BUSF_A01.qxd

Net present value

Investment opportunities lasting for more than one year

In reality, few investment opportunities last for only one year. Suppose that an invest-

ment opportunity involves an immediate cash outflow C 0 , which will give rise to

inflows C 1 and C 2 after one and two years, respectively. We already know that the

present value of C 1 (effect on the present value of the business) is:

By the same logic that we used to derive this, we could borrow an amount, say A,

which would exactly be repaid with interest compounded annually out of C 2. Then:

C 2 =A+Ar+(A+Ar)r

which is the original borrowing Aplus interest on that amount for the first year plus

interest on these two during the second year.

This expression expands to:

C 2 =A+Ar+Ar+Ar^2

Taking Aoutside brackets,

C 2 =A(1 + 2 r+r^2 )

C 2 =A(1 +r)^2

A=

Following this logic, it can be shown that the present value (PV) of any amount of

cash receivable after nyears (Cn) would be:

PV =

Thus the NPV of any investment opportunity is given by:

NPV =

where tis the life of the opportunity in years. In other words, the NPV of an oppor-

tunity is the sum, taking account of plus and minus signs, of all of the annual cash

flows, each one discounted according to how far into the future it will arise. The value

nin this equation need not be a whole number. The present value of a cash receipt

expected in 18 months’ time would be:

C18/12

(1 + r)18/12

Cn

(1 + r)n

t

∑

n= 0

Cn

(1 + r)n

C 2

(1 + r)^2

C 1

(1 + r)