Question

You are an entrepreneur starting a biotechnology firm. If your research is successful, the technology can be sold for $22 million. If your research is unsuccessful, it will be worth nothing. To fund your research, you need to raise $5.5 million. Investors are willing to provide you with $5.5 million in initial capital in exchange for 25% of the unlevered equity in the firm. a. What is the total market value of the firm without leverage? b. Suppose you borrow $0.4 million. According to MM, what fraction of the firm's equity will you need to sell to raise the additional $5.1 million you need? c. What is the value of your share of the firm's equity in cases (a) and (b)?

Answer 1

Solution:-

(a) Since investors are ready to buy 25% of the firm for $5.5 million, it means that value of the firm is as follows:

Market value of the firm= $5.5m/25%= $22 million

(b) A per Modigliani Miller (MM) theorem, the total value of a firm is not impacted by change in capital structure as the market value of a firm is dependent on the earnings potential of a business and not how the assets have been financed. Therefore, in this case the total value of the firm would still be $22 million.

Total value of firm= $22 million

Value of equity + value of debt = 22,000,000

Value of equity + 400,000= 22,000,000

Value of equity= $21,600,000 or $21.6 million

% of equity required to be sold to raise $5.1 million= ($5.1m/$21.6m)*100= 23.61%

(c) % stake remaining for entrepreneur in case (a)= 100%-25%= 75%

% stake remaining for entrepreneur in case (b)= 100%-23.61%= 76.39%

Value of entrepreneur's stake in case (a) = $22,000,000*75%= $16,500,000 or $16.5 million

Value of entrepreneur's stake in case (b) = $22,000,000*76.39%= $16,805,800 or $16.81 million