Question

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Firms HD and LD are identical except for their level of debt and the interest rates they pay on debt--HD has more debt and pays a higher interest rate on that debt. Based on the data given below, what is the difference between the two firms' ROEs? (Answer by calculating HD's ROE and LD' ROE).

(Hint: You need to find Equity and NI of the two firms to obtain ROE (=NI/EQUITY))

Applicable to Both Firms			Firm HD's Data				Firm LD's Data
Assets	$200		Debt/Assets	50%			Debt /Assets	30%
EBIT	$40		Interest rate	12%			Interest rate	10%
Tax rate	35%

FIRM HD				FIRM LD
NI				NI
EQUITY				EQUITY
ROE				ROE

Answer 1

Firm HD:

Debt/Assets = 50 %

Assets = $ 200 million

Debt = 0.5 x 200 = $ 100 million

Equity = Assets - Debt = 200 - 100 = $ 100 million

Interest Rate = 12 %

EBIT = $ 40 million

LESS: Interest Expense = 0.12 x 100 = $ 12 million

EBT = $ 28 million

LESS: Tax at 35 % = 28 x 0.35 = $ 9.8 million

Net Income = $ 18.2 million

ROE = Net Income / Equity = 18.2 / 100 = 0.182 or 18.2 %

Firm LD:

Debt/Assets = 30 %

Assets = $ 200 million

Debt = 0.3 x 200 = $ 60 million

Equity = Assets - Debt = 200 - 60 = $ 140 million

Interest Rate = 10 %

EBIT = $ 40 million

LESS: Interest Expense = 0.1 x 140 = $ 14 million

EBT = $ 26 million

LESS: Tax at 35 % = 26 x 0.35 = $ 9.1 million

Net Income = $ 16.9 million

ROE = Net Income / Equity = 16.9 / 140 = 0.1207 or 12.07 %