## Thursday, 31 July 2014

### Gontier Corporation stock currently sells for \$64.58 per share. The market requires a return of 10 percent on the firm’s stock.

Gontier Corporation stock currently sells for \$64.58 per share. The market requires a return of 10 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).)

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 = \$64.58(0.10 – 0.0575) / (1 + 0.0575) D0 = \$2.60

## Antiques ‘R’ Us is a mature manufacturing firm. The company just paid a dividend of \$12.10, but management expects to reduce the payout by 4.5 percent per year, indefinitely.

 Required: If you require a return of 11 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).)

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 = \$12.10(1 – 0.0450) / [(.11 – (–.0450)] P0 = \$74.55

### Hot Wings, Inc., has an odd dividend policy. The company has just paid a dividend of \$9.25 per share

Hot Wings, Inc., has an odd dividend policy. The company has just paid a dividend of \$9.25 per share and has announced that it will increase the dividend by \$7.25 per share for each of the next four years, and then never pay another dividend.
 Required: If you require a return of 14 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).)

Explanation:

### Rabie, Inc., has an issue of preferred stock outstanding that pays a \$5.70 dividend every year, in perpetuity.

Rabie, Inc., has an issue of preferred stock outstanding that pays a \$5.70 dividend every year, in perpetuity.

 Required: If this issue currently sells for \$80.45 per share, what is the required return? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

 Required return %

Explanation:
 The price of a share of preferred stock is the dividend divided by the required return. This is the same equation as the constant growth model, with a dividend growth rate of zero percent. Remember, most preferred stock pays a fixed dividend, so the growth rate is zero. This is a special case of the dividend growth model where the growth rate is zero, or the level perpetuity equation. Using this equation, we find the price per share of the preferred stock is:
 R = D / P0 R = \$5.70 / \$80.45 R = 0.0709, or 7.09%

### Bui Corp. pays a constant \$14.20 dividend on its stock. The company will maintain this dividend for the next ten years and will then cease paying dividends forever.

Bui Corp. pays a constant \$14.20 dividend on its stock. The company will maintain this dividend for the next ten 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 ten years, so the price of the stock is the present value of an annuity, which will be:
 P0 = \$14.20(PVIFA9%,10) P0 = \$91.13

### Suppose you know that a company’s stock currently sells for \$66.90 per share and the required return on the stock is 9 percent. You also know that the total return on the stock is evenly divided between capital gains yield and dividend yield.

Suppose you know that a company’s stock currently sells for \$66.90 per share and the required return on the stock is 9 percent. You also know that the total return on the stock is evenly divided between capital gains yield and dividend yield.

 Required: If it’s the company’s policy to always maintain a constant growth rate in its dividends, what is the current dividend per share? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

Explanation:
 We know the stock has a required return of 9 percent, and the dividend and capital gains yield are equal, so:

 Dividend yield = 1/2(.09) Dividend yield = .045 = Capital gains yield

 Now we know both the dividend yield and capital gains yield. The dividend is simply the stock price times the dividend yield, so:

 D1 = .045(\$66.90) D1 = \$3.01

 This is the dividend next year. The question asks for the dividend this year. Using the relationship between the dividend this year and the dividend next year:

 D1 = D0(1 + g)

 We can solve for the dividend that was just paid:

 \$3.01 = D0(1 + .045) D0 = \$3.01 / 1.045 D0 = \$2.88

### Raffalovich, Inc., is expected to maintain a constant 5.4 percent growth rate in its dividends, indefinitely.

Raffalovich, Inc., is expected to maintain a constant 5.4 percent growth rate in its dividends, indefinitely.

 Required: If the company has a dividend yield of 3.9 percent, what is the required return on the company’s stock? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

 Required return %

Explanation:
 The required return of a stock is made up of two parts: The dividend yield and the capital gains yield. So, the required return of this stock is:

 R = Dividend yield + Capital gains yield R = .0390 + .0540 R = .0930, or 9.30%

### The next dividend payment by Wyatt, Inc., will be \$2.50 per share. The dividends are anticipated to

The next dividend payment by Wyatt, Inc., will be \$2.50 per share. The dividends are anticipated to maintain a growth rate of 5.75 percent, forever. Assume the stock currently sells for \$48.60 per share.

 Requirement 1: What is the dividend yield? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

 Dividend yield %

 Requirement 2: What is the expected capital gains yield? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

 Capital gains yield %

Explanation: 1:
 The dividend yield is the dividend next year divided by the current price, so the dividend yield is:

 Dividend yield = D1 / P0 Dividend yield = \$2.50 / \$48.60 Dividend yield = .0514, or 5.14%

2:
 The capital gains yield, or percentage increase in the stock price, is the same as the dividend growth rate, so:

 Capital gains yield = 5.75%

### The next dividend payment by Wyatt, Inc., will be \$3.10 per share. The dividends are anticipated to

The next dividend payment by Wyatt, Inc., will be \$3.10 per share. The dividends are anticipated to maintain a growth rate of 3.75 percent, forever.

 Required: If the stock currently sells for \$49.80 per share, what is the required return? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

 Required return %

Explanation:
 We need to find the required return of the stock. Using the constant growth model, we can solve the equation for R. Doing so, we find:

 R = (D1 / P0) + g R = (\$3.10 / \$49.80) + .0375 R = .0997, or 9.97%

### Anton, Inc., just paid a dividend of \$2.40 per share on its stock. The dividends are expected to grow at

Anton, Inc., just paid a dividend of \$2.40 per share on its stock. The dividends are expected to grow at a constant rate of 6.25 percent per year, indefinitely. Assume investors require a return of 12 percent on this stock.

 Requirement 1: What is the current price? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

 Current price \$

 Requirement 2: What will the price be in four years and in sixteen years? (Do not round intermediate calculations. Round your answers to 2 decimal places (e.g., 32.16).)

 Four years \$ Sixteen years \$

Explanation: 1:
 The constant dividend growth model is: Pt = Dt × (1 + g) / (R – g) So, the price of the stock today is: P0 = D0 (1 + g) / (R – g) P0 = \$2.40 (1.0625) / (0.12 – 0.0625) P0 = \$44.35 2: The dividend at year 5 is the dividend today times the FVIF for the growth rate in dividends and five years, so: P4 = D4 (1 + g) / (R – g) P4 = D0 (1 + g)5 / (R – g) P4 = \$2.40 (1.0625)5 / (0.12 – 0.0625) P4 = \$56.52 We can do the same thing to find the dividend in Year 17, which gives us the price in Year 16, so: P16 = D16 (1 + g) / (R – g) P16 = D0 (1 + g)17 / (R – g) P16 = \$2.40 (1.0625)17 / (0.12 – 0.0625) P16 = \$116.99 There is another feature of the constant dividend growth model: The stock price grows at the dividend growth rate. So, if we know the stock price today, we can find the future value for any time in the future we want to calculate the stock price. In this problem, we want to know the stock price in Year four, and we have already calculated the stock price today. The stock price in Year four will be: P4 = P0(1 + g)4 P4 = \$44.35(1 + 0.0625)4 P4 = \$56.52 And the stock price in Year 16 will be: P16 = P0(1 + g)16 P16 = \$44.35(1 + 0.0625)16 P16 = \$116.99

### Nofal Corporation will pay a \$4.65 per share dividend next year. The company pledges to increase its dividend by 7 percent per year, indefinitely.

Nofal Corporation will pay a \$4.65 per share dividend next year. The company pledges to increase its dividend by 7 percent per year, indefinitely.

 Required: If you require a return of 11 percent on your investment, how much will you pay for the company’s stock today? (Do not round intermediate calculations. Round your answer to 2 decimal places (e.g., 32.16).)

Explanation:
 Using the constant growth model, we find the price of the stock today is: P0 = D1 / (R – g) P0 = \$4.65 / (.11 – .0700) P0 = \$116.25