Business finance : theory and practice

Chapter 4 • Investment appraisal methods
to do so. Indeed, it could even do this to raise the finance with which to make the
£10 million investment (assuming that the present value of the £12 million is greater
than £10 million).
The next question is: what is the present value of £12 million receivable after one
year with an interest rate of 10 per cent p.a.?
If we let the amount that could be borrowed (the present value of £12 million in a
year’s time) be B, then:
A 10 D
£12m = B + B ×
C 100 F
which represents the borrowing plus the interest for one year. This can be rewritten
as:
A 10 D
£12m = B 1 + = B × 1.10
C 100 F
£12m
B =
1.10
= £10.9m
‘
If we now compare the present value of the future receipt with the initial investment,
the result is an investment with a net present value (NPV) of £0.9 million
(that is, £10.9 million – £10 million). Since this is positive, the investment should be
undertaken assuming that there is not a mutually exclusive alternative with a higher
positive NPV.
The £0.9 million NPV tells us that the business can invest £10 million immediately
to gain a benefit whose present value is £10.9 million, that is, a £0.9 million increase
in the value of the business. In principle, the business could borrow £10.9 million, use
£10 million to make the investment and immediately pay out the £0.9 million to the
shareholders as a dividend. When the £12 million is received, it will exactly pay off
the £10.9 million plus the interest on it.
More generally, we can say that the NPV of an investment opportunity lasting for
one year is:
NPV = C 0 +
where C 0 is the cash flow immediately (time 0) (usually negative, that is, an outflow of
cash), C 1 is the cash flow after one year and r is the interest rate.
In practice we tend to use the NPV approach (that is, discounting future cash flows)
for investment decision making rather than the net future value approach (compounding
present cash flows), though in essence neither is superior to the other.
The reasons for favouring NPV are twofold:
l
l
C 1
1 + r
When comparing investment opportunities (choosing between one and the other),
if net future value is to be used, a decision must be made on when in the future the
value should be assessed (that is, for how many years value should be compounded).
If the competing opportunities are of unequal length (say, one lasts three
years, the other five years), this can cause difficulties.
If the opportunity is to be assessed by looking at its effect on the value of the business,
it seems more logical to look at the present effect rather than the future effect.
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