Question

A firm must choose between two mutually exclusive projects, A & B. Project A has an initial cost of $11000. Its projected net cash flows are $900, $2000, $3000, $4000, and $5000 at the end of years 1 through 5, respectively. Project B has an initial cost of $15000, and its projected net cash flows are $7000, $5000, $3000, $2000, and $1000 at the end of years 1 through 5, respectively. At what cost of capital would the firm be indifferent to the two projects (i.e. be willing to choose either one)? 3.47% 6.58% 6.82% 7.66% 7.18%

Answer 1

NPV of the two projects can be calcualted as follows. The rate at which the NPV of the two projects becomes equal so the investor is indifferent:

Substituting values of r with each of the given options we can get the following NPVs:

Cost of capital	A	B
3.47%	$     2,151.89	$     1,731.79
6.58%	$         818.76	$         724.61
6.82%	$         723.87	$         651.41
7.66%	$         400.05	$         400.01
7.18%	$         583.53	$         542.77

So at 7.66% the NPVs are equal. The difference is negligible and due to rounding off so 7.66% is the rate of indifference or the crossover rate and the correct option