Firm A and Firm B have debt-total asset ratios of 36% and 26% and returns on total assets of 8% and 12%, respectively.

Firm A and Firm B have debt-total asset ratios of 36% and 26% and returns on total assets of 8% and 12%, respectively.

  

What is the return on equity for Firm A and Firm B? (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

  

	Firm A	Firm B
Return on equity	%	%

 

Explanation:

The solution requires substituting two ratios into a third ratio. Rearranging Debt / Total assets:

Firm A	Firm B
D / TA = .36	D / TA = .26
(TA − E) / TA = .36	(TA − E) / TA = .26
(TA / TA) − (E / TA) = .36	(TA / TA) − (E / TA) = .26
1 − (E / TA) = .36	1 − (E / TA) = .26
E / TA = .64	E / TA = .74
E = .64(TA)	E = .74(TA)
Rearranging ROA = Net income / Total assets, we find:
NI / TA = .08	NI / TA = .12
NI = .08(TA)	NI = .12(TA)

Since ROE = Net income / Equity, we can substitute the above equations into the ROE formula, which yields:

  

ROE = .08(TA) / .64(TA)	ROE = .12(TA) / .74(TA)
ROE =  = .08 / .64	ROE = .12 / .74
ROE  = .1250, or 12.50%	ROE = .1622, or 16.22%