BUSF_A01.qxd

Chapter 4 • Investment appraisal methods

known as annuity tables. Even if such a table is not available, we can easily deduce the

appropriate annuity factor. It is:

1 −

where ris the annual interest rate and nthe number of years into the future that the annuity

will persist.

According to the table, the annuity factor for five years and 10 per cent is 3.791. (This only

differs from the sum of the five discount factors through rounding.)

Thus the NPV of the investment opportunity is:

−£35,000 +(£10,000 ×3.791) =+£2,910

J

L

1

(1 +r)n

G

I

1

r

Investments, particularly business investments, that give rise to a steady stream of

cash flows are, in real life, relatively rare.

How a positive NPV leads to an increase in shareholder wealth

It has been said, quite reasonably, that the essence of good investment is to buy assets

for less than they are worth. Clearly, doing this will enhance the value of the business.

When assessing an investment opportunity like the Zenith, it comes down to the ques-

tion of how much the estimated future benefits of owning the Zenith are worth to

Seagull plc. The future benefits obviously are the potential operating cost savings

(£4,000 in year 1, £6,000 in year 2 and so on).

To be able to assess whether the value of these future benefits exceeds the cost

of the asset (£20,000), it is necessary to place some value on them. As we have just seen,

the most logical way to value them is to discount each one according to how far into

the future the benefit will occur, and to sum the discounted values. Thus NPV is an

entirely logical approach to investment decision making, assuming that enhancing the

value of the shareholders’ wealth is the objective being pursued.

Discounting – a slightly different view

Staying with Example 4.1, a superficial assessment of the Zenith might be that it

should be bought because it cost £20,000 but would yield total savings of £29,000 (the

sum of the annual savings), that is, a benefit of £9,000. A second look reveals, however,

that this cannot be a correct assessment as no rational investor regards all of the £s in

the question as equivalent to one another. We should all prefer £1 today to £1 next year

and we should prefer it still more to £1 in five years’ time, even if we assume no

erosion of value through inflation. This is because if we have the £1 today we could, if

we wished, lend it so that after a year we should have not only the £1 but the interest

on it as well.

Simply adding the annual savings and comparing the total with the initial outlay

would be illogical. It would be like saying that a certain item is more expensive to

buy in France than in the UK because it costs 8 in France and only 5 in the UK,