From what we have seen so far, it seems that to make sensible investment decisions, we need a method of appraisal that both:
■ considers all of the cash flows for each investment opportunity, and
■ makes a logical allowance for the timing of those cash flows.
The third of the four methods of investment appraisal, the net present value (NPV) method, provides us with exactly this.
Consider the Billingsgate Battery example’s cash flows, which we should recall are as follows:
Time £000
Immediately Cost of machine (100)
1 year’s time Operating profit before depreciation 20 2 years’ time Operating profit before depreciation 40 3 years’ time Operating profit before depreciation 60 4 years’ time Operating profit before depreciation 60 5 years’ time Operating profit before depreciation 20
5 years’ time Disposal proceeds 20
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NET PRESENT VALUE (NPV) 161
Given a financial objective of maximising owners’ wealth, it would be easy to assess this investment if all cash inflows and outflows were to occur immediately. It would then simply be a matter of adding up the cash inflows (total £220,000) and comparing them with the cash outflows (£100,000). This would lead us to conclude that the project should go ahead because the owners would be better off by £120,000. It is, of course, not as easy as this because time is involved. The cash outflow will occur immediately, whereas the cash inflows will arise at different points in the future.
Why does time matter?
Time is an important issue because people do not normally see an amount paid out now as equivalent in value to the same amount being received in a year’s time. Thus, if we were offered
£100 in one year’s time in exchange for paying out £100 now, we would not be interested, unless we wished to do someone a favour.
Why would we see £100 to be received in a year’s time as not equal in value to £100 to be paid immediately? (There are basically three reasons.)
The reasons are:
■ interest lost
■ risk
■ inflation.
Activity 4.7
We shall now take a closer look at these three reasons in turn.
Interest lost
If we are to be deprived of the opportunity to spend our money for a year, we could equally well be deprived of its use by placing it on deposit in a bank or building society. By doing this, we could have our money back at the end of the year along with some interest earned. This interest, which is forgone by not placing our money on deposit, represents an opportunity cost.
It arises where one course of action deprives us of the opportunity to derive benefit from an alternative course of action.
An investment must exceed the opportunity cost of the funds invested if it is to be worth- while. Thus, if Billingsgate Battery Company sees putting the money in the bank on deposit as the alternative to investment in the machine, the return from investing in the machine must exceed the return from investing in the bank. If this is not the case, there is no reason to make the investment.
Risk
All investments expose their investors to risk. Thus, when Billingsgate Battery Company buys a machine on the strength of estimates made before its purchase, it must accept that things may not turn out as expected.
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162 CHAPTER 4 MAKING CAPITAL INVESTMENT DECISIONS
Can you identify the kinds of risks that the business may face?
Here are some:
■ The machine might not work as well as expected; it might break down, leading to loss of the business’s ability to provide the service.
■ Sales of the service may not be as buoyant as expected.
■ Labour costs may prove to be higher than expected.
■ The sale proceeds of the machine could prove to be less than that estimated.
You may have thought of others.
Activity 4.8
It is important to remember that the purchase decision must be taken before any of these things are known. Thus, it is only after the machine has been purchased that we find out whether, say, the forecast level of sales is going to be achieved. We can study reports and analyses of the market. We can commission sophisticated market surveys and advertise widely to promote sales. All these may give us more confidence in the likely outcome. Ultimately, however, we must decide whether to accept the risk that things will not turn out as expected in exchange for the opportunity to generate profits.
We saw in Chapter 1 that people normally expect greater returns in exchange for taking on greater risk. So, when considering the Billingsgate Battery Company’s investment opportu- nity, it is not enough to say that this business should buy the machine providing the expected returns are higher than those from investing in a bank deposit. It should expect much greater returns than the bank deposit interest rate because of the much greater risk involved. The logi- cal equivalent of investing in the machine would be an investment of similar risk. Determining how risky a particular project is, and therefore how large the risk premium should be, is a difficult task. We will consider this in more detail in the next chapter.
Inflation
If we are to be deprived of £100 for a year, when we come to spend that money it will not buy the same amount of goods and services as it would have done a year earlier. Generally, we shall not be able to buy as many tins of baked beans or loaves of bread or bus tickets as before. This is because of the loss in the purchasing power of money, or inflation, which occurs over time. Investors will expect to be compensated for this loss of purchasing power.
This will be on top of a return that takes account of what could be gained from an alternative investment of similar risk.
In practice, interest rates observable in the market tend to take inflation into account. Thus, rates offered to building society and bank depositors include an allowance for the expected rate of inflation.
What should managers do?
To summarise, managers seeking to increase the wealth of business owners should invest only when they believe the owners will be adequately compensated for the loss of interest, for the loss in the purchasing power of money invested and for the risk that the expected returns may not materialise. This normally involves checking to see whether the proposed investment will yield a return greater than the basic rate of interest (which will include an allowance for inflation) plus an appropriate risk premium.
These three factors (interest lost, risk and inflation) are set out in Figure 4.3.
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NET PRESENT VALUE (NPV) 163 Figure 4.3 Factors influencing the return required by investors from a project
There are three factors that influence the required return to investors (opportunity cost of finance).
Interest forgone
Risk premium
Inflation Required return
Dealing with the time value of money
We saw above that money has a time value: that is, £100 received today is not regarded as equivalent in value to £100 received at some future date. We cannot, therefore, simply com- pare the cash inflows with cash outflows for an investment where they arise at different points in time. Each of these cash flows must be expressed in similar terms. Only then can a direct comparison be made.
To illustrate how this can be done, let us return to the Billingsgate Battery Company exam- ple. We should recall that the cash flows expected from this investment are:
Time £000
Immediately Cost of machine (100)
1 year’s time Operating profit before depreciation 20 2 years’ time Operating profit before depreciation 40 3 years’ time Operating profit before depreciation 60 4 years’ time Operating profit before depreciation 60 5 years’ time Operating profit before depreciation 20
5 years’ time Disposal proceeds 20
Let us assume that the business could make an alternative investment with similar risk and obtain a return of 20 per cent a year.
Given that the Billingsgate Battery Company could invest its money at a rate of 20 per cent a year, what is the present (immediate) value of the expected first-year receipt of
£20,000? In other words, if instead of having to wait a year for the £20,000, and therefore be deprived of the opportunity to invest it at 20 per cent, the business could have some money now, what sum would be equivalent to getting £20,000 in one year’s time?
The business should be happy to accept a lower amount immediately than if it had to wait a year. This is because it could invest this amount at 20 per cent (in the alternative project).
Logically, the business should be prepared to accept the amount that, with a year’s income, will grow to £20,000. If we call this amount PV (for present value) we can say:
PV + (PV * 20%) = £20,000
Activity 4.9
➔
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164 CHAPTER 4 MAKING CAPITAL INVESTMENT DECISIONS
We can make a more general statement about the PV of a particular cash flow. It is:
PV of the cash flow of year n = actual cash flow of year n divided by (1 + r)n where n is the year of the cash flow (that is, how many years into the future) and r is the oppor- tunity financing cost expressed as a decimal (instead of as a percentage).
If we derive the present value (PV) of each of the cash flows associated with Billingsgate’s machine investment, we can easily make the direct comparison between the cost of making the investment (£100,000) and the subsequent benefits to be derived in years 1 to 5. We have already seen how this works for the £20,000 inflow for year 1. For year 2 the calculation would be:
PV of year 2 cash flow (that is, £40,000) = £40,000/(1 + 0.2)2 = £40,000/(1.2)2
= £40,000/1.44 = £27,778
Thus, the present value of the £40,000 to be received in two years’ time is £27,778.
See whether you can show that Billingsgate Battery would find £27,778, receivable now, equally acceptable to receiving £40,000 in two years’ time, assuming that there is a 20 per cent investment opportunity.
To answer this activity, we simply apply the principles of compounding. Income earned is reinvested and then added to the initial investment to derive its future value. Thus:
£ Amount available for immediate investment 27,778
Income for year 1 (20% * 27,778) 5,556
33,334
Income for year 2 (20% * 33,334) 6,667
40,001 (The extra £1 is only a rounding error.)
Since Billingsgate Battery can turn £27,778 into £40,000 in two years, these amounts are equivalent. That is, £27,778 is the present value of £40,000 receivable after two years (given a 20 per cent cost of finance).
Activity 4.10
That is, the amount plus income from investing the amount for the year equals the £20,000.
If we rearrange this equation, we find:
PV * (1 + 0.2) = £20,000
(Note that 0.2 is the same as 20 per cent, but expressed as a decimal.) Further rearranging gives:
PV = £20,000/(1 + 0.2) = £16,667
Thus, managers of Billingsgate Battery Company who have the opportunity to invest at 20 per cent a year should not mind whether they have £16,667 now or £20,000 in a year’s time.
In other words, £16,667 represents the present value of £20,000 received in one year’s time.
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NET PRESENT VALUE (NPV) 165
The act of reducing the value of a cash flow, to take account of the period between the present time and the time that the cash flow is expected, is known as discounting. In effect, discounting charges the project with the cost of financing it. Ignoring this financing cost would be to overlook a significant cost of undertaking the project.
Calculating the net present value
Now let us calculate the present values of all of the cash flows associated with the Billingsgate machine project and from them, the net present value of the project as a whole.
The relevant cash flows and calculations are as follows:
Time Cash flow
£000
Calculation of PV PV
£000
Immediately (time 0) (100) *(100)/(1+ 0.2)0 (100.00)
1 year’s time 20 20/(1 + 0.2)1 16.67
2 years’ time 40 40/(1 + 0.2)2 27.78
3 years’ time 60 60/(1 + 0.2)3 34.72
4 years’ time 60 60/(1 + 0.2)4 28.94
5 years’ time 20 20/(1 + 0.2)5 8.04
5 years’ time 20 20/(1 + 0.2)5 8.04
Net present value (NPV) 24.19
*Note that (1+ 0.2)0 =1.
Once again, we must decide whether the machine project is acceptable to the business. To help us, the following decision rules for NPV should be applied:
■ If the NPV is positive, the project should be accepted; if it is negative, the project should be rejected.
■ If there are two (or more) competing projects that have positive NPVs, the project with the higher (or highest) NPV should be selected.
In this case, the NPV is positive, so we should accept the project and buy the machine. The reasoning behind this decision rule is quite straightforward. Investing in the machine will make the business, and its owners, £24,190 better off than they would be by taking up the next best available opportunity. The gross benefits from investing in this machine are worth £124,190 today. Since the business can ‘buy’ these benefits for just £100,000 today, the investment should be made. If, however, the present value of the gross benefits were below £100,000, it would be less than the cost of ‘buying’ those benefits and the opportunity should therefore be rejected.
What is the maximum the Billingsgate Battery Company would be prepared to pay for the machine, given the potential benefits of owning it?
The business would logically be prepared to pay up to £124,190 since the wealth of the owners of the business would be increased up to this price – although the business would prefer to pay as little as possible.
Activity 4.11
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166 CHAPTER 4 MAKING CAPITAL INVESTMENT DECISIONS
Using present value tables
To deduce each PV in the Billingsgate Battery Company project, we took the relevant cash flow and multiplied it by 1/(1 + r)n. There is a slightly different way to do this. Tables exist (called present value tables, or discount tables) that show values of this discount factor for a range of values of r and n. Such a table appears in Appendix A at the end of the book. Take a look at it.
Look at the column for 20 per cent and the row for one year. We find that the factor is 0.833. This means that the PV of a cash flow of £1 receivable in one year is £0.833. So the present value of a cash flow of £20,000 receivable in one year’s time is £16,660 (that is, 0.833* £20,000). This is the same result, ignoring rounding errors, as we found earlier by using the equation.
What is the NPV of the Chaotic Industries project from Activity 4.2, assuming a 15 per cent opportunity cost of finance (discount rate)? (Use the table in Appendix A.)
Remember that the inflows and outflow are expected to be:
Time £000
Immediately Cost of vans (150)
1 year’s time Saving before depreciation 30
2 years’ time Saving before depreciation 30
3 years’ time Saving before depreciation 30
4 years’ time Saving before depreciation 30
5 years’ time Saving before depreciation 30
6 years’ time Saving before depreciation 30
6 years’ time Disposal proceeds from the vans 30 The calculation of the NPV of the project is as follows:
Time Cash flows
£000
Discount factor (15%)
Present value
£000
Immediately (150) 1.000 (150.00)
1 year’s time 30 0.870 26.10
2 years’ time 30 0.756 22.68
3 years’ time 30 0.658 19.74
4 years’ time 30 0.572 17.16
5 years’ time 30 0.497 14.91
6 years’ time 30 0.432 12.96
6 years’ time 30 0.432 12.96
NPV (23.49)
Activity 4.12
How would you interpret this result?
The project has a negative NPV. This means that the present values of the benefits from the investment are worth less than the initial outlay. Any amount up to £126,510 (the present value of the benefits) would be worth paying, but not £150,000.
Activity 4.13
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