Gontier Corporation stock currently sells for $64.98 per share. The market requires a return of 9 percent on the firm’s stock. Required: If the company maintains a constant 5.75 percent growth rate in dividends, what was the most recent dividend per share paid on the stock? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).) Dividend per share $ Explanation: We are given the stock price, the dividend growth rate, and the required return, and are asked to find the dividend. Using the constant dividend growth model, we get: P0 = D0 (1 + g) / (R – g) Solving this equation for the dividend gives us: D0 = P0(R – g) / (1 + g) D0 = $64.98(0.09 – 0.0575) / (1 + 0.0575) D0 = $2.00

Gontier Corporation stock currently sells for $64.98 per share. The market requires a return of 9 percent on the firm’s stock.

Required:

If the company maintains a constant 5.75 percent growth rate in dividends, what was the most recent dividend per share paid on the stock? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

Dividend per share

$

 
Explanation:

We are given the stock price, the dividend growth rate, and the required return, and are asked to find the dividend. Using the constant dividend growth model, we get:

P0 = D0 (1 + g) / (R – g)

Solving this equation for the dividend gives us:

D0 = P0(R – g) / (1 + g)

D0 = $64.98(0.09 – 0.0575) / (1 + 0.0575)

D0 = $2.00

Antiques ‘R’ Us is a mature manufacturing firm. The company just paid a dividend of $12.40, but management expects to reduce the payout by 5.25 percent per year, indefinitely. Required: If you require a return of 8 percent on this stock, what will you pay for a share today? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).) Current share price $ Explanation: The constant growth model can be applied even if the dividends are declining by a constant percentage, just make sure to recognize the negative growth. So, the price of the stock today will be: P0 = D0 (1 + g) / (R – g) P0 = $12.40(1 – 0.0525) / [(.08 – (–.0525)] P0 = $88.67

Antiques ‘R’ Us is a mature manufacturing firm. The company just paid a dividend of $12.40, but management expects to reduce the payout by 5.25 percent per year, indefinitely.

Required:

If you require a return of 8 percent on this stock, what will you pay for a share today? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

Current share price	$

 
Explanation:

The constant growth model can be applied even if the dividends are declining by a constant percentage, just make sure to recognize the negative growth. So, the price of the stock today will be:

P0 = D0 (1 + g) / (R – g)

P0 = $12.40(1 – 0.0525) / [(.08 – (–.0525)]

P0 = $88.67

Yang Corp. is growing quickly. Dividends are expected to grow at a rate of 31 percent for the next three years, with the growth rate falling off to a constant 6.1 percent thereafter. Required: If the required return is 12 percent and the company just paid a $2.80 dividend, what is the current share price? (Hint: Calculate the first four dividends.) (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).) Current share price $ Explanation: With supernormal dividends, we find the price of the stock when the dividends level off at a constant growth rate, and then find the present value of the future stock price, plus the present value of all dividends during the supernormal growth period. The stock begins constant growth after the third dividend is paid, so we can find the price of the stock in Year 3, when the constant dividend growth begins as: P3 = D3 (1 + g2) / (R – g2) P3 = D0 (1 + g1)3 (1 + g2) / (R – g2) P3 = $2.80(1.31)3(1.061) / (.12 – .061) P3 = $113.20 The price of the stock today is the present value of the first three dividends, plus the present value of the Year 3 stock price. The price of the stock today will be: P0 = $2.80(1.31) / 1.12 + $2.80(1.31)2 / 1.122 + $2.80(1.31)3 / 1.123 + $113.20 / 1.123 P0 = $92.16

Yang Corp. is growing quickly. Dividends are expected to grow at a rate of 31 percent for the next three years, with the growth rate falling off to a constant 6.1 percent thereafter.

Required:

If the required return is 12 percent and the company just paid a $2.80 dividend, what is the current share price? (Hint: Calculate the first four dividends.) (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

Current share price	$

 
Explanation:

With supernormal dividends, we find the price of the stock when the dividends level off at a constant growth rate, and then find the present value of the future stock price, plus the present value of all dividends during the supernormal growth period. The stock begins constant growth after the third dividend is paid, so we can find the price of the stock in Year 3, when the constant dividend growth begins as:

P3 = D3 (1 + g2) / (R – g2)

P3 = D0 (1 + g1)3 (1 + g2) / (R – g2)

P3 = $2.80(1.31)3(1.061) / (.12 – .061)

P3 = $113.20

The price of the stock today is the present value of the first three dividends, plus the present value of the Year 3 stock price. The price of the stock today will be:

P0   = $2.80(1.31) / 1.12 + $2.80(1.31)2 / 1.122 + $2.80(1.31)3 / 1.123 + $113.20 / 1.123

P0   = $92.16

Apocalyptica Corporation is expected to pay the following dividends over the next four years: $6.40, $17.40, $22.40, and $4.20. Afterwards, the company pledges to maintain a constant 6.00 percent growth rate in dividends, forever. Required: If the required return on the stock is 10 percent, what is the current share price? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).) Current share price $ Explanation: With supernormal dividends, we find the price of the stock when the dividends level off at a constant growth rate, and then find the present value of the future stock price, plus the present value of all dividends during the supernormal growth period. The stock begins constant growth after the fourth dividend is paid, so we can find the price of the stock at Year 4, when the constant dividend growth begins, as: P4 = D4 (1 + g) / (R – g) P4 = $4.20(1.0600) / (0.10 – 0.0600) P4 = $111.30 The price of the stock today is the present value of the first four dividends, plus the present value of the Year 4 stock price. So, the price of the stock today will be: P0 = $6.40 / 1.10 + $17.40 / 1.102 + $22.40 / 1.103 + $4.20 / 1.104 + $111.30 / 1.104 P0 = $115.92

Apocalyptica Corporation is expected to pay the following dividends over the next four years: $6.40, $17.40, $22.40, and $4.20. Afterwards, the company pledges to maintain a constant 6.00 percent growth rate in dividends, forever.

Required:

If the required return on the stock is 10 percent, what is the current share price? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

Current share price	$

 
Explanation:

With supernormal dividends, we find the price of the stock when the dividends level off at a constant growth rate, and then find the present value of the future stock price, plus the present value of all dividends during the supernormal growth period. The stock begins constant growth after the fourth dividend is paid, so we can find the price of the stock at Year 4, when the constant dividend growth begins, as:

P4 = D4 (1 + g) / (R – g)

P4 = $4.20(1.0600) / (0.10 – 0.0600)

P4 = $111.30

The price of the stock today is the present value of the first four dividends, plus the present value of the Year 4 stock price. So, the price of the stock today will be:

P0 = $6.40 / 1.10 + $17.40 / 1.102 + $22.40 / 1.103 + $4.20 / 1.104 + $111.30 / 1.104

P0 = $115.92

Hot Wings, Inc., has an odd dividend policy. The company has just paid a dividend of $8.50 per share and has announced that it will increase the dividend by $6.50 per share for each of the next four years, and then never pay another dividend. Required: If you require a return of 16 percent on the company’s stock, how much will you pay for a share today? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).) Current share price $ Explanation: The price of a stock is the PV of the future dividends. This stock is paying four dividends, so the price of the stock is the PV of these dividends discounted at the required return. So, the price of the stock is: P0 = $15.00 / 1.16 + $21.50 / 1.162 + $28.00 / 1.163 + $34.50 / 1.164 P0 = $65.90

Hot Wings, Inc., has an odd dividend policy. The company has just paid a dividend of $8.50 per share and has announced that it will increase the dividend by $6.50 per share for each of the next four years, and then never pay another dividend.

Required:

If you require a return of 16 percent on the company’s stock, how much will you pay for a share today? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

Current share price	$

 
Explanation:

The price of a stock is the PV of the future dividends. This stock is paying four dividends, so the price of the stock is the PV of these dividends discounted at the required return. So, the price of the stock is:

P0 = $15.00 / 1.16 + $21.50 / 1.162 + $28.00 / 1.163 + $34.50 / 1.164

P0 = $65.90

E-Eyes.com has a new issue of preferred stock it calls 20/20 preferred. The stock will pay a $20 dividend per year, but the first dividend will not be paid until 20 years from today. Required: If you require a return of 11.00 percent on this stock, how much should you pay today? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).) Current stock price $ Explanation: Here, we have a stock that pays no dividends for 20 years. Once the stock begins paying dividends, it will have the same dividends forever, a preferred stock. We value the stock at that point, using the preferred stock equation. It is important to remember that the price we find will be the price one year before the first dividend, so: P19 = D20 / R P19 = $20 / .1100 P19 = $181.82 The price of the stock today is simply the present value of the stock price in the future. We simply discount the future stock price at the required return. The price of the stock today will be: P0 = $181.82 / 1.110019 P0 = $25.03

E-Eyes.com has a new issue of preferred stock it calls 20/20 preferred. The stock will pay a $20 dividend per year, but the first dividend will not be paid until 20 years from today.

Required:

If you require a return of 11.00 percent on this stock, how much should you pay today? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

Current stock price

$

 
Explanation:

Here, we have a stock that pays no dividends for 20 years. Once the stock begins paying dividends, it will have the same dividends forever, a preferred stock. We value the stock at that point, using the preferred stock equation. It is important to remember that the price we find will be the price one year before the first dividend, so:

P19 = D20 / R

P19 = $20 / .1100

P19 = $181.82

The price of the stock today is simply the present value of the stock price in the future. We simply discount the future stock price at the required return. The price of the stock today will be:

P0 = $181.82 / 1.110019

P0 = $25.03

The stock price of Webber Co. is $54.30. Investors require a return of 13 percent on similar stocks. Required: If the company plans to pay a dividend of $3.80 next year, what growth rate is expected for the company’s stock price? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).) Growth rate % Explanation: We need to find the growth rate of dividends. Using the constant growth model, we can solve the equation for g. Doing so, we find: g = R – (D1 / P0) g = .13 – ($3.80 / $54.30) g = .0600, or 6.00%

The stock price of Webber Co. is $54.30. Investors require a return of 13 percent on similar stocks.

Required:

If the company plans to pay a dividend of $3.80 next year, what growth rate is expected for the company’s stock price? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

Growth rate

%

 
Explanation:

We need to find the growth rate of dividends. Using the constant growth model, we can solve the equation for g. Doing so, we find:

g = R – (D1 / P0)

g = .13 – ($3.80 / $54.30)

g = .0600, or 6.00%

Bui Corp. pays a constant $14.60 dividend on its stock. The company will maintain this dividend for the next nine years and will then cease paying dividends forever. Required: If the required return on this stock is 9 percent, what is the current share price? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).) Current share price $ Explanation: The price of any financial instrument is the present value of the future cash flows. The future dividends of this stock are an annuity for nine years, so the price of the stock is the present value of an annuity, which will be: P0 = $14.60(PVIFA9%,9) P0 = $87.53

Bui Corp. pays a constant $14.60 dividend on its stock. The company will maintain this dividend for the next nine years and will then cease paying dividends forever.

Required:

If the required return on this stock is 9 percent, what is the current share price? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

Current share price

$

 
Explanation:

The price of any financial instrument is the present value of the future cash flows. The future dividends of this stock are an annuity for nine years, so the price of the stock is the present value of an annuity, which will be:

P0 = $14.60(PVIFA9%,9)

P0 = $87.53