Firm A and firm B have debt–total asset ratios of 44% and 34% and returns on total assets of 8% and 14%, respectively.

Firm A and firm B have debt–total asset ratios of 44% and 34% and returns on total assets of 8% and 14%, respectively.

  

What is the return on equity for firm A and firm B? (Round your answers to 2 decimal places. (e.g., 32.16))

 

	Firm A	Firm B
Return on equity	%	%

Explanation:

Firm A	Firm B
D / TA = 0.44	D / TA = 0.34
(TA − E) / TA = 0.44	(TA − E) / TA = 0.34
(TA / TA) − (E / TA) = 0.44	(TA / TA) − (E / TA) = 0.34
1 − (E / TA) = 0.44	1 − (E / TA) = 0.34
E / TA = 0.56	E / TA = 0.66
E = 0.56(TA)	E = 0.66 (TA)
Rearranging ROA, we find:
NI / TA = 0.08	NI / TA = 0.14
NI = 0.08(TA)	NI = 0.14(TA)

  

Since ROE = NI / E, we can substitute the above equations into the ROE formula, which yields:

  

ROE = 0.08(TA) / 0.56(TA) = 0.08 / 0.56 = 14.29%

ROE = 0.14(TA) / 0.66 (TA) = 0.14 / 0.66 = 21.21%