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Ch05_Solutions

# Ch05_Solutions - Chapter 5 Residual Income Valuation...

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Chapter 5 – Residual Income Valuation Solutions 1. Yes, VIM earned a positive residual income: EBIT 300,000 Interest 120,000 (2,000,000 × 6%) Pretax income 180,000 Tax expense 72,000 Net income 108,000 Equity charge = Equity capital × Required return on equity = (1/3)(3,000,000) × 0.10 = 1,000,000 × 0.10 = 100,000 Residual income = Net income – Equity charge = 108,000 – 100,000 = 8,000 2. According to the residual income model, intrinsic value for a share of common stock equals book value per share plus the present value of expected future per- share residual income. Book value per share was given as \$20. Noting that debt is (2/3)(\$3,000,000) = \$2,000,000 so that interest is \$2,000,000 × 6% = \$120,000, we find that VIM has residual income of \$8,000 calculated (as in Problem 1) as follows: Residual income = Net income – Equity charge = [(EBIT – Interest)(1 – Tax rate)] – [(Equity capital)(Required return on equity)] = [(\$300,000 – \$120,000)(1 – 0.40)] – [(\$1,000,000)(0.10)] = \$108,000 – \$100,000 = \$8,000 Therefore, residual income per share is \$8,000/50,000 shares = \$0.16 per share. Because EBIT is expected to continue at the current level indefinitely, we treat the expected per-share residual income of \$0.16 as a perpetuity. With a required return on equity of 10 percent, we have Intrinsic value = \$20 + \$0.16/0.10 = \$20 + \$1.60 = \$21.60 3. With g = b × ROE = (1 – 0.80)(0.15) = (0.20)(0.15) = 0.03, P/B = (ROE – g )/( r g ) = (0.15 – 0.03)/(0.12 – 0.03) = 0.12/0.09 = 1.33 or P/B = 1 + (ROE – r )/( r g ) 1

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= 1 + (0.15 – 0.12)/(0.12 – 0.03) = 1.33 4. In this problem, interest expense has already been deducted in arriving at NMP’s pretax income of \$5.1 million. Therefore, Net income = Pretax income × (1 – Tax rate) = \$5.1 million × (1 – 0.4) = \$5.1 × 0.6 = \$3.06 million Equity charge: Total equity × Cost of equity capital = (0.1 × \$450 million) × 12% = \$45 million × 0.12 = \$5,400,000 Residual income = Net income – Equity charge = \$3,060,000 – \$5,400,000 = –\$2,340,000 NMP had negative residual income of –\$2,340,000 in 2001. 5. To achieve a positive residual income, a company’s net operating profit after taxes as a percentage of its total assets can be compared with the weighted- average cost of its capital. For SWI: NOPAT/Assets = 10 million/100 million = 10 percent WACC = (0.5)(After-tax cost of debt) + (0.5)(Cost of equity) = (0.5)(0.09) (0.6) + (0.5)(0.12) = (0.5)(0.054) + (0.5)(0.12) = 0.027 + 0.06 = 0.087 = 8.7% Therefore, SWI’s residual income was positive. Specifically, residual income equals (0.10 – 0.087) × €100 million = €1.3 million. 6. A. EVA = NOPAT – WACC × (Beginning book value of assets) = 100 – (11%) × (200 + 300) = 100 – (11%)(500) = \$45 B. RI t = E t rB t –1 = 5.00 – (11%)(30.00) = 5.00 – 3.30 = €1.70 C. RI t = (ROE t r ) × B t –1 = (18% – 12%) × (30) = €1.80 7. A. Economic value added = Net operating profit after taxes – (Cost of capital × Total capital) = \$100 million – (14% × \$700 million) = \$2 million. In the absence of information that would be required to calculate the weighted average cost of debt and equity, and given that Sundanci has no long-term debt, the only capital cost used is the required rate of return on equity of 14 percent.
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