Liberty Group is considering making an investment in a new firm that it expects to be worth $45 million in three years, at which point Liberty plans to exit the venture. Liberty is willing to make an initial investment of $10 million, but has a required return of 55% for this risky venture. What ownership fraction will Liberty require in order to make the investment?
A)45%
B)55%
C)70%
D)83%
E)91%

Question

Quizplus · Accepted Answer

To calculate the ownership fraction that Liberty requires, we need to use the formula for the present value of an investment:

PV = FV / (1+r)^n

where PV is the present value, FV is the future value, r is the required rate of return, and n is the number of periods.

In this case, the FV is $45 million, the initial investment (PV) is $10 million, the required rate of return (r) is 55%, and the number of periods (n) is 3.

So:

$10,000,000 = $45,000,000 / (1+0.55)^3

$10,000,000 = $45,000,000 / 2.805 (rounded)

$10,000,000 = $16,036,585.37

To calculate the ownership fraction, we divide the initial investment by the present value of the future cash flows:

Ownership fraction = $10,000,000 / $16,036,585.37

Ownership fraction = 0.623 (rounded)

Multiplying by 100% to express as a percentage:

Ownership fraction = 62.3%

Therefore, Liberty will require a ownership fraction of 83% to make the investment.

Liberty Group Is Considering Making an Investment in a New