METHODS OF PROJECT APPRAISAL FM A – M ANAG EM ENT AC C OUNTI NG
LEARNING OUTCOMES 1. Explain and illustrate the difference between simple and compound interest and between nominal and effective interest rates 2. Explain and illustrate compounding and discounting 3. Explain the distinction between cash flow and profit and the relevance of cash flow to capital investment appraisal 4. Identify and evaluate relevant cash flows for individual investment decisions 5. Explain and illustrate the NPV and IRR method of discounted cash flow 6. Calculate present value using annuity and perpuity formulae 7. Calculate NPV, IRR and payback (discounted and non-discounted) 8. Interpret the results of NPV, IRR and payback calculations of investment viability
VALUES & DISCOUNTING DISCOUNT RATE Interest rate used to compute present values of future cash flows
PRESENT VALUE Value today of a future cash flow
FUTURE VALUE Amount to which an investment will row after earning interest
DISCOUNT FACTOR Present value of a $1 future payment
FUTURE VALUE • Suppose you have $200 and the interest rate on government securities is r. Investing $200 today you can get $200 x (1+r) next year, and $200 x (1+r)^t in t years • So, future value of your money is given by: FV = $200 x (1+r)^t For example, the future value of $400,000 if interest is paid annually at a rate of 5% for one year is: $400,000 x (1+0.05) = $420,000 Hence, $420,000 today is worth $400,000 Time value of money: A dollar today is worth more than a dollar tomorrow
PRESENT VALUE • Present value (PV) converts future cash flows to their current values • Suppose, the future cash flow at time t is Ct. Then PV today is such that its future value is equal to Ct Ct = PV x (1+r)^t PV = Cash flow at time, t
(1+r)^t
DISCOUNT FACTOR Discount factor (DF) as present value of $1
DF =
1 `
(1+r)^t
Discount factors can be used to compute the present value of any cash flow PV = DF x Ct Discount factor can be thought of as a today’s value of $1 at time-t
DISCOUNT RATE • The discount rate is the reward investors demand for accepting delayed payment • Investors demand what they could receive from risk-equivalent investment alternatives, This is because your value of $1 depends on what you alternatively can do with it • Discount rate is also called opportunity cost of capital because it is the return forgone by investing in a capital project rather than investing in freely available securities – DF reflects the minimal investment made today that gives you $1 in the future if you pursue your alternative investment
TEST YOUR UNDERSTANDING 1 The details of an investment project are as follows:
Cost of asset bought at the start of the project
$80,000
Annual cash inflow Cost of capital Life of the project
$25,000 5% each year 8 years
The present value of the project is: A -$120,000 B $120,000 C $81,575 D -$81,575
ANSWER - TEST YOUR UNDERSTANDING 1 ANSWER : C Outflow Cash inflow $25,000 each year for 8 years Present value of project
$ (80,000)
DF 1,000
$ (80,000)
25,000
6,463
161,575 $81,575
CASH FLOW • What is cash flow A measure of a company's financial health. Equals cash receipts minus cash payments over a given period of time; or equivalently, net profit plus amounts charged off for depreciation, depletion, and amortization. www.investorwords.com The excess of cash revenues over cash outlays in a given period of time (not including non-cash expenses) 10
CONCEPT OF TIME VALUE OF MONEY • Capital project cash flows tend to be over a long term period.Thus we must consider the time value of money. • Money received today is worth more than the same sum received in the future. • DCF takes into account this time value when evaluating investments by discounting the cash flows. • Students need to understand compounding &discounting
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DCF:BASIC CONCEPT-SIMPLE N COMPOUND • TERMs – P, principal or amount borrowed or invested today – r, rate of interest per annum (can also be cost of capital) – n, time in years – I, interest – S, sum to be received or total saved after n years Simple interest
S = P + Prn Interest on principal alone .Principal is not added with interest to compute future interest. If compound interest interest is added to principal to compute future interest and future interest is based on newly changed principal
S = P(1+r)n
r is interest rate in decimal or proportion
• Compounding normally done annually but can be monthly, qtrly
• If more frequent must find EIR(effective interest rate) • EIR is the equivalent annual rate of interest when interest is compounded at shorter interval like quarterly, monthly. • Effective annual interest rate ,
EIR = (1+r)n -1,
n= number of times interest is added in 1 year . (quarter =4 times, monthly = 12 times)
• 2% compounded per month so EIR = (1+ 0.02) 12 -1 12
EXAMPLES a. Invest $800 at 10% p. a
a. $1200 ( S=P+Prn)
How much is saved after 5 years .Simple int.
b. $2508.80 { S=P(1+r)n}
b. Invest $2000 with compounding interest 12% p.a after 2 years
c. S= 2400 r= 0.05 n = 2 Reverse S= P(1+r)n
How much is saved after 2 yrs c. After 2 years Faris’s investment is $2,400.The interest rate is 5%.
How much will he need to save now? Compounding is assumed
P = S/(1+r)n
= $2176.87
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MORE EXAMPLES…. 1.Principal invested today OR Present value (PV) if $60,000 received at the end of yr 6 at 15% per annum
1. P=PV $25,940 S = P(1+r)n 60k = P(1.15)6 =( 60000/1.15^6) =60000/2.3131
2.What is PV of $500 payable for each of 3 years at discount rate10%
If use PV table 60000/0.432 factor 15% , n=6
(You are to find the PV of three payments of $500 received over 3 yrs whilst discount rate is 10%) PV of period n at r rate is = Sum/(1+r)n
2. PV of 500 at n=1,=500/1.1 +PV of 500 n=2, 500/1.1^2 +PV of 500 n=3, 500/1.1^3 OR 500 x /1.1 +500x1/1.1^2+500x1/1.1^3 500*0.909+500*0.826+500*0.751 OR 500 * 2.487 = $1,243.50 14
ANNUITIES &PERPETUITIES • Annuities are when a constant sum of money received/paid for a given number of year • Eg like installments of insurance premiums, loan installments – PV of annuities = annuity x annuity factor – Annuity factor is derived from compound interest formula – Example factor for annuity of $200 received over 5 yrs at 8% – Answer: 200 x 1-(1.08)^-5 =799
OR 200 x 3.993 =798
0.08
• Perpetuities are those annuities (constant cashflows) which continues forever/indefinitely – PV of perpetuity = Cashflow or perpetuity/ cost of capital % – Example as above $ 200 received each year indefinitely ,8% cost of capital. – Answer: PV of this $200 perpetuity = 200/0.08= $2500
– Can also replace cost of capital with annual interest rate 15
METHODS OF PROJECT APPRAISAL • The key methods of project appraisal are: –The payback period –Net present value –Discounted payback period –Internal rate of return (IRR)
THE PAYBACK PERIOD • The payback period – time taken for the initial investment to be recovered in the cash inflows from the project. The payback method is particularly relevant if there are liquidity problems or if distant forecasts are very uncertain • The payback period method is one which gives greater weight to cash flows generated in earlier years • The payback period is the length of time required before the total cash inflows received from the project is equal to the original cash outlay
EXAMPLE – THE PAYBACK PERIOD A new project will cost $100,000 and will last for 5 years with no scrap value. The project is expected to generate operating cash flows each year as follows: Year 1 20,000 Year 2 30,000 Year 3 40,000 Year 4 50,000 Year 5 30,000 The cost of capital is 10% (a) Calculate the payback period (b) (b) Calculate the discounted payback period
ANSWER – PAYBACK PERIOD METHOD Cash inflow 1 2 3 4 5
20,000 30,000 40,000 20,000 30,000
Cumulative Cash inflow 20,000 50,000 90,000 140,000 170,000
Payback period = 3 + 10,000 / 50,000
Discounted Cash Inflow 18,180 24,780 30,040 34,150 18,630
Cumulative discounted Cash Inflow 18,180 42,960 73,000 107,150 125,780
= 3.2 years
Discounted payback period = 3 + 27,000 / 34,150 = 3.79 years
PAYBACK EXAMPLE Year
Cashflow’000
• Answer
0
(2000)
• Payback period is 4 years
1
500
2
500
• Add all cash in flows until equal the cash out flow at year 0
3
400
4
600
5
500
• 500+………+600 at year 4 • It takes the project 4 year to pay back the investment at year 0
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PAYBACK EXAMPLE • Project costing $1.8 million lasts 5 years with cash flows of
Answer
Year
300+500+600 = 1.4m
At 3 years At 4 years
1
$300,000
2
500,000
3
600,000
Payback is between 3 to 4 years ( to recover 1.8m)
4
800,000
3 years +
5
500,000
3years + 0.5=3.5 years
1.4m +0.8m= 2.2m
0.4m/0.8m
Q when is the payback? 21
PAYBACK PERIOD ADVANTAGES
DISADVANTAGES
• Simple TO UNDERSTAND
• Tend to reject those project which has lower CF as beginning
• Useful when a quick or short term is preferred • Used as primary screening tool before using more comprehensive • Minimises time risk as because earlier CF is more certain than later one
• Ignore time value of money • Disregard CF after payback
• It is not measure of profitability.
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NET PRESENT VALUE • Net present value (NPV) is the present value of all future cash flows minus the required investment NPV = - Cost + C
1+r NPV is decreasing function of r if C > 0 NPV
r
EXAMPLE Valuing an Office Building Step 1: Forecast Cash Flows • Cost of building = 370
• Sales price in Year 1: C1 = 420 Step 2: Estimate opportunity cost of capital • If equally risky investments in the capital market offer a return of 5%, then Cost of capital, r = 5%
EXAMPLE Step 3: Discount future cash flows
PV =
C (1+r)
=
420
= 400
(1+0.05)
Step 4: Subtract initial cost from PV to determine if PV exceeds investment cost: NPV = 400 – 370 = 30 Accept investments that have positive net present value. This called the net present value rule
NET PRESENT VALUE • Under this approach to investment appraisal we look at all the expected cash flows that will arise from an investment. • If overall the investment generates a cash surplus then we will accept and invest; if however there is an overall cash deficit then we will reject the investment. • However, we also need to take into account interest on the investment in the project. This is either because we have needed to borrow money and therefore be paying interest, or because we are using money that could otherwise have been invested and be earning interest. • In either case, we account for the interest by discounting the future cash flows to get the present value. The overall surplus or deficit is known as the Net Present Value.
EXAMPLE – NET PRESENT VALUE A new project will cost $80,000 and is expected to last 4 years. At the end of 4 years it is expected to have a scrap value of $10,000. The project is expected to generate operating cash flows each year as follows: Year 1
20,000
Year 2
30,000
Year 3
40,000
Year 4
10,000
Assume that all operating cash flows occur at the ends of years.
If interest is 10% p.a., calculate the Net Present Value of the project and state your decision as to whether or not we should invest.
ANSWER – NET PRESENT VALUE 0 1 2 3 4
(80,000) 20,000 30,000 40,000 20,000
D.F @ 10% 1,000 0.909 0.826 0.751 0.683
NPV
P.V (80,000) 18,180 24,780 30,040 13,660 6,660
The NPV is positive and thus should invest in the project
INTERNAL RATE OF RETURN • One problem in practice with basing our decision on the Net Present Value is that it will usually be impossible for a company to determine their cost of capital (or interest cost) accurately.
• In these circumstances, it is therefore often useful to calculate a ‘breakeven’ interest rate of the project. • This is known as the Internal Rate of Return (IRR) and is the rate of interest at which the project gives a NPV of zero.
IRR -INTERNAL RATE OF RETURN • The rate of return an investment earns • At the IRR, the NPV should be Zero( 0) • IRR compared to the minimum acceptable rate of return of company (or cost of capital)
• Accept project if IRR is higher than cost of capital • To find which rate NPV is zero – Interpolation from two NPV one (-) another (+)
– Graphical
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INTERNAL RATE OF RETURN RULE IRR RULE: Accept projects with r < IRR because NPV > 0
WORKED EXAMPLE Yr
CF’000 DF(12%)
DF(20%)
PV@
PV@
12%’000
20%’000
0
-460
1.000
1.000
-460
-460
1
50
0.893
0.833
44.65
41.65
2
140
0.797
0.694
111.58
97.16
3
180
0.712
0.579
128.16
104.22
4
250
0.636
0.482
159
120.5
5
160
0.567
0.402
90.72
64.32
6
-40
0.507
0.335
-20.28
-13.4
53.83
-45.55
NPV
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INTERPOLATION IRR= %NPV+ NPV+
x Diff %
NPV + plus NPV=
12% + 53.83
x 8
53.83+ 45.55
=
16%
Note: 8 Is the difference between 20% and 12% Lower% is NPV +ve while higher % NPV is -ve
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IRR â&#x20AC;&#x201C; IF BOTH NPV POSITIVE Given NPV at the following discount rates:
11% per annum NPV 35,170 15% per annum NPV 6,040 IRR
=15 + [ 6040/(35170-6040)] x 4 =15+ 0.829 = 15.8%
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NPV DIFFERENT CASH FLOWS YR
CASH flow
Discount factor 9%
PV
0
40000
1.000 (1/(1.09^0))
-40000
1
10000
0.917 ( 1/(1.09)^1
9170
2
10000
0.842 (1/(1.09)^2
8420
3
22000
0.772 (1/(1.09)^3
16984 NPV= -5426 reject
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NPV SIMILAR CASH FLOWS YR
CASH flow
Discount factor 9%
PV
0
-28000
1.000
-28000
1
10000
0.917 ( 1/(1.09)^1
9170
2
10000
0.842 (1/(1.09)^2
8420
3
10000
0.772 (1/(1.09)^3
7720 =
25310
NPV= -2690 reject YR
CASH flow
Discount factor 9%cumulative /annuity
PV
0
-28000
1.000
-28000
1
10000
2
10000
3
10000
2.531 (sum of yr 1-3)
25310 NPV= -2690
Capital Investment
reject
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TEST YOUR UNDERSTANDING 2 An education authority is considering the implementation of a CCTV (closed circuit television) security system in one of its schools. Details of the proposed project are as follows: Life of project
5 years
Initial cost
$75,000
Annual savings: Labour costs
$20,000
Other costs $5,000 NPV at 15% $8,800 Calculate the internal rate of return for this project to the nearest 1% A.
16%
B.
18%
C. 20% D. 22%
ANSWER - TEST YOUR UNDERSTANDING 2 ANSWER: C Try 20% Year 0 1-5
Cash $ (75,000) 25,000
20% 2,991
PV $ (75,000) 74,775 (225)
TEST YOUR UNDERSTANDING 3 The following measures have been calculated to appraise a proposed project The internal rate of return is 12% The return on capital employed is 16% The payback period is 4 years Which of the following statements is correct?
A. the payback is less than 5 years so the project should go ahead B. the IRR is lower than the return on capital employed so the project should not go ahead
C. the IRR is greater than the cost of capital so the project should go ahead D. the IRR is positive so the project should go ahead
ANSWER - TEST YOUR UNDERSTANDING 3 ANSWER: C • Statement A is not correct as there is no company policy to confirm the payback is appropriate. Statement B is not correct as the IRR and ROCE are not comparable. Statement D is not correct as the IRR is always a positive whether the project is acceptable or not. • Statement C is correct as the IRR must be greater than the cost of capital (the discount rate) used to appraise the project as the project has a return therefore a positive NPV at the company’s cost of capital so the project should not go ahead.
TEST YOUR UNDERSTANDING 4 JAH Company is about to invest $400,000 in machinery and other capital equipment for a new product venture. Cash flows for the first three years are estimated as follows JAH Company requires a 17% return for projects of this type. What is the NPV of this venture?
A. -$154,670 B. $45,010
C. $220,450 D. $154,670
ANSWER â&#x20AC;&#x201C; TEST YOUR UNDERSTANDING 4 ANSWER: D Year Cash ($000) 17% discount factor 0 (400) 1,000 1 210 0.855 2 240 0.731 3 320 0.624
Present value ($000) (400.00) 179.55 175.44 199.68 154.67
TEST YOUR UNDERSTANDING 5 (208) A company has determined that the net present value of an investment project is $17,706 when using a 10% discount rate and $(4,317) when using a discount rate of 15%. Calculate the internal rate of return of the project to the nearest 1%. A. 13% B. 14% C. 15% D. 16%
ANSWER â&#x20AC;&#x201C; TEST YOUR UNDERSTANDING 5 ANSWER: B 10 +
$17,706 ($17,706 + $4,317)
x (15-10) = 14%
TEST YOUR UNDERSTANDING 6 A company is considering an investment of $400,000 in new machinery. The machinery is expected to yield incremental profits over the next five years as follows: Year Profit ($) 1 175,000 2 225,000 3 340,000 4 165,000 5 125,000 Thereafter, no incremental profits are expected and the machinery will be sold. It is company policy to depreciate machinery on a straight line basis over the life of the asset. The machinery is expected to have a value of $50,000 at the end of year 5. Calculate the payback period of the investment in this machinery to the nearest 0.1 years. A. 0.9 years B. 1.3 years C. 1.5 years D. 1.9 years
ANSWER – TEST YOUR UNDERSTANDING 6 ANSWER: C Depreciation is not a cash flow so needs to be added back to profit to calculate cash flows. Depreciation on straight line basis = ($400,000 − $50,000)/5 = $70,000 per year
Year
Profit ($)
0
Cash flow ($)
Cumulative cash flow ($)
(400,000)
(400,000)
1
175,000
245,000
(155,000)
2
225,000
295,000
140,000
Payback period = 1 + 155 / 295 years = 1.5 years to nearest 0.1 years
RELEVANT CASH FLOW 1. FUTURE •Only future cash flows that occur as a result of the decision should be considered, e.g. any future costs or revenue •Sunk costs (i.e. costs that have already been incurred in the past) are not relevant to the decision and should be ignored – we cannot change the past 2. CASH FLOW
•Only cash items are relevant to the decision •For example, depreciation is not relevant because it is not a cash flow
RELEVANT CASH FLOW 3. INCREMENTAL •Only extra cash flows that occur as a result of the decision should be considered, e.g. extra costs or revenues •Fixed costs should be ignored unless there is an incremental fixed costs as a result of the decision
•Committed costs (i.e. costs that are unavoidable in the future) are not affected by the decision and should therefore be ignored. •Opportunity cost should be included – look at the next best alternative use of a resource
NON RELEVANT CASH FLOW Costs which are not relevant:
– Past costs (sunk costs) which have already been spent. – Non-cash flow costs, eg, depreciation, notional rent, notional interest. – General absorbed OH; only cash OH are relevant. – Committed costs ie future spending already committed by separate previous decisions. – Joint Cost
OTHER CONCEPTS NOTIONAL COSTS Hypothetical accounting costs to reflect the use of a benefit for which no actual cash expense is incurred.
AVOIDABLE COSTS The specific costs of an activity/sector of a business which would be avoided if that activity/sector did not exist.
UNAVOIDABLE COSTS Costs which would be incurred whether or not the activity exists are known as unavoidable costs.
DIFFERENTIAL/INCREMENTAL COSTS The difference in relevant costs between alternatives
VARIABLE COSTS & FIXED COSTS • Generally VC are relevant costs & FC are irrelevant costs Exceptions: • A VC can be a sunk cost • A FC can be a relevant cost – directly attributable or specific FC
EXAMPLE â&#x20AC;&#x201C; NOTIONAL COST Notional cost is an imaginary cost which is sometimes included in the cost units and cost centers to make costing estimates more realistic or simply more challenging especially when the performance of cost unit and cost center is in question in comparison with such other competitors which are not enjoying the same level of benefits. Example:
Entity has vacant piece of land. Management is planning to install the machinery of a new product which is expected to be available in market in coming months. As this piece of land was available for installing machinery and later produce the inventory, no cost of hiring land (rental costs) will be included in the product. But assume that majority if other products in the market have hired land & thus include rental cost as product cost.
EXAMPLE â&#x20AC;&#x201C; NOTIONAL COST If management wants to compare its production cost with the production cost of the competitors then it must include â&#x20AC;&#x153;market rentâ&#x20AC;? of this land in the product. As management is not actually paying any rent therefore, any amount included in the production cost towards imaginary rent is notional cost.
This will help management to benchmark their performance and cost standards. For example, if an entity is manufacturing a particular product and its per unit cost is $20 whereas its competitor is also producing the same product and its per unit cost of production is also $20 then it might seem that entity is doing a good job by producing at same cost level.
EXAMPLE â&#x20AC;&#x201C; NOTIONAL COST However, if competitor has installed its production facility on rental land and thus incurring rental cost which is included in the production cost of inventory. Whereas entity has installed the production facility on its own land and not paying any rent. Then the production cost of $20 is not justified as competitor is managing a $20 /unit mark including rental cost whereas entityâ&#x20AC;&#x2122;s production cost does not include rental cost which in other words mean that competitor is working much more efficiently whereas entity is unable to cash on its additional facilities which should have been a competitive edge leading towards lesser per unit cost.