Question

Two mutually exclusive investment opportunities require an initial investment of $7 million. Investment A pays $1.5 million per year in perpetuity, while investment B pays $1.2 million in the first year, with cash flows increasing by 3% per year after that. At what cost of capital would an investor regard both opportunities as being equivalent

Answer 1

Answer:The cost of capital that will make both investments equal is 17.045%

Explanation:

Investment A

$1.5 million will be received in perpetuity we can there use perpetuity formula to Value investment A.

Value of Investment A = 1500 000/r

Investment B

$1.2 Million will be received in Investment B with a growth rate of 3% will then use Gordon's growth rate model to value investment B.

Value of investment B = (1200 000 x (1+0.03))/(r - 0.03)

Value of investment B = 1236000/(r - 0.03)

1500 000/r = 1236000/(r - 0.03)

1236000(r) = 1500000(r - 0.03)

(r - 0.03) = 1236000( r)/1500000

r - 0.03 = 0.824r

r - 0.824r = 0.03 = 0.176r = 0.03

r = 0.03/0.176 = 0.170454545

R = 17.045%

The cost of capital that will make both investments to be equal is 17.045%