BUSF_A01.qxd

Net present value

A business is faced with an investment opportunity that involves an initial investment of

£35,000, which is expected to generate annual inflows of £10,000 at the end of each of the

next five years. The business’s cost of finance is 10 per cent p.a. What is the NPV of this

opportunity?

Example 4.2

If we discounted the cash inflows using the table of discount factors in Appendix 1, the cal-

culation would be as follows:

(10,000 ×0.909) +(10,000 ×0.826) +(10,000 ×0.751) +(10,000 ×0.683) +(10,000 ×0.621)

This could be rewritten as:

10,000(0.909 +0.826 +0.751 +0.683 +0.621)

where the figures in brackets are the discount factors at 10 per cent for a series of annual

cash flows of £1 for five years. In cases like this, the calculation is made easier for us in that

tables giving the sum of discount factors, for specified periods of years and discount rates,

are readily available. There is one shown in Appendix 2 to this book. Such tables are usually

Solution

The process, shown in Example 4.1, of converting future cash flows to their present

value is known as discounting.

The business should buy the Zenith, as this would have a positive effect on its

wealth, whereas the Super would have a negative effect. It should not be prepared to

buy the Super even if it were the only such machine on the market, as to do so would

be to the detriment of the business’s wealth. The value of the business would, in

theory, fall as a result of buying the Super. Only if it were possible to negotiate a price

lower than £23,837 (the sum of the discounted savings) would the value of the annual

savings justify the cost of that machine, given the financing cost. Similarly, up to

£20,479 could be paid for a Zenith and it would continue to be a profitable investment.

It is important to recognise that the size of the initial investment is not of any direct

relevance to the decision (except to the extent that it is used in the calculation of the

NPV); only the NPV is important. Thus if the Super had a positive NPV of £480 it

would be selected in preference to the Zenith, despite the fact that the Super costs

£5,000 more to buy. The only occasion where we would need to consider the size of

the NPV in relation to the amount of investment is when there is a shortage of invest-

ment finance and projects need to compete for it. This is an aspect that we shall con-

sider in Chapter 5.

The use of tables and annuity factors

Tables are readily available that will give the discount factor 1/(1 +r)nfor a range of

values of rand n. Such a table appears in Appendix 1 to this book. Note that it is not

necessary to use the table for discounting; the calculation can easily be done from first

principles.

Sometimes an investment involves a series of identical annual cash flows (known

as an annuity) and a constant discount rate. In these circumstances there is a short cut

to the present value of those cash flows.

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