Initial Rent Rental growth rate Property growth rate Insurance Maintenance Expense growth Marginal tax rate Property tax % Selling expenses
80.00% $160,000 4.00% 30 12
Loan amount Interest rate Loan term (years) Payments (per year)
$200,000 $12,492 2.00% 2.00% $1,500 $1,500 3.00% 24.00% 2.00% 7.00%
Loan and equity calculations
Annual debt service (payment) Annual loan constant Equity investment
$9,166 5.73% $40,000 Summary loan schedule
End of year Payment Balance Interest Principal
1 $9,166 157,182 6,349 2,818
2 $9,166 154,250 6,234 2,932
3 $9,166 151,198 6,114 3,052
4 5 $9,166 $9,166 148,022 144,716 5,990 5,861 3,176 3,306
2 208,080 12,742
3 212,242 12,996
4 5 216,486 220,816 13,256 13,521
1
2
3
4
5
4,000 1,500
4,080 1,545
4,162 1,591
4,245 1,639
4,330 1,688
1,500 9,166 16,166
1,545 9,166 16,336
1,591 9,166 16,511
1,639 9,166 16,689
1,688 9,166 16,873
Property Data
Property value Rents
0 $200,000
1 204,000 12,492
BTCF (owner)
Year Property taxes Insurance Maintenance Principal and Interest Cash Outflows before taxes
18-89
Tax deductions from owning
Property taxes Interest
$4,000
$4,080
$4,162
$4,245
6,349
6,234
6,114
5,990
5,861
Total tax deductions
$10,349 2,484
$10,314 2,475
$10,276 2,466
$10,235 2,456
$10,190 2,446
16,166
16,336
16,511
16,689
16,873
2,484
2,475
2,466
2,456
2,446
13,683
13,861
14,044
14,233
14,427
$12,742
$12,996
$13,256
$13,521
Tax savings
$4,330
Net cost of owning
Cash Outflows before taxes Tax savings After tax cost
Net cost of renting
$12,492
Rents
Net Cash Flow from Owning Before Sale Cost of renting Cost of owning After Tax Cash Flow Own vs Rent
$12,492
$12,742
$12,996
$13,256
$13,521
13,683
13,861
14,044
14,233
14,427
($1,191)
($1,120)
($1,048)
($977)
($906)
1 204,000 14,280
2 208,080 14,566
3 212,242 14,857
4 5 216,486 220,816 15,154 15,457
157,182
154,250
151,198
148,022
144,716
32,538
39,265
46,187
53,311
60,643
$204,000 14,280
$208,080 14,566
$212,242 14,857
$216,486 $220,816 15,154 15,457
200,000
200,000
200,000
200,000
200,000
(10,280) 0 0 0 32,538
(6,486) 0 0 0 39,265
(2,615) 0 0 0 46,187
1,332 1,332 0 0 53,311
5,359 5,359 0 0 60,643
3
4
5
BT Cash Flow - Sale
Sales price Selling Costs Mortgage balance Benefit from sale (own - rent)
AT Cash Flow - Sale
Sales price Less selling costs Less purchase price Gain on sale Exclusion Taxable gain Tax After tax cash flow
Cash savings and IRR summary Cash flows
Year Sold 1 2 3 4 5
0 -40,000 -40,000 -40,000 -40,000 -40,000
1 $31,347 -1,191 -1,191 -1,191 -1,191
18-90
ATIRR
2 38,145 -1,120 -1,120 -1,120
45,139 -1,048 -1,048
52,334 -977
59,737
-21.63% -3.82% 2.24% 5.00% 6.43%
Problem 7-2 (a) Equity Investment = $60,000, House Value = $300,000 Less Mortgage $240,000 4% ÷ (1-.80) = 4% ÷ .20 = 20%
(b)
Year 0 1 2 3
Appr. Rate 0 0 2 3
House Price 300,000 300,000 306,000 315,180
Equity 60,000 60,000 66,000 75,180
Calculation EAHE 0% 6,000 ÷ 60,000 9,180 ÷ 66,000
10.0% 13.9%
Average Annual Rate of Appreciation: (0% + 10.0% + 13.9%) ÷ 3 = 7.97% Compounded: (1.0 *1.10*1.139) = 1.2529 Calculation: n = 3, PV = -1, PMT = 0, FV = 1.2529 solve i = 7.8% (Note the greater divergence between the arithmetic and geometric mean due to the irregular rates of appreciation.) Problem 7-3 (a) Property #1 123 Clay St. $85,000
Address Sale Price Less: Adjustment Time of Sale Location (1,000) Site (1,000) Design Construction Qlty. Number of Bedrooms (1,200) Baths Garage
Property #2 301 Cherry St. $79,000
Property #3 119 Avenue X $75,000 1,500
1,200 1,500 2,000 800
800
Total Adjustment
(3,200)
2,000
5,800
Indicated Value
$81,800
$81,000
$80,800
Comparable #2 had the fewest adjustments ($2,000) and, thus, its value of $81,000 was given the most consideration when determining the value of the property. Comparable #1 required the next fewest adjustments ($3,200), but this property is larger than the subject property and contains more amenities such as better design and a corner lot. As a result, this property was given less consideration in the determination of value than was comparable #2. Comparable #3 was given the least consideration in determining the value of the subject property. This was due to the rather large number and size of adjustments which this property required in the appraisal process. The $5,800 in adjustments which had 18-91
been made on this property indicates that it is least similar to the subject property. The estimated value of the property using the market approach to value is $81,000. (b)
Estimated Reproduction Cost of the Dwelling: $36.00 per square foot × 1,800 square feet Estimated Reproduction Cost of the Garage Estimated Land Value
$64,000 3,700 13,000
Estimated Value Using the Cost Approach
$81,500
Problem 7-4 (a) (1) Equity: Price $200,000 – Loan $160,000 = $40,000. (2) Cash out flows are assumed to occur monthly and will average $2,525. (3) Solving we have: PV = -$40,000 PMT = -$2,525 i = 20% / 12 n = 12 Solve for FV = $82,013 (4) Adding the FV of $82,013 to the loan balance of $160,000 and $8,000 in selling expenses results in $250,013 as the desired selling price @ EOY1 in order to achieve a 20% return. (5) The other issues that we must consider for doing this analysis are the time when the expenses occurred and the amount of expenses at those times. If more expenses are greater earlier rather than later in the year, then the required selling price to get 20% return will be higher. (b) (1) Equity = $40,000 Rental Income = Additional Interest = $7,200 ÷ 12 or $600 per month Net Monthly Inflow Year 2 Beginning of Year 1 = $(40,000) Monthly Outflows Year 1 $2,525 Monthly Outflows Year 2
$1,200 per month =
$600
=
-
=
+$600
Solving the cash flow to get an IRR value of 20%, we get the selling price at the end of year 2 as follows: CF0 CF1-12 CF13-24 i FV
= -$40,000 = -$2,525 = +$600 = 20%/12 = $92,108 18-92
Adding FV of $92,108 to the mortgage balance of $160,000 and $8,000 in selling expenses produces a sale price of $260,108 at end of year 2. Problem 7-5 Cash flows are summarized as follows: (a) PV = $200,000 Price -$180,000 Loan +$10,500 Acquisition fees $30,500 Equity (b) Monthly outflows: $2,000 Repairs 637.50 Interest $2,637.50 per month (c ) Year of sale: $180,000 Loan repayment 3,000 Selling expenses $183,000 (d) Solve for FV as follows: PV = -$30,500 PMTs = -$2,637.50 i = 20%/12 n = 12 Solve for FV = (X+$183,000) FV = $254,910 It appears that this is not a good investment if the expected sale price is $225,000. The investor would have to achieve a $254,910 sale price in order to earn the desired 20% return. Problem 7-6 (a)
(b)
18-93
(c)
(d)
Solution to Questions—Chapter 8 Underwriting and Financing Residential Properties
Question 8-1 What is the legislative intent of federal truth-in-lending disclosures, and what specific disclosures are required under the act? The intent of FTL legislation is to require that lenders disclose to borrowers financial information contained in loan agreements in a uniform manner. This is required so that borrowers can compare the cost of loan offers from different lenders. It should be stressed that FTL legislation does not attempt to regulate the cost of mortgage credit, but it mandates uniform disclosure of the cost of credit. Question 8-2 When would the cost of credit life insurance be included in the finance charge of an APR calculations for the truth-in-lending disclosures? When the lender requires it as a condition of obtaining a loan. Question 8-3 18-94
What assumptions about future composite rate of interest on an adjustable rate mortgage is made when determining the APR for federal truth-in-lending disclosures? The initial rate of interest remains unchanged over the life of the loan. Question 8-4 List the closing cost items, which require RESPA disclosure. What items may be excluded from disclosures under the act? What form can these disclosures take? The estimates provided by the lender generally cover costs in the following categories: (a) title search, (b) title examination and opinion, (c) title insurance, (d) attorney’s fee, (e) preparation of documents, (f) property survey, (g) credit report, (h) appraisal (i) pest inspection, (j) notary fees, (k) loan closing service fee, (l) recording fees and any transfer tax, (m) loan origination fees, (n) discount points, (o) mortgage insurance application fees, (p) assumption fees, (q) mortgage insurance premiums, (r) escrow fees (fees charged for setting up escrow accounts), and (s) prepaid mortgage interest. In addition, it is suggested, but not required, that the lender disclose (a) hazard insurance premiums and (b) escrow deposits for mortgage insurance, hazard insurance, and property taxes, if these amounts are known at the time of the advance disclosure. In practice, it would be difficult for the lender to know these latter two amounts three days after the borrower has applied for a loan. Although these two items are not likely to be estimated by the lender at the time of the advance disclosure, they will be charged to the borrower at the time of closing. The form of the advance disclosure may vary from lender to lender and still remain within the requirements of the act. Typically, the disclosure will be made in dollar amounts which will be estimates of the cost of settlement services which are to be performed. However, it is also acceptable for the lender to disclose ranges for settlement costs. For instance, a loan origination fee could be stated as ranging from $1,500 to $2,000 in the lending area where the settlement is to occur. However, the lender may not disclose a range if a specific party is required by the lender to provide a settlement service. In this case, a specific dollar amount is required. Also, the lender is under no requirement to redisclose if the estimates of settlement services provided to the borrower change prior to the time of closing. Question 8-5 What types of fees and conditions are prohibited under RESPA? Title Insurance Placement, Kickbacks and Referral Fees. Question 8-6 For what items may a lender require escrow accounts from a borrower? Property taxes, hazard insurance and mortgage default insurance premiums.
18-95
Solution to Problems—Chapter 8 Underwriting and Financing Residential Properties Problem 8-1 (a) To determine the APR: First, determine the monthly mortgage payment. PMT(i,n,PV,FV) i = n = FV = PV = Solve for PMT
5% ÷ 12 300 0 $70,000 =
$409.21
Next, determine the lender’s yield. i(PV,FV,n,PMT) PV FV n PMT Solve for i
= = = = =
$68,500 0 300 $409.21 .434869 * 12 = 5.22%
To calculate the APR, round to the nearest ¼ of a percent. APR = 5.25% (b) The APR calculated above, in all likelihood, will not be the yield that the lender receives, because the mortgage will not be held to its full term. If the borrower prepays the loan ahead of schedule, the lender’s yield will be higher. However, one of the main economic reasons that the borrower prepays is to obtain financing at a lower interest rate. Problem 8-2 Solution to credit account problem: (a) Current capacity being used is calculated as: ($3,000 + $5,000 + $8,000) / ($5,000 + $10,000 + $15,000) = 53.3% (b) If balance #2 is transferred to account #3, then capacity used would be: ($3,000 + $13,000) / ($5,000 + $15,000) = 80% (c) She must get the limit on either account #1 or #3 to increase by a total of $10,000 which is the credit limit that was lost when the balance in account #2 was transferred, otherwise the capacity used will increase and may cause the credit score to decline. 18-96
Problem 8-3 (a) Loan Amount $65,000, points 2% or $1,300 = amount disbursed at close $63,700 Payments at 5% for 30 years at start rate of 5% = $348.93 Interest due at composite rate of 7% = $65,000 or $379.93 monthly Difference (b) - (a) ($379.17 - $348.93) compound @7%, 12 months, $374.75 Add (d) to loan balance $65,374.75 Solve for IRR @ EOY, find interest rate that make PV payments and balance = $63,700 $63,700 = $348.93 (mos. 1-12) + $439.40 (mos. 12-360) i = 8% (approx.), due to 2 points and deferred interest at 7% or the portion of monthly payments deferred until EOY (b) The disclosures must be completed three days after application is made by the borrower. The APR disclosure aids the borrower in understanding the effective cost of credit with all fees and charges added to the loan. It makes comparison between loans easier. However, the APR on an ARM will almost certainly not reflect the true cost of funds to the borrower, indeed, the APR on an ARM assumes that the composite rate on the ARM will remain constant over the life of the loan and generally, this is not the case. Problem 8-4 (a) Real Estate Settlement Statement Borrower/Buyer: Loan related: Loan origination fees Prepaid interest 9/22-9/30 [(.05*84,000)÷365*9 days] Hazard insurance premium
Seller: $
2,100.00 103.56 420.00
Other: Add: Property tax refund due buyer Property tax escrow Recording fees/doc prep. Attorney’s fees-Prudent Title insurance Transfer tax Recording fees/mortgage Inspections Closing fee
(578.63) 133.33 200.00 150.00 400.00 225.00 30.00 50.00 125.00
Total fees and prepaid interest
$
3,358.26
Purchase price
105,000.00 18-97
Sale Price Less: Commission Recording fee Mortgage payoff Property tax Refund/Proration to seller Amt due seller
$ 105,000.00 6,300.00 5.00 32,715.00 578.63 $ 65,401.37
Plus: Total Fees Less: Deposit Less: Loan Amount Amount due from buyer
3,358.26 1,500.00 84,000.00 $ 22,858.26
*Note: Buyer pays $800 or a full year’s property tax in arrears on January 1 for the prior year but owns the property for only 101 of the 365 days in the year. Therefore, the seller will need to reimburse the buyer at closing for the 264 days that they owned the property or (264 ÷ 365) * 800 or $578.63. This is a credit to the buyer and charge to the seller on the closing statement. (b) APR Calculation: Prepaid finance charges Prepaid interest Loan origination fees
2,100.00
Total
$2,203.56
103.56
A. Solve for Monthly Payment: PMT(i,n,PV,FV) i = FV = PV = n = Solve for PMT
5% ÷ 12 0 $84,000 360 =
$450.93
B. Solving for the IRR: i(PV,FV,n,PMT) FV PMT n PV Solve for i
= = = = =
0 $450.93 360 $81,796.44* .860833 * 12 = 5.24%
Therefore, the APR rounds to 5.25%. *Note PV = Loan $84,000 less Points of $2,100 and Prepaid interest $103.56 Net Advanced to borrower $81,796.44 = PV C. Regular monthly payments start November 1st. Solutions to Questions—Chapter 9 Introduction to Income-Producing Properties: Leases and Market for Space 18-98
Question 9-1 How does the use of leases shift the risk of rising operating expenses from lessor to the lessee? Leases determine how much risk will be borne by the lessor versus the lessee. Future increases in market rent are compensated for by including an inflationary adjustment, such as a CPI adjustment. In the case of a CPI adjustment, the risk is shifted to the lessee, because the change in rents is not known in advance. As the lessee is responsible for any unexpected increases in the level of inflation, the lessor is insured that the real value of the lease will be preserved. The lessor can shift additional risk to the lessee by including net lease or expense stop provisions in the lease. It is important to note, however, that we would expect the lessor to accept a lower base rent as the burden of risk is shifted to the lessee. Question 9-2 What is the difference between base rents and effective rents? Base rents reflect rent that will be paid per rentable square foot of leased space. It does not include additional items such as finish out costs, expense pass throughs and other costs that are included when calculating effective rents. Question 9-3 What is meant by usable vs. rentable space? Usable space is the area actually occupied by the tenant. Rentable space is usable space plus a share of common area in a property which is included in the load factor. Question 9-4 What are CAM charges? These are expenses related to common area maintenance of hallways, lobbies, etc. that are usually prorated and passed on to tenants. Question 9-5 What are (a) pass through expenses, (b) recoverable expenses, (c) common area expenses? Give examples of each. Pass throughs are expenses such as electricity, insurance, and property taxes that are billed directly to tenants on the basis of rentable area that they occupy. Recoverables are expenses incurred by owners for specific expenses identified in a lease such as security, maintenance, utilities, etc. and are pro-rated and billed to tenants. Common areas include mallways, parking areas, lobbies, and hallways. Expenses related to these areas are referred to as common area expenses. Question 9-6 What is an estoppels? Why is it used? It is a legal document used in many circumstances. In real estate, it is used by prospective investors to determine factual information with tenants, such as amount of any rent owed, improvements promised by the current owners, etc. Question 9-7 What is meant by "loss to lease"? 18-99
Many leases reflect market conditions and rents that existed when the lease was executed. Many financial statements estimate gross rental revenue based on (1) all rental space re-leased today at prevailing rents and compare that amount to (2) actual rental revenue based on leases that have been executed at various times in the past. The difference between (1) and (2) is "loss to lease", or the difference between current market rents and rents actually collected based on lease terms with each tenant. Question 9-8 What types of expenses would property owners pay when operating and maintaining common areas? Give examples for office, retail, and warehouse properties. Common area are for the benefit of all tenants. An example for office properties would be the lobby area. For retail a good example is enclosed malls where all the area not occupied by the store itself is common area to allow pedestrians to walk from store to store and use for special events. Warehouse properties might have a loading dock that is shared by all tenants. All of these property types might have parking as a common area. The tenants would often pay a pro-rata portion of the operating expenses related to these common areas such as property taxes, insurance, utilities and maintenance.
18-100
Solutions to Problems—Chapter 9 Introduction to Income-Producing Properties: Leases and Market for Space Problem 9-1 a) Discount rate
10.00%
I. Net Lease with Steps: Year Net Rent
1 $15.00
Average rent Present value Effective rent
2 16.50
3 18.00
4 19.50
5 21.00
3 3.00% 16.97
4 3.00% 17.48
5 3.00% 18.01
3 $30.00 11.00 19.00
4 $30.00 12.00 18.00
5 $30.00 13.00 17.00
3 3.00% $23.34 11.00
4 3.00% $24.04 12.00
5 3.00% $24.76 13.00
$18.00 $67.15 $17.72
II. Net Lease with 100% CPI Adjustment: Year Exp. CPI Net Rent
1 $16.00
Average rent Present value Effective rent
2 3.00% 16.48 $16.99 $64.04 $16.89
III. Gross Lease Year Gross rent Less: expenses Net rent
1 $30.00 $9.00 21.00
Average rent Present value Effective rent
2 $30.00 10.00 20.00 $19.00 $72.74 $19.19
IV. Gross Lease with Expense Stop at $9.00 and CPI Adjustment: Year Exp. CPI Gross rent Less: expenses
1 $22.00 $9.00
2 3.00% $22.66 10.00 18-101
Plus: reimbursement Net rent
0.00 13.00
1.00 13.66
2.00 14.34
3.00 15.04
4.00 15.76
Average rent $14.36 Present value $53.94 Effective rent $14.23 Note: Effective Rent = Present Value / PVIFA, 10%, 5yrs b)
With the first type of lease, the tenant bears the risk of any unexpected change in operation expense. For the lessor, although the lease includes a step-up, higher than anticipated inflation could erode the real value of the rental income. The second alternative includes a CPI adjustment rather than fixed step-ups. The risk of unexpected inflation is shifted to the lessee. The third alternative is a gross lease. This is much riskier for the lessor than any of the net leases. The lessor bears the risk if operating expenses differ from what is expected. The fourth one is a gross lease that combines a CPI adjustment with an expense stop. This shifts the risk of any increases in expenses to the tenant, while retaining any decrease in expenses. Overall, if we rank the alternatives in terms of risk to the lessor, from the least risky to the most risky, the order should be: Gross Lease with Expense Stop and CPI Adjustments, Net Lease with CPI Adjustments, Net Lease with Steps and Gross Lease. That is: 4<2<1<3.
c)
Based on the analysis in (b), we might expect the effective rents for the four alternatives should exhibit the same order, from the least to the most risky to the lessor: 4<2<1<3. As the results showed in (a), the effective rents for four alternatives do rank the same way. The one with the most risk is also the one that offers the greatest effective rent.
Problem 9-2 (a)
Total rentable area in building if leased to one tenant: 300,000 (total building area) – 45,000 (non-rentable area) = 255,000 sq. ft. (rentable)
(b)
Load Factor for 7th floor: -
(c)
Total rentable space on 7th floor = 28,000 Common area on 7th floor = 3,000, usable area = 25,000, load = 28,000 ÷ 25,000 = 1.12
Rentable area for tenant: 5,000 usable × 1.12 load = 5,600 rentable Rent: (5,600 × $30 psf) = $168,000 or $14,000 per month 18-102
(d) If common area in lobby is included in load for all tenants, then 7th floor load could be adjusted upward as follows: ( 7th Floor Load ) × l + ( Other Common Area in Building / Total Building Rentable) or 1.12 × l + (30,000 ÷ 255,000) or 1.12 × 1.118* = 1.25 1.25 × 5,000 = 6,258 rentable space to tenant * 30,000 ÷ 255,000 = 11.8% (e)
Rent to tenant with full building load: 6,258 × $30 = $187,745 or $15,645 per month
Problem 9-3 (a) Year Cash Flows
0
1 $20
2 $21
3 $22
4 $23
5 $24
4 $27
5 $28
PV @ 10% = $82.68 Effective Rent PSF:
$21.81
(b) Year Cash Flows
0 $150,00 0
1 $24
2 $25
3 $26
PV @ 10% = $97.84 Total PV of Lease ($97.84 × 20,000 sq. ft. ) = Less PVOF Moving Allowance Less PVOF Tenant Improvements NPV of Lease Square Feet of Rentable Space NPV PSF Effective Rent
$1,956,813 50,000 (Year 0) 100,000 (Year 0) $1,806,814 $ 20,000 $ 90.34 $ 23.83
Note: Effective rent paid to the owner is still greater with these allowances than is the case in (a). Therefore, lease (b) is better for owner. (c) Year Cash Flows
0 $300,000
1 $23
2 $24
PV Rents PSF @ 10% = $94.05 18-103
3 $25
4 $26
5 $27
Total PV of Lease ($94.05 × 20,000 sq. ft.) = Less Buyout NPV of Lease Effective Rent
$ 1,880,998 300,000 $ 1,580,000 / 20,000 = $79.04 psf $20.85
The effective rent to owner of Atrium is lower than both alternatives (a) and (b) above, even if the buyout is paid monthly during year (1). Net rents would be $8 psf in year (1) and effective rent would be $21.21, which would continue to be lower than both cases (a) and (b) above. Therefore, when compared to (a) and (b), this alternative is not a good deal for the owner of Atrium.
Problem 9-4 In-line occupied area = 1,300,000 square feet Common Area = Total area – Anchor tenant occupied area - In-line occupied area = 700,000 square feet Total Maintenance cost = common area × maintenance cost psf = 700,000 × $8 = $5,600,000 Anchor contribution to CAM = $2 per s.f. × 800 s.f. = $1,600,000 CAM (Additional rent per square feet covered by in-line tenant) = (total maintenance cost – anchor contribution) / In-line occupied area = ($5,600,000 - $1,600,000) /1,300,000 = $3.08 per square feet In line tenants would have to pay $3.08 per s.f. in CAM charges, plus their base rent per square foot of rentable area. Problem 9-5 (A) Option A is best for the owner because it gives higher effective rent psf. See the calculations below Option A
18-104
Discount rate
12%
PART a Option A sq. ft. base rent Steps CAM charges CAM charge increase
10,000 $25 $1 $3 6%
Year Base rent per sf Base rent CAM Net rent
1 2 25 $26 $250,000 $260,000 $30,000 $31,800 $280,000 $291,800
3 4 5 $27 $28 $29 $270,000 $280,000 $290,000 $33,708 $35,730 $37,874 $303,708 $315,730 $327,874
Present value Effective rent
$1,085,492 $301,126
$108.55 per s.f. $30.11 per s.f.
Option B sq. ft. base rent Year 1 sales Breakpoint CAM charges CAM charge increase Overage
10,000 $23 $850,000 increasing $900,000 $3 6% 8%
Year Tenant sales Base rent per sf Base rent CAM Overage Net rent
1 2 3 4 5 $850,000 $935,000 $1,028,500 $1,131,350 $1,244,485 $23 $24 $25 $26 $27 $230,000 $240,000 $250,000 $260,000 $270,000 $30,000 $31,800 $33,708 $35,730 $37,874 $0 $2,800 $10,280 $18,508 $27,559 $260,000 $274,600 $293,988 $314,238 $335,433
Present value Effective rent
$1,050,345 $291,376
10% per year
$105.03 per s.f. $29.14 per s.f.
(B) Option B now has the higher effective rent as shown below.
18-105
Option A sq. ft. base rent Steps CAM charges CAM charge increase
10,000 $25 $1 $3 6%
Year Base rent per sf Base rent CAM Net rent
1 25 $250,000 $30,000 $280,000
2 $26 $260,000 $31,800 $291,800
3 4 5 $27 $28 $29 $270,000 $280,000 $290,000 $33,708 $35,730 $37,874 $303,708 $315,730 $327,874
Present value Effective rent
$1,085,492 $301,126
Option B sq. ft. base rent Year 1 sales Breakpoint CAM charges CAM charge increase Overage
10,000 $23 $850,000 increasing $900,000 $3 6% 8%
Year Tenant sales Base rent per sf Base rent CAM Overage Net rent
1 2 3 4 5 $850,000 $1,020,000 $1,224,000 $1,468,800 $1,762,560 $23 $24 $25 $26 $27 $230,000 $240,000 $250,000 $260,000 $270,000 $30,000 $31,800 $33,708 $35,730 $37,874 $0 $9,600 $25,920 $45,504 $69,005 $260,000 $281,400 $309,628 $341,234 $376,879
Present value Effective rent
$1,107,572 $307,251
$108.55 per s.f. $30.11 per s.f.
20% per year
$110.76 per s.f. $30.73 per s.f.
Problem 9-6 (see notes A-E below for explanation) Gross Potential Income (A) Loss to Lease (B) Vacancy & Collection Loss ( C)
1,620,000 9,550 128,160 18-106
Net Rental Income Recoveries (D) Other Income Total Income Operating Expenses (E) NOI Recurring Expenses Non-recurring Expenses Net Cash Flow
1,482,290 220,800 200,000
100,000 250,000
Notes A-E (A) 1st 6 months 40 units @ $550 @ 6 mos = $132,000 80 units @ 600 @ 6 mos = 288,000 80 units @ 800 @ 6 mos = 3 84,000 Total $804,000
First 6 months of lease (B) 10 units * (550-500) 6 mos = 3,000 20 units * (600-580) 6 mos = 2,400 10 units * (800-805) 6 mos
420,800 1,903,090 893,200 1,009,890
= (300)
350,000 659,890
2nd 6 months @ 560 = 134,400 @ 610 = 292,800 @ 810 = 388,800 816,000
Total
$1,620,000
Remaining months of lease (B) 10 units * (560-500) 3 mos = 20 units * (610-580) 4 mos = 2,400 10 units * (810-805) 5 mos = 250
$5,100
$9,550 $4,550 2nd 6 mos 4 units * 560 *6 = 13,440 6 units * 610 * 6 = 21,960 6 units * 810 * 6 = 29,160 16 64,560
( C) 4 units * 550 * 6 = 13,200 6 units * 600 * 6 = 21,600 6 units * 800 * 6 = 28,800 16 63,600 (D) 184 units @ 100 @ 12 mos = 220,800 (E) 184 units @ 400 @ 12 mos + $10,000 apt. locator = 893,200 Problem 9-7 Part (A)
SUMMER PLACE MALL Revenue: Base Rents (400,000 sq. ft. @ $20) Add: Overage Rents CAM recoveries Less: Vacancy @ 10% of Base Rents Effective Gross Income Less: Operating Expenses Maintenance/Repair Management/Admin/Leasing
8,000,000 400,000 250,000 800,000 7,850,000 1,200,000 230,000 18-107
128,160
Property Taxes Insurance Total Operating Expenses Recurring Capital Expenses Net Operating Income
1,715,000 105,000 3,250,000 160,000 3,410,000 $4,440,000
Part (B) Future Pro Formas: 1) The possibility of vacancy reduction from a high level of 10%. 2) Operating expenses in the pro forma may be underestimated as to utility expense which may not be included in the statement. 3) The likelihood of overage rents continuing or increasing from current levels. 4) A lease rollover schedule should be developed to assess the probability of lease renewal among 40 tenants. 5) A market analysis to determine the likelihood of new retail (competitive) space coming into the marketplace.
Problem 9-8 Part (A) BETTS DISTRIBUTION CENTER Rent: (200,000 sq. ft. @$7.00) Add: Recoveries @ $1.50 Insurance Property Taxes Effective Gross Income Less: Operating Expenses (NR) Property Taxes Insurance Total Operating Expenses CapEx/Improvement Allowance Net Operating Income
1,400,000 300,000 15,000 50,000 700,000 15,000 50,000 765,000 60,000
365,000 $1,765,000
825,000 $940,000
Part (B) 1) The possibility of future increases in property taxes and/or insurance. 2) An analysis of competing warehouse space in the market area. 3) Given the age (8 years) of the Center, is the Cap-ex Improvement allowance adequate for the next 5 years? 4) Is the tenant sound financially? What is the outlook for the industry in which it operates? 5) If the tenant is doing well financially, is there a possibility that we can expand the Center and increase the leasable space?
Problem 9-9 Part (A) 18-108
WEST OFFICE PLAZA Revenue: (300,000 sq. ft. @$20) Add: Other Income (parking) Recoverable Expenses Less: Vacancy Effective Gross Income Less: Operating Expenses Management/Admin/ Property Taxes Insurance Operating/Leasing Utilities Janitorial/Cleaning Business Taxes Total Operating Expenses CapEx/Improvement Allowance Net Operating Income
6,000,000 450,000 750,000 300,000 6,900,000 695,000 675,000 430,000 667,000 1,159,100 489,000 110,000 4,225,100 700,000
4,925,100 1,974,900
Part (B) 1) Market survey of competing properties to determine vacancy/rent trends. 2) Lease rollover schedule for West's 40 tenants to determine renewals/rents. 3) Adequacy of improvement allowance for an 8 year old property. 4) Review of other revenue sources (retail in lobby, cell towers, etc.) 5) Estimates of service employment growth in the relevant metro area—survey tenants to determine expansion possibilities.
Problem 9-10 (a) The second alternative below now has the highest effective rent as shown below.
18-109
Year Gross Rent Less Expenses Net Rent Average Rent Present Value Effective Rent
Year Gross Rent Less Expenses Plus Reimburse Net Rent Average Rent Present Value Effective Rent
GROSS LEASE: 1 2 40.00 40.00 20.00 22.00 20.00 18.00 16.00 68.38 16.23
3 40.00 24.00 16.00
GROSS LEASE with EXPENSE STOP: 1 2 3 38.00 38.00 38.00 20.00 22.00 24.00 0.00 2.00 4.00 18.00 18.00 18.00 18.00 75.82 18.00
4 40.00 26.00 14.00
5 40.00 28.00 12.00
4 38.00 26.00 6.00 18.00
5 38.00 28.00 8.00 18.00
GROSS LEASE WITH FREE RENT AND STEPS: Year 1 2 3 4 Gross Rent 20.00 40.00 49.00 49.00 Less Expenses 20.00 22.00 24.00 26.00 Net Rent 0.00 18.00 25.00 23.00 Average Rent 17.40 Present Value 70.92 Effective Rent 16.84
5 49.00 28.00 21.00
(b) The Year 1 rent would have to be $16.79 as shown below to have an effective rent of $18 which was the effective rent on the lease with steps in the original spreadsheet (before the changes in part a above). This results in a negative net rent in year 1 after expenses. (Goal seek was used to find the rent.)
Year Gross Rent Less Expenses Net Rent Average Rent Present Value Effective Rent
GROSS LEASE WITH FREE RENT AND STEPS: 1 2 3 4 16.79 40.00 49.00 49.00 20.00 21.00 22.00 23.00 (3.21) 19.00 27.00 26.00 18.76 75.82 18.00
5 49.00 24.00 25.00
Solution to Questions—Chapter 10 Valuation of Income Properties: Appraisal and the Market for Capital
Question 10-1 What is the economic rationale for the cost approach? Under what conditions would the cost approach tend to give the best value estimate? 18-110
The rationale for using the cost approach to valuing (appraising) properties is that any informed buyer of real estate would not pay more for a property than what it would cost to buy the land and build the structure. The cost approach is most reliable where the structure is relatively new and depreciation does not present serious complications. Question 10-2 What is the economic rationale for the sales comparison approach? What information is necessary to use this approach? What does it mean for a property to be comparable? The rationale for the market approach (otherwise known as the sales comparison approach), lies in the principle that an informed investor would never pay more for a property than what other investors have recently paid for comparable properties. The sales comparison approach to valuation is based on data provided from recent sales of properties highly comparable to the property being appraised. For a property to be comparable, the sale must be an ―arm’s-length‖ transaction or a sale between unrelated individuals. Sales should represent normal market transactions with no unusual circumstances, such as foreclosure, sales involving public entities, and so on. Question 10-3 What is a capitalization rate? What are the different ways of arriving at an overall rate to use for an appraisal? An overall rate or overall capitalization rate is the rate on the overall property (debt and equity). One way of arriving at an overall rate is to use the band of investment approach. This is based on taking into consideration the investment criteria of both the lender and the equity investor involved in a project. This is done by taking a weighted average of the equity dividend rate expected by the investor and the mortgage loan constant (expressed on an annual basis) required by the lender. Two different ways of arriving at an overall rate are the direct capitalization approach and the present value method. Question 10-4 If investors buy properties based on expected future benefits, what is the rationale for appraising a property without making any income or resale price projections? Using the direct capitalization approach, this technique is a very simple approach to the valuation of income producing property. The rationale is based on the idea that at any given point in time, the current NOI produced by a property is related to its current market value. A survey of other transactions including sales prices and NOI (NOI ÷ sales prices) indicates the cap rate that competitive investments have traded for. This survey provides cap rates that indicate what investors are currently paying relative to current income being produced. A parallel in equity securities markets would be earnings yield (or earnings per share ÷ price) or price earnings multiples (Price ÷ earnings per share). Question 10-5 What is the relationship between a discount rate and a capitalization rate? A capitalization rate is equal to the difference between the discount rate and the expected growth in income. In other words, changes in income over the economic life of the property are ignored when using a capitalization rate.
18-111
Question 10-6 What is meant by a unit of comparison? Why is it important? A unit of comparison is used in the sales comparison approach to valuation. To the extent that there are differences in size, scale, location, age, and quality of construction between the project being valued and recent sales of comparable properties, adjustments must be made to compensate for such differences. The appraiser must find an appropriate unit of comparison for a given property. Examples are price per square foot for an office building, price per cubic foot for warehouse space, price per bed for hospitals, or price per room for hotels. Question 10-7 Why do you think appraisers usually use three different approaches when estimating value? If perfect information was available, then theoretically the same value should result regardless of the methods chosen, be it cost, market, or income capitalization. Even with imperfect information, there should be some correspondence between the three approaches to value, which is the reason appraisal reports will typically contain estimates of value based on at least two approaches to determining value. Question 10-8 Under what conditions should financing be explicitly considered when estimating the value of a property? Financing should be explicitly considered when using the mortgage-equity capitalization method. With this method, the value of a property can be estimated by explicitly taking into consideration the requirements of the mortgage lender and equity investor, hence the term ―mortgage-equity capitalization‖. Question 10-9 What is meant by depreciation for the cost approach? There are three categories of depreciation for the cost approach. They are very difficult to determine and, in many cases, require the judgment of appraisers who specialize in such problems. The three categories are as follows: Physical deterioration. Functional or structural obsolescence due to the availability of more efficient layout designs and technological changes that reduce operating costs. External obsolescence that may result from changes outside of the property such as excessive traffic, noise, or pollution. Question 10-10 When may a "terminal" cap rate be lower than a "going in" cap rate? When may it be higher? A terminal cap rate may be lower than the going in cap rate if between the present time and end of a holding period interest rates are expected to fall, risk is expected to decline, or demand is expected to increase (thereby producing higher rents and/or appreciation). A higher terminal cap rate would result if the opposite changes in the three situations stated above occurred. Question 10-11 In general, what effect would a reduction in risk have on "going in" cap rates? What would this effect have if it occurred at the same time as an unexpected increase in demand? What would be the effect on property values?
18-112
A reduction in risk lowers cap rates because expected returns are lower. If this occurred at a time when demand increases, property values would rise significantly because of increases in rents from greater demand and lower cap rates. Question 10-12 What are some of the potential problems with using a "going in" capitalization rate that is obtained from previous property sales transactions to value a property being offered for sale today? Problems occur if properties being used as "comparables" have different lease terms, maturities, and credit quality of tenants. Further, if properties are older, have depreciated, have different functional design, etc. than the subject, problems can occur. In these cases cap rates must be either adjusted to reflect these differences or not used at all. Question 10-13 When estimating the reversion value in the year of sale, why is the terminal cap rate applied to NOI for the year after the holding period? When we sell a property the price paid by the next investor is an assessment of income for his expected period of ownership. Therefore, for the next investor, or potential buyer, the NOI for his first year of ownership will be the year after we sell the property. This will be the first year of his investment. Question 10-14 Is a cap rate the same as an IRR? Which is generally greater? Why? No. The cap rate is the relationship between the current NOI and present value. The IRR is the return on all future cash flows from the operation and sale of the property. Usually the IRR is greater than the cap rate. Question 10-15 Discuss the differences between using (1) a terminal cap rate and (2) an appreciation rate in property value when estimating revision values. The terminal cap rate approach to estimating a reversion value is based on the assumption that in the year of sale, investors will value the property based on the new "going in" cap rate at the time. Estimates of the terminal cap rate are made by adjusting the current or going in cap rate to reflect any depreciation that is likely to occur over the holding period. A risk premium may also be added because the cap rate is being applied to NOI several years in the future which is less certain than the current NOI that a going in cap rate would be applied to. Using a rate of appreciation to estimate the reversion value is based on the investor's expectation as to trends in property values. This could be a reflection of risk, expected cash flows, interest rates, and returns on other investments such as stocks and bonds.
18-113
Solution to Problems—Chapter 10 Valuation of Income Properties: Appraisal and the Market for Capital INTRODUCTION The homework problems in this chapter provide practice in application of all three of the appraisal approaches. The required solution procedure follows the examples in the text. However, the problems purposely do not indicate exactly which approach to use. Students should learn to determine which approach is appropriate given the information available, which is, of course, the way it works in practice. Problem 10-1 Part (a) (1) The goal is to find the present value of NOI from year 1-7 and (2) the present value of the reversion value, or selling price, at the end of year 7. Present Value of NOI in years 1-7 is as follows: End of Year 1 2 3 4 5 6 7
NOI
PV at 12%
1,000,00 892,857 0 1,000,00 797,194 0 1,000,00 711,780 0 1,200,00 762,622 0 1,250,00 709,283 0 1,300,00 658,620 0 1,339,00 605,696 0
(3) The reversion value at the end of year 7 is determined by NOI in year (8) or 1,379,170 ÷ .09 (which is the term NAI cap rate or 12% - 3%). This produces an expected sale price of $15,324,111. However, this must be discounted at 12% for 7 years to present value or $6,931,850. We add the PV of NOI ($5,138,052) + PV of REV ($6,931,850) and get a property value of $12,069,902. Part (b) The terminal cap rate is .09 or (12% - 3%). Part (c) The going in cap rate is NOI1 of $1,000,000 ÷ $12,069,902 or .082851, .083 rounded. Part (d) The difference between the "going in" cap rate of .083 and "going out" or terminal cap rate .09 is attributable to the fact that the property will be 7 years older, and holding all else constant, will trade at a discount much like properties that are 7 years older than the subject property would trade today. 18-114
Problem 10-2 (a) The property value is $22,222,222 Solution: Property Value = NOI Next Year / (Discount Rate - Growth Rate) $22,222,222 = $2,000,000 / ( 0.13 0.04 ) (b) If we survey recent sales, the cap rates indicated from recently sold properties that are comparable to the subject property should be 0.09, otherwise (1) market conditions have changed. If other properties have sold with cap rates lower than .09, property values have declined. If they have sold for higher cap rates, then property values have increased. Solution: "Going in" Cap Rate = NOI Year 1 / Property Value .09 = $2,000,000 / $22,222,222 (c) If r = 12%, the property value would be $25,000,000 Solution: Property Value = NOI Next Year / (Discount Rate - Growth Rate) $20,000,000 = $2,000,000 / ( 0.12 0.04 ) (d) Market cap rates should be falling and property values should be increasing. Problem 10-3 Office is the highest and best use of this site. The analysis for the Baker Tract is as follows: Office Rent 2,400,000 Expenses (960,000) Cash Flow 1,440,000 Cap Rate .10 Property Value Cost (10,000,000)
Retail 2,400,000 (1,200,000) 1,200,000 .11 14,400,000 10,909,090 ( 8,000,000)
Residual
2,909,090
4,400,000
Problem 10-4 Step 1, Calculate the NOI for the Office Building Solution: Rents $6,000,000 PGI or EGI 6,000,000 less: Operating Expenses 2,400,000 NOI $3,600,000 Step 2, Calculate the Building Value at Cost: Solution: 300,000 sq. ft. × $100 per sq. ft. = $30,000,000 (a) Land Value would be $10,000,000. Solution: Property Value = NOI Next Year / (Discount Rate - Growth Rate) $40,000,000 = $3,600,000 / ( 0.12 0.03 ) 18-115
Land Value = Property Value - Building Value at Cost $10,000,000 = $40,000,000 - $30,000,000 (b) Land Value would be $15,000,000 Solution: Property Value = NOI Next Year / (Discount Rate - Growth Rate) $45,000,000 = $3,600,000 / ( 0.12 0.04 ) Land Value = Property Value - Building Value at Cost $15,000,000 = $45,000,000 - $30,000,000 Percentage Change in Land Value would be a 50% increase Solution: Percentage Change = (New Land Value - Old Land Value) / Old Land Value 0.50 = ( 15,000,000 - 10,000,000 ) / 10,000,000 (c) The Land Value would be $2,727,273 Solution: Property Value = NOI Next Year / (Discount Rate - Growth Rate) $32,727,273 = $3,600,000 / ( 0.12 0.01 ) Land Value = Property Value - Building Value at Cost $2,727,273 = $32,727,273 - $30,000,000
Percentage Change in Land Value would be a 72.73% decrease Solution: Percentage Change = (New Land Value - Old Land Value) / Old Land Value -0.7273 = ( 2,727,273 - 10,000,000 ) / 10,000,000 (d) If the land owner is asking $12,000,000 for the land, the project would not be feasible (under the assumptions in (a)) because it is more than the estimated land value of $10,000,000. (e) To justify a $12 million land value, something has to give: 1. Expected Return on the Investment could increase to 12.7% from 12% Solution: Property Value = Implied Land Value + Building Value at Cost $42,000,000 = $12,000,000 + $30,000,000 Cap Rate (R) = NOI Year 1/ Property Value 0.0857 = 3,600,000 / 42,000,000 Expected Return (r) = Required Return (R) + Growth Rate 0.1157 = 0.0857 + 0.03 2. Expected growth (g) in NOI would increase from 0.03 to 0.0343 18-116
Solution: Property Value = Implied Land Value + Building Value at Cost $42,000,000 = $12,000,000 + $30,000,000
Cap Rate (R) = NOI Year 1/ Property Value 0.0857 = 3,600,000 / 42,000,000 Expected Growth (g) = Expected Return (r) - Required Return (R) 0.0343 = 0.12 0.0857 3. Building Costs would have to decrease by $2,000,000, or by $6.67 per sq. ft. and the investor will earn 12%. Solution: Max Building Costs = Expected Property Value - Amount Paid for Land $28,000,000 = $40,000,000 $12,000,000 $28,000,000 / 300,000 = $93.33 per square foot compared to $100 per square foot $100 - $93.33 = $6.67 4. Rents would have to increase from $6,000,000 to $6,300,000 or average rent per square foot from $20 to $21 and the investor would still earn 12%. Solution: Property Value = Implied Land Value + Building Value at Cost $42,000,000 = $12,000,000 + $30,000,000 NOI $3,780,000
= =
Property Value × Required Return (R) $42,000,000 × 0.09
Rents = NOI / 0.6* $6,300,000 = $3,780,000 / 0.6* *Operating Expenses are 40% of rents (1-0.4 = 0.6) and NOI is rent less operating expenses.
18-117
Problem 10-5 (a) The present value of the property would be $588,235. Solution: Property Value = NOI Next Year / (Discount Rate - Growth Rate) $588,235 = $100,000 / ( 0.13 + 0.04 ) (b) The new development would produce NOI of $200,000 and when a cap rate of .07 is applied a value of $2,857,142 is indicated. If the cost to redevelop (demolish/rebuild/release) is $1,000,000 the property could be acquired for $588,235 and a profit of $1,268,909 or (2,815,142-1,000,000588,235) could be earned. Problem 10-6 (a) The estimated value of this property is $1,172,457 Solution: End of (a) (b) Year NOI PV at 11% 1 2 3 4 5 6 7 8 9 10 11 PVCF
$100,000 105,000 110,000 115,000 120,000 125,000 130,000 135,000 140,000 145,000 150,000*
(c) REV
(d) PVREV at 11%
(e) Total PV
$90,090 85,220 80,431 75,754 71,214 66,830 62,616 58,580 54,729 51,067 $696,532
$
696,532 528,277 10 resale $1,224,809
1,500,000
528,277
*To estimate resale price. (b) The current or ―going in‖ cap rate (R) for this property is 0.0853 Solution: ―Going In‖ Cap Rate = NOI Year 1 / Total PV 0.0816 = $100,000 / $1,224,809 (c) The difference between the cap rate in (b) and the .10 terminal cap rate is caused by the fact that as properties age and depreciate over time, the production of income declines. Therefore, the expected growth in NOI from an older property should be less than that of a new property. This means that, holding all else constant, when compared to newly developed properties, a property this is 10 years old should have a higher cap rate than a new one. (d) That economic conditions today and 10 years from now will be the same. Or, that if economic conditions change, all properties and other investments will be affected in the same way, thereby not affecting the relative performance or expected returns in a disproportionate manner. 18-118
18-119
Problem 10-7 Calculation of incurable physical depreciation: Reproduction cost Less: curable physical depreciation Less: curable functional obsolescence Balance subject to depreciation
$5,000,000 300,000 200,000 4,500,000
Incurable physical depreciation (5/50 or 10%) 450,000 Calculation of depreciated cost: Reproduction cost Physical depreciation: Curable Incurable (from above) Functional obsolescence: Curable Incurable* Value of Building
$5,000,000 $300,000 450,000 200,000 207,063 3,842,937
Value of building Add land value
3,842,937 1,000,000
Total value estimate
$4,842,937
**$25,000 × (PVIFA, 45 yrs., 12%) $207,063 Problem 10-8 (a) Comparable Rent/unit #1 $550 #2 650
Price $9,000,000 6,600,000
=
Units 140 90
25,000 × 8.282516
Price/unit $64,286 73,333
=
GRM* 117 113
*
Price/unit divided by rent/unit
Thus the GRM ranges from about 113 to 117. This implies a range in value for the subject property as follows: Rent $600 600
× × ×
Units 120 120
× × ×
GRM 117 113
= = =
Est. value $8,424,000 8,136,000
Note: Because vacancy is the same for both comparables and the subject property, the vacancy can be ignored. That is, the potential gross rent multiplier can be used. If the vacancy was not the same, then using an effective gross rent multiplier would be preferred. Because the rental income is provided for in this problem, use of a rent multiplier (either gross or effective gross) is the preferred solution. However, an alternative approach to the problem would be to 18-120
estimate value based on using only the price per unit. That is, the price per unit ranges from $64,286 to $73,333. This implies a range in price for the 120 unit subject property from $7,714,320 to $8,799,960. (b) Other information that might be considered includes differences between the subject property and the comparable properties in expense ratios, financing, expected trends in rents and property values, and risk.
18-121
Problem 10-9 (a) Loan payment (PMT) = NOI / DCR = $150,000 / 1.2 = $125,000 Loan amount (using a financial calculator): PMT = $125,000; i = 10/12%, n = 20x12; FV = 0; Solve for PV PV = $1,079,423 Solve for loan balance after 5 years using financial calculator: PMT = $125,000; i = 10/12%, n = 5x12; PV = $1,079,423; Solve for FV FV = $969,348 Project NOI Year 1 2 3 4 5 6
NOI $150,000 154,500 159,135 163,909 168,826 173,891
PMT $125,000 125,000 125,000 125,000 125,000
Cash flow to equity $25,000 29,500 34,135 38,909 43,825
Resale = 173,891 / .09 = Loan balance = Cash flow from sale
$1,932,123 969,348 $ 962,775
Year 1 2 3 4 5
Cash flow to equity $25,000 29,500 34,135 38,909 43,825 + $ 962,775
PV of Cash flow to equity at 12% = $666,035 (b)
Total value Total value Total value
(c)
Cap rate
= PV of cash flow to equity + loan amount = $666,035 + $1,079,423 = $1,745,458 = NOI / Value = $150,000 / $1,745,458 = 8.59%
18-122
18-123
Problem 10-10 (a) Comparable #1 Rent (350,000 s.f. × $3.90) Vacancy and expenses (50%) NOI
$1,365,000 682,500 $682,500
Price Overall rate (682,500 / 9,400,000)
$9,400,000 7.26%
Comparable #2 Rent (300,000 s.f. × $4.10) Vacancy and expenses (50%) NOI
$1,230,000 615,000 615,000
Price Overall rate (615,000 / 7,900,000)
$7,900,000 7.79%
Comparables 1 and 2 imply an overall rate of about 7.53%. Application to the subject: Rent (320,000 s.f. × $4.00) Vacancy and expenses (50%) NOI Price = NOI / Overall rate = 640,000 / 0.0753 = $8,499,336
$1,280,000 640,000 $640,000
(b) Examples of additional information that would be desirable about the comparable properties and the subject property include the trend in NOI, property values, financing , and risk. Problem 10-11 Refer to table below, the highest land value is now $1,714,286 with a highest and best use of warehouse. The higher growth rate for warehouse was enough to change the highest and best use.
Office
$500,000.00 .13-.03
(a/c = d) Implied Property Value R $ 0.10 5,000,000.00
Retail
$600,000.00 .12-.04
0.08
7,500,000
Apartment $400,000.00 .12-.03 Warehouse .10-.03
0.09 0.07
4,444,444 5,714,286
Use
(a)
(b)
Year 1 NOI
(r-g)
(c)
18-124
(e) Building Costs $ 4,000,000.00 $ 6,000,000.00 $ 3,000,000.00 $
(d) (e) Implied Land Value 1,000,000 1,500,000 1,444,444 1,714,286
$400,000.00
4,000,000.00
Problem 10-12 (a) Rose garden has a better quality and location then other comparables. It offers all the amenities offered by other apartments and has more parking space. In sum, Rose garden should have lower going-in cap rate then all other comparables. (b) Going in cap rate = NOI/ Value = 1645000/27000000 =0.0609 This cap rate is less than the cap rates of the other comparable apartments. (c) Value of the Rose garden apartment after 5 years = NOI in year 6/ cap rate = 1645000*(1.03)^5 /(0.0609+.005) = 28,937,873 Hence the return on the investment can be calculated by using the IRR function in excel or by solving following equation: 27,000,000 = 1,645,000/(1+r)^1 +1,645,000*1.03/(1+r)^2+1,645,000*1.03^2/(1+r)^3+1,645,000*1.03^3/(1+r)^4+1,645,000*1.03^4/(1+ r)^5+28,937,873.33/(1+r)^5 Return = 7.67%. This is below the required rate of 8%. Therefore, the asking price is too high to achieve 8%. Problem 10-13 (a) The price of the apartment can be calculated by solving the following equation PV= 200,000/(1.1)^1 +210,000/(1.1)^2+ 220,000/(1.1)^3+ 230,000/(1.1)^4+ 240,000/(1.1)^5+ PV*1.03^5 /(1.1)^5 18-125
This produces: PV= PVNOI + PVREV or PV= 826,775 + [PV(1.03)5 × (1/1 + .10)5] PV= 826,775 + PV(1.159274 × .620921) PV= 826,775 + PV(.7198181) .280182PV= 826,775 PV= 2,950,849 The price will be = $2,950,850 (b) The price of the apartment in year 5 = $2,950,850*1.03^5 = $3,420,843 (c ) Value at end of year 5 can be estimated even when present value is not known. This is done in part (a) by expressing future value in terms of present value as done in solution (a) of this question or by expressing present value in terms of future value. (d) Land Value = Property Value – Building Cost = $2,950,850 - $2,300,000 = $650,850
Problem 10-14 (a) The loan increases to $403,673 from $336,394 and the value increases to $504,531from $501,960. (b) We would expect the lender to normally charge a higher interest rate for a greater loan amount. The equity investor is also likely to require a higher return on equity due to the additional risk. With a DCR of only 1.0 any drop in NOI will result in negative cash flow for the investor. Problem 10-15 (a) Warehouse is now the highest and best use with a land value of $2,214,286 as shown below:
Office
$500,000.00 .13-.03
(a/c = d) Implied Property Value R $ 0.10 5,000,000.00
Retail Apartment
$600,000.00 .12-.04 .12-.02
0.08 0.10
(a) Use
Year 1 NOI
(b) (r-g)
(c)
7,500,000 4,000,000 18-126
(e) Building Costs $ 3,500,000.00 $ 6,500,000.00 $
(d) (e) Implied Land Value 1,500,000 1,000,000 1,500,000
$400,000.00 Warehouse $400,000.00 .10-.03
0.07
5,714,286
2,500,000.00 $ 3,500,000.00
2,214,286
(b) Warehouse is still the highest and best use of the site with a land value of $2,214,286 as shown below:
Office
$500,000.00 .13-.04
(a/c = d) Implied Property Value R $ 0.09 5,555,555.56
Retail
$600,000.00 .12-.04
0.08
7,500,000
Apartment
$400,000.00 .12-.02
0.10
4,000,000
Warehouse $400,000.00 .10-.03
0.07
5,714,286
Use
(a)
(b)
Year 1 NOI
(r-g)
(c)
(e) Building Costs $ 3,500,000.00 $ 6,500,000.00 $ 2,500,000.00 $ 3,500,000.00
(d) (e) Implied Land Value 2,055,556 1,000,000 1,500,000 2,214,286
Problem 10-16 The value increases to $12,368,216 from $10,573,934 due to the lower required return and the higher resale price resulting from the lower terminal capitalization rate. (Answers may differ slightly due to rounding.)
Solutions to Questions—Chapter 11 Investment Analysis and Taxation of Income Properties Question 11-1 What are the primary benefits of investing in real estate income property? Net Income: Dollars left over after collecting rent and paying expenses but before considering taxes and financing costs. Property Sale: Expecting a price increase over a specified holding period increases investor return. Diversification: Reduces overall risk to hold many types of investments. Taxes: Preferential tax benefits. Taxable income is often less than before-tax cash flow. Question 11-2 Name the four general real estate investment styles and describe each. Identify three investment strategies within these general categories and give examples of each. (4) styles: Core, Core Plus, Value Added, Opportunistic Under Core:
Office Properties Trophy Properties Gateway Markets 18-127
Under Core Plus:
Under Value Added:
Under Opportunistic:
Properties to be re-tenanted Properties needing minor capital improvements Properties to be leveraged Properties with excess land to be developed Properties to have greater amenities (fitness center, restaurant) Properties needing major improvement (e.g., parking lot expansion, improving elevators) Raw land development Distressed assets Loans in default
Question 11-3 What factors affect a property‟s projected NOI? Expected market rents and vacancy rates Expenses associated with operating the property Nature of any leases on the property Question 11-4 What factors would result in a property increasing in value over a holding period? Inflation: This causes rents as well as the final sale price to be higher. Demand: Increased demand for space may increase value if the supply of space doesn’t increase as well. Question 11-5 How do you think expense stops and CPI adjustments in leases affect the riskiness of the lease from the lessor‟s point of view? There is less risk for the lessor with expense stops and CPI adjustments in leases. CPI Adjustments: The risk of unexpected inflation is shifted to the lessee. Expense Stops: The risk of increases in expenses is shifted to the lessee while allowing the lessor to retain the benefit of any decrease in expenses. Question 11-6 Why should investors be concerned about market rents if they are purchasing a property subject to leases? Even if the investment is an existing building that has already been leased, the income can be affected when the existing leases expire and are renewed at the market rent at the time. Question 11-7 What is meant by equity? The investor’s initial equity in the project is equal to the purchase price less the amount borrowed. The amount of equity an investor has in a property may change over time if the property value and loan balance changes, e.g., if the property value increases and the loan balance is reduced through amortization, the investor’s equity increases. Question 11-8 What are the similarities and differences between an overall rate and an equity dividend rate? Difference: The overall rate relates the entire NOI to the value of the property. The equity dividend rate relates the BTCF (or equity dividend) in the first year to the initial equity investment. 18-128
Similarity: Neither one of these is a measure of investment yield because they do not take into account future income from operations or resale of the property at the end of the holding period. Both are based on a single year, usually the first year. Question 11-9 What is the significance of a debt coverage ratio? It is a ratio of the NOI to the mortgage payment that indicates the riskiness of a loan. It is the degree to which the NOI from the property is expected to exceed the mortgage payment. Lenders typically want a debt coverage ratio (DCR) to be at least 1.2. Question 11-10 What is meant by tax shelter? The term ―tax shelter‖ refers to an investment that allows a taxpayer to reduce taxable income. Although most of the tax shelter benefits of real estate were removed by the Tax Reform Act of 1986, depreciation deductions still provide some ―shelter‖ in that they are non-cash deductions that reduce taxable income. Interest deductions on the mortgage also serve to reduce and in a sense shelter taxable income. Question 11-11 How is the gain from the sale of real estate taxed? The entire taxable gain from the sale of real estate is taxed at the same rate as ordinary income. It is still important to keep track of capital gains/losses and ordinary income gains/losses. This is due to TRA rules for passive investors and properties acquired prior to 1986. Question 11-12 What is meant by an effective tax rate? What does it measure? An effective tax rate is a tax rate that takes into account the effects of depreciation and time value of money. It measures the actual difference between the BTIRR and the ATIRR. This difference is the effective tax rate and can be less than the actual marginal tax rate. This difference is also due to the fact that the interest on the mortgage loan is deductible. Question 11-13 Do you think taxes affect the value of real estate versus other investments? Yes. Not all investments are treated alike when it comes to federal income taxes. Thus, taxes must be considered when comparing returns for investments which are not taxed in the same manner. Investments that have the same before-tax return may have quite different after-tax returns. Question 11-14 What is the significance of the passive activity loss limitation (PALL) rules for real estate investors? The PALL rules are important because, in general, passive losses cannot be used to offset income from another category. Because any tax loss from real estate is usually considered a passive loss, it cannot be used to offset income from other sources such as active income from salaries and wages or portfolio income from interest or dividends.
18-129
Solutions to Problems—Chapter 11 Investment Analysis and Taxation of Income Properties Problem 11-1 ASSUMPTIONS: Current Market Rent Gross square feet of building Net rentable square feet of building Projected Increase in Market Rent Management costs Estimated increase in CPI Vacancy rate starting year 4
Tenant
Sq. ft.
Tenant 1 Tenant 2 Tenant 3 Total
20,000 15,000 15,000 50,000
Rent per s.f.
$17.00 per s.f. 50,000 s.f. 50,000 s.f. 3.00% per year 5.00% of Effective Gross Income 3.00% per year 10.00% per year
Current Remaining pense stop Rent term (yrs) per s.f.
$15.00 $300,000 $15.50 232,500 $17.00 255,000 787,500
3 4 5
CPI adjustment
$4.00 4.50 5.00
Summary of Expense Information Dollars
per s.f.
Property tax Insurance Utilities Janitorial Maintenance
$100,000 10,000 75,000 25,000 40,000
2.00 0.20 1.50 0.50 0.80
increase increase increase increase increase
3.00% per year 3.00% per year 3.00% per year 3.00% per year 3.00% per year
Subtotal (before mgt)
250,000
5.00 (before management expenses)
Management
$39,375
0.79
Total
$289,375
$5.79
5.00% of EGI
18-130
50.00% 50.00% 50.00%
(a) EGI
Base Income: Year Tenant 1 Tenant 2 Tenant 3 Total base
1 300,000 232,500 255,000 787,500
2 300,000 232,500 255,000 787,500
3 300,000 232,500 255,000 787,500
4 371,527 232,500 255,000 859,027
5 371,527 287,005 255,000 913,532
6 371,527 287,005 295,615 954,147
CPI Adjustment: Tenant 1 Tenant 2 Tenant 3
4,500 3,488 0
9,067 7,027 3,825
13,704 10,620 7,707
0 14,267 11,648
5,573 0 15,648
11,229 4,305 0
Total CPI
7,988
19,920
32,031
25,915
21,221
15,534
Total Base and CPI
795,488
807,420
819,531
884,942
934,753
969,681
Expense Reinmursements $20,000 $23,000 7,500 9,750 0 2,250 27,500 35,000
$26,090 12,068 4,568 42,725
$0 14,455 6,955 21,409
$3,278 0 9,413 12,691
$6,655 2,532 0 9,187
862,256 0 862,256
906,351 90,635 815,716
947,444 94,744 852,699
978,868 97,887 880,982
Tenant 1 Tenant 2 Tenant 3 Total Reimbursements Potential Gross Income Vacancy Effective Gross Income
822,988 0 822,988
842,420 0 842,420
(b) Expense Reimbursements The expense reimbursements were shown above in the calculation of effective gross income. Effective gross income includes income from expense reimbursements.
(c) NOI
18-131
SUMMARY OF OPERATING EXPENSES
Property tax Insurance Utilities Janitorial Maintenance Total before management per s.f.
Management Total Expenses
Reimbursable expenses 100,000 103,000 10,000 10,300 75,000 77,250 25,000 25,750 40,000 41,200 250,000 257,500 5.00 5.15 Non reimbursable expenses 41,149 42,121 Total expenses 291,149 299,621
18-132
106,090 10,609 79,568 26,523 42,436 265,225 5.30
109,273 10,927 81,955 27,318 43,709 273,182 5.46
112,551 11,255 84,413 28,138 45,020 281,377 5.63
115,927 11,593 86,946 28,982 46,371 289,819 5.80
43,113
40,786
42,635
44,049
308,338
313,968
324,012
333,868
PROJECTED NET OPERATING INCOME Year 1 2 Base income $787,500 $787,500 Plus CPI Adjustment 7,988 19,920 Plus Reimbursements $27,500 $35,000 Total Potential Income $822,988 $842,420 Less Vacancy 0 0 Effective Gross Income 822,988 842,420 Less operating expenses: Reimbursable expenses 250,000 257,500 Non reimbursable expenses 41,149 42,121 NOI $531,838 $542,799
(d) Average Compound Rate
Annual increase in NOI over holding period:
0.57%
(e) Overall Cap Rate (Going-In Rate)
Cap. Rate:
10.64 %
18-133
3 4 5 6 $787,500 $859,027 $913,532 $954,147 32,031 25,915 21,221 15,534 $42,725 $21,409 $12,691 $9,187 $862,256 $906,351 $947,444 $978,868 0 90,635 94,744 97,887 862,256 815,716 852,699 880,982 265,225 273,182 281,377 289,819 43,113 40,786 42,635 44,049 $553,918 $501,749 $528,687 $547,114
Problem 11-2 ASSUMPTIONS: Asking Price $1,250,000 Rent year 1 $160,000 Growth-Rent 2.50% 10.00% of rents Vacancy & Coll. Loss Expenses 35.00% of EGI Loan-to-Value 70.00% Loan Interest 8.00% Loan term 30 years Appreciation rate 3.00% Holding Period 5 years Selling costs 0.00% of sale price Equity discount rate 14.00% Reinvestment rate 6.00% Equity Loan Annual Loan Payment Mortgage Balance
375,000 875,000 77,045 831,861
Year 1 PGI 160,000 Vacancy & Collection 16,000 Loss EGI 144,000 Expenses 50,400 NOI 93,600 Debt Service 77,045 BTCF 16,555 Cash flow from sale in year Sales Price Sales costs Mortgage Balance Before-tax cash flow
year
5
2 164,000 16,400
3 168,100 16,810
4 172,303 17,230
5 176,610 17,661
6 181,025 18,103
147,600 51,660 95,940 77,045 18,895
151,290 52,952 98,339 77,045 21,293
155,072 54,275 100,797 77,045 23,752
158,949 55,632 103,317 77,045 26,272
162,923 57,023 105,900 77,045 28,855
3 1.28
4 1.31
5 1.34
5 1,449,09 3 0 831,861 617,231
(a) FIRST YEAR DEBT COVERAGE RATIO (DCR) Year 1 2 Debt-Coverage Ratio 1.21 1.25 (b) TERMINAL CAPITALIZATION RATE
18-134
NOI Year 6 Resale Price Terminal Cap Rate
105,900 1,449,093 7.31%
(c) BTIRR ON EQUITY BTIRR on Equity Year BTCF BTIRR on Equity
0 (375,000) 15.08%
1 16,555
2 18,895
18-135
3 21,293
4 23,752
5 643,503
(d) NET PRESENT VALUE NPV - Equity
16,711
@
14.00%
This means that the investor can invest $16,711 more in the property and still earn a 14% IRR.
(e) PROFITABILITY INDEX Present Value BTCF Initial Equity Investment Profitability Index:
391,711 375,000 1.04
@
14.00%
This means that the investment is profitable in the sense that the investor could invest about 4% more in the property and still earn a 14% IRR. Problem 11-3 ASSUMPTIONS: Asking Price
$1,250,0 00
Tax Considerations: Building Value $1,062,5 00 Depreciation 39 years Ordinary income tax 37.00% rate 20.00% Capital gains tax rate 25.00% Depreciation recapture tax rate Loan-to-Value 70.00% Loan Interest 8.00% Loan term 30 years Payments per year 12 Holding Period 5 years Selling costs 0.00% of sale price Equity discount rate 14.00% Reinvestment rate 14.00% Equity 375,000 Loan 875,000 Annual Loan Payment 77,045 Mortgage Balance 831,861
year
5
18-136
SUMMARY LOAN INFORMATION: End of Year Payment Mortgage Balance
1 2 77,045 77,045 867,691 859,774
Interest Principal
69,736 7,309
69,129 7,916
3 4 77,045 77,045 851,201 841,91 7 68,472 67,761 8,573 9,285
18-137
5 77,045 831,861 66,990 10,055
Year Rent
1 2 160,000 164,000
Vacancy & Collection 16,000 16,400 loss Effective Gross 144,000 147,600 Income Operating Expenses 50,400 51,660 NOI 93,600 95,940 Debt Service Before-tax Cash Flow
77,045 16,555
77,045 18,895
NOI
93,600
95,940
Less: Interest Depreciation Taxable Income Tax (Savings) After-tax Cash Flow
69,736 26,108 (2,244) (830) 17,385
69,129 27,244 (433) (160) 19,055
Cash flow from sale in year Sales Price
Accumulated Depreciation Adjusted Basis
5 176,610
151,290 155,07 2 52,952 54,275 98,339 100,79 7 77,045 77,045 21,293 23,752
158,949
98,339 100,79 7 68,472 67,761 27,244 27,244 2,623 5,793 970 2,143 20,323 21,608
103,317
5 1,449,09 3 0 831,861 617,231
Sales costs Mortgage Balance Before-tax cash flow Original Cost Basis
3 4 168,100 172,30 3 16,810 17,230
1,250,00 0 135,083 1,114,91 7
Capital Gain Depreciation recapture Price appreciation
334,175 135,083
Tax on price appreciation Tax on depreciation recapture
39,819
199,093
33,771 18-138
17,661
55,632 103,317 77,045 26,272
66,990 27,244 9,083 3,361 22,911
Total capital gain tax
73,589
After-tax cash flow from sale
543,642
BTIRR on Equity Year
0 (375,00 0) 15.08% 16,711
1 16,555
0 ATCF (375,00 0) ATIRR on Equity 12.35% Effective Tax Rate 18.12% BT Equivalent Yield 19.60%
1 17,385
BTCF BTIRR on Equity NPV - Equity
@
2 3 18,895 21,293
4 5 23,752 643,503
14.00%
ATIRR on Equity Year
2 3 19,055 20,323
18-139
4 5 21,608 566,553
(a) ATIRR on Equity Year ATCF ATIRR on Equity
0 (375,00 0) 12.35%
1 17,385
2 3 19,055 20,323
4 5 21,608 566,553
(b) Effective Tax Rate 18.12% BT Equivalent Yield 19.60%
(c) The depreciation combined with the interest deductions has reduced the taxable income significantly. In fact, there are some tax losses during the holding period years resulting in some additional tax shelter if the investor can use the passive losses. The effective tax rate is 18.12% compared with the investors marginal tax rate of 37%. (d) ATIRR is 11.60%
Spreadsheet limitations: 5 year holding period. Assumes passive losses cannot be used and must be carried forward to offset taxable income in future years. Data Input Box: Asking Price $1,250,000 Tax Considerations: Building Value $1,062,500 Depreciation 39years Ordinary income tax rate 37.00% Capital gains tax rate 20.00% 25.00% Depreciation recapture tax rate Loan-to-Value 70.00% Loan Interest 8.00% Loan term 30years Payments per year 12 Holding Period Selling costs Equity discount rate Reinvestment rate
5years 0.00%of sale price 14.00% 14.00%
Equity Loan
375,000 875,000 18-140
Annual Loan Payment Mortgage Balance
77,045 850,191
year
5
SUMMARY LOAN INFORMATION: End of Year Payment Mortgage Balance Interest Principal
1 77,045 867,691 69,736 7,309
2 77,045 859,774 69,129 7,916
3 77,045 851,201 68,472 8,573
4 77,045 841,917 67,761 9,285
5 77,045 831,861 66,990 10,055
Year Rent Vacancy & Collection loss Effective Gross Income Operating Expenses NOI Debt Service Before-tax Cash Flow
1 160,000 16,000 144,000 50,400 93,600 77,045 16,555
2 164,000 16,400 147,600 51,660 95,940 77,045 18,895
3 168,100 16,810 151,290 52,952 98,339 77,045 21,293
4 172,303 17,230 155,072 54,275 100,797 77,045 23,752
5 176,610 17,661 158,949 55,632 103,317 77,045 26,272
NOI Less: Interest Depreciation Tax loss (before limitation) Accumulated tax loss Taxable income Tax After-tax Cash Flow
93,600 69,736 26,108 (2,244) (2,244) 0 0 16,555
95,940 69,129 27,244 (433) (2,677) 0 0 18,895
98,339 68,472 27,244 2,623 (44) 0 0 21,293
100,797 67,761 27,244 5,793 5,749 5,749 2,127 21,625
103,317 66,990 27,244 9,083 9,083 9,083 3,361 22,911
Cash flow from sale in year Sales Price Sales costs Mortgage Balance
5 1,449,093 0 831,861
Before-tax cash flow 617,231 Original Cost Basis Accumulated Depreciation Adjusted Basis Unused accumulated tax loss Capital Gain Depreciation recapture Price appreciation
1,250,000 135,083 1,114,917 0 343,324 135,083 199,093 18-141
Tax on price appreciation Tax on depreciation recapture Total capital gain tax
39,819 33,771 73,589
After-tax cash flow from sale
543,642
BTIRR on Equity Year BTCF BTIRR on Equity NPV - Equity
0 (375,000) 15.08% 16,711
1 16,555
2 18,895
@
14.00%
0 (375,000) 12.34%
1 16,555
2 18,895
3 21,293
4 23,752
5 643,503
3 21,293
4 5 21,625 566,553
ATIRR on Equity Year ATCF ATIRR on Equity
PROBLEM 11-4 The after-tax IRR increases to 14.11% from 12.88%.
PROBLEM 11-5
Year 0 1 2 3
New Employees 100 100 100
300 300 300
Year 0 1 2 3
New Supply
Supply 1,000,000 1,050,000 1,050,000 1,050000
50,000
Space per Employee Absorption Occupied 900,000 30,000 930,000 30,000 960,000 30,000 990,000 Occupied 900,000 930,000 960,000 990,000
Occupancy % 90% 88.57% 91.43% 94.29%
a) Current occupancy is 90% b) Absorption each year is shown in the first table above c) Occupancy each year is shown in the second table above d) Although demand is weak, occupancy is increasing because there is no new supply after year 1. So rents are likely to increase.
Solutions to Questions - Chapter 12 18-142
Financial Leverage and Financing Alternatives Question 12-1 What is financial leverage? Why is a one-year measure of return on investment inadequate in determining whether positive or negative financial leverage exists? Financial leverage is defined as benefits that may result to an investor by borrowing money at a rate of interest that is lower than the expected rate of return on total funds invested in a property. To determine whether leverage is positive (favorable) or negative (unfavorable), the investor needs to determine whether the IRR (calculated over the entire holding period) is greater than the cost of borrowed funds. A first-year measure of return such as the overall capitalization rate can not be used because it does not explicitly consider the benefits that accrue to the investor over time from changes in income and value that do not affect the cost of debt. Question 12-2 What is the break-even mortgage interest rate (BEIR) in the context of financial leverage? Would you ever expect an investor to pay a break-even interest rate when financing a property? Why or why not? The BEIR is the maximum interest rate that could be paid on the debt before the leverage becomes unfavorable. It represents the interest rate where the leverage is neutral (neither favorable or unfavorable). The BEIR remains constant regardless of the amount borrowed (that is 60, 70, or 80 percent of the property value). An equity investor probably would not pay a break-even interest rate when financing a property because the investor just earns the same after-tax rate of return as a lender on the same project. Borrowing at the BEIR provides no risk premium to the investor. Normally, a risk premium is required because the equity investor bears the risk of variations in the performance of the property. Question 12-3 What is positive and negative financial leverage? How are returns or losses magnified as the degree of leverage increases? How does leverage on a before-tax basis differ from leverage on an after-tax basis? When the before-tax or after-tax IRR are higher with debt than without debt, we say that the investment has positive or favorable financial leverage. When returns are lower with debt than without debt we say that the investment has negative or unfavorable financial leverage. Positive leverage occurs when the unlevered IRR is greater than the interest rate paid on the debt. Negative leverage occurs when the unlevered IRR is less than the interest rate paid on the debt. Returns and losses are magnified by the greater the amount of debt, the greater the return or loss to the equity investor. Leverage on a before-tax basis differs from leverage on an after-tax basis because interest is tax deductible. Therefore, we must consider the after-tax cost of debt which is different than the beforetax cost of debt. Question 12-4 In what way does leverage increase the riskiness of a loan? Leverage increases the standard deviation of return regardless of whether it is positive or negative. This means the investment is clearly riskier when leverage is used. 18-143
Because the NOI does not change when more debt is used, increasing the amount of debt increases the debt service relative to NOI. Therefore, the debt coverage ratio (DCR) may exceed the lender’s limits. With higher loan-to- value ratios and declining debt coverage ratios, risk to the lender increases. As a result, the interest rate on additional debt will also increase. Question 12-5 What is meant by a participation loan? What does the lender participate in? Why would a lender want to make a participation loan? Why would an investor want to obtain a participation loan? A participation loan is where in return for a lower stated interest rate on the loan, the lender participates in some way in the income or cash flow from the property. The lender’s rate of return depends, in part, on the performance of the property. Participations are highly negotiable and there is no standard way of structuring them. A lender’s motivation for making a participation loan includes how risky the loan is perceived relative to a fixed interest rate loan. The lender does not participate in any losses and still receives some minimum interest rate (unless the borrower defaults). Additionally, the participation provides the lender with somewhat of a hedge against unanticipated inflation because the NOI and resale prices for an income property often increase as a result of inflation. To some extent this protects the lender’s real rate of return.
18-144
An investors motivation is that the participation may be very little or zero for one or more years. This is because the loan is often structured so that the participation is based on income or cash flow above some specified breakeven point. During this time period, the borrower will be paying less than would have been paid with a straight loan. This may be quite desirable for the investor since NOI may be lower during the first couple of years of ownership, especially on a new project that is not fully rented. Question 12-6 What is meant by a sale-leaseback? Why would a building investor want to do a sale-leaseback of the land? What is the benefit to the party that purchases the land under a sale-leaseback? When land is already owned and is then sold to an investor with a simultaneous agreement to lease the land from the party it is sold to, this is called a sale-leaseback of the land. One motivation for the sale-leaseback of the land is that it is a way of obtaining 100 percent financing on the land. A second benefit is that lease payments are 100 percent tax deductible. With a mortgage, only the interest is tax deductible. The investor may deduct the same depreciation charges whether or not the land is owned, since land cannot be depreciated. This results in the same depreciation for a smaller equity investment. The investor may have the option of purchasing the land back at the end of the lease if it is desirable to do so. Question 12-7 Why might an investor prefer a loan with a lower interest rate and a participation? An investor’s motivation is that the participation may be very little or zero for one or more years. This is because the loan is often structured so that the participation is based on income or cash flow above some specified breakeven point. During this time period, the borrower will be paying less than would have been paid with a straight loan. This may be quite desirable for the investor since NOI may be lower during the first couple of years of ownership, especially on a new project that is not fully rented. Question 12-8 Why might a lender prefer a loan with a lower interest rate and a participation? A lender’s motivation for making a participation loan includes how risky the loan is perceived relative to a fixed interest rate loan. The lender does not participate in any losses and still receives some minimum interest rate (unless the borrower defaults). Additionally, the participation provides the lender with somewhat of a hedge against unanticipated inflation because the NOI and resale prices for an income property often increase as a result of inflation. To some extent this protects the lender’s real rate of return. Question 12-9 How do you think participations affect the riskiness of a loan? There is clearly some uncertainty associated with the receipt of a participation since it depends on the performance of the property. The lender does not participate in any losses and still receives some minimum interest rate (unless the borrower defaults). Additionally, the participation provides the lender with somewhat of a hedge against unanticipated inflation because the NOI and resale prices for an income property often increase as a result of inflation. To some extent this protects the lender’s real rate of return. Question 12-10 18-145
What is the motivation for a sale-leaseback of the land? One motivation for the sale-and-leaseback of the land is that it is a way of obtaining 100 percent financing on the land. A second benefit is that lease payments are 100 percent tax deductible. With a mortgage, only the interest is tax deductible. The investor may deduct the same depreciation charges whether or not the land is owned, since land cannot be depreciated. This results in the same depreciation for a smaller equity investment. The investor may have the option of purchasing the land back at the end of the lease if it is desirable to do so. Question 12-11 What criteria should be used to choose between two financing alternatives? Assuming the two financing alternatives are for roughly the same amount of funds (so financial risk due to leverage is the same), the alternative with the lowest effective interest cost should be chosen. This alternative should also result in the highest IRR on equity.
18-146
Question 12-12 What is the traditional cash equivalency approach to determine how below-market rate loans affect value? Cash equivalency was introduced in Chapter 9 where it was demonstrated that a buyer would be willing to pay more for a property with a below market interest rate loan. In that chapter, the present value of interest savings was used to indicate the additional amount which might be paid for a property. This same approach could be used to determine the additional amount that might be paid for income producing properties as analyzed in this chapter. Question 12-13 How can the effect of below-market rate loans on value be determined using investor criteria? Note: This question is not explicitly covered in the chapter. It requires students to think about how concepts from earlier chapters dealing with valuation and cash equivalency might be applied to evaluate a below-market rate loan on income property. Evaluating a below-market rate loan is like comparing two financing alternatives where one is at the market rate and one has a below-market rate. All else being equal, the below market interest rate loan should result in a higher IRRE for the property than would result with a market rate loan. The investor might therefore be willing to pay more for the property, as long as the IRRE is at least as much as it would be with the market interest rate loan.
18-147
Solutions to Problems - Chapter 12 Financial Leverage and Financing Alternatives INTRODUCTION The problems in this chapter are designed to reinforce the students’ understanding of alternative methods of structuring debt financing and how financing can affect the cash flows and the leverage of the real estate project. The conditions necessary for positive financing leverage and how the use financial leverage affects risk are also discussed. The third problem extends problem 5 in chapter 10 which involved calculation of the expected return and standard deviation for an investment. In this chapter financing is added to the problem. Instructors should emphasize that the risk (measured b the standard deviation) will always increase with leverage. However, whether the expected return increases depends on whether leverage is favorable or unfavorable. Problem 12-1 (REFER TO TEMPLATE 12_1.XLS) (a) 70% LOAN (70% and 4% are the original variables contained in the template. It must be changed for any other answer.) ASSUMPTIONS: Asking Price NOI year 1
$2,200,000 $150,000
Tax Considerations: $1,760,000 Building Value Depreciation 39 years Ord. Inc. Tax 35.00% Capital Gain 20.00% Tax years Recapture Tax 25.00%
Growth-NOI Loan-to-Value Loan Interest
2.00% 70.00% 4.00%
Loan term Payments per year Appreciation rate Holding Period Selling costs
20 12 2.00% 5 years 0.00% of sale price
Equity Loan Annual Loan Payment Mortgage Balance
660,000 1,540,000 111,985 1,261,626
SUMMARY LOAN INFORMATION: End of Year 1 Payment 111,985 Mortgage Balance 1,488,68 1 Interest 60,666
year
2 111,985 1,435,27 1 58,575
5
3 111,985 1,379,685 56,399 18-148
4 111,985 1,321,83 4 54,134
5 111,985 1,261,62 6 51,778
Principal
51,319
53,410
55,586
18-149
57,851
60,208
Year NOI Debt Service Before-tax Cash Flow NOI Less: Interest Depreciation Taxable Income Tax (Savings) After-tax Cash Flow
1 150,000 111,985 38,015
2 153,000 111,985 41,015
3 156,060 111,985 44,075
4 159,181 111,985 47,196
5 162,365 111,985 50,380
150,000 60,666 45,128 44,206 15,472 22,543
153,000 58,575 45,128 49,297 17,245 23,761
156,060 56,399 45,128 54,533 19,086 24,988
159,181 54,134 45,128 59,919 20,971 26,225
162,365 51,778 45,128 65,459 22,911 27,469
Cash flow from sale in year Sales Price Sales costs Mortgage Balance Before-tax cash flow
5
Original Cost Basis
2,200,00 0 225,641
Accumulated Depreciation Adjusted Basis
2,428,978 0 1,261,626 1,167,352
1,974,35 9
Capital Gain Tax from Sale
454,619 102,206
After-tax cash flow from sale
1,065,146
EQUITY BTCF
Year
0 (660,000)
BTIRR on Equity
17.41% Year
ATCF
0 (660,000)
ATIRR on Equity
13.18%
1 38,015
2 41,015
3 44,075
4 47,196
5 1,217,73 1
1 22,543
2 23,761
3 24,988
4 26,225
5 1,092,61 5
18-150
80% LOAN (Change 70 to 80% and 4 to 5%. All other variables are constant.) ASSUMPTIONS: Asking Price NOI year 1
$2,200,000 $150,000
Tax Considerations: $1,760,000 Building Value Depreciation 39 years Ord. Inc. Tax 35.00% 20.00% Capital Gain Tax years Recapture Tax 25.00%
Growth-NOI Loan-to-Value Loan Interest
2.00% 80.00% 5.00%
Loan term Payments per year Appreciation rate Holding Period Selling costs
20 12 2.00% 5 years 0.00% of sale price
Equity Loan Annual Loan Payment Mortgage Balance
440,000 1,760,000 139,383 1,468,806
SUMMARY LOAN INFORMATION: End of Year 1 Payment 139,383 Mortgage Balance 1,707,42 3 Interest 86,806 Principal 52,577
year
5
2 139,383 1,652,15 7 84,116 55,267
3 139,383 1,594,063
NOI Debt Service Before-tax Cash Flow
1 150,000 139,383 10,617
NOI Less: Interest Depreciation Taxable Income Tax (Savings) After-tax Cash Flow
150,000 86,806 45,128 18,066 6,323 4,294
Cash flow from sale in year Sales Price Sales costs
5
Year
81,289 58,094
4 139,383 1,532,99 6 78,316 61,066
5 139,383 1,468,80 6 75,192 64,191
2 153,000 139,383 13,617
3 156,060 139,383 16,677
4 159,181 139,383 19,799
5 162,365 139,383 22,982
153,000 84,116 45,128 23,756 8,315 5,303
156,060 81,289 45,128 29,643 10,375 6,302
159,181 78,316 45,128 35,737 12,508 7,291
162,365 75,192 45,128 42,045 14,716 8,267
2,428,978 0 18-151
Mortgage Balance Before-tax cash flow Original Cost Basis Accumulated Depreciation Adjusted Basis
Capital Gain Tax from Sale
1,468,806 960,172 2,200,00 0 225,641 1,974,35 9 454,619
After-tax cash flow from sale
102,206 857,966
18-152
EQUITY Year
0 (440,000) 19.58%
1 10,617
2 13,617
3 16,677
4 19,799
5 983,154
Year
0 (440,000) 15.36%
1 4,294
2 5,303
3 6,032
4 7,291
5 866,233
BTCF BTIRR on Equity ATCF ATIRR on Equity
(b) BEIR (To calculate the Break Even Interest Rate (BEIR), the ATIRR must first be calculated as if there were no financing.) NO LOAN (Change 80 to 0%. All other variables are constant.) ASSUMPTIONS: Asking Price NOI year 1
$2,200,000 $150,000
Tax Considerations: $1,760,000 Building Value Depreciation 39 years Ord. Inc. Tax 35.00% 20.00% Capital Gain Tax years Recapture Tax 25.00%
Growth-NOI Loan-to-Value Loan Interest
2.00% 0.00% 5.00%
Loan term Payments per year Appreciation rate Holding Period Selling costs
20 12 2.00% 5 years 0.00% of sale price
Equity Loan Annual Loan Payment Mortgage Balance SUMMARY LOAN INFORMATION: End of Year Payment Mortgage Balance Interest Principal
2,200,000 0 0 0
1 0 0 0 0
year
5
2 0 0 0 0
3 0 0 0 0
18-153
4
5 0 0 0 0
0 0 0 0
Year NOI Debt Service Before-tax Cash Flow
1 150,000 0 150,000
2 153,000 0 153,000
3 156,060 0 156,060
4 159,181 0 159,181
5 162,365 0 162,365
NOI Less: Interest Depreciation Taxable Income Tax (Savings) After-tax Cash Flow
150,000 0 45,128 104,872 36,705 113,295
153,000 0 45,128 107,872 37,755 115,245
201,571 0 45,128 110,932 38,826 117,234
207,618 0 45,128 114,053 39,919 119,263
213,847 0 45,128 117,237 41,033 121,332
Cash flow from sale in year Sales Price
5 2,428,9 78 0 0 2,428,9 78
Sales costs Mortgage Balance Before-tax cash flow
Original Cost Basis
2,200,00 0 225,641
Accumulated Depreciation Adjusted Basis
1,974,35 9
Capital Gain Tax from Sale
454,619 102,206
After-tax cash flow from sale
2,326,7 72
EQUITY Year
0 1 (2,200,00 150,000 0) 8.82.%
2 153,000
3 156,060
4 159,181
5 2,591,34 3
Year
0 1 (2,200,00 113,295 0) 6.33% 9.75%
2 115,245
3 117,234
4 119,263
5 2,448,10 4
BTCF BTIRR on Equity
ATCF ATIRR on Equity Break-even Interest Rate
The breakeven interest rate is the ATIRR on Equity divided by (1 – tax rate) or 6.33% / (1 - .35) = 9.75%. 18-154
(c) The incremental amount of financing is $220,000. The incremental payment is $2,283 and the incremental loan balance is $207,180. Thus, $220,000 = $2,283 (MPVIFA, ?%, 5 yrs) + $207,180 (MPVIF, ?%, 5 yrs).
Using a financial calculator, the yield is 11.59%. This should be compared to the IRR being earned on the property with the 70% loan which is 17.41%.
18-155
(d) To answer this question, it is helpful to prepare the following summary: IRR Before After tax
No loan 8.82% 6.33%
70% loan 17.41% 13.18%
80% loan 19.58% 15.36%
Loan Cost Before tax After tax
No loan n/a n/a
70% loan 4.00% 6.40%
80% loan 5.00% 7.04%
Incremental cost of loan 17.82% 11.40%
The 70% loan clearly has financial leverage. The return increases on both a before and after-tax basis. This occurs because the unlevered return is greater than the cost of debt. I.e., the unlevered before-tax return is 12.50% and the loan cost is 10.00%. Similarly, the unlevered after-tax return is 8.31% and the after-tax cost is debt is 10% (1-.36) = 6.40%. The leverage is also positive for the 80% loan. But this is based on all the funds borrowed having a cost less than the unleveraged return on the property. To be sure the 80% loan is favorable relative to the 70% loan we must compare the incremental cost of the 80% loan with what was already being earned on the property with the 70% loan. As noted in Part c, the incremental cost of the 80% loan is 11.59%. This is less than the 17.41% return being earned on the property with the 70% loan. Thus, the incremental leverage is favorable. Problem 12-2 (REFER TO TEMPLATE 12_2.XLS) (a) ASSUMPTIONS: Asking Price NOI year 1
$5,500,000 $400,000
Tax Considerations: $4,400,000 Building Value Depreciation 39 years Ord. Inc. Tax 35.00% 20.00% Capital Gain Tax years Recapture Tax 25.00%
Growth-NOI Loan-to-Value Loan Interest
2.00% 75.00% 4.00%
Loan term Payments per year Equity Participation Equity Participation Appreciation rate Holding Period Selling costs
20 12 40.00% of BTCF 0.00% of sales gain 2.59% 5 years 0.00% of sale price
Equity Loan
1,375,000 4,125,000 18-156
Annual Loan Payment Mortgage Balance
299,960 3,379,356
year
SUMMARY LOAN INFORMATION: End of Year 1 Payment 299.960 Mortgage Balance 3,987,53 8 Interest 162,498 Principal 137,462
2 299.960 3,844,47 5 156,898 143,063
Year NOI Debt Service Before-tax Cash Flow Equity Participation Cash Flow after Participation NOI Less: Interest Depreciation Participation Taxable Income Tax (Savings) ATCF after Participation
5
3 299.960 3,695,584 151,069 148,891
5 299.960 3,379,3 56 138,690 161,271
1 400,000 299,960 100,040 40,016 60,024
2 408,000 299,960 108,040 43,216 64,824
3 416,160 299,960 116,200 46,480 69,720
4 424,483 299,960 124,523 49,809 74,714
5 432,973 299,960 133,013 53,205 79,808
400,000 162,498 112,821 40,016 84,666 29,633 30,391
408,000 156,898 112,821 43,216 95,066 33,273 31,551
416,160 151,069 112,821 46,480 105,791 37,027 32,693
424,483 145,003 112,821 49,809 116,851 40,898 33,816
432,973 138,690 112,821 53,205 128,258 44,890 34,917
Cash flow from sale in year 5 Sales Price Sales costs Mortgage Balance Before-tax cash flow Participation in Gain BTCF after Participation
6,250,000 0 3,379,356 2,870,644 0 2,870,644
Sales Price Sales Costs Participation
6,250,000 0 0
Original Cost Basis 5,500,000 Accumulated Depreciation 564,103 Adjusted Basis
4,935,897
Capital Gain Tax from Sale
4 299.960 3,540,62 7 145,003 154,957
1,314,103 291,026
After-tax cash flow from
2,579,618 18-157
sale
18-158
EQUITY Year 0 BTCF after Participation (1,375,000 ) BTIRR on Equity 19.66% Year ATCF ATIRR on Equity
0 (1,375,000 ) 15.28%
1 60,024
2 64,824
3 69,720
4 74,714
5 2,950,45 2
1 30,391
2 31,551
3 32,693
4 33,816
5 2,614,53 6
(b) BEIR (To calculate the Break Even Interest Rate (BEIR), the ATIRR must first be calculated as if there were no financing.) NO LOAN (Change 75 to 0% and remove the participation by changing 40 to 0%. All other variables are constant.) ASSUMPTIONS: Asking Price NOI year 1
$5,500,000 $400,000
Tax Considerations: $4,400,000 Building Value Depreciation 39 years Ord. Inc. Tax 35.00% 20.00% Capital Gain Tax years Recapture Tax 25.00%
Growth-NOI Loan-to-Value Loan Interest
2.00% 0.00% 4.00%
Loan term Payments per year Equity Participation Equity Participation Appreciation rate Holding Period Selling costs
20 12 40.00% of BTCF 0.00% of sales gain 2.59% 5 years 0.00% of sale price
Equity Loan Annual Loan Payment Mortgage Balance
5,500,000 0 0 0
SUMMARY LOAN INFORMATION: End of Year 1 Payment 0 Mortgage Balance 0 Interest 0 Principal 0
year
5
2
3 0 0 0 0
4 0 0 0 0
18-159
5 0 0 0 0
0 0 0 0
Year NOI Debt Service Before-tax Cash Flow Equity Participation Cash Flow after Participation NOI Less: Interest Depreciation Participation Taxable Income Tax (Savings) ATCF after Participation
1 400,000 0 400,000 0 400,000
2 408,000 0 408,000 0 408,000
3 416,160 0 416,160 0 416,160
4 424,483 0 424,483 0 424,483
5 432,973 0 432,973 0 432,973
400,000 0 112,821 0 287,179 100,513 299,487
408,000 0 112,821 0 295,179 103,313 304,687
416,160 0 112,821 0 303,339 106,169 309,991
424,483 0 112,821 0 311,663 109,082 315,401
432,973 0 112,821 0 320,152 112,053 320,920
2 408,000
3 416,160
4 424,483
5 6,682,97 3
2 304,687
3 309,991
4 315,401
5 6,279,89
Cash flow from sale in year 5 Sales Price
6,250,00 0 0 0 6,250,00 0 0 6,250,00 0
Sales costs Mortgage Balance Before-tax cash flow Participation in Gain BTCF after Participation
Sales Price Sales Costs Participation
6,250,000 0 0
Original Cost Basis 5,500,000 Accumulated Depreciation 564,103 Adjusted Basis 4,935,897 Capital Gain Tax from Sale
1,314,103 291,026
After-tax cash flow from sale
5,958,97 4
EQUITY Year 0 1 BTCF after Participation (5,500,000 400,000 ) BTIRR on Equity 9.78% Year 0 1 ATCF (5,500,000 299,487
18-160
ATIRR on Equity Break-even Interest Rate
) 7.07% 10.88%
4
18-161
(b) continued - Projected cost of participation. Cost of Participation Year Debt service Loan balance
0
Participation Loan amount
4,125,000 4,125,000 6.27%
Cash flows to lender IRR on Loan
1 299,960
2 299,960
40,016
43,216
399,976
343,176
3 4 5 299,960 299,960 299,960 3,379,35 6 46,480 49,809 53,205
346,440 349,769 3,732,52 1
Using a financial calculator, the IRR of the cash flows to the lender is 6.27%. This is the effective before tax cost of the loan including the participation. (Note that this was done with annual cash flows for simplicity.) (c) Summary IRR Before tax After tax
No loan 9.78 7.07
With loan 19.66 15.28
Yes, there is favorable leverage. The IRR increases on both a before and after-tax basis. Problem 12-3 (REFER TO TEMPLATE 12_3AB.XLS) (8% interest rate and 3% NOI and appreciation are the original variables contained in the template. It must be changed for any other answer.) (a) Asking Price Rent year 1 Growth-NOI Loan-to-Value Loan Interest Loan term Appreciation rate Holding Period Selling costs Required DCR
$1,500,000 $100,000 2.00% 70.00% 4.50% 20 years 2.00% 5 years 0.00% of sale price 1.20
Equity Loan
450,000 1,050,000 18-162
Annual Loan Payment Mortgage Balance Year NOI Debt Service BTCF DCR
79,714 868,350
year
5
1 100,000 79,714 20,286
2 102,000 79,714 22,286
3 104,040 79,714 24,326
4 106,121 79,714 26,407
5 108,243 79,714 28,529
1.25
1.28
1.31
1.33
1.36
18-163
Cash flow from sale in year Sales Price
5 1,656,12 1 0 868,350 787,771
Sales costs Mortgage Balance Before-tax cash flow BTIRR on Equity Year BTCF BTIRR on Equity
0 (450,000) 16.16%
1 20,286
2 22,286
3 24,326
4 26,407
5 816,301
In this case the DCR is greater than 1.25. Thus, the first-year NOI is 25% higher than necessary to support the debt service. Based on this criteria, the loan would probably be acceptable. (b) The maximum loan amount would be $1,083,995 Step 1, Calculate the payment: Payment = NOI Year 1 / DCR $83,333 = $100,000 / 1.2 Step 2, Calculate the loan amount: PMT = $83,333 N = 20 I = 4.5 Solve for the present value PV = $1,083,995
(c) (Change 4.5 to 6.5% and 2 to 5%. All other variables are constant.) Asking Price Rent year 1 Growth-NOI Loan-to-Value Loan Interest Loan term Appreciation rate Holding Period Selling costs Required DCR
$1,500,000 $100,000 5.00% 70.00% 6.50% 20 years 5.00% 5 years 0.00% of sale price 1.20
Equity Loan Annual Loan Payment Mortgage Balance
450,000 1,050,000 93,942 898,686
Year NOI Debt Service
1 100,000 93,942
year 2 105,000 93,942
5 3 110,250 93,942 18-164
4 115,763 93,942
5 121,551 93,942
BTCF
6,058
11,058
16,308
21,820
27,608
DCR
1.06
1.12
1.17
1.23
1.29
18-165
Cash flow from sale in year Sales Price
5 1,914,42 2 0 898,686 1,015,73 7
Sales costs Mortgage Balance Before-tax cash flow
BTIRR on Equity Year BTCF
0 (450,000)
BTIRR on Equity
20.11%
1 6,058
2 11,058
3 16,308
4 21,820
5 1,043,34 5
The DCR is now much less than 1.2 and it is barely above 1.0. This does not provide a safety margin for the lender. It is not likely that this loan would be made.
Problem 12-4 (REFER TO TEMPLATE 12_4.XLS) ASSUMPTIONS: Purchase Price NOI Loan to Value Ratio Loan Interest Rate Payments per Year Annual Payment Increase Required DCR Holding Period Year NOI Debt Service DCR
Mont h 0 1 2 3 4 5
3,250,000 125,000 80.00%
1 125,000 100,000 1.25
5.50% 12 3.50% 1.25 5 years 2 125,000 103,500 1.21
3 125,000 107,123 1.17
Beginning Balance
Interest
Principal
2,600,000.00 2,603,583.33 2,607,183.09 2,610,799.35 2,614,432.18
11,916.67 11,933.09 11,949.59 11,966.16 11,982.81
(3,583.33) (3,599.76) (3,616.26) (3,632.83) (3,649.48)
4 125,000 110,872 1.13
5 125,000 114,752 1.09
Payment
Ending Balance
Loan to Value Ratio
8,333.33 8,333.33 8,333.33 8,333.33 8,333.33
2,600,000.00 2,603,583.33 2,607,183.09 2,610,799.35 2,614,432.18 2,618,081.66
80.00% 80.11% 80.22% 80.33% 80.44% 80.56%
18-166
6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54
2,618,081.66 2,621,747.86 2,625,430.88 2,629,130.77 2,632,847.62 2,636,581.50 2,640,332.50 2,644,100.69 2,647,594.49 2,651,104.29 2,654,630.19 2,658,172.24 2,661,730.53 2,665,305.13 2,668,896.11 2,672,503.55 2,676,127.53 2,679,768.11 2,683,425.38 2,687,099.42 2,690,488.41 2,693,892.94 2,697,313.08 2,700,748.89 2,704,200.45 2,707,667.82 2,711,151.09 2,714,650.33 2,718,165.60 2,721,696.98 2,725,244.55 2,728,808.38 2,732,076.10 2,735,358.80 2,738,656.55 2,741,969.41 2,745,297.45 2,748,640.75 2,751,999.37 2,755,373.39 2,758,762.87 2,762,167.88 2,765,588.50 2,769,024.80 2,772,153.47 2,775,296.48 2,778,453.90 2,781,625.79 2,784,812.22
11,999.54 12,016.34 12,033.22 12,050.18 12,067.22 12,084.33 12,101.52 12,118.79 12,134.81 12,150.89 12,167.06 12,183.29 12,199.60 12,215.98 12,232.44 12,248.97 12,265.58 12,282.27 12,299.03 12,315.87 12,331.41 12,347.01 12,362.68 12,378.43 12,394.25 12,410.14 12,426.11 12,442.15 12,458.26 12,474.44 12,490.70 12,507.04 12,522.02 12,537.06 12,552.18 12,567.36 12,582.61 12,597.94 12,613.33 12,628.79 12,644.33 12,659.94 12,675.61 12,691.36 12,705.70 12,720.11 12,734.58 12,749.12 12,763.72
(3,666.21) (3,683.01) (3,699.89) (3,716.85) (3,733.88) (3,751.00) (3,768.19) (3,493.79) (3,509.81) (3,525.89) (3,542.06) (3,558.29) (3,574.60) (3,590.98) (3,607.44) (3,623.97) (3,640.58) (3,657.27) (3,674.03) (3,389.00) (3,404.53) (3,420.13) (3,435.81) (3,451.56) (3,467.38) (3,483.27) (3,499.23) (3,515.27) (3,531.38) (3,547.57) (3,563.83) (3,267.72) (3,282.70) (3,297.75) (3,312.86) (3,328.04) (3,343.30) (3,358.62) (3,374.01) (3,389.48) (3,405.01) (3,420.62) (3,436.30) (3,128.67) (3,143.01) (3,157.42) (3,171.89) (3,186.43) (3,201.03) 18-167
8,333.33 8,333.33 8,333.33 8,333.33 8,333.33 8,333.33 8,333.33 8,625.00 8,625.00 8,625.00 8,625.00 8,625.00 8,625.00 8,625.00 8,625.00 8,625.00 8,625.00 8,625.00 8,625.00 8,926.88 8,926.88 8,926.88 8,926.88 8,926.88 8,926.88 8,926.88 8,926.88 8,926.88 8,926.88 8,926.88 8,926.88 9,239.32 9,239.32 9,239.32 9,239.32 9,239.32 9,239.32 9,239.32 9,239.32 9,239.32 9,239.32 9,239.32 9,239.32 9,562.69 9,562.69 9,562.69 9,562.69 9,562.69 9,562.69
2,621,747.86 2,625,430.88 2,629,130.77 2,632,847.62 2,636,581.50 2,640,332.50 2,644,100.69 2,647,594.49 2,651,104.29 2,654,630.19 2,658,172.24 2,661,730.53 2,665,305.13 2,668,896.11 2,672,503.55 2,676,127.53 2,679,768.11 2,683,425.38 2,687,099.42 2,690,488.41 2,693,892.94 2,697,313.08 2,700,748.89 2,704,200.45 2,707,667.82 2,711,151.09 2,714,650.33 2,718,165.60 2,721,696.98 2,725,244.55 2,728,808.38 2,732,076.10 2,735,358.80 2,738,656.55 2,741,969.41 2,745,297.45 2,748,640.75 2,751,999.37 2,755,373.39 2,758,762.87 2,762,167.88 2,765,588.50 2,769,024.80 2,772,153.47 2,775,296.48 2,778,453.90 2,781,625.79 2,784,812.22 2,788,013.25
80.67% 80.78% 80.90% 81.01% 81.13% 81.24% 81.36% 81.46% 81.57% 81.68% 81.79% 81.90% 82.01% 82.12% 82.23% 82.34% 82.45% 82.57% 82.68% 82.78% 82.89% 82.99% 83.10% 83.21% 83.31% 83.42% 83.53% 83.64% 83.74% 83.85% 83.96% 84.06% 84.16% 84.27% 84.37% 84.47% 84.57% 84.68% 84.78% 84.89% 84.99% 85.10% 85.20% 85.30% 85.39% 85.49% 85.59% 85.69% 85.79%
55 56 57 58 59 60
2,788,013.25 2,791,228.95 2,794,459.39 2,797,704.64 2,800,964.76 2,804,239.82
12,778.39 12,793.13 12,807.94 12,822.81 12,837.76 12,852.77
(3,215.70) (3,230.44) (3,245.25) (3,260.12) (3,275.06) (3,290.07)
9,562.69 9,562.69 9,562.69 9,562.69 9,562.69 9,562.69
(a) BALLOON PAYMENT AT END OF YEAR 5 = $2,807,529.90 (b) LOAN-TO-VALUE RATIO AT END OF YEAR 5 = 86.39%
18-168
2,791,228.95 2,794,459.39 2,797,704.64 2,800,964.76 2,804,239.82 2,807,529.90
85.88% 85.98% 86.08% 86.18% 86.28% 86.39%
Problem 12-5 (a) Payment at 4%, 30 years using a financial calculator is $4,774.15 per month. Note, calculated as if the loan had an interest rate of 4%. (b) Interest accrues at 6%. On $1,000,000 this is $60,000 per year or $50,000 per month. In this case, payments do not cover the interest, although the loan would not be amortized in 30 years. For this reason, the future value of the loan will be greater than the initial loan amount, even though monthly payments are made. We can find the loan balance after one year as follows:
Payment
Interest
Principle
1 $4,774.15 $5,000.00 -$225.85 2 $4,774.15 $5,001.13 -$226.98 3 $4,774.15 $5,002.26 -$228.11 4 $4,774.15 $5,003.40 -$229.25 5 $4,774.15 $5,004.55 -$230.40 6 $4,774.15 $5,005.70 -$231.55 7 $4,774.15 $5,006.86 -$232.71 8 $4,774.15 $5,008.02 -$233.87 9 $4,774.15 $5,009.19 -$235.04 10 $4,774.15 $5,010.37 -$236.22 11 $4,774.15 $5,011.55 -$237.40 12 $4,774.15 $5,012.74 -$238.58 Sum of the interest payments equals $60,075.79
Balance $1,000,000.00 $1,000,225.85 $1,000,452.82 $1,000,680.93 $1,000,910.19 $1,001,140.58 $1,001,372.13 $1,001,604.84 $1,001,838.71 $1,002,073.75 $1,002,309.97 $1,002,547.37 $1,002,785.95
(c) Using the same approach as above we can get the balance after 5 years. PV = -1,000,000 i = 6% / 12 = .5% pmt = 4,774.15 (from part a) n = 60 (to get balance after 60 months) Solve for FV FV = $1,015,757.36 (d) To amortize the loan over the remaining 25 years, we can use a financial calculator as follows: PV = -$1,015,757.36 i = 6% / 12 = .5% n = 300 (300 months remaining loan term) FV = 0 (to amortize the loan) Solve for pmt pmt = $6,544.54 18-169
18-170
Problem 12-6 (REFER TO TEMPLATE 12_6.XLS) Purchase price
$1,250,000 Loan amount Interest rate $100,000 Loan term 5.00% Monthly payment $100,000 Annual payment 50.00%
Initial NOI Growth in NOI Base for participation Participation % of NOI Terminal cap rate Participation in price increase
$1,125,00 0 5.50% 20 $7,738.73 $92,864.7 9
8.00% 50.00%
Resale price Purchase price Increase in value Participation in sale Loan balance at resale
$2,036,118 $1,250,000 $786,118 $393,059 $713,075
Year
NOI 0 1 2 3 4 5 6 7 8 9 10 11
Excess over base $100,000 $105,000 $110,250 $115,763 $121,551 $127,628 $134,010 $140,710 $147,746 $155,133 $162,889
0 5,000 10,250 15,763 21,551 27,628 34,010 40,710 47,746 55,133
Participatio Debt n service
Lender cash flow -$1,125,000 $92,865 $92,865 $92,865 $95,365 $92,865 $97,990 $92,865 $100,746 $92,865 $103,640 $92,865 $106,679 $92,865 $109,870 $92,865 $113,220 $92,865 $116,738 $92,865 $1,226,565 *
0 2,500 5,125 7,881 10,775 13,814 17,005 20,355 23,873 420,626 IRR
*Includes participation in NOI, Resale, and loan balance
18-171
9.10%
Problem 12-7 (REFER TO TEMPLATE 12_7.XLS) (a) Purchase price
$1,250,000 Loan amount Interest rate $100,000 Loan term 5.00% Monthly payment $100,000 Annual payment 50.00%
Initial NOI Growth in NOI Base for participation Participation % of NOI Terminal cap rate Conversion percentage
$1,125,00 0 6.50% 20 $8,387.70 $100,652. 37
8.00% 60.00%
Resale price $2,036,118 Conversion value $1,221,671 Loan balance at resale $738,692 Lender cash flow if no default $1,221,671 (lender gets higher of conversion value or loan balance) $1,221,671 (lender gets property if less than loan balance at Lender cash flow if default allowed resale) Year Debt service 0 1 2 3 4 5 6 7 8 9 10
$100,652 $100,652 $100,652 $100,652 $100,652 $100,652 $100,652 $100,652 $100,652 $100,652
Lender cash flow -1,125,000 $100,652 $100,652 $100,652 $100,652 $100,652 $100,652 $100,652 $100,652 $100,652 $1,322,323 *
IRR
9.50%
*Includes debt service plus either loan balance, conversion value or default proceeds. Note: In this case the lender would want to convert to ownership in the property because 60% of the resale value is greater than the loan balance. 18-172
(b) Purchase price
$1,250,000 Loan amount Interest rate $100,000 Loan term 5.00% Monthly payment $100,000 Annual payment 50.00%
Initial NOI Growth in NOI Base for participation Participation % of NOI Terminal cap rate Conversion percentage
$1,125,00 0 6.50% 20 $8,387.70 $100,652. 37
8.00% 60.00%
Resale price $1,130,000 Conversion value $678,000 Loan balance at resale $738,692 Lender cash flow if no default $738,692 (lender gets higher of conversion value or loan balance) $738,692 (lender gets property if less than loan balance at Lender cash flow if default allowed resale) Year Debt service 0 1 2 3 4 5 6 7 8 9 10
$100,652 $100,652 $100,652 $100,652 $100,652 $100,652 $100,652 $100,652 $100,652 $100,652
Lender cash flow -$1,125,000 $100,652 $100,652 $100,652 $100,652 $100,652 $100,652 $100,652 $100,652 $100,652 $839,344 *
IRR
6.39%
*Includes debt service plus either loan balance, conversion value or default proceeds. Note: In this case the lender would not want to convert because the mortgage balance after 10 years is greater than 60% of the resale value. Thus, the return is essentially the same as the interest rate on the mortgage of 6.5%. The rounding (6.39% vs. 6.5%) is due to the fact that we assumed all the cash flows occurred at the end of each year rather than monthly.
18-173
(c) Purchase price
$1,250,000 Loan amount Interest rate $100,000 Loan term 5.00% Monthly payment $100,000 Annual payment 50.00%
Initial NOI Growth in NOI Base for participation Participation % of NOI Terminal cap rate Conversion percentage
$1,125,00 0 6.50% 20 $8,387.70 $100,652. 37
8.00% 60.00%
Resale price Conversion value Loan balance at resale Lender cash flow if no default Lender cash flow if default allowed
$625,000 $375,000 $738,692 $738,692 (lender gets higher of conversion value or loan balance) $625,000 (lender gets property if less than loan balance at resale)
Year Debt service 0 1 2 3 4 5 6 7 8 9 10
$100,652 $100,652 $100,652 $100,652 $100,652 $100,652 $100,652 $100,652 $100,652 $100,652
Lender cash flow -$1,250,000 $100,652 $100,652 $100,652 $100,652 $100,652 $100,652 $100,652 $100,652 $100,652 $725,652 *
IRR
5.49%
*Includes debt service plus either loan balance, conversion value or default proceeds. Note: If the borrower did not default, the lender’s return would be the same as part b. In this case, however, we assume that the borrower defaults and the lender gets the property and sells it for its estimated resale value of $625,000. Thus, the lender’s return would be 5.49 percent as shown above. 18-174
Problem 12-8 This question is like an example in the chapter. (a) Reinvestment Rate = 2% + 1.5% YMF156 = [(5% - 3.5%)/12] x 20,000,000(MIFPVA, 5%, 24mos.) = $569,847 If the 2-year treasury rate was 4%, then the lender’s reinvestment rate would be 5.5% (or 4% +1.5%), which is greater than the original interest rate (of 5%). Therefore, the lender will not charge a YMF, because the loan balance can now be reinvested at a rate greater than the original rate.
18-175
Problem 12-9 (REFER TO TEMPLATE 12_9.XLS) The before tax IRR on equity is now 14.59% and the after tax IRR on Equity is 10.70%. The lender’s return is 6.18%.
Solutions to Questions—Chapter 13 Risk Analysis Question 13-1 What is meant by partitioning the internal rate of return? Why is this procedure meaningful? To illustrate what is meant by partitioning the IRR, remember that the IRR is made up of two components of cash flow: 1. cash flow from operations 2. cash flow from the sale of the investment Partitioning is done to obtain some idea of the relative weights of these components of return and to get an idea of the timing of the receipt of the largest portion of that return. Partitioning is meaningful because it helps the investor to determine how much of the return is from annual operating cash flow and how much is from the projected resale cash flow. Operating cash flow is generally more certain than projected resale cash flow. Therefore, the greater the proportion of resale cash flow versus operating cash flow, the greater the risk facing the investor. This could be useful in comparing multiple investments. Question 13-2 What is a risk premium? Why does such a premium exist between interest rates on mortgages and rates of return earned on equity invested in real estate? A risk premium is a higher expected rate of return paid to an investor as compensation for incurring additional risk on a higher risk investment. In general, investors are considered risk averse and must be compensated more for the higher risk of some investments. This premium exists between mortgage interest rates and returns on equity invested in real estate because the equity investor is assuming more risk than the mortgage lender. The lender assumes less risk because a lender would have first claim on the property should there be a default. If this were not the case, the investor would be better off lending on real estate than investing in it. Question 13-3 What are some of the types of risk that should be considered when analyzing real estate and other categories of investment? Business Risk Financial Risk Liquidity Risk Inflation Risk Management Risk Interest Rate Risk Legislative Risk Environmental Risk Question 13-4 18-176
What is the difference between business risk and financial risk? Business risk is the risk of loss due to fluctuations in economic activity that affect the variability of income produced by a property. Financial risk (or debt financing referred to as financial leverage) magnifies the business risk. Financial risk increases as the amount of debt increases. Question 13-5 Why is the variance (or standard deviation) used as a measure of risk? What are the advantages and disadvantages of this risk measure? Lower variability in returns is considered by many analysts to be associated with lower risk and vice versa. Therefore, by using a statistical measure of variance, one has an indication of the extent risk is present in an investment. The standard deviation gives us a specific range over which we can expect the actual return for each investment to fall in relation to its expected return. It has the advantage of being relatively easy to calculate. It has the disadvantage of treating both higher than expected returns and lower than expected returns the same. It could be argued, however, that investors should be more concerned about returns being lower than expected or lower than some threshold return.
18-177
Question 13-6 What is meant by a „ real option‟ ? A real option is an option related to investment in tangible assets like real estate that involves the option to wait to decide whether to invest additional capital based on future economic conditions. Land can be viewed as having the option to invest additional capital in the future to construct a building. Question 13-7 What is meant by the term „overage‟ for retail space ? Overage refers to the rent that is paid above the minimum rent in the lease where the rent is based on a percentage of the tenant’s sales once sales exceeds a specified breakpoint. The total rent is the minimum rent plus the overage rent. Question 13-8 How does the use of scenarios differ from sensitivity analysis ? Sensitivity analysis involves changing one variable at a time, such as the market rent or the vacancy rate. Scenarios involve changing several variables at once for each scenario, e.g., a pessimistic, most likely, and optimistic scenario. For each scenario there might be a different assumption about market rents, vacancy rates, and the resale price because they are interrelated. Question 13-9 How does the use of Monte Carlo Simulation differ from using scenarios? Scenario analysis allows you to indicate the probability of a particular scenario occurring whereas Monte Carlo Simulation allows you to specify a probability distribution for inputs that are uncertain. Each iteration of the simulation can, in effect, result in a different scenario. By having a hundred or more iterations in the Monte Carlo Simulation, the output is a probability distribution that indicates the likelihood of different scenarios occurring.
18-178
Solutions to Problems—Chapter 13 Risk Analysis INTRODUCTION
Problem 13-1 Investment A Year 1 2 3 4
BTCF $5,000 10,000 12,000 15,000
PV $4,501 8,103 8,753 9,849
4 (sale)
120,000
78,792 $109,998*
*Difference from $110,000 due to rounding of IRR. The BTIRR for Investment A is 11.09 percent. This is used as the discount rate for calculating the present value. Present value of BTCFO is $31,206 Present value of BTCFS is $78,792 Investment B Year 1 2 3 4
BTCF $2,000 4,000 1,000 5,000
PV $1,774 3,145 697 3,092
4 (sale)
180,000
111,301 $120,009*
*Difference from $120,000 due to rounding of IRR. The BTIRR for Investment B is 12.77 percent. This is used as the discount rate for calculating the present value. Present value of BTCFO is $8,708 Present value of BTCFS is $111,301 (a) The BTIRR for investment A is 11.09% and the BTIRR for investment B is 12.77%. 18-179
(b)
For investment A PVATCFO is $31,206 / $110,000 or 28% and PVATCFS is $78,792 / $110,000 or 72%. For investment B PVATCFO is $8,708 / $120,000 or 7% (rounded) and PVATCFS is $111,301 / $120,000 or 93%.
(c)
Investment B is much more dependent on the reversion. It might be considered more risky because there is often more uncertainty about the estimated resale price than the cash flow from operations -especially when there are leases on the property.
18-180
Problem 13-2 INVESTMENT I
Optimistic Most Likely Pessimistic
(1) Estimate d BTIRR
(2) Expected Return
(3) Deviatio n (1) - (2)
15.00 10.00 5.00
10.00 10.00 10.00
5.00 0.00 -5.00
(4) Squared
(5)
(6) Product
Deviatio n 25.00 0.00 25.00
Probabili ty 0.20 0.60 0.20
(4) × (5)
Variance Std Deviation
10.00 3.16
(4) Squared
(5)
(6) Product
Deviatio n 36.00 1.00 81.00
Probabili ty 0.20 0.60 0.20
(4) × (5)
Variance Std Deviation
24.00 4.90
5.00 0.00 5.00
INVESTMENT II
Optimistic Most Likely Pessimistic
(1) Estimate d BTIRR
(2) Expected Return
(3) Deviatio n (1) - (2)
20.00 15.00 5.00
14.00 14.00 14.00
6.00 1.00 -9.00
7.20 0.60 16.20
The expected BTIRR and standard deviation of the BTIRR are calculated above for Investment I and II. The expected BTIRR is higher for Investment II (14% vs. 10%) but the standard deviation is also higher for investment II vs. investment I (4.90% vs. 3.16%). Thus, based on this criteria, Investment II has a higher expected BTIRR but is also riskier. We cannot say that one is better than the other. It depends on whether Mike Riskless feels that the higher expected BTIRR for Investment II is sufficient to compensate him for the extra risk. Additional Comment: It is interesting to note that for any of the three scenarios (growth, stability and decline), Investment II never has a lower return than Investment I. Thus, it could be said that Investment II dominates Investment I. This is a slightly different way of evaluating the risk (referred to as stochastic dominance). In this case, it leads to a different conclusion than if only the variance or standard deviation is evaluated.
18-181
Problem 13-3 (REFER TO TEMPLATE 13_3.XLS) ASSUMPTIONS:
Scenario Probability NOI Change in NOI Sale Price Asking Price
(a) Pessimistic Scenario Year NOI Resale Total IRR Most-Likely Scenario Year NOI Resale Total IRR Optimistic Scenario Year NOI Resale Total IRR
Pessimistic 30% $200,000 -2.00% $1,800,00 0 $2,000,00 0
Most-Likely Optimistic 40% 30% $200,000 $200,000 0.00% 3.00% $2,000,000 $2,200,000
0 (2,000,00 0)
1 200,000
2 196,000
3 192,080
4 188,238
5 184,474
(2,000,00 0) 7.93%
200,000
196,000
192,080
188,238
1,800,000 1,984,474
0 (2,000,00 0)
1 200,000
2 200,000
3 200,000
4 200,000
5 200,000
(2,000,00 0) 10.00%
200,000
200,000
200,000
200,000
2,000,000 2,200,000
0 (2,000,00 0)
1 200,000
2 206,000
3 212,180
4 218,545
5 225,102
218,545
2,200,000 2,425,102
(2,000,00 0) 12.12%
200,000
206,000
212,180
(b) Expected IRR Pessimistic Most-likely Optimistic
IRR 7.93% 10.00% 12.12%
Probability IRR × Prob. 30.00% 2.38% 40.00% 4.00% 30.00% 3.64% 18-182
Total (Expected IRR)
10.01%
18-183
(c) Variance & Standard Deviation Square of IRR -Expected IRR Pessimistic Most-likely Optimistic Variance Std. Dev.
Probability
0.04% 0.00% 0.04%
30.00% 40.00% 30.00%
IRR × Prob. 0.01% 0.00% 0.01% 0.0263% 1.62%
(d)
We can’t tell. Although the IRR is higher, the standard deviation is higher, as well. The decision would be up to the risk averseness of the investor. The investor would need to decide if the higher return is enough to compensate for the extra risk. Problem 13-4 (REFER TO TEMPLATE 13_4.XLS) ASSUMPTIONS:
Scenario Probability NOI Change in NOI Sale Price
Pessimistic Most-Likely Optimistic 30% 40% 30% 200,000 -2.00% 1,800,000
200,000 200,000 0.00% 3.00% 2,000,000 2,200,000
Holding Period Asking Price Loan Amount Loan Term Loan Interest Rate Payments per Year
5 2,000,000 1,500,000 15 years 10.00% 12
Equity Annual Debt Service Mortgage Balance
500,000 193,429 1,219,749 end of year
5
18-184
(a) IRR AND STANDARD DEVIATION OF RETURN ON EQUITY: Pessimistic Scenario Year 0 NOI Debt Service BTCF Resale (500,000) Total (500,000) IRR 2.82%
1 200,000 193,429 6,571
2 196,000 193,429 2,571
3 192,080 193,429 (1,349)
4 188,238 193,429 (5,191)
6,571
2,571
(1,349)
(5,191)
1 200,000 193,429 6,571
2 200,000 193,429 6,571
3 200,000 193,429 6,571
4 200,000 193,429 6,571
6,571
6,571
6,571
6,571
1 200,000 193,429 6,571
2 206,000 193,429 12,571
3 212,180 193,429 18,751
4 218,545 193,429 25,116
6,571
12,571
18,751
25,116
5 184,474 193,429 (8,955) 580,251 571,295
Most-Likely Scenario Year NOI Debt Service BTCF Resale Total IRR
0
(500,000) (500,000) 10.42%
Optimistic Scenario Year 0 NOI Debt Service BTCF Resale (500,000) Total (500,000) IRR
17.07%
Expected IRR Pessimistic Most-likely Optimistic Total (Expected IRR)
IRR 2.82% 10.42% 17.07%
Variance & Standard Deviation Square of IRR -Expected IRR Pessimistic 0.53% Most-likely 0.00% Optimistic 0.48%
Probability IRR × Prob. 30.00% 0.85% 40.00% 4.17% 30.00% 5.12% 10.14%
Probability IRR × Prob. 30.00% 40.00% 30.00%
0.16% 0.00% 0.14% 18-185
5 200,000 193,429 6,571 780,251 786,822
5 225,102 193,429 31,673 980,251 1,011,92 4
Variance Std. Dev.
0.3050% 5.52%
(b) The IRR has only increased slightly (from 10.01% to 10.14%). However, the standard deviation has increased from 1.62% to 5.52%. The return does not appear to have increased sufficiently to justify the additional risk. It should be noted that the standard deviation (and thus the risk ) will always increase with more debt. Whether or not the expected IRR increases depends on the degree of leverage. In this case, leverage is only marginally positive.
18-186
Problem 13-5 The value of the land at the end of the year if the NOI is $150,000 is as follows: Property Value = NOI / (Discount rate – growth rate) Property Value = $150,000 / (.12 - .02) = $1,500,000 Land value = Property Value – Construction Cost Land value = $1,500,000 - $1,000,000 = $500,000 The value of the land at the end of the year if NOI is $75,000 is as follows: Property Value = NOI / (Discount rate – growth rate) Property Value = $75,000 / (.12 - .02) = $750,000 Land value = Property Value – Construction Cost Land value = $750,000 - $1,000,000 Land value = 0 since it would not be developed because the property value if constructed is less than the construction cost The expected land value in one year is therefore (.60 × $500,000) + (.40 × $0) = $300,000. The value today is found by discounting the expected value in one year by the 12% discount rate. Land value - $300,000 / 1.12 = $267,857.
Solutions to Questions—Chapter 14 Disposition and Renovation of Income Properties Question 14-1 What factors should an investor consider when trying to decide whether to dispose of a property that he has owned for several years? The factors are based on an incremental, or marginal, return criteria that should be utilized by investors when faced with such decision making. The investor should evaluate the expected future performance of the property and then compare the IRR for holding versus sale of the property. The investor must consider whether the net funds obtained from the sale of the property (after tax and expenses) can be reinvested at a greater rate of return (ATIRR) than the return that would be earned if the property is not sold. Tax laws in effect at the time of purchase/sale of a property. Tax law changes affect the relative benefits of existing versus new investors in the same property. Question 14-2 Why might the actual holding period for a property be different from the holding period that was anticipated when the property was purchased? An investor purchases a real estate investment based on the benefits expected to be received over an anticipated holding period. That is, the investor computes the various measures of investment performance based on expectations at the time the property is purchased. After the property is 18-187
purchased, however, many things can change that affect the actual performance of the property. These same factors may affect the investor’s decision as to whether the property continues to meet his investment objectives. For example, market rents may not be increasing as fast as expected, thus reducing the investor’s cash flow. Tax laws may have changed, as they did in 1986, thus changing the benefit for some investors more than others. The point is that a periodic evaluation should be made to determine whether properties should be sold. Question 14-3 What is the marginal rate of return? How is it calculated? The marginal rate of return is the return gained by holding the property for one additional year. The marginal rate of return considers what the investor could get in the future by keeping the property versus what he could get today by selling the property. The marginal rate of return is calculated on the benefit of receiving the ATCF from operations for one additional year and the ATCF from the sale of the property at the end of the additional year. The actual formula is on page 427 of the text. Question 14-4 What causes the marginal rate of return to change over time? How can the marginal rate of return be used to decide when to sell a property? Increasing rents and increases in the value of the property tend to increase the MRR. Equity buildup from the price appreciation and loan repayment, however, tends to lower the MRR. Also, because the depreciation deduction is fixed but rents are rising, the relative amount of tax benefits from depreciation decreases each year. The property should be sold when the marginal rate of return falls below the rate at which funds can be reinvested. Question 14-5 Why might the after-tax internal rate of return on equity (ATIRRe) differ for a new investor versus an existing investor who keeps the property? This could be due to tax law changes that affect the relative benefits of existing versus new investors in the same property. If the tax law becomes less favorable as it did in 1986, this tends to favor existing investors. If the tax law becomes more favorable, as it did in 1981 when ACRS was passed and depreciable lives were shortened considerably, then new investors tend to be favored. Tax law changes tend to affect the turnover or sale of real estate. It is important to understand these concepts since tax laws are always subject to change and these changes affect the relative risk and return opportunities for new and existing investors.
18-188
Question 14-6 What factors should be considered when deciding whether to renovate a property? To determine whether a property should be renovated, consider the incremental benefit associated with renovating the property versus not renovating the property. Question 14-7 Why is refinancing often done in conjunction with renovation? When properties are renovated, the investor often uses that opportunity to refinance the entire property. Thus, the investor may be able to borrow funds in addition to what is needed for the renovation, especially if the investor plans to obtain a new loan on the entire property rather than obtain a second mortgage to cover the renovation costs. The total amount of funds that the investor will be able to borrow is usually based on a percentage of the estimated value of the property after renovation is completed. Question 14-8 Why would refinancing be an alternative to sale of the property? Refinancing would increase financial leverage. Refinancing at a higher loan-to-current-value ratio may provide the investor with additional funds to invest. This, to some extent, is an alternative to sale of the property. No taxes have to be paid on funds received by additional borrowing, whereas taxes would have to be paid if the property is sold. Question 14-9 How can tax law changes create incentives for investors to sell their properties to other investors? Tax law changes affect the relative benefits of existing versus new investors in the same property. If the tax law becomes less favorable as it did in 1986, this tends to favor existing investors. If the tax law becomes more favorable, as it did in 1981 when ACRS was passed and depreciable lives were shortened considerably, then new investors tend to be favored. Tax law changes tend to affect the turnover or sale of real estate. It is important to understand these concepts since tax laws are always subject to change and these changes affect the relative risk and return opportunities for new and existing investors. Question 14-10 How important are taxes in the decision to sell a property? Taxes are important for a number of reasons. If a property is sold, capital gains tax must usually be paid. This increases the opportunity cost of selling versus keeping the property. Also, tax laws may have changed since the property was purchased. This means that the depreciation deductions available to a new investor might be better or worse than that which the current owner is using. This affects the return that a new investor can get relative to that which the current owner can get by keeping the property. Question 14-11 Are tax considerations important in renovation decisions? Yes. First, the improvements may result in an increased depreciable basis and more tax deductions. Second, there may be tax credits available for renovating the property. Question 14-12 What are the benefits and costs of renovation? 18-189
In general, renovation can have many benefits, including increasing rents, lowering vacancy, lowering operating expenses and increasing the future property value. Question 14-13 Do you think renovation is more or less risky than a new investment? Renovation can be more risky because of the uncertainty as to the cost of the renovation. It is often easier to estimate the costs of new construction relative to the costs of renovating an older building that may have hidden structural and environmental problems.
18-190
Question 14-14 What is meant by the “incremental cost of refinancing?” When the interest rate is higher on the larger loan amount, the incremental cost of the additional funds borrowed is even higher than the rate on the larger loan. This is due to the fact that the higher rate has to be paid on all the funds borrowed, not just the additional funds. For refinancing to be a profitable strategy, the effective cost of the debt must be less than the unlevered return on the projects being financed. Question 14-15 In general, what kinds of tax incentives are available for rehabilitation of real estate income property? There are several tax incentives for rehabilitation. For example, investment tax credits are available for certain rehabilitation expenditures. A property placed in service before 1936 may be eligible for a 10% credit and a building that is a certified historic structure may be eligible for a 20% credit. There are also credits available for renovation of low-income housing. Question 14-16 Why would an investor consider doing an exchange or an installment sale? Both an exchange and an installment sale are ways of deferring capital gain taxes so that they are recognized in the future rather than at the time of sale.
18-191
Solutions to Problems—Chapter 14 Disposition and Renovation of Income Properties INTRODUCTION The four problems in this chapter deal with disposition and renovation decisions. Students are also expected to recognize that refinancing is also an alternative to disposition (part g of problem 3), and refinancing is often a part of renovation (part b of problem 4). Problem 14-1 (a) Sale price Mortgage balance Capital gain tax Cash flow
If sold today $2,000,000 1,000,000 250,000 $ 750,000
If sold next year $2,100,000 900,000 255,000 $ 945,000
Marginal return = (Cash flow if sold next year + NOI over next year - Cash flow if sold today) / Cash flow if sold today Marginal return = ($945,000 + $50,000 - $ 750,000) / $750,000 = 32.67%. (b) This appears to be a very attractive return. The property should be held for another year unless the investor feels that a higher return can be earned investing the $750,000 elsewhere at the same or lower risk. Problem 14-2 After-tax cash flow from operations if renovated After-tax cash flow from operations if not renovated Incremental cash flow from operations
$60,000 - 50,000 $10,000
Sale proceeds if renovated Sale proceeds if not renovated Incremental cash flow from sale
$2,400,000 2,100,000 $ 300,000
Renovation costs
$250,000
(a) Return from renovation = ($10,000 + $300,000 - $250,000) / $250,000 = 24% (b) This appears to be an attractive return, but it must be weighed against the risk of renovation. The investor needs to consider whether the $250,000 can be invested elsewhere at a higher return with the same or less risk.
18-192
Problem 14-3 (a) CASH FLOW FROM SALE: Sale Price (received by investor) Sales costs Mortgage Balance Before-tax Cash Flow
2,200,000 88,000 1,338,696 773,304
Sale Price Sales Costs Original Cost Basis 2,000,000 Accumulated Depreciation 130,909 Adjusted Basis
2,200,000 88,000
1,869,091
Capital Gain Depreciation recapture Price appreciation
242,909 130,909 112,000
Tax on price appreciation Tax on depreciation recapture
22,400 32,727
Total Capital Gain Tax
55,127
After-Tax Cash Flow from Sale
718,177
(b) Cash flow if not sold: Year
3 286,110 143,055 143,055 95,780 47,275
4 291,832 145,916 145,916 95,780 $ 50,136
Net Operating Income Less: Interest Depreciation Taxable Income (loss) Tax
143,055 62,878 65,455 14,723 5,153
Before-Tax Cash Flow Less Tax After-Tax Cash Flow
47,275 5,153 42,122
Rents Less Operating Expenses Net Operating Income Less Debt Service Before-Tax Cash Flow
$
$
$
5 297,669 148,834 148,834 95,780 53,055
6 303,622 151,811 151,811 95,780 $ 56,031
145,916 61,281 65,455 19,181 6,713
148,834 59,606 65,455 23,774 8,321
151,811 57,850 65,455 28,507 9,977
154,847 56,008 65,455 33,385 11,685
50,136 6,713 43,423
53,055 8,321 44,734
56,031 9,977 $ 46,054
59,068 11,685 47,383
$
$
18-193
$
$
7 309,695 154,847 154,847 95,780 59,068
(c) Cash flow if sold after 5 years:
CASH FLOW FROM SALE: Sale Price Sales costs Mortgage Balance Before-tax Cash Flow Sale Price Sales Costs Org. Cost Basis Accum Dep Adj Basis
2,550,403 153,024 1,157,419 1,239,960 2,550,403 153,024 2,000,000 458,182 1,541,818
Capital Gain Depreciation recapture Price appreciation
855,561 458,182 397,379
Tax on price appreciation Tax on depreciation recapture
79,476 114,545
Total Capital Gain Tax
194,021
After-Tax Cash Flow from Sale
1,045,938
(d) IRR (selling after 5 additional years vs. selling today): End of Year Before-Tax Cash Flow After-Tax Cash Flow Before-Tax IRR After-Tax IRR
2 (718,177) (718,177)
3 47,275 42,122
4 50,136 43,423
17.52% 13.20%
18-194
5 53,055 44,734
6 56,031 46,054
7 1,299,027 1,093,321
(e) 3
Sale price Mortgage balance Selling expenses B.T.C.F.
2,266,000 1,305,794 135,960 824,246
Sale price Selling expenses
2,266,000 135,960
Orig. Cost basis Accum Deprec. Adjusted basis
2,000,000 196,364 1,803,636
Capital gains Tax From Sale ATCF From Sale
326,404 75,099 749,147
Year
2 -718,177
Cash Flows
3 791,269
The IRR on the above cash flows is 10.18%. which is also the Marginal Rate of Return. (f) When a property is sold after just one year, this often pulls down the return compared to what it would be holding it for a few more years because the selling costs are being incurred so soon after the property was acquired. If the property is held for five years, the selling costs are, in effect, spread over all five years. Of course, there are other factors that could lower the return each year depending on projected rents, expenses and changes in property value. (g) Carson might consider refinancing. For example, a new loan for 80% of the value would result in a loan of $1,760,000. After paying off the loan balance of $1,338,696 he would have additional funds of $421,304 which could be used as equity capital to purchase Royal Palms. (h) The answer depends on the return that Carson could get by reinvesting the capital in Royal Palms, assuming he must sell Royal Oaks and not refinance as discussed in part g. If Carson expects a return over the next 5 years that is greater than 13.20% by investing in Royal Palms, he should consider selling Royal Oaks. (i) Holding Period
2
1 2 3 4 5
-718,177 -718,177 -718,177 -718,177 -718,177
3
791,269 42,122 42,122 42,122 42,122
4
861,827 43,423 43,423 43,423
18-195
5
935,602 44,734 44,734
6
1,012,723 46,054
7
IRR
1,093,321
10.18% 12.52% 13.08% 13.22% 13.20%
MRR 10.18% 15.04% 14.32% 13.68% 13.10%
Problem 14-4 (a) IF NOT RENOVATED RETURN FOR NEXT 5 YEARS Data Input Box for Yrs 3-7: 850,000 Tax Considerations: 800,000 Building Value (original) 2.0% Depreciable Life (in years) Ord. Inc. tax 2.0% Capital Gain tax 938,469 Recapture tax 4.0% 561,254 4.50% 18 12 7
Current Value Original Cost Basis Rent/NOI Growth Operating Expenses (% of Rent) Property Growth Resale Value Selling Costs Loan Amount / Current Balance Interest Rate Loan Term Remaining (in years) Payments per Year Total Holding Period (in yrs)
600,000 39 35% 20% 25%
NO RENOVATION: Loan Annual Pmt Mortg Bal
561,254 45,551 394,636
CASH FLOW FROM OPERATIONS: 4 5
3
Net Operating Income Less Debt Service Before-Tax Cash Flow $
52,000 45,551 6,449
Net Operating Income Less: Interest Depreciation Taxable Income (loss) Tax Before-Tax Cash Flow Less Tax After-Tax Cash Flow
$
in year 7
53,040 45,551 7,489
54,101 45,551 $ 8,550
52,000 24,833 15,385 11,783 4,124
53,040 23,881 15,385 13,775 4,821
6,449 4,124 2,325
7,489 4,821 2,668
$
$
18-196
$
6
7
55,183 45,551 9,632
56,286 45,551 $10,736
54,101 22,885 15,385 15,831 5,541
55,183 21,844 15,385 17,954 6,284
56,286 20,755 15,385 20,147 7,051
8,550 5,541 3,009
9,632 6,284 3,348
10,736 7,051 $ 3,684
$
$
CASH FLOW FROM SALE: Sale Price (received by investor) Sales costs Mortgage Balance Before-tax Cash Flow Sale Price Sales Costs Org. Cost Basis Accum Dep Adj Basis
938,469 37,539 447,697 453,233 938,469 37,539 800,000 107,692
(years 1 to 7) 692,308
Capital Gain Depreciation recapture Price appreciation
208,622 107,692 100,930
Tax on price appreciation Tax on depreciation recapture
20,186 26,923
Total Capital Gain Tax
47,109
After-Tax Cash Flow from Sale
406,124
IF RENOVATED IF RENOVATED: Additional Equity Loan Annual Pmt Mortg Bal
50,000 711,254 56,328 593,576
in year 7 3 62,400 56,328 6,072 $
5 64,272 66,200 56,328 56,328 7,944 $ 9,873 $
7 6 68,186 70,232 56,328 56,328 11,859 $13,904
Net Operating Income Less: Interest Depreciation Taxable Income (loss) Tax
62,400 35,080 20,513 6,807 2,382
64,272 33,993 20,513 9,766 3,418
66,200 32,850 20,513 12,837 4,493
68,186 31,649 20,513 16,024 5,608
70,232 30,387 20,513 19,332 6,766
Before-Tax Cash Flow Less Tax After-Tax Cash Flow
6,072 2,382 3,690 $
7,944 3,418 4,526 $
9,873 4,493 5,380 $
11,859 5,608 6,250
13,904 6,766 $ 7,138
Net Operating Income Less Debt Service Before-Tax Cash Flow
$
$
4 -
18-197
8
72,339
CASH FLOW FROM SALE: Sale Price Sales costs Mortgage Balance Before-tax Cash Flow
1,205,645 48,226 593,576 563,844
Sale Price Sales Costs Org. Cost Basis Accum Dep Adj Basis
1,205,645 48,226 1,000,000 133,333 866,667
Capital Gain Depreciation recapture Price appreciation
290,753 133,333 157,419
Tax on price appreciation Tax on depreciation recapture
31,484 33,333
Total Capital Gain Tax
64,817
After-Tax Cash Flow from Sale
499,026 2 (250,000) (200,000) (50,000)
ATCF assuming renovation ATCF assuming no renovation Incremental Cash Flow IRR on Incremental A.T. Cashflows
16.75%
(b) Data Input If Renovated with Refinance: NOI Yr 1 After Renovation 62,400 NOI Growth 3.0% Terminal Cap Rate 6.0% Renovation Costs 200,000 Total New Loan Amount 735,000 (70% loan) Interest Rate Loan Term (in years) Payments per Year Dep. Life of Renovation Holding Period Years Since Purchase IF RENOVATED: Additional Equity Loan Annual Pmt Mortg Bal
5.00% 20 12 39 5 2
26,254 735,000 58,208 613,393
3 3,690 2,325 1,365
in year 7
18-198
4 4,526 2,668 1,858
5 5,380 3,009 2,371
6 6,250 3,348 2,902
7 506,164 409,808 96,357
3 -
7 8 70,232 72,339 58,208 $ 12,024
Net Operating Income Less Debt Service Before-Tax Cash Flow $
62,400 58,208 4,192 $
64,272 58,208 6,064
5 6 66,200 68,186 58,208 58,208 $ 7,992 $ 9,978
Net Operating Income Less: Interest Depreciation Taxable Income (loss) Tax
62,400 36,251 20,513 5,636 1,973
64,272 35,128 20,513 8,631 3,021
66,200 33,947 20,513 11,740 4,109
68,186 32,706 20,513 14,967 5,239
Before-Tax Cash Flow Less Tax After-Tax Cash Flow
4,192 1,973 2,219 $
6,064 3,021 3,043
7,992 4,109 $ 3,883 $
9,978 12,024 5,239 6,411 4,739 $ 5,612
$
4 -
CASH FLOW FROM SALE: Sale Price Sales costs Mortgage Balance Before-tax Cash Flow Sale Price Sales Costs Org. Cost Basis Accum Dep Adj Basis
1,205,645 48,226 613,393 544,026 ######## 48,226 1,000,000 133,333 866,667
Capital Gain Depreciation recapture Price appreciation
290,753 133,333 157,419
Tax on price appreciation Tax on depreciation recapture
31,484 33,333
Total Capital Gain Tax
64,817
After-Tax Cash Flow from Sale
479,209
ATCF assuming renovation ATCF assuming no renovation Incremental Cash Flow
70,232 31,401 20,513 18,318 6,411
2 (226,254) (200,000) (26,254)
IRR on Incremental A.T. Cashflows
3 2,219 2,325 (106)
4 3,043 2,668 375
5 3,883 3,009 874
6 7 4,739 484,821 3,348 409,808 1,391 75,013
24.51%
(c) The return for part b is higher because of the additional leverage. This also increases the risk.
18-199
(d) It appears that renovation makes sense given the relatively high IRR (15.75%) from renovation. Of course, this depends on what alternatives are available. If the renovation is done, it probably makes sense to refinance at the same time given that there is equity that has built up on the property. Although this also increases the risk, the amount of leverage is still typical.
Problem 14-5 The IRR on the incremental cash flows resulting from renovation drops to 1.84% from 24.13%. Problem 14-6 The marginal rate of return (MRR) starts off higher and decreases at a faster rate over time as shown below. Holding Period Original MRR New MRR 1 14.56% 14.56% 2 14.19% 13.81% 3 13.85% 13.17% 4 13.55% 12.62% 5 13.28% 12.14% 6 13.04% 11.72% 7 12.81% 11.36% 8 12.61% 11.03% 9 12.42% 10.74% 10 12.24% 10.47%
Problem 14-7 part a Sale price Adjusted basis Capital gain
$2,000,000 $1,500,000 $500,000
Sale price Mortgage Balance Equity
$2,000,000 $1,750,000 $250,000
Profit ratio Down Payment Seller Financing Interest rate Installment payments Ordinary income tax rate
assumed by seller
200% $50,000 $200,000 10.00% $50,000 35% 18-200
Capital gain tax rate
20%
Year Installment Payment x Profit Ratio = Gain to report x Capital gain tax rate = Capital gain tax
0 1 2 3 4 Total $50,000 $50,000 $50,000 $50,000 $50,000 $250,000 200% 200% 200% 200% 200% $100,000 $100,000 $100,000 $100,000 $100,000 $500,000 20% $20,000
20% $20,000
20% $20,000 $100,000
End yr balance Interest x Ordinary income tax rate Ord income tax
$200,000 $150,000 $100,000 $20,000 $15,000
$50,000 $10,000
$0 $5,000
$50,000
35% 1750
$17,500
Installment Payment Less ordinary income tax Less capital gain tax After tax cash flow Discount rate PV
7.00% $160,067
20% $20,000
20% $20,000
35% 7000
35% 5250
35% 3500
$50,000
$50,000
$50,000
$50,000
$50,000 $250,000
$0 $20,000 $30,000
$7,000 $20,000 $43,000
$5,250 $20,000 $39,750
$3,500 $20,000 $36,500
$1,750 $20,000 $33,250
Cash Sale Sale price Gain to report Tax Mortgage balance After Tax Cash Flow (PV)
$2,000,000 $500,000 $100,000 $1,750,000 $150,000
The installent sale has a larger present value ($160,067) than the cash sale ($150,000). Part b. Exchange versus Regular Sale and Purchase New Prop Calc of tax savings if exchanged: Sale Price if sold today Adjusted Basis today Gain if sold today Capital Gain Tax Rate Tax if sold today
$2,000,000 1,500,000 $500,000 20% $100,000
Calc of add dep benefits if not 18-201
exchanged: Depreciable life Add depreciation if sale & purchase new Ord inc. tax rate Dep. tax savings if sale & purchase new
30 $16,667 35% $5,833
Calc of additional tax at end of holding period if exchanged: Holding period 5 Additional Gain at sale of exchanged prop Deferred gain $500,000 Less: difference in accum dep $83,333 Net $416,667 Cap gains tax rate at end of holding 20% period Additional tax at sale of exchanged $83,333 prop Calc of return on tax savings from exchange: PV PMT FV N Rate
($100,000) $5,833 $83,333 5 2.67%
This means that by paying the taxes today instead of doing the exchange the investor is only earning 2.67% on his or her money. This is quite low suggesting that it is better to do the exchange. Solutions to Questions—Chapter 15 Financing Corporate Real Estate
Question 15-1 What are the main reasons that corporations may choose to own real estate? There are a number of reasons a corporation may decide to own (rather than lease) real estate. It may find that owning is less expensive than leasing when considering the cost of leasing and the tax benefits of owning. The corporation may also want to have more control over the real estate than is possible with leasing. It may also feel that owning real estate provides diversification of its asset base. Question 15-2 What factors would tend to make leasing more desirable than owning? The cost of leasing may be less than the cost of owning the space, especially if the company can not use the tax benefits associated with owning. The company may also be concerned about the effect that owning real estate may have on its income and balance sheets. It may also prefer the 18-202
flexibility associated with leasing, especially if the company only plans to use the space for a short period of time.
Question 15-3 Why might the cost of a mortgage loan be greater than the cost of using unsecured corporate debt to finance corporate real estate? Mortgage loans are typically on a non-recourse basis for real estate income property. This means that the risk of default must be built into the mortgage interest rate. A corporation with a high credit rating may find that it can borrow money at a cheaper rate based on the credit worthiness of the corporation. That is, the corporation may be less risky than a specific property that the company wants to finance. Question 15-4 Why might the riskiness of cash flow from the residual value of the real estate differ from the riskiness of cash flow from the corporation‟s core business? What would cause these cash flows to be correlated? The residual value of the real estate depends on factors affecting the supply and demand for space where the property is located. This might be quite different from factors that affect the supply and demand for the products and / or services offered by the corporation. Question 15-5 What would cause the rate of return for an investor that purchases real estate and leases it to the corporation to differ from the rate of return earned by the corporation on the incremental investment in owning versus leasing the same property? One reason these returns might differ is that the corporation may be taxed quite differently than the investor, e.g., they may have very different marginal tax rates. The cost of financing to the investor may also be quite different that that for the corporation. Question 15-6 Why might the decision to own rather than lease real estate have an unfavorable effect on the corporation‟s financial statements? Real estate may have a lower current return than the typical investment that the corporation makes. Thus, owning the real estate lowers the company’s return on assets. If the real estate is highly levered, it can also make the corporation look more risky. Question 15-7 Why is the value of corporate real estate often considered “hidden” from shareholders? Real estate is shown on the corporation’s books at its historical cost less book depreciation. Thus, if the properties owned by the corporation have increased in value rather than decreased, this is not reflected on the company’s balance sheet. Question 15-8 How does the analysis of a sale-leaseback differ from the analysis of owning versus leasing? The main difference is that if the property is already owned, capital gains tax must be paid if the property is sold.
18-203
Question 15-9 Why is the cost of financing with a sale-leaseback essentially the same as the return from continuing to own? Both of these calculations use the same marginal cash flows. The difference is just in how the return is interpreted. Question 15-10 Why might it be argued that corporations do not have a comparative advantage when investing in real estate as a means of diversification from the core business? Corporations do not typically hold real estate in a large number of geographic areas and may not hold a variety of different types of properties. Thus, they cannot diversify their real estate holdings as much as a large institutional investor that holds a much larger and more diversified portfolio. Question 15-11 Why has real estate often been a key factor in corporate restructuring? Many corporations do not understand the value of their real estate holdings, especially based on its highest and best use which could be for a different use than being used by the corporation. Thus, real estate often presents an opportunity for management (or takeover investors) to restructure the way the real estate is used. Excess real estate may be sold as a source of corporate financing. Question 15-12 Why might refinancing be considered an alternative to a sale-leaseback? Sale and leaseback of real estate is essentially a way to obtain financing. Thus, refinancing the real estate without selling it may accomplish the same objective of raising funds. Question 15-13 What factors might cause the highest and best use of real estate to change during the course of typical lease term? Market conditions can change such that the property and / or the underlying land owned by the corporation is more valuable to someone who wants to use it for a different purpose, e.g., there could be an increases in the demand for office space in an area surrounding a property currently being used for warehouse space. Question 15-14 Why should corporations have their real estate appraised on a regular basis? Having the real estate appraised helps the corporation determine whether property is being used at its highest and best use. The results of the appraisals might also be reported to shareholders in a special report or note to the financial statements to reduce the problem of ―hidden value‖. Question 15-15 What factors would tend to affect the value of a lease? The value of a lease to the corporate lessor will increase if market rental rates rise above the contract rate in the lease. This means that the corporation is benefiting from the below market rental rate.
18-204
Solutions to Problems—Chapter 15 Financing Corporate Real Estate INTRODUCTION The three problems in this chapter parallel the lease versus own and sale-leaseback examples in the chapter. Emphasis should be on the interpretation of the rate of return calculations from the point of view of the corporate decision maker. Problem 15-1 ASSUMPTIONS: Increase in sales Costs of Goods Sold Increase in Corporate Overhead Personal property Tax rate
Own Sales Costs of goods sold Gross income
$2,500,0 00 1,000,00 0 1,500,00 0
Operating expenses: Business 300,000 Real estate 225,000 Lease payments 0 Interest Depreciation Taxable income Tax Income after tax Plus: Depreciation Principal
141,750 92,308 740,942 155,598 585,344 92,308 0
2,500,00 LEASE: 0 1,000,00 Annual lease pmt. 450,000 0 300,000 Lease term 15 2,500,00 Operating 0 Expenses 21.00%
Lease
Difference (OwnLease) $2,500,0 $0 00 1,000,00 0 0 1,500,00 0 0 0 300,000 0 225,000 0 450,000 (450,000 ) 0 141,750 0 92,308 525,000 215,942 110,250 45,348 414,750 170,594 0 92,308 0 0 18-205
225,000
PURCHASE: Purchase Price 4,500,000 Land
900,000
Building
3,600,000
Depreciable life 39 Resale Value 5,000,000 Interest-only loan: 3,150,000 Amoun t Interest rate 4.50%
After-tax cash flow
677,652 414,750 262,902
Cash flow from Sale - Owning Resale
$5,000,0 00 3,150,00 0
Mortgage Balance Resale Basis Gain Tax After-tax Cash Flow
$5,000,0 00 3,115,38 5 1,884,61 5 395,769 1,454,23 1
Incremental Analysis Owning vs. Leasing Ye 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 ar O (3,850 677, 677, 677, 677, 677, 677, 677, 677, 677, 677, 677, 677, 677, 677, 2,131 wn ,000) 652 652 652 652 652 652 652 652 652 652 652 652 652 652 ,883 Le (2,500 414, 414, 414, 414, 414, 414, 414, 414, 414, 414, 414, 414, 414, 414, 414,7 ase ,000) 750 750 750 750 750 750 750 750 750 750 750 750 750 750 50 Differe (1,350 262, 262, 262, 262, 262, 262, 262, 262, 262, 262, 262, 262, 262, 262, 1,717 nce ,000) 902 902 902 902 902 902 902 902 902 902 902 902 902 902 ,133
18-206
(a) ATIRR (lease): 14.38% (b) ATIRR (own): 16.44% (c) ATIRR (owning vs. leasing difference): 19.59% (d) Other factors to consider in a lease vs. own decision include space requirements, amount of time space is needed, risk bearing, management expertise, maintenance, special purpose buildings, tax considerations, access to capital markets, control, and effect on financial statements. Problem 15-2
ASSUMPTIONS: Increase in sales Costs of Goods Sold Increase in Corporate Overhead Tax rate Number of years property owned
2,500,000 1,000,00 0 300,000
Annual lease pmt.
21.00%
Operating Expenses Resale Value
5
4,500,00 0 900,000
15 Building
3,600,00 0 39
Lease term
Own Sales Cost of goods sold Gross income Operating expenses: Business Real estate Lease payments Interest Depreciation Taxable income Tax Income after tax Plus: Depreciation Principal
Purchase Price 450,000 Land
SALE-LEASEBACK
$2,500,000 1,000,000 1,500,000 300,000 225,000 0 141,750 92,308 740,942 155,598 585,344 92,308 0
225,000 Depreciable life 5,700,00 Value Today 4,850,000 0 Interest-only loan: 3,150,00 Amou 0 nt Interest rate 4.50% Lease Difference (OwnLease) $2,500,000 $0 1,000,000 0 1,500,000 0 300,000 225,000 450,000 0 0 525,000 110,250 414,750 0 0
18-207
0 0 -450,000 141,750 92,308 215,942 45,348 170,594 92,308
After-tax cash flow Cash Flow From Sale Owning Resale Mortgage balance Resale Basis Gain Tax After-tax Cash Flow
677,652
414,750
262,902
Year 5 (today) $4,850,000 3,150,000 $4,850,000 4,038,462 811,538 170,423 1,529,577
18-208
Cash Flow From Sale Owning Resale Mortgage balance Resale Basis Gain Tax After-tax Cash Flow
Year 20 $5,700,000 3,150,000 $5,700,000 2,653,846 3,046,154 639,692 1,910,308
Incremental Analysis Sales-Leaseback Ye 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 ar O (1,529 677, 677, 677, 677, 677, 677, 677, 677, 677, 677, 677, 677, 677, 677, 2,587 wn ,577) 652 652 652 652 652 652 652 652 652 652 652 652 652 652 ,960 Le 414, 414, 414, 414, 414, 414, 414, 414, 414, 414, 414, 414, 414, 414, 414,7 ase 750 750 750 750 750 750 750 750 750 750 750 750 750 750 50 Differe (1,529 262, 262, 262, 262, 262, 262, 262, 262, 262, 262, 262, 262, 262, 262, 2,071 nce ,577) 902 902 902 902 902 902 902 902 902 902 902 902 902 902 ,592 ATIRR (owning vs. leasing difference): 17.61% (a) After-tax Cash Flow: $1,529,577 The answers to parts (b) and (c) are the same because the cost of obtaining financing and the return from continuing to own the property are essentially the same, the only difference being your perspective, i.e. one person’s cost is another person’s return. (d) In considering a sale-leaseback, the firm should consider the implications for its financial statements; its ability to shelter capital gains; its possible use as an anti-takeover device; its role as a signaling device; and its ability to provide capital to refinance high-priced debt or fund growth opportunities. Problem 15-3 (a) This causes the cost of owning to increase since the corporation can not use the tax benefits. (b) If the real estate does not increase in value, the lease IRR remains the same but ATIRR associated with owning goes down because there is less benefit of owning. (c) A lower interest rate increases the benefit of owning.
Problem 15-4 (a) The IRR for owning versus leasing drops to 14.33% from 16.39% as a result of the lower lease rate. Owning is less attractive and leasing is more attractive. 18-209
(b) The IRR for owning versus leasing increases to 17.05% from 16.39% as a result of the lower interest rate. Owning is more attractive due to the lower cost of financing ownership. Solutions to Questions—Chapter 16 Financing Project Development Question 16-1 What are the sources of risk associated with project development? Sources of risk associated with project development include market risks and project risks. Market risks are the result of unexpected changes in general market conditions affecting the supply and demand for space. Project risks are the result of choosing a specific location to develop a property and the design of the project. Question 16-2 What are some development strategies that many developers follow? Why do they follow such strategies? Business strategies used by developers can be categorized in three general ways: 1) owning and managing projects for many years, 2) selling projects after the lease-up phase, and 3) developing land and buildings for lease in a master-planned development or ―build to suite‖ for single tenants. Following a particular strategy allows the developer to have a balance between use of external contractors, architects, real estate brokers, leasing agents, and property managers and having this expertise within the firm. Question 16-3 What contingencies are commonly found in permanent or take-out loan commitments? Why are they used? What happens if they are not met by the developer? Contingencies commonly found in permanent or take-out loan commitments include: 1) a maximum amount of time to obtain a construction loan commitment, 2) a date for completion of construction, 3) minimum rent-up (leasing) requirements and an approval of major leases, 4) an expiration date of the permanent loan commitment and any provisions for extensions, and 5) an approval by the permanent lender of design changes and substitution of any building materials. Question 16-4 What is a standby commitment? When and why is it used? A standby commitment is an agreement by a lender to provide permanent financing for a property once construction is complete. It is used by a developer to obtain construction financing, because construction lenders typically require the commitment of a permanent lender before a construction loan will be made. The permanent lender may receive a fee for making the commitment to provide permanent financing, if necessary. A standby commitment is often used by developers who are still shopping for permanent financing, but need a commitment in order to obtain the construction loan. Thus, the standby commitment is like an option that the developer can use as a source of financing, but may choose not to if a better alternative is found. Question 16-5 A presale agreement is said to be equivalent to a take-out commitment. What will the construction lender be concerned about if the developer plans to use such an agreement in lieu of a take-out? A presale agreement differs from a take-out commitment in that proceeds from the sale of a property are used to repay the construction loan rather than the permanent loan. The construction 18-210
lender must be sure that the agreement requires the buyer to purchase the property at an amount that is sufficient enough to pay off the construction loan and that there will be no contingencies in the agreement that allow the purchaser to cancel the agreement. Question 16-6 What is the major concern construction lenders express about the income approach to estimating value? Why do they prefer to use the cost approach when possible? In the latter case, if the developer has owned the land for five years prior to development would the cost approach be more effective? Why or why not? The income approach usually provides a good indication of the expected value of an incomeproducing property once construction is complete and it has been leased-up. The projected value should exceed construction costs, if this is not the case, the project is not feasible and the loan should not be made. Assuming that the project is feasible, using the cost approach would provide a more conservative estimate of value, especially if the land has appreciated in value from its original cost to the developer. Question 16-7 What do we mean by overage in a retail lease agreement? How might it be calculated? Retail leases often specify a minimum rent that must be paid by tenants, as well as a percentage rent provision whereby the tenant pays rent based on a percentage of sales revenue once sales revenue exceeds a specified minimum amount. The amount by which the total rent exceeds the minimum rent is referred to as overage rent. Question 16-8 What are "gross ups" in determining tenant reimbursements for operating expenses? Why are they used? Gross ups are used by developers to increase reimbursable operating expenses to be paid by tenants based on reimbursable expenses that would be expected when the property is fully occupied. This way, as actual expenses are incurred by the developer as the property leases up, the developer is receiving funds from tenants ―in advance‖ and will have adequate cash flow today expense prior to full occupancy. Question 16-9 What is sensitivity analysis? How might it be used in real estate development? Sensitivity analysis is a way of determining how sensitive the expected results of projects are to changes in the underlying assumptions. This is an excellent way of evaluating the riskiness of a real estate development project. Question 16-10 It is sometimes said that land represents “residual” value. This statement reflects the fact that improvement costs do not vary materially from one location to another whereas rents vary considerably. Hence, land values reflect changes in rents (both up and down) from location to location. Do you agree or disagree? If improvement costs do not vary significantly between different locations, then the difference in rents may be often attributable to differences in the productivity or suitability of the land for that development and hence the land value becomes the residual value. (Author’s note: In recent years there has been more of an awareness that once a development is complete, some of the income may reflect a return on the ―business‖ aspects of the development, e.g., a successful hotel 18-211
that is a part of a national franchise or a nursing home. Thus, the appraiser must be careful not to attribute this business value to the land.) Question 16-11 Why is the practice of “holdbacks” used? Who is involved in this practice? How does it affect construction lending? Holdbacks are used by construction lenders to be sure that a developer has met all of his or her obligations before all of the funds from the construction loan are given to the developer.
18-212
Solutions to Problems—Chapter 16 Financing Project Development Problem 16-1 (a) Gross Revenue Vacancy Expenses Net Operating Income
240 Unit Proposal $ 2,851,200 142,000 997,920 $ 1,710,720
250 Unit Revised Proposal $ 2,970,000 148,500 1,782,000 $ 1,782,000
Cost Return on Total Cost
$22,000,000 7.78%
$22,800,000 7.82%
The project becomes slightly more feasible because the land cost per unit declines from (2,800,000/240) = $11,667 to (2,800,000/250) = $11,200, which partially explains why developers tend to maximize density on sites where feasible. Profitability would be even better if operating expenses (35%) would not increase proportionately with rents. A regulatory body could be persuaded to increase density if it wanted to provide more housing for its community residents and perhaps increase its property tax revenues. It would be against it if the added density caused an increase in traffic, decreased open/green space and was unfair to other developers seeking approval of projects with lower densities. (b) Assume a 240 percent luxury project at 83,000 per unit. In order to get an 8% return on cost, we can approximate the rents required to achieve this as follows: (1) NOI = [Building Cost + Land Cost] × Return on Cost NOI = [(83,000 * 240) + 2,800,000] × .08 = $1,817,600 (2) Given that NOI is 60% of rents, we have: NOI = 0.60(Rent) 1,817,600 = 0.60(Rent) Rent = $3,029,333 Rents would have to be: $3,029,333/ (240 × 12) =$1,052 per month per unit. This is an increase from $990 per month to $1,052 per month per unit, or $62 per unit per month on average. The developer would have to complete a more refined market analysis to determine what the competition is asking for rents for comparable units and consider whether the location is suitable for an upgraded level of ―luxury units‖ in that submarket/location. Problem 16-2 Parker Road Plaza The following conventions were used: Depreciation Schedule: Category Capital Improvements (90%)
Depreciation Period 31.5 years 18-213
Method S/L
Tenant Improvements (10%)
7.0 years
DDB
The total amount to be depreciated is the total direct costs financed, $11,865,000, plus the estimated interest carry. These costs are split between capital improvements (90% of the total) and tenant improvements (10% of the total). The mid-year convention was not used on either the 31.5 year straightline depreciation for capital improvements or the 7 year double declining balance used for the tenant improvements. However, the use of double declining balance does allow for switching to straight-line after the fourth year (with a double declining balance and a depreciation period of 7 years.)
18-214
Amortization Schedule: Category Construction loan fees Permanent loan fees
Depreciation Period 1 year10 years
Method S/L S/L
The construction loan fee and the permanent loan fee are amortized over the lives of each loan, respectively. The construction loan fee of $253,591 is amortized over the one year construction time period, while the permanent loan fee of $316,988 is amortized over the ten year life of the permanent loan. If the property is sold before the end of the depreciation/amortization periods, the basis in the property must be adjusted for the amount of accumulated depreciation/amortization already taken. (a) Gross revenue Vacancy Expenses Net operating income
240 Unit Proposal $2,851,200 142,160 997,920 $1,710,720
250 Unit Revised Proposal $2,970,000 148,500 1,039,500 $1,782,000
Cost:
$22,000,000
$22,800,000
Return on total cost
7.78%
7.82%
The project becomes slightly more feasible because the land cost per unit declines from (2,800,000 ÷ 240) = $11,667 to (2,800,000 ÷ 250) = $11,200 which partially explains why developers tend to maximize density on sites where feasible. Profitability would be even better if operating expenses (35%) would not increase proportionately with rents. A regulatory body could be persuaded to increase density if it wanted to provide more housing for its community residents and perhaps increase its property tax revenues. It would be against it if the added density caused an increase in traffic, decreased open/green space and was unfair to other developers seeking approval of projects with lower densities. (b) Assume a 240 percent luxury project at 83,000 per unit. In order to get an 8% return on cost, we can approximate the rents required to achieve this as follows: (1) (2)
(83,000 * 240) + 2,800,000 * .08 = 1,817,600 (NOI) Given that NOI is 60% of rents we have: NOI = .60 (R) 1,817,600 = .60 (R) 3,029,333 = (R)
Rents would have to be: $3,029,333 ÷ (240 * 900) ÷ 12 = $1,026 per month per unit. This is an increase from $990 per month to $1,026 per month per unit, or $36 per unit per month on average. The developer would have to complete a more refined market analysis to determine what the competition is asking for 18-215
rents for comparable units and also consider whether the location is suitable for an upgraded level of ―luxury units‖ in that submarket/location. PART I (a) General Project Description A. Site and Proposed Improvements Site Area (in acres) Gross Buildable Area (GBA) Gross Leasable (GLA) Percent Leasable Area Floor Area Ratio (Site Area)
12 190,000 sq. feet 175,000 sq. feet 92.11% 36.35%
B. Development Period
12 months
18-216
C. Loan Information Construction Loan: Loan Term % of Construction $ Drawn the 1st 6 months % of Construction $ Drawn the last 6 months Interest Rate Construction Loan Fee
12 months 60.00% 40.00% 13.00% 2.00%
Permanent Loan: Debt Amortization Term of Loan Interest Rate Permanent Loan Fee
20 years 10 years 12.00% 2.50%
D. Anticipated Hold After Completion
5 years
Summary of Cost Information for Parker Road Plaza A. Land and Site Improvement
Costs
% of Total Costs
Cost/(GBA)
14.5%
$11.84
8.9% 100.0%
$7.29 $81.58
ft. Site Acquisition and Closing Costs Site Improvements
$2,250,000 $750,000
B. Construction Costs Total Hard Costs @ $54.00/(GBA) ft. $10,260,000 Total Soft Costs (exc. interest) @ $4.50/(GBA) ft.$885,000 Project Costs w/o Interest Carry and Loan Fees$14,115,000 Interest Carry and Loan Fees Construction Interest Construction Loan Fees Permanent Loan Fees Unfinanced Soft Costs TOTAL PROJECT COSTS
$814,537 253,591 316,988 $1,385,117 $15,500,117
PART I (b) Summary of Construction Loan Terms Site Improvements Total Hard Construction Costs Total Soft Construction Costs Total Costs Which Will Be Financed
$750,000 $10,260,000 $855,000 $11,865,000
Estimated Interest Carry (calculated below) 814,537 Total Loan Amount $12,679,537
18-217
Interest Carry for Parker Road Plaza Construction Loan Repayment Schedule and Yield Calculation for Construction Lender (a) (b) (c) (d) (e) (f) Total Draws Payments Interest (g) Total Monthly Direct Monthl Interest Principal × (13%/12) Payments (d) Draws y Costs + (e) (a) + (b) 0 $0 $0 $0 1 1,865,500 0 1,186,500 $0 $0 2 1,865,500 12,854 1,199,354 12,854 12,854 3 1,865,500 25,847 1,212,347 25,847 25,847 4 1,865,500 38,981 1,225,481 38,981 38,981 5 1,865,500 52,257 1,238,757 52,257 52,257 6 1,865,500 65,676 1,252,176 65,676 65,676 7 791,000 79,242, 870,242 79,242 79,242 8 791,000 88,669 879,669 88,669 88,669 9 791,000 98,199 889,199 98,199 98,199 10 791,000 107,832 898,832 107,832 107,832 11 791,000 117,569 908,569 117,569 117,569 12 791,000 127,412 918,412 $12,679,53 127,412 12,806,950 7 Total $11,865,00 $814,537 $12,679,537 $12,679,53 814,537 $13,494,075 0 7
(g) Ending Bal. (g) Prev Bal + (c) (d) $0 1,186,500 2,385,854 3,598,200 4,823,681 6,062,438 7,314,614 8,184,856 9,064,525 9,953,724 10,852,556 11,761,125 0
Yield to Lender: The yield to the lender is calculated as the interest rate needed to equate the present value of the construction loan fee to the present value of the cash flow stream of the lender which is calculated from the Construction Loan Repayment Schedule as column (d) minus column (a).
Month 0 1 2 3 4 5 6 7 8 9 10 11 12
Cash Flows 253,591 (1,186,500) (1,186,500) (1,186,500) (1,186,500) (1,186,500) (1,186,500) (791,000) (791,000) (791,000) (791,000) (791,000) 11,888,537
Yield to Construction Lender =
17.58%
PART I (c) Summary of Permanent Loan Terms 18-218
$0
Total Loan Debt Amortization Term of Loan Interest Rate Debt Service/Month Debt Service/Year 2.50% Permanent Loan Fee
$12,679,537 20 10 12.00% $139,613 $1,675,352 $316,988
18-219
Pro Forma Statement of Cash Flows - Construction Period Draws Per Year Draws Per Year (0) (1) Cost Breakdown $2,250,00 Site Acquisition & Closing $750,000 Costs Site Improvements 10,260,000 Hard Costs 855,000 Soft Costs Permanent Loan Fee 316,988 Construction Loan Fee 253,591 Construction Interest 814,537 Total $2,820,579 $12,679,537 Total Construction Cash $2,820,579 12,679,537 Outflow Less: Total Draws 0 12,679,537 Total Equity Needed $2,820,579 $0 PART II (d) Pro Forma Operating Statement - Parker Road Plaza CASHFLOWS (EOP) 2 3 INCOME: Rent Increase @ 5.00% Minimum Rent $18.50 $3,237,50 $3,339,37 0 5 Average (% of gross sales) 3.00% 52,500 118,650 Tenant Reimbursement (per $8.00 1,400,000 1,470,000 GLA) GROSS POTENTIAL $4,690,00 $4,998,02 INCOME 0 5 Vacancy Allowance 1,407,000 249,401 EXPECTED GROSS $3,283,00 $4,738,62 INCOME 0 4 EXPENSES Operating Expenses (per $14.00 $2,450,00 2,572,500 GLA) 0 Management Fee (% of EGI) 5.00% 164,150 236,931 Total Expenses $2,614,15 $2,809,43 0 1 NET OPERATING INCOME $668,850 1,929,193 Less: Debt Service
1,675,352
1,675,352
BEFORE TAX CASH FLOW
$(1,006,50 2)
$253,841
Total
$2,250,000 750,000 10,260,000 855,000 316,988 253,591 814,537 $15,500,117 $15,500,117 12,679,537 $2,820,579
4
5
6
$3,569,3 44 118,769 1,543,50 0 $5,301,6 13 265,081 $5,036,5 32
$3,747,8 11 263,095 1,620,67 5 $5,631,5 81 281,579 $5,350,0 02
$3,935,2 01 341,881 ,701,709
2,701,12 5 251,827 $2,952,9 52 2,083,58 1 1,675,35 2 $408,229
2,836,18 1 267,500 $3,103,6 81 2,246,32 1 1,675,35 2 $570,969
,997,990
Depreciation and Amortization Schedule - Parker Road Plaza A. Depreciable Costs Site Improvements (on/off)
$750,000 18-220
$5,978,7 91 98,940 $5,679,8 52
83,993 $3,261,9 83 ,417,869 ,675,352 $742,517
Hard Costs Soft Costs & Construction Interest Total Depreciable Costs
$10,260,000 $1,669,537 $12,679,537
B. Depreciation Schedule
Depreciation
Period Capital Improvements (90% of Total) Tenant Improvement (10% of Total)
11,411,584 1,267,954
C. Amortization Schedule
31.5 yrs. 7 yrs. Amortization
Period Construction Loan Fees Permanent Loan Fees Total Amortized Costs Add: Land Total Project Costs
253,591 316,988
1 yr. 10 yrs. 570,579 2,250,000 $15,500,177
18-221
Adjusted Basis at the End of Year 6 Item Total Cost Land Capital Improvements Tenant Improvements Permanent Loan Fees Construction Loan Fees Total
Less: Accum Deprec/Amort. $0 1,811,362 1,047,915 158,494 253,591 $3,271,362
$2,250,000 11,411,584 1,267,954 316,988 253,591 $15,500,117
Adjusted Basis $2,250,000 9,600,221 220,039 158,494 0 $12,228,755
Sale of Parker Road Plaza Sale Price
$18,400,000
Less: Selling Expenses Mortgage Balance BTCF (sale)
368,000 11,632,757 $6,399,243
Gain In Year of Sale: Sale Price Less: Selling Expenses Adjusted Basis Total Gain Tax @28%
$18,400,000 368,000 12,228,755 $5,803,245 1,624,909
BTCF(sale) - Tax ATCF(sale)
$6,399,243 1,624,909 $4,774,335
PART II (d) and (e) Profitability Analysis - Parker Road Plaza Before Tax Cash Flows: Year 0 1 Equity ($2,820,579) ($0) BTCF Operation BTCF Sale Total BTCF
($2,820,579) $(0)
BTIRR BTNPV @ 16% Taxable Income: NOI
2
3
4
5
6
($1,006,502)
$253,841
$408,22 9
$570,969
$742,517
($1,006,502)
$253,841
= =
16.14% $22,639
$668,850
$1,929,193
18-222
$408,22 9
$2,083,581
$570,969
$2,246,32
$6,399,24 3 $7,141,76 1
$2,417,869
1 Less: Interest Depreciation Capital Improvements Tenant Improvements Amortization Construction loan fees Permanent Loan Fee Taxable Income
0
Tax @28%;
0
1,512,797
1,492,181
1,468,950
1,442,773
1,413,276
362,272
362,272
362,272
362,272
362,272
362,272
258,766
184,883
132,024
110,020
31,699
31,699
31,699
31,699
31,699
(253,591 (1,600,191) ) (71,005) (448,053)
(215,726)
35,826
277,553
500,601
(60,403)
10,031
77,715
140,168
253,591
18-223
After Tax Cash Flows: Total ($2,820,579 ($0) BTCF ) Less: 0 (71,005) Taxes* ATCF ($2,820,579 $71,005 ) *included taxes from sale in year 6
($1,006,502 ) (448,053)
$253,841
$408,229
$570,969
$7,141,761
(60,403)
10,031
77,715
1,765,077
($558,448)
$314,244
$398,198
$493,254
$5,376,683
=
13.77%
ATIRR
PART II (e) Based on the BTNPV and BTIRR, this project exceeds the required before tax hurdle rate of 16%. Therefore, Kudhner should move forward and develop Parker Road Plaza. Problem 16-3 Timbercreek Office Building (a) General Project Description A. Site and Proposed Improvements Site Area (in Acres) Gross Buildable Area (GBA) Gross Leasable Area (GLA) Percent Leasable Area Floor Area Ratio (Site Area) B. Development Period C. Loan Information Construction Loan: Loan Term % of Construction $ Drawn the 1st 6 Months % of Construction $ Drawn the Last 6 Months Interest Rate Construction Loan Fee Permanent Loan: Debt Amortization Term of Loan Interest Rate Permanent Loan Fee E. Anticipated Hold After Completion
1.3 31,200 sq. ft. 26,520 sq. ft. 85.00% 55.10% 12 months
12 months 100.00% 0.00% 13.00% 1.50% 25 years 8 years 11.50% 4.00% 5 years
Summary of Cost Information for Proposed Office Building Land and Site Improvements Site Acquisition and Closing Costs Site Improvements
Costs TBD $2,400,00 0 18-224
Percent of Total Costs 0.0%
Cost per Sq. Ft. GBA $0.00
Project Costs w/o Interest Carry and Loan Fees Interest Carry and Loan Fees Construction Interest Construction Loan Fees Permanent Loan Fees Unfinanced Soft Costs TOTAL DEVELOPMENT COSTS
$2,400,00 0 $230,637 39,460 105,225 $375,322 $2,775,32 2
18-225
13.5% 100.0%
$12.03 $88.95
Estimation of Loan Costs and Equity Requirements for the Development Site Improvements $2,400,000 Total Direct Costs Which Will Be Financed $2,400,000 Estimated Interest Carry (calculated below) 230,637 Total Loan Amount $2,630,637 Total Development Costs $2,775,322 Less: Total Loan Amount 2,630,637 Total Equity Requirements for Development $144,685 Estimated Interest Carry for Proposed Office Building Construction Loan Repayment Schedule (a) (b) (c) (d)
Monthly
Draws Direct Costs
Interest
0 1 2 3 4 5 6 7 8 9 10 11 12
$0 400,000 400,000 400,000 400,000 400,000 400,000 0 0 0 0 0 0
$0 0 4,333 8,714 13,141 17,617 22,141 26,714 27,004 27,296 27,592 27,891 28,193
Total Monthly Draws (a) + (b) $0 400,000 404,333 408,714 413,141 417,617 422,141 26,714 27,004 27,296 27,592 27,891 28,193
Total
$2,400,000
$230,637
$2,630,637
(b) Summary of Permanent Loan Terms Total Loan Debt Amortization Term of Loan Interest Rate Debt Service/Month Debt Service/Year 4.00% Permanent Loan Fee
Payments Principal
$2,630,63 7 $2,630,63 7
(e)
(f)
Interest (g) × (13%/12)
Total Payments (d) + (e)
$0 4,333 8,714 13,141 17,617 22,141 26,714 27,004 27,296 27,592 27,891 28,193
$0 4,333 8,714 13,141 17,617 22,141 26,714 27,004 27,296 27,592 27,891 2,658,831
$0 400,000 804,333 1,213,047 1,626,188 2,043,805 2,465,947 2,492,661 2,519,665 2,546,961 2,574,553 2,602,444 0
$230,637
$2,861,275
$0
$2,630,637 25 years 8 years 11.50% $26,740 $320,875 $105,225
Pro Forma Statement of Cash Flows - Construction Period Draws per Year Draws per Year (0) (1) Cost Breakdown Site Acquisition & Closing Costs TBD 18-226
(g) Ending Bal. (g) Prev Bal + (c) - (d)
Total $0
Site Improvements Permanent Loan Fee Construction Loan Fee Construction Interest Total Total Construction Cash Outflow Less: Total Draws Total Equity Needed
$2,400,000
$114,685
230,637 $2,630,637
2,400,000 105,225 39,460 230,637 $2,775,322
$114,685 0 $114,685
$2,630,637 2,630,637 $0
$2,775,322 2,630,637 $114,685
$105,225 39,460
18-227
Pro Forma Operating Statement - Parker Road Plaza CASHFLOWS (EOP) 2 INCOME: Rent Increase @ 3.00% yr. Minimum Rent $19.00 / GLA $503,880 ft. Tenant Reimbursement (per $3.25 86,190 GLA)
3
4
$518,996 $534,556
5
6
91,439
$550,60 $567,121 3 94,182 97,008
$607,772 $626,005
644,784 664,129
88,776
GROSS POTENTIAL INCOME Vacancy Allowance
$590,070
EXPECTED GROSS INCOME
$442,553
$577,383 $594,705
$612,54 $630,923 6
251,940
259,498
267,283
275,302 283,561
Total Expenses
$251,940 0
259,498
267,283
275,302 283,561
NET OPERATING INCOME
$190,613
$317,885 $327,422
Less: Debt Service
320,875
320,875
320,875
$337,24 $347,362 5 320,875 320,875
BEFORE TAX CASH FLOW
($130,26 3)
($2,990)
$6,547
$16,369 $26,486
3
4
5
6
$2,990
$6,547
$16,369
$26,486
$16,369
$1,002,787 $1,029,273
EXPENSES Operating Expenses (per GLA)
147,518
$9.50 / GLA ft.
Sale of Proposed Office Building Sale Price Less: Selling Expenses Mortgage Balance BTCF (sale)
31,300
32,239
33,206
$3,656,400* 146,258 2,507,396 $1,002,787
Profitability Analysis for Proposed Office Building Year 0 1 2 Equity ($144,685 ($0) ) BTCF $130,263 Operation BTCF Sale Total BTCF ($144,685 ($0) ($130,263) ) BTIRR BTNPV @ 16%
30,389
= = 18-228
($2,990)
29.64% $190,459
$6,547
(c) Without considering the equity requirements for the land, a positive BTNPV exists when you discount the equity cash flows at 16%. (d) Unfortunately, if the asking price of the land was $195,000, the BTIRR would fall to 15.78%. Additionally, the BTNPV of 16% would become negative and the project would no longer meet Spain Development Company’s hurdle rate of 16%. Before Tax Cash Flows Year Equity Proposed Land Price BTCF Operation BTCF Sale Total BTCF BTIRR BTNPV @ 16%
0 ($144,685) (195,000)
($339,685)
1 ($0)
($0) = =
18-229
2
4
5
6
($130,263) ($2,990)
$6,547
$16,369
($130,263) ($2,990)
$6,547
$16,369
$26,486 $1,002,787 $1,029,273
15.78% ($4,541)
3
Problem 16-4 (a) The yield to the lender is now 15.11% vs. 15.45% and the after tax IRR to the investor is 17.73% vs. 17.35%. (b) The yield to the lender is now 15.89% vs. 15.45% and the after tax IRR to the investor is 17.00% vs. 17.35%. Solutions to Questions—Chapter 17 Financing Land Development Projects Question 17-1 How might land development activities be specialized? Why is this activity different from project development discussed in the preceding chapter? Firms can specialize in the acquiring raw land in suburban fringe areas and developing sites for single family detached units or for multiple uses, such as combinations of single family units, multifamily apartments, and cluster housing. Land developers and builders or project developers may, or may not, be the same entities. Land developers may or may not have the expertise to undertake building construction and/or project development. Question 17-2 What is an option contract? How is it used in land acquisition? What should developers be concerned with when using such options? What contingencies may be included in a land option? Option contracts are used to reserve a parcel of land so that it will not be sold to someone else, while the developer does preliminary analysis of the site. The developer should be concerned about the price of the option and the length of time until a decision is made. Contingencies might include passing an environmental inspection, being able to get the land rezoned, or receiving any necessary permits for development. Question 17-3 What are some of the physical considerations that a developer should be concerned with when purchasing land? How should such considerations be taken into account when determining the price that should be paid? The developer should be concerned about the physical characteristics of the land and how this affects the number of parcels that can be developed, as well as the cost of developing them. Examples of important physical characteristics include the land’s size, topography, soil condition, amenities, and accessibility. Question 17-4 In land development projects, why do lenders insist on loan repayment rates in excess of sales revenue? What is a release price? A lender doesn’t want to wait until the last parcel sells for the development loan to be completely repaid. Thus, a lender will normally insist on a loan repayment rate that is greater than the rate for which parcels are expected to sell. The release price is the dollar amount of a loan that must be repaid when a lot is sold. Release prices may vary with different types of lots. Typically, the release price is set at an amount that results in the loan being repaid by the time a certain percentage, e.g. 80 percent, of the lots are sold. Note, this does not mean that the developer must pay back an amount that is greater than the sale price of the lot. 18-230
Question 17-5 What are the unique risks of land development projects from the developer‟s and lender‟s point of view? Land development can be quite risky for both the developer and the lender, especially when compared to existing projects. During the development period, a developer must be concerned about changing market conditions that subsequently affects the price and rate at which parcels are sold. The cost to develop the site can also be greater than anticipated. Ultimately, the same factors affect the lender’s risks because proceeds from the sale of parcels are used to repay the loan. Lenders get paid as lots are sold. As a result, the rate at which lots sell affects the lender’s, as well as the developers rate of return. A higher release price might reduce this risk to the lender. However, if the release price is too high, the developer may not have sufficient funds to successfully develop the project.
18-231
Solutions to Problems—Chapter 17 Financing Land Development Projects Problem 17-1 Part (A) Revised revenues: 32 @ $103,000 = $3,296,000 32 @ $118,000 = 3,776,000 16 @ $125,000 = 2,000,000 Total Revenue $9,072,000 Less: Land development cost $71,000 @ 80 = $5,680,000 Land cost $1,000,000 Gross Profit from Sales $2,392,000 Administration $1,134,000 Net Profit $1,250,000 Margin on gross revenue: Return on cost:
Required land cost to achieve ROC:
$9,072,000 $5,680,000 $ 855,200* $2,536,800 $1,134,000 $1,402,800
13.8% 18.8%
15.5% 21.5%
Part (B) If the land could be acquired for approximately $855,200*, then return on cost ROC would return to about 21% and the margin would exceed 13.8%. (see right hand column above)
Problem 17-2 (a) Calculation of the Release Price Per Parcel Note to users of the 10th edition: This edition of the book uses a simplified approach to calculate the release price. The answer is identical to the previous edition if the release price is not accelerated and the loan is repaid exactly when the last lot is sold. The accelerated release price differs slightly from the previous edition but is easier to calculate. Neither approach is more ―correct‖ than the other. We have simply taken a simpler approach to accelerating the release price that no longer requires calculating the Total Interest Cary (TLF). Thus, the answer that follows will differ slightly from the answer shown for the previous edition which uses a slightly different accelerated release price.
Month
Draw
Cumulati Monthly Cumulati MPVIF ve ve @ Deluxe Standard Units Sales Sales 11%
0 1
600,000 600,000
0 0
0 0
0 0
0 0
2
600,000
0
0
0
0 18-232
PV Draws
0 1.00000 600000 0 .99092 594549.958 7 0 .98192 589149.422
Monthly Sales 0 0 0
3
600,000
0
0
0
4
300,000
4
3
7
5
300,000
4
3
14
6
300,000
4
3
21
4 4 4 4 4 4 2 2 2 2 2 2 2 2 2 2 2 2 60
3 3 3 3 3 3 5 5 5 5 5 5 5 5 5 5 5 5 87
28 35 42 49 56 63 70 77 84 91 98 105 112 119 126 133 140 147 147
7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Total PV
3,300,000 3,227,382
PV of Draws PV of Revenue PV Revenue / PV Draws Release Price
3 0 .97300 583797.941 2 260,000 260,000 .96416 289247.534 9 260,000 520,000 .95540 286620.183 2 260,000 780,000 .94672 284016.696 8 260,000 1,040,000 .93812 0 260,000 1,300,000 .92960 0 260,000 1,560,000 .92116 0 260,000 1,820,000 .91279 0 260,000 2,080,000 .90450 0 260,000 2,340,000 .89628 0 256,000 2,596,000 .88814 0 256,000 2,852,000 .88007 0 256,000 3,108,000 .87208 0 256,000 3,364,000 .86416 0 256,000 3,620,000 .85631 0 256,000 3,876,000 .84853 0 256,000 4,132,000 .84082 0 256,000 4,388,000 .83319 0 256,000 4,644,000 .82562 0 256,000 4,900,000 .81812 0 256,000 5,156,000 .81069 0 256,000 5,412,000 .80332 0 5,412,000 3,227,382 4,771,981 0
0 250681 248404 246148 243912 241696 239501 237325 235170 233034 227364 225299 223253 221225 219215 217224 215251 213296 211358 209438 207536 205651 4,771,981
3,227,382 4,771,981 67.6319% 81.1583%
The ratio of the PV of Revenue to PV of Draws above (67.6319%) is what the release price would be if it was not accelerated and the loan would be repaid exactly when the last lot is sold. Increasing this by 20% (67.6319% × 1.20) gives us the accelerated release price as a percent of revenue (81.1583%) For each lot type: Deluxe Deluxe
= =
$38,000 × .811583 $30,840.15
Standard
=
$36,000 × .811583 18-233
Standard
=
29,216.98
(b) Price of each parcel: Number of Parcels 60 87
Deluxe Standard Total
Price per Parcel $38,000 $36,000
Total $2,280,000 3,132,000
147
$5,412,000
Construction Period Approval Period Likely Financing Terms improvement costs carry. Loan interest is
6 Months 6 Months 40.00% of the land acquisition cost, 100 percent of (subject to appraisal and feasibility analysis), and interest draws are to be made as improvements are completed, and to be paid monthly.
Interest Rate
11.00% (or prime of 9% plus 2%) 3 points to be paid at closing.
Treetop Associated Group - Estimate of Costs to be Funded by Loan Proceeds: 40.00% Land Acquisition Costs Financed $600,000 Direct Development Costs 2,700,000 Total Direct Costs Which Will Be Financed
$3,300,000
Estimated Interest Carry (calculated below) Total Loan Amount
299,222 $3,599,222
Treetop Associated Group - Schedule of Estimated Monthly Cash Draws for Development Costs: Month Amount Closing $600,000 1 600,000 2 600,000 3 600,000 4 300,000 5 300,000 6 300,000 Total
$3,300,000
Treetop Associated Group - Estimated Monthly Absorption Rate After Loan Closing: Cumulative Cumulative Monthly Unit Sales Sales * Standard ** Sales Volume Revenue Month Deluxe
Close
0
0
0 18-234
0
$0
Monthly Revenue Rate (percent of total) 0.000000%
1-3 4-6 7-12 13-18 19-24
0 4 4 2 2
0 3 3 5 5
0 21 63 105 147
0 780,000 2,340,000 3,876,000 5,412,000
Total
12
16
147
$5,412,00 0
* Price ** Price
= =
0 260,000 260,000 256,000 256,000
0.000000% 4.804139% 4.804139% 4.730229% 4.730229% 100.000000 %
$38,000 $36,000
Treetop Associated Group - Determining the Duration of the Construction Loan: The month in which the loan repayment occurs must be determined to solve for the interest carry. Because the bank wants the loan paid off 20% faster than the revenue is generated, the loan must be totally repaid when 83.33333% (100% / 120%) of the revenue is collected.
Target Revenue Amount
= 83.3333% = 83.3333% = $4,510,000
x x
Total Revenue $5,412,000
The following table illustrates the relationship between the percentage of revenue at which the bank wants the loan paid off, and the month in which this occurs.
Month 4-6 7-12 13-18 19 20 21
Cluster 12 24 12 2 2 2
Standard 9 18 30 5 5 5
Cumulative Sales ($) $780,000 2,340,000 3,876,000 4,132,000 4,388,000 4,644,000
Monthly Sales Revenue $260,000 260,000 256,000 256,000 256,000 256,000
-- Repaid during this month
Treetop Associated Group - Estimate of Interest Carry:
(c) Treetop Associated Group - Loan Repayments Schedule:
Month
Interest 0
0
Total
Principal
Payments Interest
600,000 18-235
Total
BalanceCash Flow 600,000 (492,023)
1
5,500
605,500
0
5,500
2
11,050
611,050
0
11,050
3
16,652
616,652
0
16,652
4
22,304
322,304
211,012
22,304
5
23,325
323,325
211,012
23,325
6
24,354
324,354
211,012
24,354
7
25,393
25,393
211,012
25,393
8
23,692
23,692
211,012
23,692
9
21,974
21,974
211,012
21,974
10
20,242
20,242
211,012
20,242
11
18,493
18,493
211,012
18,493
12
16,728
16,728
211,012
16,728
13
14,947
14,947
207,765
14,947
14
13,180
13,180
207,765
13,180
15
11,396
11,396
207,765
11,396
16 17 18 19 20 21 22 23 24
9,596 7,779 5,946 4,096 2,229 345 0 0 0 299,222
9,596 207,765 7,779 207,765 5,946 207,765 4,096 207,765 2,229 207,765 345 37,996 0 0 0 0 0 0 3,599,222 3,599,222
9,596 7,779 5,946 4,096 2,229 345 0 0 0 299,222
18-236
5,500 1,205,50 (600,000) 0 11,050 1,816,55 (600,000) 0 16,652 2,433,20 (600,000) 2 233,316 2,544,49 (88,988) 5 234,336 2,656,80 (88,988) 8 235,366 2,770,15 (88,988) 0 236,405 2,584,53 211,012 2 234,703 2,397,21 211,012 2 232,986 2,208,17 211,012 5 231,253 2,017,40 211,012 5 229,504 1,824,88 211,012 6 227,740 1,630,60 211,012 3 222,712 1,437,78 207,765 5 220,945 1,243,19 207,765 9 219,161 1,046,83 207,765 0 217,361 848,661 207,765 215,545 648,675 207,765 213,711 446,856 207,765 211,861 243,187 207,765 209,994 37,651 207,765 38,341 0 37,996 0 0 0 0 0 0 0 0 0 3,898,443 15.44%Lender's Yield
(d) Treetop Associated Group - Estimated Project Costs and Equity Requirements Land and Development Costs: Site 1,500,000 Site Closing 50,000 Site Improvements 2,700,000 Construction Interest 299,222 Const. Loan Fee 107,977 Total Direct Costs 4,657,198 Operating Expenses: Selling Commissions Property Taxes General & Admin. Total Indirect Costs
270,600 38,000 60,000 368,600
Total Project Costs - Loan Amount Total Equity Required
5,025,798 3,599,222 1,426,577
Percent Financed
71.61%
(e) Treetop Associated Group - Schedule of Cash Flows Quarter 0 1 2 3 4 5 6 7 8 Inflow: Sales 0 0 780,000 780,000 780,000 768,000 768,000 768,000 768,000 Loan Draw 600,000 1,833,20 969,983 71,059 55,463 39,523 23,322 6,671 0 2 Total Inflow 600,000 1,833,20 1,749,98 851,059 835,463 807,523 791,322 774,671 768,000 2 3 Outflows: Site Purch. 1,500,000 Closing 50,000 Loan Fee 107,977 0 633,035 633,035 633,035 623,296 623,296 453,526 0 Loan Princ. Pmt. Loan interest 0 33,202 69,983 71,059 55,463 39,523 23,322 6,671 0 Direct Costs 1,800,00 900,000 0 Gen & Admin 7500 7500 7500 7500 7500 7500 7500 Prop. Tax 19000 19000 Sales Exp. 0 39,000 39,000 39,000 38,400 38,400 38,400 38,400 Total Outflow 1,657,977 1,833,20 1,649,51 750,594 753,997 708,719 692,517 506,097 64,900 2 8 Net Cash (1,057,97 0 100,465 100,465 81,465 98,804 98,804 268,574 703,100 18-237
7) NPV @ IRR
15%
85,148 20.31%
Problem 17-3 Note: The solution below assumes the first draw is in month 1 – not month 0 as might be implied by the question in the book, which says the first draw is at loan closing which might be interpreted as month 0. Using month 1 for the first draw is more consistent with the book example and reality.
18-238
(a) Price of each parcel
Deluxe Standard Total
Number of Parcels 18 57 75
Price per Parcel $24,000 13,500
Total $432,000 769,500 $1,201,500
Construction Period 4 months Likely Financing Terms 0.00% of the land cost, 100 percent of improvement costs (subject to appraisal and feasibility analysis.) Loan draws are to be made as improvements are completed, interest is to be paid monthly. Interest Rate 13.00% (or prime rate of 11% plus 2%) 3 points to be paid at closing
Land and Development Costs: Site 225,000 Site Closing 10,000 Site Improvements 775,000 35,527 Construction Interest Const. Loan Fee 24,316 Total Direct 1,069,843 Costs Operating Expenses: Selling Commissions Property Taxes General & Admin. Total Indirect Costs
60,075 7,000 44,000 111,075
Total Project Costs - Loan Amount Total Equity Required
1,180,918 810,527 370,391
Percent Financed
68.64%
18-239
PRESENT VALUES, ACCELERATION, & RESALE PRICE: Cumulative Monthly Cumulative Month Draw Standard Delux Units Sales Sales 0 0 0 0 0 0 0 1 193,750 0 0 0 0 0 2 193,750 0 0 0 0 0 3 193,750 0 0 0 0 0 4 193,750 5 4 9 163,500 163,500 5 0 5 4 18 163,500 327,000 6 0 5 4 27 163,500 490,500 7 7 1 35 118,500 609,000 8 7 1 43 118,500 727,500 9 7 1 51 118,500 846,000 10 7 1 59 118,500 964,500 11 7 1 67 118,500 1,083,000 12 7 1 75 118,500 1,201,500 13 0 0 75 0 1,201,500 14 0 0 75 0 1,201,500 15 0 0 75 0 1,201,500 16 0 0 75 0 1,201,500 17 0 0 75 0 1,201,500 18 0 0 75 0 1,201,500 19 0 0 75 0 1,201,500 20 0 0 75 0 1,201,500 21 0 0 75 0 1,201,500 22 0 0 75 0 1,201,500 23 0 0 75 0 1,201,500 24 0 0 75 0 1,201,500 Total 775,000 57 18 75 1,201,500 Present Value 754,457 1,106,721
PV Draws PV Revenue
754,457 1,106,72 1 68.1705 PV Rev / PV % Draw Acceleration 25.00% Release Price 85.2131 %
Total revenue is $1,021,500 as shown above.
18-240
MPVIF @ 13% 1.00000 .98928 .97868 .96819 .95782 .94755 .93740 .92735 .91741 .90758 .89785 .88823 .87871 .86929 .85998 .85076 .84164 .83262 .82370 .81487 .80614 .79750 .78895 .78050 .77213
PV Draws 0 191673.54 189619.33 187587.13 185576.72 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 754,457
M
LOAN SCHEDULE AND LENDER'S IRR
Month
Interest 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Lender's Yield
0 0 2,099 4,221 6,365 7,024 5,591 4,142 3,093 2,032 961 0 0 0 0 0 0 0 0 0 0 0 0 0 0 35,527
Total Draw
Paymen ts Principal Interest
0 193,750 0 0 195,849 0 2,099 197,971 0 4,221 200,115 139,323 6,365 7,024 139,323 7,024 5,591 139,323 5,591 4,142 100,977 4,142 3,093 100,977 3,093 2,032 100,977 2,032 961 89,625 961 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 810,527 810,527 35,527
22.85%
18-241
Total 0 2,099 4,221 145,689 146,347 144,914 105,119 104,070 103,010 90,585 0 0 0 0 0 0 0 0 0 0 0 0 0 0 846,055
Balance Cash Flow 0 24,316 193,750 (193,750) 389,599 (193,750) 587,570 (193,750) 648,362 (54,427) 516,062 139,323 382,329 139,323 285,494 100,977 187,609 100,977 88,664 100,977 0 89,625 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
The loan is repaid by the end of the 10th month. (b) The total interest is $35,527 as shown above. The release price for each lot is 85.2131% of the lot sale price. (See above for calculation of the release price as a 85.2131% percent of sales revenue.) For the standard lot .852131 × $13,500 = $11503.76 For the deluxe lot . 852131 × $24,000 = $20,451.14 The loan repayment schedule is shown above. Total cash payments to the bank will be $810,527. (c) Total equity requirements will be $177,842 + $11,000 = $188,842 (see below). DEVELOPER'S CASH FLOW, NPV AND IRR Quarter Inflow: Sales Loan Draw Interest Draw Total Inflow Outflows: Site Purch. Closing Loan Fee Loan Pmt. Interest Cost Direct Costs Gen & Admin Prop. Tax Sales Exp. Total Outflow Net Cash
0
1
2
0 0 490,500 0 581,250 193,750 0 6,32018,980 0 587,570 703,230
3
4
355,500 0 9,267 364,767
355,500 0 961 356,461
0 417,970 0 6,320 18,980 0 581,250 193,750 11,000 11,000
302,932 9,267
89,625 961
11,000
24,525 0 259,316 598,570 666,225
17,775
11,000 7,000 17,775
340,975
126,360
225,000 10,000 24,316
($259,316) ($11,000) $37,005
Net Present Value Internal Rate of Return
(21,199)
$23,793 $230,100
18%discount rate
8.19%
The investor’s IRR is only 8.19%, which is significantly below the 18% required return. Thus, the land should not be developed.
18-242
Problem 17-4 (a) No acceleration PV Draws PV Revenue PV Rev / PV Draw Acceleration Release Price
754,457 1,106,721 68.1705% 0.00% 68.1705%
LOAN SCHEDULE AND LENDER'S IRR Month
Payments Interest Total Draw Principa Interest l 0 0 0 1 0 193,750 0 0 2 2,099 195,849 0 2,099 3 4,221 197,971 0 4,221 4 6,365 200,115 111,459 6,365 5 7,326 7,326 111,459 7,326 6 6,198 6,198 111,459 6,198 7 5,057 5,057 80,782 5,057 8 4,237 4,237 80,782 4,237 9 3,408 3,408 80,782 3,408 10 2,570 2,570 80,782 2,570 11 1,722 1,722 80,782 1,722 12 866 866 80,782 866 13 0 0 0 0 14 0 0 0 0 15 0 0 0 0 16 0 0 0 0 17 0 0 0 0 18 0 0 0 0 19 0 0 0 0 20 0 0 0 0 21 0 0 0 0 22 0 0 0 0 23 0 0 0 0 24 0 0 0 0 44,068 819,068 819,068 44,068
Lender's Yield 21.06% 18-243
Total 0 2,099 4,221 117,824 118,784 117,656 85,839 85,019 84,190 83,352 82,504 81,648 0 0 0 0 0 0 0 0 0 0 0 0 863,136
Balance Cash Flow 0 24,572 193,750 (193,750) 389,599 (193,750) 587,570 (193,750) 676,226 (82,291) 572,093 111,459 466,832 111,459 391,108 80,782 314,563 80,782 237,188 80,782 158,976 80,782 79,916 80,782 0 80,782 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
18-244
10% acceleration PV Draws PV Revenue PV Rev / PV Draw Acceleration Release Price
754,457 1,106,721 68.1705% 10.00% 74.9875%
LOAN SCHEDULE AND LENDER'S IRR Month
Payments Interest Total Draw Principa Interest l 0 0 0 1 0 193,750 0 0 2 2,099 195,849 0 2,099 3 4,221 197,971 0 4,221 4 6,365 200,115 122,605 6,365 5 7,205 7,205 122,605 7,205 6 5,955 5,955 122,605 5,955 7 4,691 4,691 88,860 4,691 8 3,779 3,779 88,860 3,779 9 2,858 2,858 88,860 2,858 10 1,926 1,926 88,860 1,926 11 984 984 88,860 984 12 32 32 3,001 32 13 0 0 0 0 14 0 0 0 0 15 0 0 0 0 16 0 0 0 0 17 0 0 0 0 18 0 0 0 0 19 0 0 0 0 20 0 0 0 0 21 0 0 0 0 22 0 0 0 0 23 0 0 0 0 24 0 0 0 0 40,115 815,115 815,115 40,115
Lender's Yield 21.79%
18-245
Total 0 2,099 4,221 128,970 129,810 128,559 93,551 92,640 91,718 90,786 89,844 3,033 0 0 0 0 0 0 0 0 0 0 0 0 855,230
Balance Cash Flow 0 24,453 193,750 (193,750) 389,599 (193,750) 587,570 (193,750) 665,080 (71,145) 549,681 122,605 433,031 122,605 348,862 88,860 263,781 88,860 177,779 88,860 90,844 88,860 2,968 88,860 0 3,001 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
30% acceleration PV Draws PV Revenue PV Rev / PV Draw Acceleration Release Price
754,457 1,106,721 68.1705% 30.00% 88.6216%
LOAN SCHEDULE AND LENDER'S IRR Month
Payments Interest Total Draw Principa Interest l 0 0 0 1 0 193,750 0 0 2 2,099 195,849 0 2,099 3 4,221 197,971 0 4,221 4 6,365 200,115 144,896 6,365 5 6,964 6,964 144,896 6,964 6 5,469 5,469 144,896 5,469 7 3,959 3,959 105,017 3,959 8 2,864 2,864 105,017 2,864 9 1,757 1,757 105,017 1,757 10 639 639 59,598 639 11 0 0 0 0 12 0 0 0 0 13 0 0 0 0 14 0 0 0 0 15 0 0 0 0 16 0 0 0 0 17 0 0 0 0 18 0 0 0 0 19 0 0 0 0 20 0 0 0 0 21 0 0 0 0 22 0 0 0 0 23 0 0 0 0 24 0 0 0 0 34,337 809,337 809,337 34,337
Total 0 2,099 4,221 151,262 151,860 150,366 108,975 107,881 106,774 60,237 0 0 0 0 0 0 0 0 0 0 0 0 0 0 843,673
Balance Cash Flow 0 24,280 193,750 (193,750) 389,599 (193,750) 587,570 (193,750) 642,789 (48,854) 504,856 144,896 365,429 144,896 264,371 105,017 162,218 105,017 58,959 105,017 0 59,598 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Lender's Yield 23.17%
(b) In the loan schedule for zero acceleration shown in part (a) the loan is repaid in month 12 when the last lot is sold. Part ( C ) Lender’s yield is shown below each of the loan schedules above. 18-246
Solutions to Questions—Chapter 18 Partnerships, Joint Ventures, and Syndications Question 18-1 What is the difference between an IRR preference and an IRR lookback? With an IRR preference the investor receives all additional cash flow from sale (after each party has received capital equal to their initial investment) until they have received a specified IRR. With an IRR lookback the cash flow after each party has received capital equal to their initial investment is split in a predetermined proportion. An IRR preference will always give the investor a return that is equal to or better than what the return would be with an IRR lookback. Question 18-2 What is the advantage of the limited partnership ownership form for real estate syndications? The advantage of a limited partnership is that any tax losses can be allocated to the partners to reduce their personal taxable income. Question 18-3 How can the general partner-syndicator structure the partnership to offer incentives to limited partners? The syndicator can offer the limited partner a greater proportion of the tax losses and a greater proportion of the cash flow that is available for distribution. Question 18-4 Why is the Internal Revenue Service concerned with how partnership agreements in real estate are structured? The IRS does not want the allocation of taxable income (or losses) to differ from the allocation of cash flow in an extreme manner such that there is no ―substantial economic effect‖ of the allocations. Question 18-5 What is the main difference between the way a partnership is taxed versus the way a corporation is taxed? Corporations can not allocate losses to shareholders. Also, corporations are taxed at the corporate level and shareholders are taxed on dividends they receive. Partnerships are not taxed at the partnership level. Question 18-6 What are special allocations? The term ―special allocation‖ refers to allocations of income (losses) in different proportions to the partners. For example, the limited partner may be allocated all of the tax losses but only half of the cash flow. Question 18-7 What causes the after-tax IRR (ATIRRe) for the general partner to differ from that of the limited partner? The ATIRRe for the general partner can differ from that of the limited partner due to differences in the way cash flow and taxable income is allocated to each partner as well as differences in their marginal tax rate. 18-247
Question 18-8 What is the significance of capital accounts? What causes the balance in a capital account to change each year? The capital accounts are used to keep track of allocations to each partner of cash flow and taxable income. They increase when the partner is allocated income and decrease if the partner is allocated losses. They also increase when the partner makes a cash contribution to the partnership and decrease when cash is distributed to the partner. Question 18-9 How does the risk associated with investment in a partnership differ for the general partner versus a limited partner? The general partner is personally liable for the debts of the partnership whereas the limited partner has ―limited liability‖ like shareholders in a corporation.
18-248
Question 18-10 What are the different ways that the general partner is compensated? General partners can receive a number of different fees for structuring the partnership, acquiring property on behalf of the partnership, managing the partnership, etc. They may also receive an allocation of cash flow from operations and/or sale of properties. Question 18-11 How do you think the federal tax policy affects the desirability of investing in real estate partnerships? The depreciable life for real estate income property has varied considerably over time as federal tax policy has shifted in its desire to encourage investments in real estate. This impacts the ability of investors to invest in properties that can generate losses for tax purposes. One of the benefits of a partnership compared to a corporate structure is the ability to use these tax losses to offset other sources of income to the investor. Question 18-12 What concerns should an investor in a real estate syndication have regarding general partners? The investor should be concerned about the general partner’s ability to manage the partnership including acquisition and /or development of properties, property management, etc. The investor should also be concerned about whether the general partner is likely to act in the best interest of the limited partner. Question 18-13 Differentiate between public and private syndications? What is an accredited investor? Why is the distinction used? Private partnerships are exempt from registration requirements of Regulation D of the Securities Act of 1933 which can substantially reduce the costs of setting up a partnership. An accredited investor is one that meets certain criteria that, in general, apply to investors who can afford to invest in the partnership and who should understand the risks associated with the investment. If the securities are sold only to accredited investors, it is not necessary to provide investors with the information otherwise required to obtain an exemption under Regulation D. Question 18-14 How are general partners usually compensated in a syndication? What major concerns should investors consider when making an investment with a syndication General partners can receive a number of different fees for structuring the partnership, acquiring property on behalf of the partnership, managing the partnership, etc. They may also receive an allocation of cash flow from operations and/or sale of properties. The investor should be concerned about the general partner’s ability to manage the partnership including acquisition and /or development of properties, property management, etc. The investor should also be concerned about whether the general partner is likely to act in the best interest of the limited partner. Question 18 – 15 What is the main difference between organizing a real estate venture a corporation versus a general partnership? How does a limited partnership have some of the characteristics of both? A corporation provides limited liability to shareholders whereas partners in a general partnership have liability. But a corporation is taxed at the entity level and dividends paid to shareholders may also be subject to taxation. Partnerships are not taxed at the partnership level. Taxable 18-249
income and losses flow to the partner’s tax return. If there are tax losses, this also flows to the partner’s tax return which can offset other taxable income whereas with a corporation the tax losses cannot be pass through to the shareholders. A limited partnership is taxed like a general partnership but the limited partners do not have any personal liability. The liability is incurred by the general partner in the limited partnership.
18-250
Solutions to Problems—Chapter 18 Partnerships, Joint Ventures, and Syndications INTRODUCTION The problems in this chapter parallel that of the example in the textbook. We have assumed the syndication expenses can not be expensed or amortized. That is, they are capitalized but not depreciated. Note that this is similar to the tax treatment of land. The proper way of handling syndication fees is somewhat controversial and depends on the specific nature of the syndication expense. Some commentators have suggested that syndication costs might be amortizable over the life of a limited partnership, but most practitioners are dubious of this position. Most writers suggest that fees paid for services rendered in connection with acquisition of the property can be capitalized as part of the basis of the acquired asset and depreciated over the recovery period of that asset. Examples of service relating to the acquisition of an asset include negotiation of a lease of the partnership’s property, negotiation of the partnership’s purchase of real estate, and legal and brokerage fees paid by the syndication with respect to acquisition of the asset. However, legal and marketing fees related to the creation of the syndication securities are capitalized but cannot be depreciated. Rather, these fees would be deductible only upon termination or liquidation of the partnership (see Promoters‟ and Managers‟ Compensation, Page 511). For simplicity, we have chosen to simply assume that all ―syndication fees‖ are capitalized but not depreciated. However, the instructor may want to bring this issue to the attention of the students.
18-251
Problem 18-1 Table 1
Year
Initial Investment $100,000,00 0 0 1 2 3 4 5
Cash flow from Operations
$2,000,000 $4,000,000 $9,000,000 $12,000,00 0 $14,000,00 0
IRR
Total Cash flow $100,000,00 0 $2,000,000 $4,000,000 $9,000,000 $12,000,000 $164,000,00 0
ABC fund return from operations
Newtown Developer s Inc. return from operations
Remaining operating cash flow to be split
ABC fund from sale for 11% IRR
$2,000,000 $2,250,000 $2,250,000
$0 $1,750,000 $2,750,000
$0 $0 $4,000,000
$45,000,000 $2,000,000 $2,250,000 $4,250,000
$2,250,000
$2,750,000
$7,000,000
$5,750,000
$2,250,000
$2,750,000
$9,000,000
$51,345,38 1
14.77%
Table 1 continued.. Newtown Developers Inc. return of initial Year investment 0 1 2 3 4 5 $55,000,000
ABC fund cash flow for 11% IRR
$58,095,381 11.00%
Remaining cash flow from sale to be split
Newtown Developers Inc. Check -$55,000,000 $0 $1,750,000 $4,750,000 $6,250,000 $43,654,619 $84,077,309
$0 $0 $0 $0 $0 $0
Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
18-252
IRR
12.62%
Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
18-253
Cash flow from Operations
Year
1 2 3 4 5
ABC fund Inc. return from operations
$2,000,000 $4,000,000 $9,000,000 $12,000,000 $14,000,000
$2,000,000 $2,250,000 $2,250,000 $2,250,000 $2,250,000
Newtown Developers Inc. return from operations
$0 $1,750,000 $2,750,000 $2,750,000 $2,750,000
Remaining operating cash flow to be split
$0 $0 $4,000,000 $7,000,000 $9,000,000
Year 0 1 2 3 4 5
ABC fund Inc. cash flow from Operations
ABC fund Inc. return of initial investment
ABC fund additional cash flow from Sale
$2,000,000 $2,250,000 $4,250,000 $5,750,000 $6,750,000
$45,000,000 $2,000,000 $2,250,000 $4,250,000 $5,750,000 $45,000,000 $6,345,381 $58,095,381
Total Cash Flow
11.00%
ABC fund Inc.
Year
Newtown Developers Inc.
0 1 2 3 4 5
$45,000,000 $2,000,000 $2,250,000 $4,250,000 $5,750,000 $79,922,691
-$55,000,000 $0 $1,750,000 $4,750,000 $6,250,000 $84,077,309
IRR
17.30%
12.62%
Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
18-254
Problem 18-2 (REFER TO TEMPLATE 18_1.XLS) ASSUMPTIONS: COST BREAKDOWN 1,000,000 Land Improvements Points Subtotal Organization fee Syndication expenses
9,000,000 100,000 10,100,000 100,000 100,000
Total funding required Years amortized
10,300,000 5
FINANCING 8,000,000 Loan Amount Interest rate 4.75% Term 25 Points 100,000 Pmts / Year 12 Amortized over loan term Annual Pmt 547,313
PARTNERSHIP FACTS AND EQUITY REQUIREMENTS Equity Cash Tax. Income Alloc. gain capital distrib. contribution Operations Operations Sale General partner 10.00% 10.00% 10.00% 15.00% Limited Partners 90.00% 90.00% 90.00% 85.00% # of Limited Partners 35
Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-255
OPERATING AND TAX PROJECTIONS Potential gross income Projected growth in PGI Vacancy and coll. Loss Operating Expenses Depreciable Life Projected Resale Ordinary income tax rate Capital gain tax rate Selling Expenses Holding Period
1,300,000 2.00% 10.00% of PGI 35.00% of EGI 39 years 12,750,000 24.00% 24.00% 5.00% 5 years
INITIAL EQUITY REQUIREMENTS Land 1,000,000 9,000,000 Improvemen ts Points on Loan 100,000 Organization fee 100,000 100,000 Syndication fee Total 10,300,000 8,000,000 Less loan Equity General Partner Limited Partners
2,300,000 230,000 2,070,000
4 359,302 7,461,680
5 350,175 7,264,542
6 340,604 7,057,83 4
3 1,326,00 0 132,600
4 1,352,520
5 1,379,57 0 137,957
6 1,407,16 2 140,716
1,217,268 426,044 791,224 547,313 243,912
1,241,61 3 434,565 807,049 547,313 259,736
1,266,44 6 443,256 823,190 547,313 275,877
Loan Information: Year Interest Loan Balance
Depreciation per year
2 376,309 7,828,996
3 368,007 7,649,69 1
230,769
STATEMENT OF BEFORE-TAX CASH FLOW Year 2 Potential gross income 1,300,000 Vacancy and collection loss Effective gross income
130,000
135,252
1,170,000
Operating Expenses Net operating income Debt service Before-tax cash flow
409,500 760,500 547,313 213,187
1,193,40 0 417,690 775,710 547,313 228,397
Distribution of BTCF General Partner Limited Partners
21,319 191,869
22,840 205,558
24,391 219,520
25,974 233,762
27,588 248,289
3 775,710 368,007 230,769
4 791,224 359,302 230,769
5 807,049 350,175 230,769
6 823,190 340,604 230,769
STATEMENT OF INCOME (LOSS) Year Net operating income Less: Interest
2 760,500 376,309 230,769
Depreciation Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-256
Amortization of: Organization fee Loan fee Taxable income
20,000 4,000 129,422
20,000 4,000 152,934
20,000 4,000 177,153
20,000 4,000 202,105
20,000 84,000 147,816
Distribution of Taxable Income General Partner 12,942 Limited Partners 116,480
15,293 137,640
17,715 159,437
20,210 181,894
14,782 133,035
Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-257
CALCULATION OF CAPITAL GAIN Sales Price Sales Costs Original costs basis Accumulated depreciation Adjusted basis Total taxable gain
12,750,000 637,500 10,100,000 1,153,846 8,946,154 3,166,346
Allocation of Gain General Partner Limited Partners
474,952 2,691,394
CAPITAL ACCOUNTS - LIMITED PARTNERS Year 0 Equity 2,070,000 Plus Income(loss) Plus Gain from Sale Less Cash Distributed Total for Year Balance
(75,389) 1,994,611
2,070,000 2,070,000
1
2
3
4
5
116,480
137,640
159,437
181,894
(191,869)
(205,558 ) (67,916) 1,926,69 4
(219,520)
(233,762 ) (51,868) 1,814,74 3
133,035 2,691,394 (248,289)
(60,083) 1,866,611
2,576,140 4,390,882
CAPITAL ACCOUNTS – GENERAL PARTNER Year
0 230,000
Equity Plus Income(loss) Plus Gain from Sale Less Cash Distributed Total for Year 230,000 Balance 230,000
1
2
3
4
5
12,942
15,293
17,715
20,210
(21,319) (8,377) 221,623
(22,840) (7,546) 214,077
(24,391) (6,676) 207,401
(25,974) (5,763) 201,638
14,782 474,952 (27,588) 462,146 663,784
(a) ATIRR: AFTER-TAX CASH FLOW AND ATIRR - LIMITED PARTNERS Year 0 Operation: BTCF (2,070,000 ) Taxable Income Taxes 0
1
2
3
4
5
191,869
205,558
219,520
233,762
248,289
116,480 27,955
137,640 33,034
159,437 38,265
181,894 43,655
133,035 31,928
Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-258
ATCF
(2,070,000 )
163,913
172,524
181,255
190,108
Reversion: BTCF Capital gain Taxes ATCF Total ATCF
ATIRR
(2,070,000 )
163,913
172,524
181,255
190,108
216,361
4,390,88 2 2,691,39 4 491,978 3,898,90 4 4,115,26 5
20.48%
Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-259
(b) ATIRR: AFTER-TAX CASH FLOW AND ATIRR - GENERAL PARTNER Year 0 Operation: BTCF (230,000 ) Taxable Income Taxes 0 ATCF (230,000 ) Reversion: BTCF Capital gain Taxes ATCF Total ATCF
ATIRR
(230,000 )
1
2
3
4
5
21,319
22,840
24,391
25,974
27,588
12,942 3,106 18,213
15,293 3,670 19,169
17,715 4,252 20,139
20,210 4,851 21,123
14,782 3,548 24,040
21,123
663,784 474,952 86,820 576,964 601,004
18,213
19,169
20,139
26.51%
(c) The general partner receives a higher IRR. This is due to the fact that the general partner is allocated a higher proportion of the gain (and therefore the cash flow) at sale of the property.
Problem 18-3 Before tax cash flow: Net operating income Less debt service (interest only) Before-tax cash flow
$ 250,000 -200,000 $50,000
Taxable income: Net operating income Less depreciation Less interest cost Taxable income
$250,000 250,000 200,000 $-200,000
(a) Capital Accounts after First Year of Operations
Initial equity contribution
A's Capital Account $500,000
B's Capital Account 0
Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-260
Less loss allocation Less cash flow distribution Ending balance
$-180,000 -45,000 $275,000
$-20,000 -5,000 $-25,000
(b) Cash from sale Sales price Less mortgage balance Cash flow
$3,000,000 2,000,000 $1,000,000
Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-261
(c) Cash distributions from sale Cash flow from sale (from part b) Distribution to A: Initial investment $500,000 Less prior distrib. -45,000 Distribution to A Remaining cash Distribution to A (50%) Distribution to B (50%)
$1,000,000
455,000 $545,000 272,500 272,500
(d) Capital gain from sale after 1 year: Sales price Purchase price Depreciation taken Adjusted basis Gain Allocation of gain to A Allocation of gain to B
$3,000,000 $2,500,000 250,000 2,250,000 $750,000 375,000 375,000
(e) Capital Accounts after Sale of Building Balance prior to sale Return of original equity Less previous cash distribution 50 percent remaining cash proceeds 50 percent of gain Ending balance
A's Capital Account $275,000 -455,000 -272,500 375,000 $-77,500
B's Capital Account $-5,000 NA -272,500 375,000 $77,500
Problem 18-4 The general partner’s return is now 19.40% versus 27.03% and the limited partner’s return is also 19.40% versus 18.93%. The general partner’s return drops and the limited partner’s return increases so that the returns are exactly the same for both partners because there are now no ―special allocations.‖ Contribution of equity allocations of all income and capital gains is the same percentage for a particular partner, even though the limited partner’s percentage differs from the general partner. Solutions to Questions—Chapter 19 The Secondary Mortgage Market: Pass-Through Securities Question 19-1 What is the secondary mortgage market? List three reasons why it is important. The secondary mortgage market is the ―after‖ market in which mortgages are sold and resold. The secondary mortgage market is important for the following: (1) it enables mortgage banking Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-262
companies to sell existing mortgages and thereby replenish funds with which new loans can be originated, (2) it facilitates the geographic low of funds, and (3) it increases the investing options available to individuals and institutions. Question 19-2 What were the three principal activities of FNMA under its 1954 charter? What is its principal function now? In 1954, Congress rechartered FNMA, assigning it three separate and distinct activities: (1) enhancement of secondary market operations in federally insured and guaranteed mortgages, (2) management of direct loans previously made and, where necessary, liquidation of properties and mortgages acquired by default, and (3) management of special assistance programs, including support for subsidized mortgage loan programs. Eventually, the investment by life insurance companies in common stocks and bonds grew at the expense of mortgages. Mortgage companies and other originators became concerned because their traditional source of funds from secondary mortgage sales diminished. Industry related associations advocated that FNMA’s secondary market operations be expanded to include its principal function today: namely, holding mortgages. Question 19-3 Name two ways that FNMA currently finances its secondary mortgage operations. To provide a financial base to operate FNMA, the Charter Act also authorized issuance of nonvoting preferred and common stock for the financing of secondary market operations. Additional funding came from FNMA’s issuance of notes and debt instruments. Question 19-4 When did GNMA come into existence? What was its original function? What is its main function now? The Government National Mortgage Association was created by the Housing and Urban Development Act of 1968. Originally, it was organized to perform three principal functions: (1) management and liquidation of mortgages previously acquired by FNMA; the liquidation of the portfolio acquired from FNMA at the time of its partition comes through regular principal repayments and sales; (2) special assistance lending in support of certain federal subsidized housing programs; GNMA, also known as ‖Ginnie Mae,‖ is authorized to purchase mortgages, which are originated under various housing programs designed by FHA, to provide housing in areas where it cannot be provided by conventional market lending; and (3) provision of a guarantee for FHA-VA mortgage pools, which would provide a guarantee for mortgage-backed securities. By providing the buyer with a guarantee of timely payment of interest and principal, GNMA was, in essence, guaranteeing monthly payments of interest and principal from amortization. This guarantee enabled originators of FHA and VA mortgages to pool or package mortgages and to issue securities, called pass-through securities, which were collateralized by the mortgages, and were based on the notion of investors buying an undivided security interest in a pool of mortgages with interest and principal passed through to investors as received from borrowers. Question 19-5 Why was the formation of FHLMC so important? Period of intermittent rate volatility, particularly during the mid- and late 1960s, was also causing liquidity problems that plagued thrifts. The Federal Home Loan Mortgage Corporation Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-263
(FHLMC) was established to provide a secondary market and, hence, liquidity for conventional mortgage originators.
Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-264
Question 19-6 What is a mortgage-related security? What are the similarities and differences between mortgage securities and corporate bonds? Many originators are no longer willing to take the interest rate risk associated with originating loans with funds obtained from deposits and have found a way, through securitization, to raise funds and shift interest rate risk to various classes of investors. Large mortgage originators place mortgages in pools and sell securities of various types, using the mortgages in these pools as collateral. With the aid of investment bankers, large originators can issue securities in small denominations that are purchased by numerous investors. Like corporate bonds, mortgage securities are: underwritten by investment banks, rated by independent bond a-rating agencies, sold through an underwriting syndicate, and issued with fixed-coupon rates and specific maturities. However, unlike corporate bonds, mortgage securities are ―overcollateralized.‖ Question 19-7 Name the principal types of mortgage-related securities. What are the difference between them? The major types of mortgage-backed securities currently in use are: mortgage-backed bonds (MBBs), mortgage pass-through securities (MPTs), mortgage pay-through bonds (MPTBs), collateralized mortgage obligations (CMOs). The major difference between them is whether they are more like bonds where the issuer owns the mortgage pool and pays interest to investors, versus principal and interest flowing directly to the investors. Question 19-8 There are several ways that mortgages can be sold in the secondary market. Choose two and compare and contrast their length of distribution channel, relative ease of transaction, and efficiency as it relates to maximizing funds flow from sale. Essentially, mortgages are originated by lenders and are pooled by them or sold to FNMA or FHLMC. If pooled by the originator, the originator will work with a securities underwriter to issue the securities. These securities are then sold through security dealers to individuals and institutional investors. In the early 1980s both FNMA and FHLMC instituted swap programs in which originators pool mortgages, then swap them for pass-through securities simultaneously issued by Fannie Mae or Freddie Mac. Depending on market interest rates, the originator may then choose to sell part or all of the mortgage securities at a premium or a discount. These securities could be sold directly by the originator to institutional investors, to security dealers, or through the trading department operated by FHLMC. By swapping securities for mortgages, the originator has more flexibility when deciding whether to own securities or how and when such securities will be sold to raise cash. Question 19-9 What is the function of the optional delivery commitment? Under the optional delivery, originators pay Fannie Mae a fee for the ―right but not the obligation‖ to sell (deliver) their mortgages to Fannie Mae. Hence, if interest rates increase, originators can sell mortgages to Fannie Mae, but if interest rates fall, they can retain the option to sell mortgages to another party for a better price (or even to re negotiate a price with Fannie Mae). Question 19-10 What is a mortgage swap certificate? In a mortgage swap, an originator pools mortgages, then swaps them for pass-through mortgage securities issued simultaneously by Fannie Mae or Freddie Mac. Mortgage swap certificates are the securities guaranteed by FNMA and FHLMC. Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-265
Question 19-11 Name five important characteristics of mortgage pools. Tell why each is important. (1) Guarantee against default on mortgages by both private mortgage insurers and government agencies reduces the inherent risk of such securities. (2) Mortgages are grouped according to payment patterns, maturity and security which helps investors predict with some confidence the cash flow pattern that they can expect to receive. (3) A mixture of interest rates enables a faster accumulation of larger pools for securitization. The coupon rate promised to investors purchasing securities is generally based on the lowest interest rate on any mortgage in the pool, less servicing and guarantee fees. This means that for two security issues bearing the same coupon rate, expected cash flows to investors in the pool containing mortgages with different rates will be less variable than cash flows from the pool with the same interest rates
Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-266
(4) The risk of default is usually greatest in the early years of the life of a mortgage. Inclusion of seasoned mortgages in pools tends to reduce the possibility of prepayment because of default. (5) Geographic diversity of the mortgages in the pool is important because it may affect the likelihood of prepayment and default. Certain regions of the country may be affected more by economic downturns and resulting unemployment than others and, hence, may have higher default rates. A mortgage pool with more geographic diversity tends to insulate investors from cash flow irregularities. Question 19-12 In general, would a falling rate of market interest cause the price of an MPT security to increase or decrease? Would the increase or decrease be greater if the security was issued at a discount? Would an increase in prepayment be likely or unlikely? Describe with an example. The market value of an MPT security will increase as the market interest rate fells. An increase or decrease will affect MPTs in the same manner whether they are issued at a discount, a premium or par. As interest rates decrease below the rates of individual mortgages in a pool, borrowers will begin to refinance their loans assuming they are able to secure lower rates. Conversely, as interest rates rise above those of individual mortgages in a pool, borrowers will be less apt to prepay as their ability to secure rates below that of the market diminishes.
Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-267
Solutions to Problems—Chapter 19 The Secondary Mortgage Market: Pass-Through Securities Problem 19-1 ASSUMPTIONS: Principal Coupon rates: (Bond 1) Annual (Bond 2) Zero Term in years Initial Years into future Investors interest rate Market interest rate Number of compounding periods (a)
$10,000 10.50% 0.00% 25 years 5 12.00% 9.50% 50
Initial price of each bond (compounded annually):
Annual compounding on both MBBs Principal Coupon rate Term Investors interest rate
Bond 1 $10,000.00 10.50% 25 12.00%
Bond 2 $10,000.00 0.00% 25 12.00%
The present value of the coupon payments The present value of the principal Initial price of each bond
$8,235.30
$0.00
$588.23 $8,823.53
$588.23 $588.23
The price of the annual coupon bond is the present value of 25 payments at 10.5% times the initial principal discounted at the investor’s required rate of return plus the present value of the initial principal discounted for 25 periods at the same rate of return. The price of the zero-coupon bond is the present value of the initial principal discounted for 25 periods at the investor’s required rate of return. (b) Initial price of each bond (compounded semi-annually): Semi-annual compounding on both MBBs Principal Coupon rate Term Investors interest rate Number of compounding periods
$10,000.00 10.50% 25 12.00% 50
$10,000.00 0.00% 25 12.00% 50
Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-268
The present value of the coupon payments The present value of the principal Initial price of each bond
$8,274.98
$0.00
$542.88 $8,817.86
$542.88 $542.88
Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-269
(c) Value each bond at the end of the fifth year. Market interest rates fall to 9.50% and the bonds are compounded annually: Future Value Principal Coupon rate Term Market interest rate The present value of the coupon payments The present value of the principal Value of bond in dollars Value of the bond in % of par
$10,000.00 10.50% 20 9.50%
$10,000.00 0.00% 20 9.50%
$9,253.00
$0.00
$1,628.24 $10,881.24 108.81%
$1,628.24 $1,628.24 16.28%
Problem 19-2 ASSUMPTIONS: Number of mortgages in initial pool Average mortgage balance Initial mortgage pool balance Prepayment rate Coupon rate (a)
Price MBS’s under different market interest rates. (a) Pool
Yea Balance r 0 $7,500,000 1 6,322,619 2 3 4 5 6 7 8 9 10
75 $100,000 $7,500,000 10.00% 12.00%
5,262,449 4,308,352 3,450,483 2,680,246 1,990,325 1,374,848 829,928 355,460 0
(b) (c) Principal due to Principal and
(d)
Total Principal Prepaymen Interest Pmts and Interest t $750,00 0 632,262 526,245 430,835 345,048 268,025 199,032 137,485 82,993 0
$1,327,38 1 1,186,622 1,059,346 944,036 839,246 743,526 655,283 572,416 491,067 398,115
(e)
Pool Factor
$2,077,381
1.0000 0.8430
1,818,884 1,585,591 1,374,872 1,184,294 1,011,551 854,316 709,901 574,060 398,115
0.7017 0.5744 0.4601 0.3574 0.2654 0.1833 0.1107 0.0474 0.0000
The price that Green could obtain is determined by discounting the total principal and interest payments including any prepayment (column d) by the market interest rate. Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-270
Market Interest Rate 11.00% 12.00% 9.00%
Price of the Pool $7,740,598 $7,500,000 $8,264,095
Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-271
(b) The pool factor at any given time is the outstanding principal balance divided by the initial principal of the pool. At the end of year 5: Outstanding pool balance Initial pool balance Pool factor
$2,680,246 7,500,000 0.3574
If the market interest rate is 12.00%, the price that Green could obtain is the PV of the remaining cash flows discounted at the current market interest rate. (Take the PV of column d for years 6-10.) Market Interest Rate 12.00%
Price of the pool after 5 years $2,680,246
(c) Issuance of 100 Mortgage Pass Through Securities: (10.00% prepayment rate and 9.50% market interest rate are the original variables contained in the template. It must be changed for any other answer.) Assuming that Green does not service or guarantee the mortgages, the price obtained will be the PV of the total cash flows less servicing and guarantee fees (column f) discounted by the market rate of interest.
Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-272
Data Input Box: Number of mortgages in initial pool Average mortgage balance Initial mortgage pool balance Prepayment rate Coupon rate Servicing and Guarantee Fee Mortgage rate Market interest rate
75 $100,000 $7,500,000 10.00% 11.50% 0.5% 12.0% 9.50%
Issuance of 100 Mortgage Pass Through Securities (MPT) (a)
Year 0 1 2 3 4 5 6 7 8 9 10
Pool Balance $7,500,000 6,322,619 5,262,449 4,308,352 3,450,483 2,680,246 1,990,325 1,374,848 829,928 355,460 0 Price to Green $8,002,077
(b)
(c) Principal and Interest Pmts to Issuer
(d) Total Principal and Interest Pmts to Issuer (b)+(c)
(e) Guarantee and Service Fees (a)x(0.5%)
Principal due to Prepayment 750,000 632,262 526,245 430,835 345,048 268,025 199,032 137,485 82,993 0
1,327,381 1,186,622 1,059,346 944,036 839,246 743,526 655,283 572,416 491,067 398,115
2,077,381 1,818,884 1,585,591 1,374,872 1,184,294 1,011,551 854,316 709,901 574,060 398,115
37,500 31,613 26,312 21,542 17,252 13,401 9,952 6,874 4,150 1,777
(f) (g) Total Pmt to Payments Individual to Investors Investor (d)-(e) (f)/100 ($75,000) 2,039,881 20,399 1,787,271 17,873 1,559,279 15,593 1,353,330 13,533 1,167,042 11,670 998,150 9,981 844,364 8,444 703,027 7,030 569,910 5,699 396,338 3,963 IRR 11.50%
Value of MPT $80,021
Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-273
(d) Issuance of 100 Mortgage Pass Through Securities: (Change 10.00% prepayment rate to 20.00% and 9.50% market interest rate to 8.00%. All other variables are constant.) ASSUMPTIONS: Data Input Box: Number of mortgages in initial pool Average mortgage balance Initial mortgage pool balance Prepayment rate Coupon rate Servicing and Guarantee Fee Mortgage rate Market interest rate
75 $100,000 $7,500,000 20.00% 11.50% 0.5% 12.0% 8.00%
Issuance of 100 Mortgage Pass Through Securities (MPT) (a)
Year 0 1 2 3 4 5 6 7 8 9 10
Pool Balance $7,500,000 5,572,619 4,080,946 2,932,965 2,055,663 1,391,220 893,984 528,135 265,996 87,327 0
(b)
(c)
Principal due to Prepayment 1,500,000 1,114,524 816,189 586,593 411,133 278,244 178,797 105,627 53,199 0
Price to Green $8,213,080
Principal and Interest Pmts to Issuer
(d) Total Principal and Interest Pmts to Issuer (b)+(c)
(e) Guarantee and Service Fees (a)x(0.5%)
1,327,381 1,045,863 821,506 642,665 499,990 385,938 294,330 219,889 157,389 97,806
2,827,381 2,160,387 1,637,695 1,229,257 911,123 664,182 473,127 325,516 210,588 97,806
37,500 27,863 20,405 14,665 10,278 6,956 4,470 2,641 1,330 437
(f) (g) Total Pmt to Payments Individual to Investors Investor (d)-(e) (f)/100 ($75,000) 2,789,881 27,899 2,132,524 21,325 1,617,291 16,173 1,214,593 12,146 900,844 9,008 657,226 6,572 468,657 4,687 322,875 3,229 209,258 2,093 97,370 974 IRR 11.50%
Value of MPT $82,131
Problem 19-3 (a) See result for 7.5% in the table below. Discount rate Price to Green 7.50% 9.50% 8.50% 10.50% 11.50%
$1,069,843 $1,000,000 $1,033,908 $967,969 $937,679
Value of MPT $26,746 $25,000 $25,848 $24,199 $23,442
Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-274
(b) See result for 11.5% in the table above. Solution to Questions—Chapter 20 The Secondary Mortgage Market: CMOs and Derivative Securities Question 20-1 What is a mortgage pay-through bond (MPTB)? How does it resemble a mortgage-backed bond (MBB)? How does it differ? MPTBs are issued against mortgage pools and, like MPTs, cash flows from the pool are passed through to security holders. However, unlike an MPT, this security is a bond and not an undivided equity ownership interest in a mortgage pool. Like the MBB, the MPTB is a debt obligation of the issuer, who retains ownership of the mortgage pool. Question 20-2 Are the overcollateralization requirements the same for mortgage pay-through bonds as for the mortgage-backed bonds? Most pay-through issues are based on residential pools and, like MBBs, will generally be overcollateralized (1) more mortgages in the pool than the sum of the securities issued against it or (2) additional collateral in the form of U.S. government bonds or other agency obligations. Question 20-3 Name two different ways that MPTBs can be overcollateralized. The are overcollateralized in two ways: (1) more mortgages in the pool than the sum of the securities issued against it or (2) additional collateral in the form of U.S. government bonds or other agency obligations. Question 20-4 What is a CMO? Explain why a CMO has been called as much of a marketing innovation as a financial innovation. A CMO is a type of mortgage-backed security where a pool of mortgages is used as collateral for several different classes of securities. Each class has different investment characteristics which would appeal to different types of investors. The CMO is a marketing innovation, as well as, a financial innovation, because the different classes of securities can be marketed to a variety of investors with different investment goals. Question 20-5 What is meant by a derivative investment? A derivative security derives its value from another security, index, or financial claim. Because the value of mortgage-backed securities (MBS), such as MPTs and CMOs, are based on pools of mortgages, both are referred to as derivatives. IOs and POs are also examples of derivatives. Question 20-6 Name the four major classes of mortgage-related securities. As an issuer, explain the reasons for choosing one type over another. The four major classes of mortgage-backed securities are mortgage-backed bonds (MBBs), mortgage pass-through securities (MPTs), mortgage pay-through bonds (MPTBs) and collateralized mortgage obligations (CMOs). The issuer may choose one type over another due to differences in the amount of risk that might be incurred. For example, the issuer retains the Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-275
prepayment risk on MBBs, whereas the investors incur this risk with MPTs. Also, the issuer may find that there is more market for one type of than versus another at any given time. Question 20-7 What is the major difference between a CMO and the other types of mortgage-related securities? CMOs differ because there are different classes or tranches of securities that are issued. The classes vary in terms of their priority of receipt of principal including prepayment; they hence differ in terms of maturity and risk. Question 20-8 Why are CMOs overcollateralized? CMOs are overcollateralized to provide additional interest income as a cushion to meet contractual payments on securities. This cushion is especially important when a decrease in interest rates leads to accelerated prepayment. Mortgages that pay the highest interest rates are prepaid first, whereas securities with the lowest coupon (i.e., the class A) receive additional principal from prepayment.
Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-276
Question 20-9 What is the purpose of the accrual tranche? Could a CMO exist without a Z class? What would be the difference between the CMO with and without the accrual class? The purpose of the accrual tranche is to provide additional cash flow to shorten the maturity of the higher priority tranches. That is, the interest not going to the Z tranche is used as additional principal for the A tranche until it is completely repaid, then the B tranche until it is repaid, etc. Question 20-10 Which tranches in a CMO issue are least subject to price variances related to changes in market interest rates? Why? Changes in market interest rates affect the market value of a tranche. Tranches with the greatest duration (time-weighted maturity) are affected most by changes in interest rates. This will be the lowest priority tranches, e.g., the C tranche has a longer duration than the A tranche. Note that even though a change in interest rates may have a greater impact on the duration of the A tranche than the C tranche, the C tranche still has a longer duration, which is what affects a security’s sensitivity to changes in interest rates. Question 20-11 What is the primary distinction between mortgage-related securities backed by residential mortgages and those backed by commercial mortgages? The key risk with residential mortgage-related securities is prepayment. Default risk is eliminated when the securities are backed by a federal agency. Commercial mortgages on the other hand are not backed by any federal agencies and therefore default risk must be incurred by investors. Prepayment risk is generally not as significant with commercial mortgage backed securities because these loans typically have significant prepayment penalties and ―lock-out‖ provisions. Question 20-12 Name the major types of credit enhancement used for commercial-backed mortgage securities. Forms of credit enhancement include issuer or third-party guarantees, surety bonds and letters of credit, advance payment agreements, loan substitutions and repurchase agreements, lease assignments, over collateralization, and cross-collateralization and cross default. Credit also can be enhanced with commercial mortgage-backed securities through the CMO structure. In this case, the lower priority classes incur any losses from default before the higher classes. Question 20-13 What is a “floater”/”inverse-floater” tranche in a CMO offering? A floater is a CMO tranche that has a variable interest rate. It is supported by an inverse-floater that is structured so that the sum of interest on the floater and inverse floater sum to a fixed interest amount. Question 20-14 What is the role of the “scaler” in structuring an (F) and (IF) structure? A scaler is used to adjust the ratio of the relative composition of interest to be received by the f (floater) and IF (inverse floater) tranches. Question 20-15 Why would anyone want to purchase an (F) or (IF) derivative type of investment? Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-277
Investors may have different expectations about the change in interest rates. Purchasers of a floater may expect rates to rise and purchasers of an inverse floater may expect rates to fall. An inverse floater also can be used by lenders to hedge a portfolio of adjustable rate mortgage loans that they hold. Question 20-16 What are (IO) and (PO) strips? Which tends to be more volatile in price? Why? An IO strip receives only the interest from a pool of mortgages. A PO strip receives only the principal. An IO tends to be more volatile because it only receives interest from mortgages that have not been prepaid. Prepayment causes investors in a PO to get repaid sooner, but they still receive all of the principal from the entire pool of mortgages.
Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-278
Question 20-17 In what ways is a CMBS structure different from a CMO backed by residential mortgages? Why is default risk in a CMBS offering given more attention? A CMBS is subject to default risk because there are no government agencies that insure the mortgages against default or guarantee the payments as in the case of a CMO backed by residential mortgages. Default risk is borne first by the lower rated trances in the CMBS. Because there are typically prepayment penalties and ―lockout‖ provisions associated with commercial mortgages, prepayment risk is not a significant concern for CMBS. Question 20-18 How do CDOs differ from CMBS? Difference between CDO and CMBS is that CMBS is a subset of CDO. In CMBS the underlying assets are commercial based mortgages but in CDO the underlying asset can be Real Estate ABS, Non-real Estate ABS, Leveraged Loans, Middle Market Leveraged Loans, Trust preferred securities, CMBS or any combination of these asset classes. So CDO adds another level of complexity to the securitization process.
Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-279
Solution to Problems—Chapter 20 The Secondary Mortgage Market: CMOs and Derivative Securities Problem 20-1 (a) The Initial WAC is simply the coupon rate of each tranche weighted by the initial tranche balance Tranche A B Z
Balance 40,500,000 22,500,000 45,000,000
Total
$108,000,000
Weighting 37.50% 20.83% 41.67%
Coupon Rate 8.25% 9.00% 10.00%
Weighted Avg Coupon 3.09% 1.87% 4.17% WAC = 9.13%
(b) To calculate the maturity of each tranche, the yearly interest and principal paid on each tranche must be calculated. Remember that the interest that would have been paid on the Z tranche is applied first to pay down the principal on the A tranche. The Z tranche accrues interest which is added to its principal until all preceding tranches are paid off. The format for this portion of the solution comes directly from Exhibit 18-2. Mortgage Pool Year Beg. Bal Payment Interest 1 $112,500.00 $18,308.86 11,250.0 0 2 105,441.14 $18,308.86 10,544.1 1 3 97,676.40 $18,308.86 9,767.64 4 89,135.18 $18,308.86 8,913.52 5 79,739.85 $18,308.86 7,973.98 6 69,404.97 $18,308.86 6,940.50 7 58,036.61 $18,308.86 5,803.66 8 45,531.42 $18,308.86 4,553.14 9 31,775.70 $18,308.86 3,177.57 10 16,644.42 $18,308.86 1,664.44 Tranche A Amount Rate Year
Beg. Bal
1 $40,500.00 2 28,941.14 3 16,226.40 4 2,240.18 5 0.00
Principal End Bal $7,058.86 $105,441.14 $7,764.74 $97,676.40 $8,541.22 $9,395.34 $10,334.87 $11,368.36 $12,505.20 $13,755.72 $15,131.29 $16,644.42
$89,135.18 $79,739.85 $69,404.97 $58,036.61 $45,531.42 $31,775.70 $16,644.42 $0.00
$40,500 8.25% Interest
Principal
End Bal
3,341.25 $11,558.86 $28,941.14 2,387.64 12,714.74 16,226.40 1,338.68 13,986.22 2,240.18 184.82 2,240.18 0.00 0.00 0.00 0.00
Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-280
6 7 8 9 10
0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00
0.00 0.00 0.00 0.00 0.00
Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-281
Tranche B Amount Rate Year
$22,500 9.00%
Beg. Bal
Interest
1 $22,500.00 2 22,500.00 3 22,500.00 4 22,500.00 5 9,355.35 6 0.00 7 0.00 8 0.00 9 0.00 10 0.00
Principal
End Bal
$2,025.00 $0.00 $22,500.00 2,025.00 0.00 22,500.00 2,025.00 0.00 22,500.00 2,025.00 13,144.65 9,355.35 841.98 9,355.35 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
(c) The weighted average coupon each year is found by weighting the coupon rate for each class by the outstanding balance of that class.
A B 8.25% 9.00% Balance Balance
Coupon End of Year 0 1 2 3 4 5 6 7 8 9
40500 28941 16226 2240 0 0 0 0 0 0
22500 22500 22500 22500 9355 0 0 0 0 0
Z 10.00% Balance
Total Balance
45000 49500 54450 59895 65885 64905 53537 41031 27276 12144
108000 100941 93176 84635 75240 64905 53537 41031 27276 12144
WAC
9.14% 9.28% 9.45% 9.69% 9.88% 10.00% 10.00% 10.00% 10.00% 10.00%
Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-282
(d) Tranche a
Year
Beg. Bal
1 $40,500.00 2 28,941.14 3 16,226.40 4 2,240.18 5 0.00 6 0.00 7 0.00 8 0.00 9 0.00 10 0.00
Interest
Principal
End Bal
3,341.25 $11,558.86 $28,941.14 2,387.64 12,714.74 16,226.40 1,338.68 13,986.22 2,240.18 184.82 2,240.18 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
P V at
8.50%
Cash Flow 14,900.11 15,102.39 15,324.89 2,425.00 0.00 0.00 0.00 0.00 0.00 0.00
$40,309
Tranche B
Year
Beg. Bal
1 $22,500.00 2 22,500.00 3 22,500.00 4 22,500.00 5 9,355.35 6 0.00 7 0.00 8 0.00 9 0.00 10 0.00
Interest
Principal
End Bal
$2,025.00 $0.00 $22,500.00 2,025.00 0.00 22,500.00 2,025.00 0.00 22,500.00 2,025.00 13,144.65 9,355.35 841.98 9,355.35 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
P V at
9.50%
Cash Flow 2,025.00 2,025.00 2,025.00 15,169.65 10,197.33 0.00 0.00 0.00 0.00 0.00
$22,110
Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-283
Tranche Z
Year
Beg. Bal
Interest
0 1 $45,000.00 2 49,500.00 3 54,450.00 4 59,895.00 5 65,884.50 6 64,904.97 7 53,536.61 8 41,031.42 9 27,275.70 10 12,144.42
4,500.00 4,950.00 5,445.00 5,989.50 6,588.45 6,490.50 5,353.66 4,103.14 2,727.57 1,214.44
Total Payment
End Bal
0.00 $49,500.00 0.00 54,450.00 0.00 59,895.00 0.00 65,884.50 7,567.98 64,904.97 17,858.86 53,536.61 17,858.86 41,031.42 17,858.86 27,275.70 17,858.86 12,144.42 13,358.86 0.00 IRR P V at
9.75%
Cash Flow ($45,000) 0.00 0.00 0.00 0.00 7,567.98 17,858.86 17,858.86 17,858.86 17,858.86 13,358.86 10.00% $45,768
(e) Residual Class
Year
Total in pool
0 1 $18,308.86 2 $18,308.86 3 $18,308.86 4 $18,308.86 5 $18,308.86 6 $18,308.86 7 $18,308.86 8 $18,308.86 9 $18,308.86 10 $18,308.86
Other Classes
Residual
($4,500.00 ) $16,925.11 1,383.75 17,127.39 1,181.47 17,349.89 958.96 17,594.65 714.20 17,765.30 543.55 17,858.86 450.00 17,858.86 450.00 17,858.86 450.00 17,858.86 450.00 13,358.86 4,950.00 IRR
19.10%
Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-284
(f) Assuming 10% prepayment Mortgage Pool Year
Beg. Bal
1 $112,500.00 2 94,191.14 3 77,835.74 4 63,245.90 5 50,254.84 6 38,715.96 7 28,502.79 8 19,510.99 9 11,665.33 10 4,943.88
Payment
Interest
$18,308.86 11,250.00 $16,355.40 9,419.11 $14,589.84 7,783.57 $12,991.06 6,324.59 $11,538.88 5,025.48 $10,213.17 3,871.60 $8,991.80 2,850.28 $7,845.66 1,951.10 $6,721.45 1,166.53 $5,438.27 494.39
Principal
End Bal
$18,308.86 $16,355.40 $14,589.84 $12,991.06 $11,538.88 $10,213.17 $8,991.80 $7,845.66 $6,721.45 $4,943.88
$94,191.14 $77,835.74 $63,245.90 $50,254.84 $38,715.96 $28,502.79 $19,510.99 $11,665.33 $4,943.88 $0.00
End Bal
Cash Flow
Prepayment 11250.00 9419.11 7783.57 6324.59 5025.48 3871.60 2850.28 1951.10 1166.53 494.39
Tranche A
Year
Beg. Bal
1 $40,500.00 2 17,691.14 3 0.00 4 0.00 5 0.00 6 0.00 7 0.00 8 0.00 9 0.00 10 0.00
Interest
Principal
3,341.25 $22,808.86 $17,691.14 1,459.52 17,691.14 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
P V at
8.50%
26,150.11 19,150.66 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
$40,369
Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-285
Tranche B
Year
Beg. Bal
1 $22,500.00 2 22,500.00 3 18,885.74 4 0.00 5 0.00 6 0.00 7 0.00 8 0.00 9 0.00 10 0.00
Interest
Principal
End Bal
$2,025.00 $0.00 $22,500.00 2,025.00 3,614.26 18,885.74 1,699.72 18,885.74 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
P V at
9.50%
Cash Flow 2,025.00 5,639.26 20,585.46 0.00 0.00 0.00 0.00 0.00 0.00 0.00
$22,232
Tranche Z
Year
Beg. Bal
0 1 $45,000.00 2 49,500.00 3 54,450.00 4 58,745.90 5 45,754.84 6 34,215.96 7 24,002.79 8 15,010.99 9 7,165.33 10 443.88
Interest
Total Payment
4,500.00 4,950.00 5,445.00 5,874.59 4,575.48 3,421.60 2,400.28 1,501.10 716.53 44.39
0.00 $49,500.00 0.00 54,450.00 1,149.10 58,745.90 18,865.65 45,754.84 16,114.37 34,215.96 13,634.77 24,002.79 11,392.08 15,010.99 9,346.76 7,165.33 7,437.99 443.88 488.27 0.00
End Bal
IRR P V at
9.75%
Cash Flow ($45,000) 0.00 0.00 1,149.10 18,865.65 16,114.37 13,634.77 11,392.08 9,346.76 7,437.99 488.27 10.00% $45,588
Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-286
Residual
Year
Total in pool
0 1 $29,558.86 2 $25,774.52 3 $22,373.42 4 $19,315.65 5 $16,564.37 6 $14,084.77 7 $11,842.08 8 $9,796.76 9 $7,887.99 10 $5,438.27
Other Classes
Residual
($4,500.00 ) $28,175.11 1,383.75 24,789.92 984.60 21,734.56 638.86 18,865.65 450.00 16,114.37 450.00 13,634.77 450.00 11,392.08 450.00 9,346.76 450.00 7,437.99 450.00 488.27 4,950.00 IRR
16.10%
(g) 10 percent price increase after issue Tranche A
Year
Beg. Bal
0 1 $40,500.00 2 17,691.14 3 0.00 4 0.00 5 0.00 6 0.00 7 0.00 8 0.00 9 0.00 10 0.00
Interest
Principal
End Bal
3,341.25 $22,808.86 $17,691.14 1,459.52 17,691.14 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 P V at
8.50%
Cash Flow
26,150.11 19,150.66 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
10% Price Increase ($44,550) 26,150.11 19,150.66 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00
$40,369 YTM
1.18%
Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-287
Tranche B
Year
Beg. Bal
0 1 $22,500.00 2 22,500.00 3 18,885.74 4 0.00 5 0.00 6 0.00 7 0.00 8 0.00 9 0.00 10 0.00
Interest
Principal
End Bal
$2,025.00 $0.00 $22,500.00 2,025.00 3,614.26 18,885.74 1,699.72 18,885.74 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 P V at
9.50%
Cash Flow
2,025.00 5,639.26 20,585.46 0.00 0.00 0.00 0.00 0.00 0.00 0.00
10% Price Increase ($24,750) 2,025.00 5,639.26 20,585.46 0.00 0.00 0.00 0.00 0.00 0.00 0.00
$22,232 YTM
5.12%
Class Z
Year
Beg. Bal
0 1 $45,000.00 2 49,500.00 3 54,450.00 4 58,745.90 5 45,754.84 6 34,215.96 7 24,002.79 8 15,010.99 9 7,165.33 10 443.88
Interest
4,500.00 4,950.00 5,445.00 5,874.59 4,575.48 3,421.60 2,400.28 1,501.10 716.53 44.39
Total Payment
End Bal
0.00 $49,500.00 0.00 54,450.00 1,149.10 58,745.90 18,865.65 45,754.84 16,114.37 34,215.96 13,634.77 24,002.79 11,392.08 15,010.99 9,346.76 7,165.33 7,437.99 443.88 488.27 0.00
Cash Flow
($45,000) 0.00 0.00 1,149.10 18,865.65 16,114.37 13,634.77 11,392.08 9,346.76 7,437.99 488.27
YTM PV at
10% Price Increase ($49,500) 0.00 0.00 1,149.10 18,865.65 16,114.37 13,634.77 11,392.08 9,346.76 7,437.99 488.27 8.18%
9.75%
$45,588
Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-288
Problem 20-2 (a) Beginning Balance Prepayment Rate Interest Rate
Period 1 2 3 4 5 6 7 8 9 10
= = =
Beginning Balance $1,000,000 930,971 856,419 775,903 688,945 595,032 493,605 384,063 265,759 137,990
$1,000,000 0.00 0.08 Interest IO/Strip $80,000 74,478 68,513 62,072 55,116 47,603 39,488 30,725 21,261 11,039
Principal PO/Strip $69,029 74,552 80,516 86,957 93,914 101,427 109,541 118,304 127,769 137,990
PO Prepayment $0 0 0 0 0 0 0 0 0 0
Ending Balance $930,971 856,419 775,903 688,945 595,032 493,605 384,063 265,759 137,990 0
The price of the IO and PO strips is the PV of the cash flows at 8% PV/Price at 8%
IO/Strip $360,838
PO/Strip $639,162
(b) If interest rates increase to 10% then the price of the IO and PO is the PV of the respective cash flows at 10%
PV/Price at 10%
IO/Strip $337,113
PO/Strip $578,608
The percentage change in the IO and PO price is: IO/Strip PO/Strip % change in price -6.57% -9.47% The PO strip has the greatest change in price which demonstrates it has greater amounts of convexity than the IO (c) Cash flow schedule at 0% prepayment Beginning Balance = Prepayment Rate = Interest Rate =
Period 1 2 3 4 5
Beginning Balance $1,000,000 930,971 856,419 775,903 688,945
$1,000,000 0.00 0.08
Interest IO/Strip $80,000 74,478 68,513 62,072 55,116
Principal PO/Strip $69,029 74,552 80,516 86,957 93,914
PO Prepayment $0 0 0 0 0
Ending Balance $930,971 856,419 775,903 688,945 595,032
Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-289
6 7 8 9 10
595,032 493,605 384,063 265,759 137,990
47,603 39,488 30,725 21,261 11,039
101,427 109,541 118,304 127,769 137,990
0 0 0 0 0
493,605 384,063 265,759 137,990 0
The price of the 0% prepayment IO and PO strips is the PV of the cash flows at 6% PV/Price at 6%
IO/Strip $387,480
PO/Strip $709,390
Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-290
Cash flow schedule at 20% prepayment Beginning Balance = Prepayment Rate = Interest Rate =
Period 1 2 3 4 5 6 7 8 9 10
Beginning Balance $1,000,000 730,971 526,241 371,518 255,578 169,623 106,785 61,730 30,369 9,695
$1,000,000 0.20 0.08
Interest IO/Strip $80,000 58,478 42,099 29,721 20,446 13,570 8,543 4,938 2,430 776
Principal PO/Strip $69,029 58,536 49,474 41,637 34,839 28,913 23,698 19,015 14,601 9,695
PO Prepayment $200,000 146,194 105,248 74,304 51,116 33,925 21,357 12,346 6,074 0
Ending Balance $730,971 526,241 371,518 255,578 169,623 106,785 61,730 30,369 9,695 0
The price of the 20% prepayment IO and PO strips is the PV of the cash flows at 6% IO/Strip $221,902
PV/Price at 6%
PO/Strip $833,574
Problem 20-3 (a) Scale = 50% / 50% = 1.0 (F) Floater (IF) Inverse Floater
Scale 0.50 0.50
$1,000,000 1,000,000
Interest Rate 0.08 0.08
Interest Payable $80,000 80,000 $160,000
Maximum cap for (F) (160,000 / 1,000,000) - .08 of 16%
=
0.080 increase in the interest rate or an interest rate
Maximum floor for (IF) (.08) × 1 of 0%
=
0.080 decrease in the interest rate or an interest rate
(b) Scale = 60% / 40% = 1.5 (F) Floater (IF) Inverse Floater
$1,200,000 800,000
Scale 0.60 0.40
Interest Rate 0.08 0.08
Interest Payable $96,000 64,000 $160,000
Maximum cap for (F) Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-291
(160,000 / 1,200,000) - .08 of 13.33% Maximum floor for (IF) -(.053) × (1.5) of 0%
=
0.053 increase in the interest rate or an interest rate
=
-0.080 decrease in the interest rate or an interest rate
Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-292
(c) Impact of 2% increase in interest rate under 50% proportions Scale (F) Floater $1,000,000 0.50 (IF) Inverse 1,000,000 0.50 Floater
Interest Rate 0.10 0.06
Interest Payable $100,000 60,000 $160,000
F receives $100,000 and IF receives $60,000 Impact of 2% increase in interest rate under 60% / 40% proportions Scale Interest Rate (F) Floater $1,200,000 0.60 0.10 (IF) Inverse 800,000 0.40 0.05 Floater
Interest Payable $120,000 40,000 $160,000
F receives $120,000 and IF receives $40,000 Impact of 2% decrease in interest rate under 50% proportions Scale (F) Floater $1,000,000 0.50 (IF) Inverse 1,000,000 0.50 Floater
Interest Rate 0.06 0.10
Interest Payable $60,000 100,000 $160,000
F receives $60,000 and IF receives $100,000 Impact of 2% decrease in interest rate under 60% / 40% proportions Scale Interest Rate (F) Floater $1,200,000 0.60 0.06 (IF) Inverse 800,000 0.40 0.11 Floater
Interest Payable $72,000 88,000 $160,000
F receives $72,000 and IF receives $88,000 Summary Yield
Proportions
of Issue
2% increase in interest rate
2% decrease in interest rate
Case (a) (F) (IF)
50% 50%
8% 8%
10 6
6 10
Case (b) (F) (IF)
60% 40%
8% 8%
10 5
6 11
Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-293
In case (a) there is an equal impact of changing interest rates on the F and IF yields, that is, each either increases or decreases by 2%. In case (b) however, IF investors will experience greater volatility in yield. This is because the proportion of each class comprising the tranche is now 60 - 40. Therefore, for each 1% change in the underlying interest rate, IF investors will realize a change in yield of 1.5%.
Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-294
Problem 20-4 See table below: Prepayme IRR on nt Rate Residual 0.00% 19.10% 5.00% 17.33% 10.00% 16.10% 15.00% 15.53% 20.00% 14.99% 25.00% 14.74% 30.00% 14.74%
Problem 20-5 See below: Libor
(F) Rate 0% 1% 2% 3% 4% 5% 6% 7% 8%
0.00% 1.00% 2.00% 3.00% 4.00% 5.00% 6.00% 7.00% 8.00%
(IF) Rate 24.00% 21.00% 18.00% 15.00% 12.00% 9.00% 6.00% 3.00% 0.00%
F interest
IF Interest
Total interest $0 $1,200,000 $1,200,000 150,000 1,050,000 1,200,000 300,000 900,000 1,200,000 450,000 750,000 1,200,000 600,000 600,000 1,200,000 750,000 450,000 1,200,000 900,000 300,000 1,200,000 1,050,000 150,000 1,200,000 1,200,000 0 1,200,000
Note that the inverse floater now starts at a higher rate with Libor equal to 0% and decreases at a faster rate than before. Problem 20-6
Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-295
See below:
IRR on IO and PO vs. Prepayment IRR of IO
35% 30%
30.00% 25.32% 20.62% 15.91% 11.19% 6.45% 1.70%
5.38% 6.57% 7.90% 9.37% 10.94% 12.59% 14.30%
IO
25%
PO IRR
Prepayment 0.00% 5.00% 10.00% 15.00% 20.00% 25.00% 30.00%
IRR of PO
20% 15% 10% 5% 0% 0%
5%
10%
15%
20%
25%
30%
Prepayment rate
Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-296
Problem 20-7 The returns to the subordinated tranche = 11.17% The returns to the residual = -4.92%
Solutions to Problems—Chapter 20 Appendix The Secondary Mortgage Market: CMOs and Derivative Securities Problem 20A-1 (a) Interest Payments of a Corporate Bond= Final Payment of a Corporate Bond =
$10,000 $100,000
Annual Payments of a Mortgage Final Payment of a Mortgage Bond
$16,275 $61,693
= =
Duration Calculation of a Corporate Bond: Weighting Period Payment Factor 0 1 10,000 1.0 2 10,000 2.0 3 10,000 3.0 4 10,000 4.0 5 10,000 5.0 5 100,000 5.0
Present Value
Weighted PV of Payment
0.9091 0.8264 0.7513 0.6830 0.6209 0.6209
14,795 26,901 36,693 44,464 50,527 191,532 $364,903
Total Duration Duration Duration
= = =
Total weighted present value of payments $364,903 \ $100,000 3.65 years
(b) New price for corporate bond if interest rate falls from 10% to 7% Difference Duration % Change in Price New Price New Price
= = = = =
10% - 7% = 3.00% 4.17 years -11.37% Old Price * (1 + % Change) $88,628
New price for mortgage bond if interest rate falls from 10% to 7% Difference Duration % Change in Price New Price New Price
= = = = =
10% -7% = 3.00% 3.65 years -9.95% Old Price × (1 + % Change) $90,048
Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-297
Solutions to Questions—Chapter 21 Real Estate Investment Trusts (REITs) Question 21-1 What are the general requirements regarding income, investments, and dividends with which a REIT must comply to maintain its qualification to be taxed as a REIT? In general, at least 75 percent of gross income must be from rents, interest on obligations secured by mortgages, gains from the sale of certain assets, or income attributable to investments in other REITs. At least 75 percent of the value of a REIT’s assets must consist of real estate assets, cash, and government securities. A REIT must distribute 90 percent of its taxable income to shareholders as a dividend. December 18, 2015 enactment of the Protecting Americans from Tax Hikes Act of 2015 (PATH Act) featured significant changes to various real estate investment trust (REIT) rules. Example: Currently, no more than 25% of the assets of a REIT (by value) can consist of securities of one or more TRS. The PATH Act reduces the percentage limitation to 20%. This provision applies to 2018 and later taxable years. Question 21-2 What are the two principal types of REITs? The two principal types of REITs are mortgage and equity. Question 21-3 List and characterize equity REITs based on their property types. Industrial/Office: REITs that specialize in owning industrial, office and/or a mix of industrial and office properties. These REITs can be further divided based on the property location in which they invest, such as CBD versus suburban. Retail: REITs that specialize in owning retail properties. These REITs can be further segregated into retail subcategories, such as neighborhood centers, regional malls, outlet centers, and/or free-standing retail properties. Residential: REITs that specialize in owning residential properties. These REITs can be further segregated into residential subcategories, such as multi-family apartments, manufactured home communities, student housing and/or military housing. Lodging/Resorts: REITs that specialize in owning lodging/resorts properties, including hotels, resorts and/or motels. Health Care: REITs that specialize in owning health care related facilities, including hospitals, senior housing, medical office and/or related health care facilities that are leased back to private health care providers who operate such facilities. Self-Storage: REITs that specialize in owning self-storage facilities. Timber: REITs that specialize in owning timberland. Infrastructure: REITs that specialize in owning various types of infrastructure, including railroads, electric and gas transmission and distribution, cell towers and other forms of infrastructure. Diversified or Specialty: REITs that own a variety of different product types or property types that are not otherwise classified, such as golf courses, prisons, data centers, etc. Equity trusts may be broken down into the following categories: Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-298
1. 2. 3. 4. 5. 6. 7. 8. 9.
Blank or ―blind pool‖ check trusts. Purchasing, or Specified Trusts. Mixed Trusts. Leveraged REITs versus Unleveraged REITs. Finite-Life versus NonFinite-Life REITs. Closed-end versus Open-end REITs. Exchange trusts. Developmental-Joint Venture Equity REITs. Health-Care REITs.
Question 21-4 What is the difference between earnings per share (EPS), funds from operations (FFO), adjusted funds from operations (AFFO), and dividends per share? Earnings per share (EPS) is based on accounting income which is reduced by any depreciation and amortization which are non-cash deductions. EPS is calculated as GAAP net income minus preferred stock dividends divided by number of common shares outstanding. FFO is calculated by adding back depreciation and amortization and other non-cash deductions to earnings minus any capital gains from property sales. Although subject to different methods of calculation, AFFO is usually calculated by subtracting from FFO (i) normalized recurring expenditures that are capitalized by the REIT and then amortized, and (ii) straight-lining of rents. The resulting AFFO calculation is sometimes referred to as the cash available for distribution (CAD) or funds available for distribution (FAD). Dividends per share is what the REIT actually distributes to shareholders and is calculated as dividends paid divided by number of common shares outstanding. Question 21-5 Explain how an investor in an equity REIT may receive a current dividend, part of which may be tax-deferred. Part of the dividend paid by a REIT may represent ―return of capital.‖ This can occur when the dividends per share exceeds earnings per share. Question 21-6 What are some important lease provisions which investors should be aware of when analyzing the financial statements of REITs? When analyzing the financial statements of REITs, investors should consider the effect of lease provisions such as provisions for tenant improvements and free rents, leasing commissions and lease guarantees. The accounting treatment of these provisions can affect the reported FFO for one REIT versus another REIT. Question 21-7 What is a mortgage REIT? A mortgage REIT is a REIT that primarily invests in mortgages rather than equity ownership.
Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-299
Solutions to Problems—Chapter 21 Real Estate Investment Trusts (REITs) Problem 21-1 (a) Assuming dividends are set at 90% × EPS, or $2.03 per share EPS: (Net Income) / (Shares Outstanding) = $2.26 NOI: (Income from Operations) + (Depreciation and Amortization) / (Shares Outstanding) = $5.10 FFO: (Net Income) + (Depreciation and Amortization) / (Shares Outstanding) = $4.46 ROC: (Dividend per Share) - (EPS) = ($0.11) Cash Retention per Share: (FFO) - (Dividend per Share) = $2.43 Net Assets per Share: (Net Assets) / (Shares Outstanding) = $30.40 Equity or Book Value per Share: (Shareholders equity) / (Shares Outstanding) = $21.20 ROA: (NOI) / (Net Assets) = 16.8% ROE: (FFO) / (Equity) = 21.0% (b) Assuming that National paid a minimum dividend of $2.03 per share (90% of EPS) and investors capitalized dividends paid by National at .08, the indicated price would by $2.03 / .08, or $25.37. However, market research indicates that investors are paying 12 × FFO for comparable REITs. In National’s case this would be 12 × $4.46, or $53.52. Assuming National’s dividend is $2.03, its cash retention would be $2.43 per share and its investors would not realize any recovery of capital. Indeed, the full amount of the dividend would be taxed at ordinary rates. If a minimum payout is chosen, Blue Street may want to evaluate National’s ability to provide a much higher dividend payout as opposed to the cash retention of $2.43 per share. To have a dividend yield equal to that of comparable REITs , using the share price of $53.52 suggested by the FFO multiple above, National should consider paying a dividend of around 8% of $53.52 or about $4.28. In this case it would not be retaining as much cash and the amount of dividend paid that exceeds $2.26 would be considered return of capital and not taxed when paid. The basis of the investor’s stock would be reduced by the amount of return of capital which would result in additional capital gain when the stock is sold. Alternatively, if National chooses to retain more cash flow, its plan for future property acquisitions or use of its cash flow should be evaluated carefully in order to justify paying 12 × FFO. (c) Net Revenue $100,000,000 Operating expenses 40,000,000 NOI (from properties) 60,000,000 NOI / Cap rate = $60m / .10 = $600 million Equity = Net Asset Value – Liabilities Equity = $600 million - $92 million = $508 million Equity / shares = $508 million / 10 million = $50.80 per share Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-300
Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-301
Problem 21-2 Approach 1 Balance Sheet - Date of Offering Assets Properties @ Cost $100,000,000 Tenant Improvements 10,000,000 Other Capital Costs: Financing Fees 900,000 Lease Commissions 600,000 Total Net Assets $111,500,000 $111,500,000
Liabilities Mortgage Loan
$30,000,000
Shareholder Equity
81,500,000
Total Liabilities & Equity
Operating Statement
Net Revenue Less: Operating Expenses Management Expenses G&A Expense Less Amortization: Lease Commission Financing Fees Less Depreciation: Buildings Tenant Improvements Income from Operations Less Interest Net Income
(1) $15,000,000
Year (2) $15,750,000
(3) $16,537,500
5,700,000 750,000 450,000
5,985,000 787,500 472,500
6,284,250 826,875 496,125
120,000 90,000
120,000 90,000
120,000 90,000
2,000,000 250,000 5,640,000 2,400,000
2,000,000 250,000 6,045,000 2,400,000
2,000,000 250,000 6,470,250 2,400,000
$3,240,000
$3,645,000
$4,070,250
Relevant Ratios for Year One Assuming dividends are set at $4.00 per share EPS: (Net Income) / (Shares Outstanding) = $3.24 NOI: (Income from Operations) + (Depreciation and Amortization) / (Shares Outstanding) = $8.10 FFO: (Net Income) + (Depreciation and Amortization) / (Shares Outstanding) = $5.70 ROC: (Dividend per Share) - (EPS) = $0.76 Cash Retention per Share: (FFO) - (Dividend per Share) = $1.70 Net Assets per Share: (Net Assets) / (Shares Outstanding) = $111.50 Equity or Book Value per Share: (Assets) - (Liabilities) = $81.50 ROA: (NOI) / (Net Assets) = 7.3% ROE: (FFO) / (Equity) = 7.0% Approach 2 Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-302
Balance Sheet - Date of Offering Assets Properties @ Cost $100,000,000 Tenant Improvements 10,000,000 Other Capital Costs: Financing Fees 900,000 Lease Commissions 600,000 Total Net Assets $111,500,000 $111,500,000 Operating Statement
Liabilities Mortgage Loan
$30,000,000
Shareholder Equity
81,500,000
Total Liabilities & Equity
(1) $15,000,000
Year (2) $15,750,000
(3) $16,537,500
5,700,000 750,000 450,000
5,985,000 787,500 472,500
6,284,250 826,875 496,125
Lease Commission (expensed) 600,000 Financing Fees (expensed) 900,000
0 0
0 0
Net Revenue Less: Operating Expenses Management Expenses G&A Expense
Less Depreciation: Buildings Tenant Improvements Income from Operations Less Interest
2,000,000 2,000,000 2,600,000 2,400,000
2,000,000 2,000,000 4,505,000 2,400,000
2,000,000 2,000,000 4,929,750 2,400,000
Net Income
$200,000
$2,105,000
$2,529,750
Relevant Ratios for Year One Assuming dividends are set at $4.00 per share EPS: (Net Income) / (Shares Outstanding) = $.20 NOI: (Income from Operations) + (Depreciation and Amortization) / (Shares Outstanding) = $8.10 FFO: (Net Income) + (Depreciation and Amortization) / (Shares Outstanding) = $4.20 ROC: (Dividend per Share) - (EPS) = $3.80 Cash Retention per Share: (FFO) - (Dividend per Share) = $1.70 Net Assets per Share: (Net Assets) / (Shares Outstanding) = $111.50 Equity or Book Value per Share: (Assets) - (Liabilities) = $81.50 ROA: (NOI) / (Net Assets) = 7.3% ROE: (FFO) / (Equity) = 7.0% (a) Note that major differences occur in the above ratios under each approach. Using the $4.00 dividend in each case, note the changes in EPS and ROC in particular. Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-303
EPS ROC
Approach 1 $3.24 0.76
Approach 2 $0.20 3.80
Although Approach 1 provides the highest EPS, it provides a lower ROC. As a result if a $4.00 dividend is paid, more will be taxable to shareholders. FFO per share, which is the focus of many investors, is $5.70 per share for method 1 but $4.20 per share for method 2. Clearly the adoption of accounting treatment should be carefully considered by Robust.
Problem 21-3 (a)
FFO = $8 + $2 = $10 per share FFO × FFO Multiple = $10 × 10 = $100 per share
(b) (c)
$6 / (.12 - .02) = $60 $10.00 per share × 1 million shares = $10 million $10 million / .08 = $125 million value of properties $125 million - $40 million liabilities = $85 million NAV $85 million / 1 million shares = $85 per share Solutions to Questions—Chapter 22 Real Estate Investment Performance and Portfolio Considerations
Question 22-1 What are some of the difficulties of obtaining data to measure real estate investment performance? It is difficult obtaining data to measure real estate investment performance because properties do not sell frequently like stocks and bonds. Also, when properties do sell, the sale price is generally not publicly available. This makes it difficult to compare the investment performance with stocks and bonds. Question 22-2 What are the distinguishing characteristics between REIT data and the NCREIF Property Index? The NCREIF index measures the investment performance of real estate by using appraised values (rather than actual sale prices) for properties held by institutional investors that are members of the National Council of Real Estate Investment Fiduciaries (NCREIF). Because REITs are publicly traded, actual transactions prices are available for these stocks. Because REITs are operating companies, however, their value reflects both the performance of properties held by the REIT, as well as the ability of the REIT’s management to operate the company successfully. Question 22-3 What is the difference between arithmetic and geometric mean returns? The arithmetic mean adds the returns that occur over time and divides the sum by the total number of returns. The geometric mean is calculated by add one to each return and taking the product of the returns that occur over time. The geometric mean is the nth root of this product. The geometric mean is considered more appropriate in measuring the mean (i.e., average) of rates of return that occur over time. Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-304
Question 22-4 What statistical concept do many portfolio managers use to represent risk when considering investment performance? The standard deviation (square root of the variance) of returns is typically used as a measure of risk. Question 22-5 When NCREIF returns and REIT returns are compared, NCREIF returns exhibit a much lower pattern of variation. Why might this be the case? NCREIF returns are based on using the quarterly appraised value of the properties as estimates for the value of the property, whereas REIT returns are based on actual transaction prices. The appraisal process tends to result in smoother changes in estimates of value over time as markets change, in part due to the fact that appraisers must rely on historical information. Question 22-6 Mean returns for portfolios are calculated by taking the weighted average of the mean returns for each investment in the portfolio. Why won‟t this approach work to calculate the standard deviation of portfolio returns? This approach would not take into consideration the way returns for different properties in the portfolio are correlated over time. The correlation of returns between each property and all other properties in the portfolio affects the standard deviation of the returns for the entire portfolio. The less returns are correlated between properties, the lower the portfolio standard deviation. Question 22-7 What is the difference between covariance and correlation? Why are these concepts so important in portfolio analysis? Correlation is calculated by dividing the covariance of two returns by the product of the standard deviation of the two returns. Both measure the degree to which returns move together over time. The advantage of the correlation coefficient is that it always ranges from -1 to +1 which makes it easier to compare for different investment alternatives.
Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-305
Question 22-8 Results reported in the chapter showed that by including either REITs or the NCREIF Index in a portfolio containing S&P 500 securities, corporate bonds, and T bills, diversification benefits resulted. Why was this true? Did those benefits come about for the same reason for each category of real estate investment? Diversification benefits resulted by including either REITs or the NCREIF Index in a portfolio because real estate investment returns are not highly correlated with returns for stocks, bonds and T bills. The diversification benefits come about for the same general reason for both REITs and the NCREIF Index although these two measures differ in the way they are calculated and what they measure as discussed in questions 2 and 5 above. Question 22-9 Results presented in the chapter are based on historical data. Of what use are these results to a portfolio manager who may be making an investment decision today? Elaborate. Results based on historical data suggest that real estate can add diversification benefits to a portfolio of stocks and bonds. This result in not likely to change since real estate returns should continue to be affected by different economic factors than stocks and bonds and ,thus, returns between these categories of investments will not be highly correlated. The exact mix of assets in the portfolio, i.e., the percentage invested in real estate versus other assets, is likely to differ over time, however, so portfolio managers making decisions today should do their own analysis using the concepts presented in the chapter. Question 22-10 Why should an investor consider investing globally? Investor should consider investing globally because by doing so it can diversify portfolio risk and hence will be able to achieve higher return for the same level of risk or same return with lower level of risk. Question 22-11 What are the risks of global investment? Some of the risks associated with global investing are: government instability in host country, political issues, different rules and regulations, and change in exchange rates. Question 22-12 How can derivative security be used to hedge portfolio risk? Derivative security can be used to hedge portfolio risk by taking opposite position then what is taken in the underlying security. Say for instance if the investor takes a long position in any security, it can hedge against the downside movement of prices by taking long position in ―puts‖. If the investor takes a short position in any security, it can hedge against the upward movement of prices by taking long position in ―calls‖. Similarly, opposite position in indexes can be taken for hedging risk for different securities constituting a portfolio.
Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-306
Solutions to Problems—Chapter 22 Real Estate Investment Performance and Portfolio Considerations Problem 22-1
Period Ending 1 2 3 4 5 6 7 8 9 10 11 12 13
ET&T Common Stock Fund Unit Quarterly Value Dividend 701.00 8.28 752.50 8.11 850.52 10.30 953.75 9.81 1,047.57 12.05 1,221.70 14.17 1,443.90 17.18 1,263.31 14.91 1,258.56 13.84 1,526.72 18.32 1,616.81 19.73 1,624.08 19.98 1,560.25 18.88
MREAF Real Estate Fund Unit Quarterly Value Dividend 70.00 2.17 80.05 2.14 90.80 2.01 100.50 2.01 99.14 1.87 95.50 1.81 93.77 1.79 80.31 1.54 77.34 1.49 76.53 1.44 78.42 1.51 79.01 1.53 81.75 1.55
(a) Calculate the HPR for each investment The formula to be used is ((Pt - Pt-1) + Dt) / Pt-1 where Dt = Dividends or cash distributions in time period t Pt = Price in time period t Pt-1 = Price in time period t-1
Period 1 2 3 4 5 6 7 8 9 10 11 12 13 Total
(a) Common Stock Fund NA 8.50% 14.39% 13.29% 11.10% 17.97% 19.59% -11.47% .72% 22.76% 7.19% 1.69% -2.77%
(b) Real Estate Fund NA 17.41% 15.94% 12.90% 0.51% -1.85% 0.06% -12.71% -1.84% 0.81% 4.44% 2.70% 5.43%
102.98%
43.81%
(b) Calculate Arithmetic Mean return Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-307
Mean HPR for Common Stock Fund = Mean HPR for Real Estate Fund =
102.98% / 12 = 43.81% / 12 =
8.58% 3.65%
Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-308
Calculate the Standard Deviation Period 1 2 3 4 5 6 7 8 9 10 11 12 13
Stock Fund (HPRa - HPRa) (HPRa - HPRa) -0.0008 0.0581 0.0471 0.0252 0.0939 0.1101 -0.2006 -0.0786 0.1418 -0.0139 -0.0690 -0.1135
Real Estate fund (HPRb - HPRb) (HPRb - HPRb)
0.0000 0.0034 0.0022 0.0006 0.0088 0.0121 0.0402 0.0062 0.0201 0.0002 0.0048 0.0129
Total
0.1376 0.1229 0.0925 -0.0314 -0.0550 -0.0359 -0.1636 -0.0549 -0.0284 0.0079 -0.0095 0.0178
0.1115
0.0790
Variance of Common Stock Fund= Standard Deviation =
0.1115 / 12 0.0964
=
0.0093
Variance of Real Estate Fund Standard Deviation
0.0790 / 12 0.0811
=
0.0066
= =
Calculate the Geometric Mean Stock Fund Period (1 + HPRa) 1 2 1.0850 3 1.1439 4 1.1329 5 1.1110 6 1.1797 7 1.1959 8 0.8853 9 1.0072 10 1.2276 11 1.0719 12 1.0169 13 .9723 Geometric Mean of Stock Fund = Geometric Mean of Real Estate Fund
0.0189 0.0151 0.0085 0.0010 0.0030 0.0013 0.0268 0.0030 0.0008 0.0001 0.0001 0.0003
Real Estate Fund (1 + HPRb) 1.1741 1.1594 1.1290 1.0051 0.9815 1.0006 0.8729 0.9816 1.0081 1.0444 1.0270 1.0543 0.0814 =
0.0333
Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-309
(c) Correlation between Common Stock Fund and Real Estate Fund Correlation between Stock Fund and Real Estate Fund [Std. Dev. (a) × Std. Dev. (b)] COVab
Period 1 2 3 4 5 6 7 8 9 10 11 12 13
=
=
[COVab] /
[HPRa - HPRa] × [HPRb - HPRb] / N
(HPRa - HPRa)
(HPRb - HPRb)
[HPRa - HPRa] * [HPRb - HPRb]
-0.0008 0.0581 0.0471 0.0252 0.0939 0.1101 -0.2006 -0.0786 0.1418 -0.0139 -0.0690 -0.1135
0.1376 0.1229 0.0925 -0.0314 -0.0550 -0.0359 -0.1636 -0.0549 -0.0284 0.0079 -0.0095 0.0178
-0.0001 0.0071 0.0044 -0.0008 -0.0052 -0.0040 0.0328 0.0043 -1.0040 -0.0001 0.0007 -0.0020
Total
0.0331
Covariance between Stock Fund and Real Estate Fund = Correlation between Stock Fund and Real Estate Fund .081) =
= 0.0028 = 0.3530
0.0331 / 12.00 0.0028 / (.096 ×
(d) In order for a portfolio of assets to provide diversification, the standard deviation of the portfolio must be less than the weighted average standard deviations of the individual assets. Standard Deviation of Common Stock Fund Standard Deviation of Real Estate Fund The portfolio will be comprised of
Period 1 2 3 4 5 6 7 8 9
Common Stock Fund NA 0.0850 0.1439 0.1329 0.1110 0.1797 0.1959 -0.1147 0.0072
= =
0.0964 0.0811 50.00% Common Stock and 50.00% Real Estate Equities
Real Estate Fund NA 0.1741 0.1594 0.1290 0.0051 -0.0185 0.0006 -0.1271 -0.0184
Portfolio NA 0.1296 0.1517 0.1309 0.0580 0.0806 0.0983 -0.1209 -0.0056
Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-310
10 11 12 13
0.2276 0.0719 0.0169 -0.0277
0.0081 0.0444 0.0270 0.0543
0.1179 0.0582 0.0219 0.0133
1.0298
0.4381
0.7339
Weighted Average Standard Deviation (each asset weighted 50%) = Portfolio Standard Deviation = 0.0731
0.0888
Because the portfolio’s standard deviation is less than the weighted average of the individual standard deviations, the portfolio does provide an element of diversification.
Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-311
(e) Optional Weight of Common Stock 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100%
Portfolio Return 3.65% 4.14% 4.64% 5.13% 5.62% 6.12% 6.61% 7.10% 7.60% 8.09% 8.58%
Portfolio Risk 8.11% 7.69% 7.39% 7.22% 7.20% 7.31% 7.57% 7.94% 8.42% 8.99% 9.64%
(f) Based on the exhibit below, it would appear that substantial risk reduction occurs as more of the real estate fund is combined with the stock fund. However, mean returns on the portfolio increase sharply as more common stock is added. How much stock should be combined with real estate will depend on the degree of risk aversion of the portfolio manager, however, the trade off between risk and return can be clearly seen in the Exhibit.
Portfolio of Stocks and Real Estate Return vs. Risk 10%
Return
8% 6% 4% 2% 7%
8%
9%
10%
Risk
Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-312
Problem 22-2 See below:
The standard deviation of the portfolio for 50% S&P stocks and 50% leveraged real estate (NPI) is 9.55% versus 10.94% before. The more negative the correlation the greater the diversification benefits and the lower the portfolio standard deviation. Solutions to Questions—Chapter 23 Real Estate Investment Funds: Structure, Performance, Benchmarking, and Attribution Analysis Question 23-1 What are the primary differences between an open-end and closed-end fund? Why would an investor choose to invest in one or the other? An open-end fund allows investors to invest or withdraw capital from the fund overtime. A closed end fund is usually closed to new investment after a specified amount of capital is raised. It does not allow investors to withdraw funds until fund objectives are achieved and is liquidated. Open end funds may be thought of as ongoing funds that expand or contract as investors make additional investments or withdraw capital from the fund. Closed end funds are usually more focused and may have a finite life. Open end funds are usually well diversified whereas a closed Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-313
end fund often has a focus on a particular property type or geographic area. Closed end funds are often used for riskier investments. The fund that is best for an investor depends on their expected returns, need for liquidity and need for diversification. Question 23-2 What is the difference between a time-weighted return and an internal rate of return? When reporting historical investment performance to investors in a core fund, which return would be more likely to be reported? What return would likely be used for an opportunity fund? Unlike the IRR, time-weighted returns (TWR) are not impacted by the amount of capital invested each period, however, in order to calculate a TWR, an appraisal must be made each period. An IRR does not require an appraisal but is impacted by the amount of funds invested each period. A core fund generally has stabilized investments that can be valued each period and are usually open end. The manager has no control over the flow of capital in or out of the fund each period. Thus, when measuring performance, the TWR is usually considered best for core funds. Opportunity funds often include properties such as development projects or properties that are not yet stabilized, e.g., may require repositioning, renovation and lease-up. These investments are usually held in closed end funds and the manager has control over the amount of capital invested. Thus, the IRR is usually considered best for opportunity funds. Question 23-3 Which fund, core or opportunistic, would you expect to have higher returns? Why? Which would be expected to have greater volatility in returns? Why? Opportunistic funds take on riskier investments such as properties requiring significant renovation and development projects. They also use more leverage than a core fund which invests mainly in stabilized properties and may also be well diversified geographically and by property type. Because they are more focused and may require a longer period of time before reaching stabilized occupancy and expected cash flow, most opportunity funds are riskier and are expected to earn a higher return than core funds. Question 23-4 What is meant by a target return? How does it relate to an investment benchmark? When managers create funds and performance is to be measured and reported to investors, a ―benchmark‖ is usually chosen to compare how the fund is performing relative to other investment funds. For example, an open and core fund may choose the NPI (see chapter) as both its benchmark and target return. However, to the extent that such a fund has a strategy that differs as to property type and/or location from those represented by the benchmark index, the manager may choose a target return which may be higher or lower than the benchmark. For example, if a fund manager creates a core fund but adopts a strategy to overweight the fund in a certain geographic region (e.g., the ―sunbelt‖), it will be less diversified than properties represented in the index. Therefore, the manager may choose the NPI as a benchmark index but may add a premium to it when specifying its target return. This premium compensates investors for less diversification and perhaps greater risk when compared to the benchmark index. Similarly, if a core fund manager chooses to overweight its investment portfolio with a certain property type (e.g., apartments) because that sector is expected to do well, it may add a premium to the benchmark when defining its target return. So in both of the latter cases, the target return will equal the NPI benchmark, plus a premium for the added risk and less diversification. Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-314
Question 23-5 When comparing investment funds, what is the difference between committed capital and invested capital? Why may this matter for investors? A Capital Commitment usually refers to the total amount that any one investor has agreed to invest in a fund. Depending on the type of fund, there may be many commitments made at different times during the marketing phase of the fund. Consequently, there will be a time lag between commitments made during the fund marketing stage and when capital is invested. Managers ―call capital‖ in from investors who then contribute capital immediately prior to the time when they are ready to make investments in properties). The difference between commitments, contributions, and invested capital o is important for investors because different fees may be charged on each category. Also, investment performance measurement may be affected: (1) at the ―fund level‖ as capital is called by managers and (2) at the ―property level‖ when actual property acquisitions are made. Question 23-6 When evaluating investment funds, what is meant by performance at the ―fund level‖ and at the ―property level‖? What would generally cause a difference between the two? What is this difference called? The term ―property level returns‖ refers to the returns on the properties independent of the ownership structure used to hold the properties such as an open end fund. Thus property level returns do not include the impact of fees paid to the fund manager or any leverage that the manager obtained to finance the fund that is not tied to specific properties. The term ―fund level returns‖ refers to the returns that investors receive after considering fees paid to the fund manager, leverage used by the fund, cash balances and any other non-real estate investments in the fund ( such as treasuries or even REITs for liquidity). When fund returns are less than property level returns this is sometimes called ―cash drag‖ or ―administrative drag‖. However, it also is possible that fund returns may exceed property returns because of leverage which affects fund returns but not property returns. Question 23-7 When thinking about the extent of discretion that fund managers have when making property acquisitions, under which fund structures would a manager tend to have the greatest discretion? Under which structures would they tend to have the least discretion? Why? Open end Fund managers usually have greatest discretion because fund objectives are usually broad as to property types and location. Closed end fund managers usually have less discretion because fund objectives are more specific. Managers usually have least discretion when managing ―separate accounts‖. The latter are usually designed to meet the needs of a single client who may want to approve investments and limit the discretion of the fund manager when making decisions. Question 23-8 When reporting property values to investors in funds, which fund types would generally require more frequent appraisals than others? Why?
Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-315
Open end funds require more frequent appraisals because investors can add or withdraw capital over time. Therefore, values must be determined to establish unit investment values when investors buy or sell units in the fund. Closed end funds typically do not allow capital to be withdrawn. Thus, it isn’t as necessary to establish values. However, these funds will require periodic appraisals when reporting performance to investors. Question 23-9 What are the objectives of performing an attribution analysis? How could fund managers be evaluated by using an attribution analysis? The purpose of attribution analysis is to explain why the performance of a fund differs from its benchmark. This is done by breaking down the difference between the fund’s return and the benchmark return and investigating whether differences are due to superior management when selecting properties, or allocating capital among different property types and different geographic areas. Question 23-10 When evaluating fund performance, what is meant by ―style drift‖? How might style drift impact investment returns and volatility? Style drift occurs when a fund manager promotes the fund as having a certain style such as being a core fund but then takes on investments that reflect a different fund style such as opportunistic. This might result in higher returns but it usually subjects investors to more risk than they were told to expect. This could mean that expected returns may be higher, but will be more volatile. Question 23-11 Why should risk be considered in attribution analysis? A find might appear to have done better (worse) than the benchmark because it invested in riskier (less risky) properties in one or more sectors. Adjusting the risk of the returns for each sector to have the same risk as the benchmark allows comparison more on an apples-to-apples basis. Question 23-12 What is the purpose of a clawback provision in the calculation of a promote? The promote might be calculated on the sale of each property with a true-up once all the properties are sold, and the fund is liquidated. If the properties performed well in the early years but the poorly later on in the life of the fund, the promote that was paid to the manager could turn out to be larger than it should be after the true-up. The clawback provision allows for the excessive promote to be paid back to investors from the manager.
Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-316
Solutions to Problems—Chapter 23 Real Estate Investment Funds: Structure, Performance, Benchmarking, and Attribution Analysis Problem 23-1 FUND A: Capital Commitment $500,000,000 Year 1 2 3 4 5 TOTAL
Capital Contribution $200,000,000 $300,000,000
Capital Returned 0 0 0 100.000,000 50,000,000
Capital Fee on Fee on Invested Commitment Investment 200,000,000 2,250,000 0 500,000,000 2,250,000 0 500,000,000 0 3,000,000 400,000,000 0 2,400,000 350,000,000 0 2,100,000 4,500,000 7,500,000
Total Fee 2,250,000 2,250,000 3,000,000 2,400,000 2,100,000 12,000,000
FUND B: Capital Commitment $500,000,000 Year 1 2 3 4 5 TOTAL
Capital Contribution $300,000,000 $200,000,000
Capital Returned 0 0 0 50,000,000 100,000,000
Capital Fee on Fee on Invested Commitment Investment 300,000,000 2,500,000 0 500,000,000 2,500,000 0 500,000,000 0 2,750,000 450,000,000 0 2,475,000 350,000,000 0 1,925,000 5,000,000 7,150,000
Total Fee 2,500,000 2,500,000 2,750,000 2,475,000 1,925,000 12,150,000
(a)
Fund B will charge more in total fees than Fund A during the five years projected but that could change after year five depending on how much capital each fund returns to investors from sale of properties.
(b)
Although Fund A charged a lower fee on committed capital during the investment period, they are receiving a higher fee in the invested capital starting in year 3. But they have not caught up to Fund B after 5 years. So, they would need to hold properties longer than 5 years to catch up to Fund A.
Problem 23-2 Initial Investment= $2,000,000 Target Return to Investors = 10% IRR, then a 25% promote is paid to manager (a)
$2,000,000 = $50,000 / (1.1) + $50,000 / (1.1)2 + $50,000 / (1.1)3 + X / (1.1)3 Solving for (X) = $2,496,499
Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-317
This is the amount paid to investors when properties are sold to earn 10% IRR. The same answer could be found in a spreadsheet using goal seek to find the amount to make the IRR 10%. Note: Fund manager is also normally receiving a management fee that was already deducted when calculating the cash flows each year. This may also include a disposition fee. So, the manager is still receiving fees which in this case will be in addition to the promote. (b) At a sale price of $3 million the fund manager will receive 25% of ($3,000,000 - $2,496,499) = $125,875. (c) After the promote, the investor receives the sale price less the promote in the year of sale or $3,000,000 - $125,875 = $2,874,125. (d) IRR to equity now equals: $2,000,000 = $50,000 / (1+i) + $50,000 / (1+i)2 + $50,000 / (1+i)3 + $2,874,125 / (1+i)3 Solving for (i), the IRR is = 15.08% Problem 23-3 Quarterly Fund Performance (a)
Beginning Equity: $ 50 Million $ 20 Million $ 500 Million $ 570 Million -$300 Million $ 270 Million
(b)
(Cash) (Other investments) (Properties) (Total Assets) (Fund Debt) (MVBE: market value beginning equity)
What is MVEE? Ending equity = Beginning equity + NOI + change in property value + Contributions – Distributions – fees + interest income – interest expense Ending equity = $270 + $10 + $5 + $200 - $25 - $2 +$0.20 – $4.50 = $453.70
(c) be:
If all cash flows occurred at the end of the quarter, the quarterly IRR for the fund would
Fund return = ($10 - $2 + $0.20 -$4.50 + $5) / $270 = 3.22% Or Fund return = ($453.7 - $270 - $200 + $25) / $270 = 3.22% Note: Property appreciation = $655 – ($500 + $175 - $25) = $5 Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-318
(d) In cases when cash inflows and outflows occur many times during the quarter, rather than performing an IRR calculation, the Modified Dietz Return (RD) is used to approximate the IRR: First, solve for CFW to adjust the denominator in RD for timing of cash flows during the quarter: CFW = [ 1 CD × (90 – 30) ÷ 90 ] + [ 1 CD × (90 – 60) ÷ 90] + [ 1 CD × (90 – 90) ÷ 3
3
3
90] = [ 1 $25 × (90 – 30) ÷ 90 ] + [ 1 $25 × (90 – 60) ÷ 90] + [ 1 $25 × (90 – 90) 3
÷ 90]
3
3
= [ $8.33 × (60 ÷ 90) ] + [$8.33. × (30 ÷ 90) ] + [ $8.33 × (0 ÷ 90) ] CFW = $8.33 Note when the distributions are even amounts each month this result is simply 1/3 of the distributions or 1/3 * $25 = $8.33 We can now solve for the Modified Dietz Return, which is a close approximation to the quarterly IRR. Fund return = ($10 - $2 + $0.20 -$4.50 +$5) / ($270 - $8.33) = 3.32% This return is slightly higher than the return calculated in part c assuming all cash flows occur at the end of the quarter because we are now assuming the distributions occur monthly. Thus, the investor starts getting money sooner than the end of the quarter which combined with monthly compounding results in a slightly higher return. (e)
Returns ―Before Fees‖: (1) Add back to distributions, the $2 million in fees paid to fund manager. This makes a total of $27 million available for distributions ―before fees‖. So, the numerator to the return does not have the fee taken out and the denominator adjustment reflects that there is now $2 more to distribute so the Modified Dietz adjustment is now $27/3 instead of $25/3. (2) The denominator adjustment in the Modified Dietz formula is now 1/3* 27 = $9 Fund return = ($10 + $0.20 -$4.50 +$5) / ($270 - $9) = 4.10%
(f) Returns at the ―property level‖ would be determined by focusing only on those operating cash flows related to properties in the fund and ignoring cash balances, leverage, fund fees, etc. Note: NOI = $10 and is assumed to occur at the rate of $3.33 per month during the quarter. Property appreciation was $5. RD (Property Level) Property return = ($10 + $5) / ($500 – 1/3 × $10) = 3.02 % Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-319
Note that the fund returns even is higher even though there is some cash drag and fund management fees. The favorable leverage increased the fund return compared to the unleveraged property return. Of course this also results in more risk for the fund compared to the property itself.
Problem 23-4 Comparing IRR with Arithmetic Mean (a) Year 0 1 2 3 4 5
Fund Value Return Return Relative 100 110 10.00% 1.1000 120 9.09% 1.0909 110 -8.33% 0.9167 105 -4.55% 0.9545 100 -4.76% 0.9524
Arithmetic mean Geometric mean
0.29% 0.00%
(b)
Arithmetic Mean Return .29%
(c)
Geometric Mean Return
(d)
The Geometric Mean reflects annual compounding for each period. The Arithmetic Mean does not reflect any compounding of the return. Even though an investment of $100 would still be worth $100 after 5 years, and the Geometric Mean (IRR) is zero, the Arithmetic Mean shows a 0.37% return.
0%
Problem 23-5 (a)
Relative to the Industry Index, Bluestone is over weighted in office (35% vs. 10%) and in retail (40% vs. 15%). It is underweighted in apartments, industrial and hotels.
(b)
Relative to the Industry Index, Bluestone is overweighed in the South (35% vs. 15%). It is underweighted in the East and has the same allocations in the North and West.
(c)
Bluestone underperformed the Industry Index (8.7% - 9.8%) or by 1.1%. What was this due to? ATTRIBUTION ANALYSIS: Property Type
ALLOCATION
Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-320
Brinson-Hood-Beebower (BHB) Allocation Sector
Industry Index
Fund
Industry Diff in weights x Index Returns Ind. Index Ret.
Weights Apartment Hotel Industrial Office Retail TOTAL
20.00% 0.00% 5.00% 35.00% 40.00% 100.00%
35.00% 10.00% 30.00% 10.00% 15.00% 100.00%
12.00% 14.00% 8.00% 6.00% 8.00% ---
Fund
Industry Index
-1.80% -1.40% -2.00% 1.50% 2.00%
-1.70%
SELECTION
Selection Sector
Industry Index
Weight Apartment Hotel Industrial Office Retail TOTAL
Selection Allocation Cross product Fund Benchmark
35.00% 10.00% 30.00% 10.00% 15.00% 100.00%
Returns 14.00% 16.00% 10.00% 4.00% 10.00%
12.00% 14.00% 8.00% 6.00% 8.00%
Diff in returns x Benchmark 0.70% 0.20% 0.60% -0.20% 0.30% 1.60%
1.6% -1.7% -1.0% -1.1%
ANALYSIS: The fund did a better job selecting individual properties, but its property type allocation decision hurt its performance. The interaction of the two was -1%. (d) ATTRIBUTION ANALYSIS: Geographic Region ALLOCATION
Sector
Fund
Industry Index
Industry Index Returns
Diff in weights × Ind. Index
Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-321
Ret.
North South East West TOTAL
Weights 30.00% 35.00% 35.00% 15.00% 10.00% 25.00% 25.00% 25.00% 100.00% 100.00%
12.00% 14.00% 8.00% 6.00% ---
Industry Index
Industry Index
-0.60% 2.80% -1.20% 0.00% 1.00%
SELECTION
Fund
Sector Weight North South East West TOTAL
30.00% 35.00% 10.00% 25.00% 100.00%
Returns 11.00% 12.00% 7.00% 2.00%
12.00% 14.00% 8.00% 6.00%
Diff in returns × Benchmark weight -0.30% -0.70% -0.10% -1.00% -2.10%
Summary Selection Allocation Cross product Fund - Benchmark
-2.1% 1.0% 0.0% -1.1%
ANALYSIS: When allocation is broken down into geographic areas, we see that the fund did a good job of picking what geographic areas to be in with allocation giving them a 1.0% higher return. But property selection is now -2.1%. This might appear to be a conflict with the results above when allocation was by property type. But because we are not using geographic areas to analyze allocation, the property types that they picked within the geographic areas is now captured in the selection effect. Another way we could have done this is to do the breakdown by combinations of region and division in a single analysis, e.g., south apartments, south retail, etc. which would result in 5 property types times 4 regions or 20 different combinations with weights and returns for each to compare to the benchmark. But we don’t have the data in this problem to do that.
Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-322
(e) The total allocation effect is the same at -1.70% but the contribution of each sector is now more meaningful and indicates that all but the allocation to industrial hurt performance. Brinson-Fachler (BF) Allocation Alternative Methodology
Sector
Fund
Benchmark Weights 35.00% Apartment 20.00% 0.00% 10.00% Hotel 5.00% 30.00% Industrial 35.00% 10.00% Office 40.00% 15.00% Retail TOTAL 100.00% 100.00%
Benchmark Relative Return =Sector Benchmark Returns Total Benchmark Return 2.20% 4.20% -1.80% -3.80% -1.80%
Diff in weights × Benchmark Relative Return -0.33% -0.42% 0.45% -0.95% -0.45% -1.70%
(f) The total allocation effect is the same at -1.00% but the contribution of each sector is now more meaningful and indicates that all but the allocation to the North helped performance.
Sector North South East West TOTAL
Fund Weights 30.00% 35.00% 10.00% 25.00% 100.00%
Benchmark
Benchmark Relative Return =Sector Benchmark Returns Total Benchmark Return
35.00% 15.00% 25.00% 25.00% 100.00%
2.20% 4.20% -1.80% -3.80%
Diff in weights × Benchmark Relative Return -0.11% 0.84% 0.27% 0.00% 1.00%
(g) We can risk-adjust the return as follows: RAP = RS − (RB − RF) × (βS − 1) RAP = 14% − (9.8% -1%) × (1.25 − 1) RAP = 11.8% The risk-adjusted apartment return of 11.8% is now slightly less than the benchmark apartment return of 12%. Note that the overall benchmark return of 9.8% is used for the risk adjustment rather than the apartment benchmark return. This is because the risk adjustment is based on how the ―market‖ performed as proxied by the industry benchmark. Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-323
Problem 23-6 (a) Investment Preferred return
$100 8%
Fund Cash Flow for Distribution After Management Fee
Year 0 1 2 3 4 5 6 7 8 9 10
$5.00 $10.00 $20.00 $30.00 $50.00 $40.00 $30.00 $20.00 $10.00 $5.00
Beginning Capital Balance
then 80 /20 split after catchup
Pref Return
$100 $103.00 $101.24 $89.34 $66.49 $21.81
$8.00 $8.24 $8.10 $7.15 $5.32 $1.74
Beg Capital Contribution & Balance plus Distributions to Pref Return Pref Return ($100) $108.00 $5.00 $111.24 $10.00 $109.34 $20.00 $96.49 $30.00 $71.81 $50.00 $23.55 $23.55 IRR
Ending Capital Balance $103.00 $101.24 $89.34 $66.49 $21.81 $0.00
8.00%
The preferred return of 8% is reached in year 6 as shown above. The IRR on the cash flows in the Pref Return column is 8% and the capital account balance goes to zero indicating that the money has been return to the investor plus an 8% return on the outstanding capital balance each year. (b) Only $23.55 of the fund distributions in Year 6 was needed to achieve the preferred return. The remainder will be split 80% to the investor and 20% to the manager. (c) Fund Cash Total Flow less Distributions Pref Return to Investors
Year 0 1 2 3 4 5 6 7 8 9 10
$0.00 $0.00 $0.00 $0.00 $0.00 $16.45 $30.00 $19.92 $10.00 $5.00
Distribution Investor to Manager Total as Promote cash flow ($100) $5.00 $5.00 $10.00 $10.00 $20.00 $20.00 $30.00 $30.00 $50.00 $50.00 $36.71 $3.29 $36.71 $24.00 $6.00 $24.00 $16.00 $4.00 $16.00 $8.00 $2.00 $8.00 $4.00 $1.00 $4.00 $16.29 IRR
15.11%
The investor will earn 15.11% over the 10 years. Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-324
(d) The manager will receive $16.29 million total up to year 10.
Problem 23-7 Following is a summary of the statistics for each of the measures:
Variance Stdev Mean
Fund Return 0.17% 4.10% 14.60%
Benchmark Return 0.0636% 2.52% 11.20%
Fund Benchmark 0.03% 1.85% 3.40%
Risk-free rate 0.00% 0.00% 2.0000%
Fund Exces Benchmark return Excess return 0.17% 0.06% 4.10% 2.52% 12.60% 9.20%
(a) The Sharpe ratio for the fund is 12.60% / 4.1% = 3.07 The Sharpe ratio for the benchmark is 9.20% / 2.52% = 3.65. The fund has a lower Sharpe ratio (lower return per unit of risk) (b) The first step is to calculate the correlation and covariance between the fund returns and the benchmark returns. The result is a follows: Correlation Covariance
0.9547 0.00099 = correlation x Stdev Prop x Stdev Benchmark
Beta = Covariance / Variance of the benchmark Beta = 0.00099 / .000636 = 1.55 (1.5535 if additional decimal places used) Beta could also have been found by a regression or trendline of the fund returns vs the benchmark returns as shown below :
(c) The Treynor ratio for the fund is 12.6% / 1.5535 = 8.11% The Treynor ratio for the benchmark is 9.20% / 1 = 9.20% Thus, the fund also has a lower Treynor ratio (lower return per unit of beta risk) Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-325
(d) The tracking error is 1.85% (standard deviation of the difference in returns between the fund and the benchmark). (e) The beta for the fund is 1.5535 as shown above. (f) To calculate Jensen’s alpha we first need to calculate the expected fund return.
Expected return = 2% + 9.2% × 1.5535 = 16.29%
Jensen’s alpha is the actual return less the expected return. Jensen’s alpha = 14.60% - 16.29% = -1.69%
The fund appears to have more risk per unit of return than the benchmark as indicated by the lower Sharpe ratio and the lower Treynor ratio. The fund has a higher beta which suggests that it should have a higher expected return. But its expected return is greater than the actual return over the 10 years resulting in a negative alpha. Based on these risk measures, the fund does not appear to be a good investment.
Copyright © 2022 McGraw Hill. All rights reserved. No reproduction or distribution without the prior written consent of McGraw Hill.
1-326