Question

Question 36

There are two firms: Firm U and Firm L. Both firms have $50M total assets and $8M EBIT (earnings before interest and taxes). Firm U is an unleveraged firm without debt. Firm L is a leveraged firm with 50% of debt and 50% of common equity. The pre-tax cost of debt for Firm L is 10%. Both firms have 40% corporate tax rate. Calculate the return on equity (ROE) for firm U.

		9.6%
		13.2%
		16.0%
		19.2%

Question 37

Based on the information from Question 36, what’s the return on equity (ROE) for firm L

		9.6%
		13.2%
		16.0%
		19.2%

Question 38

Based on the information from Question 36, what’s the difference of the total dollars paid to all investors in Firm L and Firm U?

		$3.2 million
		$4.8 million
		$5.8 million
		$1.0 million

Answer 1

Q. 36) Return on equity (ROE) for firm U = Net income / Equity

Here,

a) Net income = EBIT * (1 - Tax rate @ 40% or 0.40)

Net income = $8 Million * (1 - 0.40)

Net income = $4.80 Million

b) Total assets = Total liabilities & Equity

As it is unlevered firm, so there is no debt or liabilities.

Total assets = Equity = $50 Million

Now put the values into formula,

ROE for firm U = $4.80 million / $50 million

ROE for firm U = 0.0960 or 9.60%

Q. 37) ROE for firm L = Net income / Equity

Here,

a) Total assets = Total liabilities and Equity

Liabilities & equity are 50% each & total asset is $50 million

Equity = 50% * Total liabilities & equity

Equity = 50% * $50 million = $25 million

Debt = Total liabilities & equity - Equity

Debt = $50 million - $25 million = $25 million

b) Net income = (EBIT - Interest) * (1 - Tax rate @ 40% or 0.40)

Net income = ($8 million - ($25 million of debt * 10% rate)) * (1 - 0.40)

Net income = ($8 million - $2.50 million) * 0.60

Net income = $5.50 million * 0.60

Net income = $3.30 million

Now put the values into formula,

ROE for firm L = $3.30 million / $25 million

ROE for firm L = 0.1320 or 13.20%

Note : Here, total liabilities assumed as debt only.

Q. 38) a) Dollars paid to all investors in firm U :

Firm U's capital consists of equity only & hence whole net income is paid in dollars to equity investors.

So, Dollars paid = Net income

Dollars paid = $4.80 million (refer Ans. Of Q. 36)

b) Dollars paid to all investors in firm L :

Firm L's capital consists of both ie. equity & debt. Hence interest in dollars is paid to debt investors & net income in dollars is paid to equity investors.

Dollars paid = Interest to debt investors + Net income to equity investors

Dollars paid (refer Ans. Of Q. 37) = $2.50 million + $3.30 million

Dollars paid = $5.80 million

c) Difference of total dollars paid to all investors in firm L & firm U = Dollars paid by firm L - Dollars paid by firm U

Difference = $5.80 million - $4.80 million

Difference = $1.0 million