In the below problem, why is the Equity not adjusted? because if the income changes, then equity has to change also.
An analyst finds return-on-equity (ROE) a good measure of management performance and wants to compare two firms: Firm A and Firm B. Firm A reports net income of $3.2 million and has a ROE of 18. Firm B reports income of $16 million and has an ROE of 16. A review of the notes to the financial statements for Firm A, shows that the earnings include a loss from smelting operations of $400,000 and that the firm has exited this business. In addition, the firm sold the smelting equipment and had a gain on the sale of $300,000. A similar review of the notes for Firm B discloses that the $16 million in net income includes $2.6 million gain on the sale of no longer needed office property. Assume that the tax rate for both firms is 36%, and that the notes describe pre-tax amounts. Which of the following is closest to the “normalized” ROE for Firm A and for Firm B, respectively?
A) 17.1 and 16.9. B) 16.0 and 18.0. C) 18.4 and 14.3.
Your answer: C was correct!
The ROE for Firm A is adjusted for the $400,000 loss on discontinued operations and the $300,000 non-recurring gain. The ROE for Firm B is adjusted to remove the effects of the $2.6 million one-time gain. The first step in this problem is to solve for equity using ROE. Then, “normalize” net income by adjusting for discontinued operations and non-recurring items. Then, solve for “normalized” ROE. Firm A: 18% = 3,200,000 / EquityA EquityA = 17,777,778 (rounding) Normalized Net IncomeA = 3,200,000 + (1 – 0.36)(400,000 – 300,000) Normalized ROEA = 3,264,000 / 17,777,778 = 18.360% Firm B: 16% = 16,000,000 / EquityB EquityB = 100,000,000 Normalized Net IncomeB = 16,000,000 + (1 – 0.36)(–2,600,000) Normalized ROEB = 14,336,000 / 100,000,000 = 14.336% 18.360 and 14.336 are closest to 18.4 and 14.3