Investment Appraisal
Investment appraisal decides whether a capital investment – a new machine, building or project – is worthwhile. BA2 uses three techniques, all based on cash flows:
Net present value (NPV) – discount every cash flow at the cost of capital and add them up; accept if the NPV is positive.
Internal rate of return (IRR) – the interest rate at which the NPV is zero, estimated from two NPVs; accept if it is above the cost of capital.
Payback period – how long it takes to get the original investment back (the discounted payback period does the same with discounted cash flows); the shorter the better.
1 Introduction
In this chapter we will apply the discounting techniques covered in the previous chapter to the appraisal of capital investments.
The decisions are based on the cash the investment will pay out and bring in – not on accounting profit. Only relevant cash flows count (chapter 18): the future cash that changes because the investment is made. Unless told otherwise, assume that the initial cost is paid now (time 0) and that the other cash flows arise at the ends of the years (time 1 = one year from now, and so on).
2 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.
Decision rule: if the NPV is positive, accept the investment; if it is negative, reject it. A positive NPV means the investment earns more than the cost of capital – it is the surplus, in today’s money, after paying for the interest.
Discount each year’s cash flow with the discount factor for that year (from the present value table). If the same amount arises every year, the annuity factor can be used instead (chapter 19). The factors used in this chapter are:
Year | 10% | 15% |
0 | 1.000 | 1.000 |
1 | 0.909 | 0.870 |
2 | 0.826 | 0.756 |
3 | 0.751 | 0.658 |
4 | 0.683 | 0.572 |
5 | 0.621 | 0.497 |
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 $10,000.
The project is expected to generate operating cash flows each year as follows:
Year | Operating cash flow ($) |
1 | 20,000 |
2 | 30,000 |
3 | 40,000 |
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.
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3 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.
The higher the interest rate, the lower the NPV. So the IRR is estimated by calculating the NPV at two rates – ideally one giving a positive NPV and one a negative NPV – and assuming the NPV falls in a straight line between them:
IRR = lower rate + [NPV at lower rate ÷ (NPV at lower rate − NPV at higher rate)] × (higher rate − lower rate)
(If the NPV at the higher rate is negative, ‘minus a negative’ means its size is added: 6,660 − (−2,160) = 8,820.)
Decision rule: accept the investment if its IRR is higher than the cost of capital. The IRR also shows the margin for error: if the cost of capital is thought to be 10% and the IRR is nearly 14%, the estimate of the cost of capital could be quite wrong and the decision would still be right.
For the project detailed in Example 1:
Calculate the net present value at interest of 15% and hence estimate the Internal Rate of Return of the project.
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The graph shows the project’s NPV at different interest rates (red dots: the two NPVs calculated above). The NPV falls as the rate rises and crosses zero at the IRR. Because the line is really a slight curve, the straight-line estimate of 13.78% is only approximate – the exact IRR of this project is about 13.7%. This is why the two rates used should be close to the IRR, and why the exam will tell you which rates to use.
4 Payback Period
One problem with basing decisions on the net present value of a project is that the cash flows are only estimates, and if the estimates are wrong then the decision could be wrong.
It is likely to be the earlier cash flows that are the most certain whereas the further into the future that we are estimating the more uncertain the cash flows are likely to be.
The payback period is the number of years it takes to get back the original investment in cash terms. The shorter the payback period, the more certain we are that the project will actually pay for itself.
The discounted payback period is exactly the same except that it takes into account the time value of money by measuring how many years it takes to get back the original investment looking at the discounted cash flow each year.
Payback is found by adding up the cash inflows year by year (the cumulative cash inflow) until they reach the original investment. If it is recovered part-way through a year, the part of the year is usually estimated by assuming the cash comes in evenly through that year. The payback period ignores everything after payback, so it is used alongside NPV, not instead of it.
A new project will cost $100,000 and will last for 5 years with no scrap value.
The project is expected to generate operating cash flows each year as follows:
Year | Operating cash flow ($) |
1 | 20,000 |
2 | 30,000 |
3 | 40,000 |
4 | 50,000 |
5 | 30,000 |
The cost of capital is 10%.
(a) Calculate the payback period
(b) Calculate the discounted payback period
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The discounted payback period is always longer than the simple payback period, because discounting makes each year’s inflow smaller. Strictly, discounting assumes each cash flow arrives at the end of its year, so the discounted payback is sometimes stated simply as ‘within 4 years’ rather than apportioned.
Method | Decision rule | Takes account of the time value of money? |
Net present value | Accept if positive | Yes |
Internal rate of return | Accept if higher than the cost of capital | Yes |
Payback period | The shorter the better | No |
Discounted payback period | The shorter the better | Yes |
5 Test your knowledge
Two quick checks before you move on: work through the flashcards to fix this chapter’s terms and definitions, then sit the objective questions for exam-style practice. Both mark themselves and explain the answers as you go.
Investment Appraisal
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