Question

I need 450 words.

Explain why the NPV of a relatively long-term project, defined as one for which a high percentage of its cash flows are expected in the distant future, is more sensitive to changes in the required rate of return than is the NPV of a short-term project. In addition, please provide an example to better demonstrate your explanation.

Answer 1

The reason for the phenomenon is the nature of compounding.
The formula for discounting of a cash flow is:
Cash flow/(1+r)^t
where
r = discount rate per period, and
t = number of the year [1,2,3 etc].
The value of CF/(1+i)^t decreases more than proportionately
[in geometric proportion] as t increases, which means that the
cash flows in the later years are discounted more heavily than
the earlier years. This being so, any change in interest rates
affects the value of the later cash flows more.
Example:
Consider two projects with cash flows as below;
A = -10000, 2000, 3000, 3000, 5000, 5000
B = -10000, 9000,9000
The NPVs with 10% discount rate are:		% Change
A = -10000+ 2000/1.1+3000/1.1^2+3000/1.1^3+5000/1.1^4+5000/1.1^5=	$    3,071.14
B = -10000+9000/1.1+9000/1.1^2 =	$    5,619.83
The NPVs with 12% discount rate are:
A = -10000+ 2000/1.12+3000/1.12^2+3000/1.12^3+5000/1.12^4+5000/1.12^5=	$    2,327.36	-24.22%
B = -10000+9000/1.12+9000/1.12^2 =	$    5,210.46	-7.28%
As can be seen Project A's NPV is affected to a larger % for a 2% change in
discount rate in comparison with the % change in the NPV of Project B.