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APPENDIX G LEARNING OBJECTIVES 1. DISTINGUISH BETWEEN SIMPLE AND COMPOUND INTEREST. 2. SOLVE FOR FUTURE VALUE OF A SINGLE AMOUNT. 3. SOLVE FOR FUTURE VALUE OF AN ANNUITY. 4. IDENTIFY THE VARIABLES FUNDAMENTAL TO SOLVING PRESENT VALUE PROBLEMS. 5. SOLVE FOR PRESENT VALUE OF A SINGLE AMOUNT. 6. SOLVE FOR PRESENT VALUE OF AN ANNUITY. 7. COMPUTE THE PRESENT VALUE OF NOTES AND BONDS.
8. COMPUTE THE PRESENT BUDGETING SITUATIONS.
VALUES
IN
CAPITAL
9. USE A FINANCIAL CALCULATOR TO SOLVE TIME VALUE OF MONEY PROBLEMS.
APPENDIX G REVIEW Value of Interest 1.
(L.O. 1) Interest is payment for the use of another person’s money. The amount of interest involved in any financing transaction is based on three elements: a. Principal: The original amount borrowed or invested. b. Interest Rate: An annual percentage of the principal. c. Time: The number of years that the principal is borrowed or invested.
2.
Simple interest is computed on the principal amount only. Simple interest is usually expressed as: Interest = Principal X Rate X Time
3.
Compound interest is computed on principal and on any interest earned that has not been paid or withdrawn. It is the return on (or growth of) the principal for two or more time periods.
Future Value of a Single Amount 4.
(L.O. 2) The future value of a single amount is the value at a future date of a given amount invested assuming compound interest. Future value is usually expressed as: FV = P X (1 + i)n FV = future value of a single amount P = principal i = interest rate for one period n = number of periods
5.
The Future Value of 1 table is used for obtaining a 5-digit decimal number which is multiplied by the principal to calculate the future value.
Future Value of an Annuity 6.
(L.O. 3) The future value of an annuity is the sum of all the payments (receipts) plus the accumulated compound interest on them. In computing the future value of an annuity, it is necessary to know the (1) interest rate, (2) the number of compounding periods, and (3) the amount of the periodic payments or receipts. When the periodic payments or receipts are the same in each period, the future value can be computed by using a future value of an annuity of 1 table.
Present Value Variables 7.
(L.O. 4 and 5) The present value is based on three variables: (1) the dollar amount to be received (future amount), (2) the length of time until the amount is received (number of periods), and (3) the interest rate (the discount rate). PV = FV/(1 + i) PV = present value FV = future value i = interest rate
8.
The present value of 1 may also be determined through tables that show the present value of 1 for n periods.
Present Value of an Annuity 9.
(L.O. 6) In computing the present value of an annuity, it is necessary to know (1) the discount rate, (2) the number of discount periods, and (3) the amount of the periodic receipts or payments. When the future receipts are the same in each period, there are two other ways to compute the present value. First, the annual cash flow can be multiplied by the sum of the three present value factors. Second, annuity tables may be used.
Time Periods and Discounting 10.
Discounting may also be done over shorter periods of time such as monthly, quarterly, or semiannually. When the time frame is less than one year, it is necessary, to convert the annual interest rate to the applicable time frame.
Computing the Present Value of a Long-Term Note or Bond 11.
(L.O. 7) The present value (or market price) of a long-term note or bond is a function of three variables: (1) the payment amounts, (2) the length of time until the amounts are paid, and (3) the discount rate. When the investor’s discount rate is equal to the bond’s contractual interest rate, the present value of the bonds will equal the face value of the bonds.
Computing the Present Values in Capital Budgeting Situations 12.
(L.O. 8) The decision to make long-term capital investments is best evaluated using discounting techniques that calculate the present value of the cash flows involved in a capital investment.
13.
If the net present value of a capital investment is positive, the proposal should be accepted (make the investment). If the net present value is negative, the proposal should be rejected.
Using a Financial Calculator 14.
(L.O. 9) Financial calculators can be used to solve the same and additional problems as those solved with time value of money tables. The amounts for all of the known elements of a time value of money problem are entered into a financial calculator and it solves for the unknown element. Financial calculators are particularly useful in situations involving interest rates and compounding periods not presented in the compound interest tables.
LECTURE OUTLINE A.
Nature of Interest 1. Interest is payment for the use of another person’s money. It is the difference between the amount borrowed or invested (called the principal) and the amount repaid or collected. 2. The amount of interest involved in any financing transaction is based on: a.
Principal (p): The original amount borrowed or invested,
b.
Interest Rate (i): An annual percentage of the principal,
c.
Time (n): The number of years that the principal is borrowed or invested.
3. Simple interest is computed on the principal amount only.
4. Compound interest is computed on principal and on any interest earned that has not been paid or withdrawn. It is the return on the principal for two or more time periods. B.
Future Value of a Single Amount 1. The future value of a single amount is the value at a future date of a given amount invested assuming compound interest. 2. The future value of a single amount can be computed using the following formula: FV = p X (1 + i )n p = principal; i = interest rate; n = number of periods. 3. Another way to compute the future value of a single amount is to use Table 1, which shows the future value of 1 for n periods. 4. Using Table 1, the future value of a single amount is computed by multiplying the principal by the appropriate future value of 1 factor.
C.
Future Value of an Annuity 1. An annuity is an equal dollar amount of payments or receipts. 2. The future value of an annuity is the sum of all the payments (receipts) plus the accumulated compound interest on them. 3. In computing the future value of an annuity, it is necessary to know the: a.
interest rate,
b.
number of compounding periods,
c.
amount of the periodic payments or receipts.
4. The future value of an annuity can be computed by using Table 2, which shows the future value of 1 to be received periodically for a given number of periods.
D.
Present Value Variables 1. The present value is based on the: a.
dollar amount to be received (future amount),
b.
length of time until the amount is received (number of periods),
c.
interest rate (the discount rate).
2. The process of determining the present value is referred to as discounting the future amount.
E.
Present Value of a Single Amount 1. The present value of a single amount is the value today of a future amount to be received (or paid), assuming compound interest. 2. The present value of a single amount can be computed using the following formula: PV = FV รท (1 + i )n FV = future amount; i = interest rate; n = number of periods. 3. Another way to compute the present value of a single amount is to use Table 3, which shows the present value of 1 for n periods. 4. Using Table 3, the present value of a single amount is computed by multiplying the future amount by the appropriate present value of 1 factor.
F.
Present Value of an Annuity 1. The present value of an annuity is the value today of a series of future receipts or payments, discounted assuming compound interest. 2. In computing the present value of an annuity, one needs to know the: a.
discount rate.
b.
number of discount periods.
c.
amount of the periodic receipts or payments.
3. The present value of an annuity can be computed by using Table 4, which shows the present value of 1 to be received periodically for a given number of periods.
G.
Computing the Present Value of a Long-Term Note or Bond 1. The present value (or market price) of a long-term note or bond is a function of the: a.
payment amounts.
b.
length of time until the amounts are paid.
c.
discount rate.
2. The payment amounts are made up of two elements: a.
a series of interest payments (an annuity),
b.
the principal amount (a single sum).
3. To compute the present value of the bond, one must discount both the interest payments and the principal amount. a.
Multiply the principal amount by the appropriate present value factor from Table 3.
b.
Multiply the amount of the interest payments by the appropriate present value factor from Table 4.
c.
Add the present value of the principal amount to the present value of the interest payments to determine the present value of the bond.
4. Since interest on bonds is paid semiannually, the discount rate used in computing the present value of the bonds is the semiannual rate.
H.
Computing the Present Values in a Capital Budgeting Decision 1. The decision to make long-term capital investments is best evaluated using discounting techniques that recognize the time value of money. This is done by calculating the present value of the cash flows involved in a capital investment. 2. When the present value of the cash receipts (inflows) from a capital investment exceeds the present value of the cash payments (outflows), the net present value is positive, and the investment should be accepted. 3. When the present value of the cash payments (outflows) for a capital investment exceeds the present value of the cash receipts (inflows), the net present value is negative, and the investment should be rejected.
I.
Using Financial Calculators. 1. Financial calculators can be used to solve present and future value problems using the following keys. a.
N = Number of periods
b.
I = interest rate per period
c.
PV = present value (occurs at the beginning of the first period)
d.
PMT = payment (all payments are equal, and none are skipped)
e.
FV = future value (occurs at the end of the last period)
10 MINUTE QUIZ Circle the correct answer. True/False 1.
Simple interest is computed on the principal and any interest earned that has not been paid or received. True
2.
The future value of an annuity is the sum of all the payments plus the accumulated compound interest on them. True
3.
False
In computing the present value of an annuity, it is necessary to know the discount rate, the number of discount periods, and the amount of the periodic payments. True
5.
False
The process of determining the present value is referred to as discounting the present amount. True
4.
False
False
To compute the present value of a bond, both the interest payments and the principal amount must be discounted. True
False
Multiple Choice 1.
Interest that is computed on the principal and any interest earned is called a. simple interest. b. present interest. c. future interest. d. compound interest.
2.
The value at a future date of a given amount invested assuming compound interest is the a. compounded value of a single amount. b. compounded value of an annuity. c. future value of a single amount. d. future value of an annuity.
3.
The process of determining the present value is referred to as discounting the a. compound amount. b. future amount. c. present amount. d. simple amount.
4.
In computing the present value of an annuity, it is not necessary to know the a. discount rate. b. number of discount periods. c. amount of the periodic payments. d. year the payments will begin.
5.
Cogswell Company issued 6%, 10-year bonds that pay interest semiannually. The discount rate of interest for such bonds is 8%. In computing the present value of these bonds, the appropriate discount rate is a. 8%. b. 6%. c. 4%. d. 3%.
ANSWERS TO QUIZ True/False 1. 2. 3. 4. 5.
False True False True True
Multiple Choice 1. 2. 3. 4. 5.
d. c. b. d. c.
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