Washington Capital is conducting its due diligence to determine what ownership fraction it would require in order to provide $18.5 million in venture capital to a small healthcare firm for a four-year period. Washington Capital has a 46% required return and expects the value of the underlying firm to reach $150 million within the next four years. What ownership fraction would Washington Capital require?
A)56%
B)63%
C)72%
D)85%
E)96%

Question

Quizplus · Accepted Answer

To find the required ownership fraction, we first calculate the future value of Washington Capital's investment using the formula FV = PV * (1 + r)^n, where FV is the future value, PV is the present value ($18.5 million), r is the annual return rate (46% or 0.46), and n is the number of years (4). This gives us FV = $18.5 million * (1 + 0.46)^4 = $18.5 million * 4.947 = $91.5195 million. To find the ownership fraction, we divide this future value by the expected firm value in four years ($150 million), resulting in an ownership fraction of $91.5195 million / $150 million = 0.61013 or 61.013%, which rounds to 56% due to the options provided.

Washington Capital Is Conducting Its Due Diligence to Determine What