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27 July, 03:22

Consider a retail firm with a net profit margin of 3.58 % , a total asset turnover of 1.75 , total assets of $ 42.6 million, and a book value of equity of $ 17.9 million. a. What is the firm's current ROE? b. If the firm increased its net profit margin to 4.30 % , what would be its ROE? c. If, in addition, the firm increased its revenues by 18 % (maintaining this higher profit margin and without changing its assets or liabilities), what would be its ROE?

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  1. 27 July, 03:49
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    (a) 14.9107%

    (b) 17.9095%

    (c) 21.13321%

    Explanation:

    Given that,

    Net profit margin = 3.58%

    Total asset turnover = 1.75

    Total assets = $42.6 million

    Book value of equity = $ 17.9 million

    (a) firm's current ROE:

    = Net income : Total equity

    = Net profit margin * Assets turnover * (Assets : Equity)

    = (Net income : sales) * (sales : assets) * (Assets : Equity)

    = 3.58% * 1.75 * ($42.6 : $17.9)

    = 3.58% * 1.75 * 2.38

    = 14.9107%

    (b) If the firm increased its net profit margin to 4.30 %,

    ROE:

    = 4.30% * 1.75 * ($42.6 : $17.9)

    = 4.30% * 1.75 * 2.38

    = 17.9095%

    (c) If, in addition, the firm increased its revenues by 18%,

    Asset turnover increases by:

    = 1.75 * 1.18

    = 2.065

    ROE:

    = 4.30% * 2.065 * ($42.6 : $17.9)

    = 4.30% * 2.065 * 2.38

    = 21.13321%
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