Question

A bias-neutral venture capitalist is contemplating investing $11 million in a start-up company. Company net income at end of year three is expected to be $4 million. Given the three year length of his investment, his firm requires a 45% internal rate of return compounded annually. Given that the market for the company’s product line is expected to be national, the price to earnings ratio is expected to be 20. Neither future investments nor change in earnings projection is expected prior to the end of the investment term. There are currently 5 million shares outstanding.

Using the Sahlman Ownership proportion Formula, compute rounded to the nearest thousandth the percentage of ownership in a start-up company that the venture capitalists should seek and enter digits for in the form (#.###) in the corresponding answer box below. For example, 27.3% would be entered 0.273, 100% would be entered as 1.000. Answers will be graded correct if within +/- 1% of the correct answer.

Answer 1

The firm requires a 45% return on the investment of $11 million after 3 years.

Therefore,

Their investment value after 3 years = Investmentx(1+r)ⁿ

Where,

n=3

r = 45% = 0.450

Investment = $11 million

Investment worth after 3 years = 11x(1+0.450)³ = $33.535 Mn
Expected net income after 3 years = $4 Mn

Expected Price/ Earning Ratio = 20

Value of company at end of year 3 = Net Income x P/E ratio = 4x20 = $80 Mn

Therefore the firm needs to recieve $33.535 at the end of 3 years out of $80 Mn

Ownership required = 33.535/80 = 0.419 = 41.9%