Question

Last year FBGS Inc. had sales of $325,000 and a net income of $19,000, and its year-end assets were $250,000. The firm's total-debt-to-total-capital ratio was 15.0%. The firm finances using only debt and common equity and its total assets equal total invested capital. Based on the DuPont equation, what was the ROE?

Answer 1

Solution :

As per the Du pont Equation

Return on equity = Equity multiplier * Total asset turnover * Profit margin

= ( Assets / Common equity ) * ( Sales / Assets ) * ( Net Income / sales )

As per the information given in the question we have

Assets = $ 250,000   ; Sales = $ 325,000      ; Net Income = $ 19,000

Total assets = Total capital

We know that total assets = $ 250,000 = Total capital

Total debt to total capital ratio = 15.0% = 0.15

The Formula for calculating the total debt to total capital = Total Debt / Total Capital

Thu we have

0.15 = Total Debt / $ 250,000

Total Debt = $ 250,000 * 0.15 = $ 37,500

Further we know that

Debt + Common equity = Total capital

$ 37,500 + Common equity = $ 250,000

Thus Common equity = $ 250,000 - $ 37,500 = $ 212,500

Applying the available information in the ROE Formula we have

= ( $ 250,000 / $ 212,500 ) * ( $ 325,000 / $ 250,000 ) * ( $ 19,000 / $ 325000 )

= 1.176471 * 1.3 * 0.058462

= 0.089412

= 8.9412 %                                                              

= 8.94 % ( when rounded off to two decimal places )

Thus based on the DuPont equation, the ROE = 8.94 %