Question

You are an entrepreneur starting a biotechnology firm. If your research is​ successful, the technology can be sold for $ 27 million. If your research is​ unsuccessful, it will be worth nothing. To fund your​ research, you need to raise ​$5.6 million. Investors are willing to provide you with ​$5.6 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 ​$0.7 million. According to​ MM, what fraction of the​ firm's equity will you need to sell to raise the additional ​$4.9 million you​ need?

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

Answer 1

Given
Project Value can be
i) 27 Million
ii) 0 Million

Funding Needed 5.6 million

A.
An investor is willing to pay 5.6 million for 30% equity

Which Means market value of Firm = (5.6/30) * 100
= 18.6667 Million
Market Value Of Firm (without Leverage) = 18.6667

B.
Borrow ​ 0.7 Million

According to​ MM Theory: proposition 1
The Value of the firm (with Leverage/Debt) = Value of the firm (without Debt/Leverage)

We have the Value of the firm (without debt) = 18.6667 = Value of the firm (with Debt)
The Value of the firm (With Debt) = Value of Debt + Value of Equity

18.6667 = 0.7 (GIVEN) + Value of Equity
Value of Equity = 18.6667 - 0.7 = 17.9667

According to​ MM Theory: proposition 2
Financial leverage is in direct proportion to the cost of equity. With an increase in debt, the equity shareholders perceive a higher risk. Hence, expect a higher return, thereby increasing the cost of equity.
Funding Needed = 4.9 million
Percentage of Equity = (4.9/17.9667) * 100
= 27.27273%

C.
Value of My Share in case
a).
Market Value of Equity = 18.6667
Investor's Share = 30%
My share = 70%
Value of My Share of the firm's equity =.70*18.6667
= 13.0667

b).
Market Value of Equity = 17.9667
Investor's Share = 27.273%
My share = 72.727%
Value of My Share of the firm's equity =.72727*17.9667
= 13.0667

In Both Cases, The cases Value of My Share of the firm's equity is the same.

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