Question

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?

Applicable to both firms

Assets $400

EBIT $60

Tax rate 30%

FIRMS HD DATA

debt ratio is 50%

interest rate is 12%

FIRMS LD DATA

debt ratio os 20%

interest ratio is 8%

a. 0.98%

b. 1.02%

c. 1.42%

d. 0.87%

e. 0.95%

Please show all work

Answer 1

Answer: The correct answer is D i.e. 0.87%

For HD:

Debt = Assets * Debt Ratio
Debt = $400 * 50%
Debt = $200

Interest = Debt * Interest Rate
Interest = $200 * 12%
Interest = $24

EBT = EBIT – Interest
EBT = $60 - $24
EBT = $36

Net Income = EBT – (EBT*tax rate)
Net Income = $36 – ($36 * 30%)
Net Income = $36 - $10.8
Net Income = $25.2

Equity = Assets – Debt
Equity = $400 - $200
Equity = $200

ROE = Net Income / Equity
ROE = $25.2 / $200
ROE = 0.126 or 12.6%

For LD:

Debt = Assets * Debt Ratio
Debt = $400 * 20%
Debt = $80

Interest = Debt * Interest Rate
Interest = $80 * 8%
Interest = $6.4

EBT = EBIT – Interest
EBT = $60 - $6.4
EBT = $53.6

Net Income = EBT – (EBT*tax rate)
Net Income = $53.6 – ($53.6 * 30%)
Net Income = $53.6 - $16.08
Net Income = $37.52

Equity = Assets – Debt
Equity = $400 - $80
Equity = $320

ROE = Net Income / Equity
ROE = $37.52 / $320
ROE = 0.1173 or 11.73%

Difference between firms’ ROE = ROE of HD – ROE of LD
Difference between firms’ ROE = 12.6% - 11.73%
Difference between firms’ ROE = 0.87%