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%
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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