The Jackson-Timberlake Wardrobe Co. just paid a dividend of $1.60 per share on its stock. The dividends are expected to grow at a constant rate of 6 percent per year indefinitely.

The Jackson-Timberlake Wardrobe Co. just paid a dividend of $1.60 per share on its stock. The dividends are expected to grow at a constant rate of 6 percent per year indefinitely. Investors require a return of 10 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 12 years? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Explanation

Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.

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 = $1.60(1.06)/(.10 − .06)

P0 = $42.40

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 = $1.60(1.06)4/(.10 − .06)

P3 = $50.50

We can do the same thing to find the dividend in Year 13, which gives us the price in Year 12, so:

P12 = D12(1 + g)/(R − g) = D0(1 + g)13/(R − g)

P12 = $1.60(1.06)13/(.10 − .06)

P12 = $85.32

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 =$42.40(1 + .06)3

P3 = $50.50

And the stock price in 12 years will be:

P12 = P0(1 + g)12

P12 = $42.40(1 + .06)12

P12 = $85.32

Red, Inc., Yellow Corp., and Blue Company each will pay a dividend of $3.10 next year. The growth rate in dividends for all three companies is 4 percent. The required return for each company’s stock is 7 percent, 10 percent, and 13 percent, respectively. What is the stock price for each company?

Red, Inc., Yellow Corp., and Blue Company each will pay a dividend of $3.10 next year. The growth rate in dividends for all three companies is 4 percent. The required return for each company’s stock is 7 percent, 10 percent, and 13 percent, respectively. What is the stock price for each company?

Explanation

Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.

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 = $3.10/(.07 − .04) = $103.33

Yellow stock price = $3.10/(.10 − .04) = $51.67

Blue stock price = $3.10/(.13 − .04) = $34.44

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 Perfect Rose Co. has earnings of $2.00 per share. The benchmark PE for the company is 13.

The Perfect Rose Co. has earnings of $2.00 per share. The benchmark PE for the company is 13.

 
a. What stock price would you consider appropriate?

b. What if the benchmark PE were 16?

Explanation

Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.

Using the equation to calculate the price of a share of stock with the PE ratio:

P = Benchmark PE ratio × EPS

So, with a PE ratio of 13, we find:

P = 13($2.00)

P = $26.00

And with a PE ratio of 16, we find:

P = 16($2.00)

P = $32.00

Grateful Eight Co. is expected to maintain a constant 4.4 percent growth rate in its dividends indefinitely. If the company has a dividend yield of 6.2 percent, what is the required return on the company’s stock?

Grateful Eight Co. is expected to maintain a constant 4.4 percent growth rate in its dividends indefinitely. If the company has a dividend yield of 6.2 percent, what is the required return on the company’s stock?

Explanation

Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.

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 = .062 + .044

R = .1060, or 10.60%

An investment offers a total return of 17 percent over the coming year. Janice Yellen thinks the total real return on this investment will be only 12 percent.

An investment offers a total return of 17 percent over the coming year. Janice Yellen thinks the total real return on this investment will be only 12 percent.

 What does Janice believe the inflation rate will be over the next year?

Explanation

Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.

The Fisher equation, which shows the exact relationship between nominal interest rates, real interest rates, and inflation is:

(1 + R) = (1 + r)(1 + h)

h = (1 + .17)/(1 + .12) – 1

h = .0446, or 4.46%

Thanks

A Japanese company has a bond outstanding that sells for 95 percent of its ¥100,000 par value. The bond has a coupon rate of 5.4 percent paid annually and matures in 16 years.

A Japanese company has a bond outstanding that sells for 95 percent of its ¥100,000 par value. The bond has a coupon rate of 5.4 percent paid annually and matures in 16 years.


What is the yield to maturity of this bond (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Explanation

Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.

Here we need to find the YTM of a bond. The equation for the bond price is:

P = ¥95,000 = ¥5,400(PVIFAR%,16) + ¥100,000(PVIFR%,16)

Notice the equation cannot be solved directly for R. Using a spreadsheet, a financial calculator, or trial and error, we find:

R = YTM = 5.89%

Calculator Solution:

Enter

16

±¥95,000

¥5,400

¥100,000

N

I/Y

PV

PMT

FV

Solve for

5.89%

Thanks

Treasury bills are currently paying 9 percent and the inflation rate is 2.9 percent.

Problem 7-12 Calculating Real Rates of Return [LO4]

Treasury bills are currently paying 9 percent and the inflation rate is 2.9 percent.

a.
What is the approximate real rate of interest? (Enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

b. What is the exact real rate? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Explanation

Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.

The approximate relationship between nominal interest rates (R), real interest rates (r), and inflation (h) is:

R ≈ r + h

Approximate r = .09 – .029

Approximate r = .061, or 6.10%

The Fisher equation, which shows the exact relationship between nominal interest rates, real interest rates, and inflation is:

(1 + R) = (1 + r)(1 + h)

(1 + .09) = (1 + r)(1 + .029)

r = (1 + .09)/(1 + .029) – 1

r = .0593, or 5.93%

Thanks

Janicex Co. is growing quickly. Dividends are expected to grow at a rate of 24 percent for the next three years, with the growth rate falling off to a constant 6 percent thereafter. If the required return is 11 percent and the company just paid a dividend of $1.90, what is the current share price ?

Janicex Co. is growing quickly. Dividends are expected to grow at a rate of 24 percent for the next three years, with the growth rate falling off to a constant 6 percent thereafter. If the required return is 11 percent and the company just paid a dividend of $1.90, what is the current share price ?

Answer

Thank you!