Controlling interests in the stock of other companies

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controlling interests in the stock of other companies. h. The value of operations is the present value of all the future free cash flows that are expected from current assets-in-place and the expected growth of assets-in-place when discounted at the weighted average cost of capital: . WACC 1 FCF V 1 t t t 0) time op(at The terminal, or horizon value, is the value of operations at the end of the explicit forecast period. It is equal to the present value of all free cash flows beyond the forecast period, discounted back to the end of the forecast period at the weighted average cost of capital: . g WACC ) g 1 ( FCF g WACC FCF V N 1 N N) time op(at The free cash flow model defines the total value of a company as the value of operations plus the value of nonoperating assets plus the value of growth options. 7-3 A perpetual bond is similar to a no-growth stock and to a share of preferred stock in the following ways: 1. All three derive their values from a series of cash inflows--coupon payments from the perpetual bond, and dividends from both types of stock. 2 All three are assumed to have indefinite lives with no maturity value (M) for the perpetual bond and no capital gains yield for the stocks. 7-4 The first step is to find the value of operations by discounting all expected future free cash flows at the weighted average cost of capital. The second step is to find the total corporate value by summing the value of operations, the value of nonoperating assets, and the value of growth options. The third step is to find the value of equity by subtracting the value of debt and preferred stock from the total value of the corporation. The last step is to divide the value of equity by the number of shares of common stock. 35
SOLUTIONS TO END-OF-CHAPTER PROBLEMS 7-1 D 0 = $1.50; g 1-3 = 5%; g n = 10%; D 1 through D 5 = ? D 1 = D 0 (1 + g 1 ) = $1.50(1.05) = $1.5750. D 2 = D 0 (1 + g 1 )(1 + g 2 ) = $1.50(1.05) 2 = $1.6538. D 3 = D 0 (1 + g 1 )(1 + g 2 )(1 + g 3 ) = $1.50(1.05) 3 = $1.7364. D 4 = D 0 (1 + g 1 )(1 + g 2 )(1 + g 3 )(1 + g n ) = $1.50(1.05) 3 (1.10) = $1.9101. D 5 = D 0 (1 + g 1 )(1 + g 2 )(1 + g 3 )(1 + g n ) 2 = $1.50(1.05) 3 (1.10) 2 = $2.1011. 7-2 D 1 = $1.50; g = 6%; r s = 13%; 0 P ˆ = ? 0 P ˆ = g r D s 1 = 06 . 0 13 . 0 50 . 1 $ = $21.43. 7-3 P 0 = $22; D 0 = $1.20; g = 10%; 1 P ˆ = ?; r s = ? 1 P ˆ = P 0 (1 + g) = $22(1.10) = $24.20. r s = 0 1 P D + g = 22 $ ) 10 . 1 ( 20 . 1 $ + 0.10 36
= 22 $ 32 . 1 $ + 0.10 = 16.00%. r s = 16.00%. 7-4 D ps = $5.00; V ps = $50; r ps = ? r ps = ps ps v D = 00 . 50 $ 00 . 5 $ = 10%. 37
7-5 0 1 2 3 | | | | D 0 = 2.00 D 1 D 2 D 3 2 P ˆ Step 1: Calculate the required rate of return on the stock:
Step 3: Calculate the PV of the expected dividends:
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Step 5: Calculate the PV of 2 P ˆ : PV = $58.11/(1.123) 2 = $46.08. Step 6: Sum the PVs to obtain the stock’s price: 0 P ˆ = $4.42 + $46.08 = $50.50. Alternatively, using a financial calculator, input the following: CF 0 = 0, CF 1 = 2.40, and CF 2 = 60.99 (2.88 + 58.11) and then enter I/YR = 12.3 to solve for NPV = $50.50.

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