Question

You are an entrepreneur starting a biotechnology firm. If your research is​ successful, the technology can be sold for $24 million. If your research is​ unsuccessful, it will be worth nothing. To fund your​ research, you need to raise ​$2.4 million. Investors are willing to provide you with ​$2.4 million in initial capital in exchange for 50% of the unlevered equity in the firm.

a. What is the total market value of the firm without​ leverage?

b. Suppose you borrow ​$0.3 million. According to​ MM, what fraction of the​ firm's equity will you need to sell to raise the additional ​$2.1 million you​ need?

c. What is the value of your share of the​ firm's equity in cases ​(a​) and ​(b​)?

Answer 1

a) Total Market value of the equity without leverage = Fund Raised / Share of Capital

Total Market value of the equity without leverage = $2.4 / 50%

Total Market value of the equity without leverage = $4.8 Million

b) Total value of firm is $4.8 million.

Equity Value After Debt = $4.8 Million - $0.03 Million = $4.5 Million

Fraction of equity = Amount to be raised / Current Equity

Fraction of equity = 2.10 / 4.5

Fraction of equity = 46.67%

c)

(a) Value of Share = Total value * 50% = $4.8 Million * 50% = $2.4 Million

(b) Value of Share = Total value * (1 - 46.67%) = $4.5 Million * 53.33% = $2.4 Million