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

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%

The cost of capital that  an investor would regard both opportunities as being equivalent is 15%

Investment A

Perpetuity =1,500,000

Present value= 1,500,000/r

Investment B

First year =1,200,000

Present Value= 1,200,000 / ( r - 3%)

Now let calculate the rate

1,500,000/r =1,200,000 / (r - 3%)

1,500,000(r - 3% ) = 1,200,000r

(1,500,000×r) - (1,500,000×3%)= $1,200,000r

1,500,000r - 45,000 = 1,200,000r

1,500,000-1,200,000=45,000

$300,000r = 45,000

r = 45,000/300,000

r= 0.15 ×100

r = 15%

Inconclusion The cost of capital that  an investor would regard both opportunities as being equivalent is 15%

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