Math Problem Statement

You are an entrepreneur starting a biotechnology firm. If your research is​ successful, the technology can be sold for

$ 33$33

million. If your research is​ unsuccessful, it will be worth nothing. To fund your​ research, you need to raise

$ 3.8$3.8

million. Investors are willing to provide you with

$ 3.8$3.8

million in initial capital in exchange for

50 %50%

of the unlevered equity in the firm.

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

b.

Suppose you borrow

$ 0.4$0.4

million. According to​ MM, what fraction of the​ firm's equity will you need to sell to raise the additional

$ 3.4$3.4

million you​ need?

c. What is the value of your share of the​ firm's equity in cases

​(a​)

and

​(b​)?

Question content area bottom

Part 1

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

The market value without leverage is

​$enter your response here

million.  ​(Round to one decimal​ place.)

Part 2

b.

Suppose you borrow

$ 0.4$0.4

million. According to​ MM, what fraction of the​ firm's equity will you need to sell to raise the additional

$ 3.4$3.4

million you​ need?

The fraction of the​ firm's equity you will need to sell is

enter your response here​%.

​(Round to the nearest whole​ percentage.)

Part 3

c. What is the value of your share of the​ firm's equity in cases

​(a​)

and

​(b​)?

The value of your share of the​ firm's equity in case

​(a​)

is

​$enter your response here

million.  ​(Round to one decimal​ place.)

Part 4

The value of your share of the​ firm's equity in case

​(b​)

is

​$enter your response here

million.  ​(Round to one decimal​ place.)

Solution

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Math Problem Analysis

Mathematical Concepts

Market Value of Firm
Modigliani-Miller Theorem
Equity Financing
Leverage

Formulas

Total market value = Capital raised / Fraction of equity sold
Fraction of equity to sell = Additional equity needed / Total market value
Value of share = Share percentage × Total market value

Theorems

Modigliani-Miller Theorem

Suitable Grade Level

Undergraduate - Finance/Economics