Red, Inc., Yellow Corp., and Blue Company each will pay a dividend of $2.35 next year. The growth rate in dividends for all three companies is 4 percent. The required return for each company’s stock is 6 percent, 9 percent, and 12 percent, respectively. What is the stock price for each company?

Red, Inc., Yellow Corp., and Blue Company each will pay a dividend of $2.35 next year. The growth rate in dividends for all three companies is 4 percent. The required return for each company’s stock is 6 percent, 9 percent, and 12 percent, respectively. What is the stock price for each company?

We can use the constant dividend growth model, which is:

Pt = Dt × (1 + g)/(R – g)

So the price of each company’s stock today is:

Red stock price = $2.35/(.06 − .04) = $117.50

Yellow stock price = $2.35/(.09 − .04) = $47.00

Blue stock price = $2.35/(.12 − .04) = $29.38

As the required return increases, the stock price decreases. This is a function of the time value of money: A higher discount rate decreases the present value of cash flows. It is also important to note that relatively small changes in the required return can have a dramatic impact on the stock price.

The Jackson-Timberlake Wardrobe Co. just paid a dividend of $1.70 per share on its stock. The dividends are expected to grow at a constant rate of 5 percent per year indefinitely. Investors require a return of 15 percent on the company's stock.

The Jackson-Timberlake Wardrobe Co. just paid a dividend of $1.70 per share on its stock. The dividends are expected to grow at a constant rate of 5 percent per year indefinitely. Investors require a return of 15 percent on the company's stock.

a.    What is the current stock price? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
b.    What will the stock price be in 3 years? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
c.    What will the stock price be in 20 years? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

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 = $1.70(1.05)/(.15 − .05)

P0 = $17.85

The dividend at Year 4 is the dividend today times the FVIF for the growth rate in dividends and four years, so:

P3 = D3(1 + g)/(R − g) = D0(1 + g)4/(R − g)

P3 = $1.70(1.05)4/(.15 − .05)

P3 = $20.66

We can do the same thing to find the dividend in Year 21, which gives us the price in Year 20, so:

P20 = D20(1 + g)/(R − g) = D0(1 + g)21/(R − g)

P20 = $1.70(1.05)21/(.15 − .05)

P20 = $47.36

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 three years, and we have already calculated the stock price today. The stock price in three years will be:

P3 = P0(1 + g)3

P3 =$17.85(1 + .05)3

P3 = $20.66

And the stock price in 20 years will be:

P20 = P0(1 + g)20

P20 = $17.85(1 + .05)20

P20 = $47.36