Question

You are an entrepreneur starting a biotechnology firm. If your research is​ successful, the technology can be sold for $21 million. If your research is​ unsuccessful, it will be worth nothing. To fund your​ research, you need to raise ​$4.8 million. Investors are willing to provide you with ​$4.8 million in initial capital in exchange for 30% of the unlevered equity in the firm.

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

b. Suppose you borrow ​$0.8 million. According to​ MM, what fraction of the​ firm's equity will you need to sell to raise the additional​$4.0 million you​ need?

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

Answer 1

a) Capital needed = $4.8 million | Unlevered Equity to be given = 30%

We need to find the Value of the firm without leverage.

As investors are valuing $4.8 million for 30% of firm's Unlevered equity, we can use that valuation to calculate the Firm's unlevered equity's value.

Value of 30% Unlevered equity = $4.8 million

Value of 30% Unlevered equity = 30% * Value of the firm's Unlevered equity

Value of the firm's Unlevered equity = $4.8 million / 30%

Value of the firm's Unlevered equity = $16 million

b) Borrowing = $0.8 million | Remaining needed = $4 million

As MM theorem, Value of the firm remains same irrespective of its Capital Structure. Therefore, with borrowing of $0.8 million, firm's value remains the same at $16 million however, with 0.8 million being the debt and remaining the equity.

Value of firm's Levered equity = Value of Unlevered equity - Borrowing

Value of firm's Levered equity = 16 million - 0.8 million

Value of firm's Levered equity = $15.2 million

Since additional $4 million are required for funding, we need to calculate the percentage of equity you need to sell for it.

Percentage of Equity for $4 million = Funding requirement / Value of firm's levered equity

Percentage of Equity for $4 million = 4 million / 15.2 million

Percentage of Equity for $4 million = 26.32% or 26%

c) Case (a): Raise $4.8 million by selling 30% of Unlevered equity

Case (b): Borrow $0.8 million and sell 26.32% of Levered equity for remaining $4 million

Case (a): We have already calculated Value of Unlevered equity in part (a).

Value of the firm's Unlevered equity = $16 million

Now after selling 30% equity, we can find the Value of your share in firm's equity.

Value of Your share = Value of the firm * (1 - Percentage equity sold)

Value of Your share = $16 million * (1 - 30%)

Value of Your share = $16 million * 70%

Value of Your share in Firm's equity for part (a) = $11.2 million

Case (b): For case (b), we have already calculated Value of Levered equity of the firm in part (b).

Value of firm's Levered equity = $15.2 million

Percentage of Equity sold= 26.32%

Value of Your share = Value of the firm * (1 - Percentage equity sold)

Value of Your share = $15.2 million * (1 - 26.32%)

Value of Your share = $15.2 million * 73.68%

Value of Your share in Firm's equity for part (b) = $11.2 million