Stocks and Their Valuation
Chapter 10
Stocks and Their Valuation
Learning Objectives
Solutions to End-of-Chapter Problems
10-1 D0 = $1.25; g1-3 = 6%; gn = 4%; D1 through D5 = ?
D1 = D0(1 + g1) = $1.25(1.06) = $1.3250.
D2 = D0(1 + g1)(1 + g2) = $1.25(1.06)2 = $1.4045.
D3 = D0(1 + g1)(1 + g2)(1 + g3) = $1.25(1.06)3 = $1.4888.
D4 = D0(1 + g1)(1 + g2)(1 + g3)(1 + gn) = $1.25(1.06)3(1.04) = $1.5483.
D5 = D0(1 + g1)(1 + g2)(1 + g3)(1 + gn)2 = $1.25(1.06)3(1.04)2 = $1.6103.
10-2 = $1.35/(12% – 6%) = $22.50
10-3 D1 = $0.55; g = 6%; rs = 12%; = ?
10-4 P0 = $22; D0 = $1.10; g = 7%; = ?; rs = ?
= P0(1 + g) = $22(1.07) = $23.54.
= + g = + 0.06 = + 0.06 = 11.35%. rs = 11.35%.
10-5 a. The terminal, or horizon, date is the date when the growth rate becomes constant. This occurs at the end of Year 2.
b. 0 1 2 3 | | | | 1.50 1.77 2.09 2.19
31.29 =
The horizon, or terminal, value is the value at the horizon date of all dividends expected thereafter. In this problem it is calculated as follows: c. The firm’s intrinsic value is calculated as the sum of the present value of all dividends during the supernormal growth period plus the present value of the terminal value. Using your financial calculator, enter the following inputs: CF0 = 0, CF1 = 1.50, CF2 = 1.77 + 31.29 = 33.06, I/YR = 10, and then solve for NPV = $28.69.
10-6 The firm’s free cash flow is expected to grow at a constant rate, hence we can apply a constant growth formula to determine the total value of the firm.
Firm value = FCF1/(WACC – g) = $145,000,000/(0.12 – 0.06) = $2,416,666,667.
To find the value of an equity claim upon the company (share of stock), we must subtract out the market value of debt and preferred stock. This firm happens to be entirely equity funded, and this step is unnecessary. Hence, to find the value of a share of stock, we divide equity value (or in this case, firm value) by the number of shares
Stocks and Their Valuation
Learning Objectives
Solutions to End-of-Chapter Problems
10-1 D0 = $1.25; g1-3 = 6%; gn = 4%; D1 through D5 = ?
D1 = D0(1 + g1) = $1.25(1.06) = $1.3250.
D2 = D0(1 + g1)(1 + g2) = $1.25(1.06)2 = $1.4045.
D3 = D0(1 + g1)(1 + g2)(1 + g3) = $1.25(1.06)3 = $1.4888.
D4 = D0(1 + g1)(1 + g2)(1 + g3)(1 + gn) = $1.25(1.06)3(1.04) = $1.5483.
D5 = D0(1 + g1)(1 + g2)(1 + g3)(1 + gn)2 = $1.25(1.06)3(1.04)2 = $1.6103.
10-2 = $1.35/(12% – 6%) = $22.50
10-3 D1 = $0.55; g = 6%; rs = 12%; = ?
10-4 P0 = $22; D0 = $1.10; g = 7%; = ?; rs = ?
= P0(1 + g) = $22(1.07) = $23.54.
= + g = + 0.06 = + 0.06 = 11.35%. rs = 11.35%.
10-5 a. The terminal, or horizon, date is the date when the growth rate becomes constant. This occurs at the end of Year 2.
b. 0 1 2 3 | | | | 1.50 1.77 2.09 2.19
31.29 =
The horizon, or terminal, value is the value at the horizon date of all dividends expected thereafter. In this problem it is calculated as follows: c. The firm’s intrinsic value is calculated as the sum of the present value of all dividends during the supernormal growth period plus the present value of the terminal value. Using your financial calculator, enter the following inputs: CF0 = 0, CF1 = 1.50, CF2 = 1.77 + 31.29 = 33.06, I/YR = 10, and then solve for NPV = $28.69.
10-6 The firm’s free cash flow is expected to grow at a constant rate, hence we can apply a constant growth formula to determine the total value of the firm.
Firm value = FCF1/(WACC – g) = $145,000,000/(0.12 – 0.06) = $2,416,666,667.
To find the value of an equity claim upon the company (share of stock), we must subtract out the market value of debt and preferred stock. This firm happens to be entirely equity funded, and this step is unnecessary. Hence, to find the value of a share of stock, we divide equity value (or in this case, firm value) by the number of shares