HW FIN 3331
HW FIN 3331
Chapter 9
9.1. Warr Corporation just paid a dividend of $1.50 a share (that is, D0 = $1.50). The dividend is expected to grow 7% a year for 3 years and then at 5% a year thereafter. What is the expected dividend per share for each of the next 5 years?
D0 = $1.50; g1-3 = 7%; gn = 5%; D1 through D5 = ?
D1 = D0(1 + g1) = $1.50(1.07) = $1.6050.
D2 = D0(1 + g1)(1 + g2) = $1.50(1.07)2 = $1.7174.
D3 = D0(1 + g1)(1 + g2)(1 + g3) = $1.50(1.07)3 = $1.8376.
D4 = D0(1 + g1)(1 + g2)(1 + g3)(1 + gn) = $1.50(1.07)3(1.05) = $1.9294.
D5 = D0(1 + g1)(1 + g2)(1 + g3)(1 + gn)2 = $1.50(1.07)3(1.05)2 = $2.0259.
9.2. Thomas Brothers is expected to pay $0.50 per share dividend at the end of the year (that is, D1 = $0.50). The dividend is expected to grow at a constant rate of 7% a year. The required rate of return on the stock, Rs, is 15%. What is the stock’s value per share?
D1 = $0.50; g = 7%; rs = 15%; P(hat) 0 = ?
9.14. Microtech Corporation is expanding rapidly, and it currently needs to retain all of its earnings, hence it does not pay any dividends. However, investors expect Microtech to begin paying dividends, with the first dividend of $1.00 coming 3 years from today. The dividend should grow rapidly – at a rate of 50 percent per year – during Years 4 and 5. After Year 5, the company should grow at a constant rate of 8 percent per year. If the required return on the stock is 15 percent, what is the value of the stock today?
Solution:
Calculate the expected dividends:
D3 = 1.00
D4 = 1.00(1.50) = 1.50
D5 = 1.50(1.50) = 2.25
Calculate the PV of the expected dividends:
PV(Div) = $1.00/(1.15)3 + $1.50/(1.15)4 + $2.25/(1.15)5 = $2.634
Compute D6 = 2.25 (1.08) = 2.43; Then P5 = D6 /(r - g) = 2.43 / (0.15 - 0.08) = $34.71
Calculate the PV of P5 = $34.71/(1.15)5 = $17.257
Sum the two PVs to obtain the stock’s price: P0 = $2.634.483 + $17.257 = $19.891
Alternatively, using a financial calculator input the following:
CF0 = 0
CF1 = 0, F01 = 2,
C02 = 1.00
Chapter 9
9.1. Warr Corporation just paid a dividend of $1.50 a share (that is, D0 = $1.50). The dividend is expected to grow 7% a year for 3 years and then at 5% a year thereafter. What is the expected dividend per share for each of the next 5 years?
D0 = $1.50; g1-3 = 7%; gn = 5%; D1 through D5 = ?
D1 = D0(1 + g1) = $1.50(1.07) = $1.6050.
D2 = D0(1 + g1)(1 + g2) = $1.50(1.07)2 = $1.7174.
D3 = D0(1 + g1)(1 + g2)(1 + g3) = $1.50(1.07)3 = $1.8376.
D4 = D0(1 + g1)(1 + g2)(1 + g3)(1 + gn) = $1.50(1.07)3(1.05) = $1.9294.
D5 = D0(1 + g1)(1 + g2)(1 + g3)(1 + gn)2 = $1.50(1.07)3(1.05)2 = $2.0259.
9.2. Thomas Brothers is expected to pay $0.50 per share dividend at the end of the year (that is, D1 = $0.50). The dividend is expected to grow at a constant rate of 7% a year. The required rate of return on the stock, Rs, is 15%. What is the stock’s value per share?
D1 = $0.50; g = 7%; rs = 15%; P(hat) 0 = ?
9.14. Microtech Corporation is expanding rapidly, and it currently needs to retain all of its earnings, hence it does not pay any dividends. However, investors expect Microtech to begin paying dividends, with the first dividend of $1.00 coming 3 years from today. The dividend should grow rapidly – at a rate of 50 percent per year – during Years 4 and 5. After Year 5, the company should grow at a constant rate of 8 percent per year. If the required return on the stock is 15 percent, what is the value of the stock today?
Solution:
Calculate the expected dividends:
D3 = 1.00
D4 = 1.00(1.50) = 1.50
D5 = 1.50(1.50) = 2.25
Calculate the PV of the expected dividends:
PV(Div) = $1.00/(1.15)3 + $1.50/(1.15)4 + $2.25/(1.15)5 = $2.634
Compute D6 = 2.25 (1.08) = 2.43; Then P5 = D6 /(r - g) = 2.43 / (0.15 - 0.08) = $34.71
Calculate the PV of P5 = $34.71/(1.15)5 = $17.257
Sum the two PVs to obtain the stock’s price: P0 = $2.634.483 + $17.257 = $19.891
Alternatively, using a financial calculator input the following:
CF0 = 0
CF1 = 0, F01 = 2,
C02 = 1.00