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
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