Question

A company has an investment project that would cost $10 million today and yield a payoff of $15 million in 4 years.

a. Should the firm undertake the project if the interest rate is 11 percent? 10 percent?

b. Can you figure out the exact cutoff for the interest rate between profitability and non-profitability?

Answer 1

In order to conclude whether or not the firm should undertake the project, we will have to calculate the present value of the future cash inflows/yield. If the present value of future yield is more than the present investment to be made, then it will be considered a profitable investment.

Part A -

Present Value = Future Value x [1/(1+r)ⁿ]

where r is the rate of interest, and n is the term or number of years.

a) If we consider the interest rate as 11%
then, present value = 15,000,000 x [1/(1+0.11)⁴]
= 9,880,964.6121
Since present value is less than investment of 10 million. Therefore, the firm should not undertake the project.

b) If we consider the interest rate as 10%
then, present value = 15,000,000 x [1/(1+0.10)⁴]
= 10,245,201.8304
Since present value is more than investment of 10 million. Therefore, the firm should undertake the project.

Part B -

To find out the exact cut off interest rate (break even interest rate). Consider the findings in part A above.

a change in interest rate of 1% (11%-10%) has led to a change in presnt value of 364,237.2183 (10,245,201.8304 - 9,880,964.6121).

Therefore, how much reduction in interest rate from 11% would lead to present value being 10 million should be calculated by cross multiplying.

1%	364237.2183
?	119035.3879 (i.e. 10,000,000-9,880,964.6121)

? = (119035.3879x1)/364237.2183
= .3268

Therefore at inrerest rate = 10.6732% (i.e. 11 - .3268) there is neither profit nor loss from investment.