A firm evaluates all of its projects by applying the IRR rule. A project under consideration has the following cash flows:

Problem 9-7 Calculating IRR [LO5]
A firm evaluates all of its projects by applying the IRR rule. A project under consideration has the following cash flows:
  
Year    Cash Flow
0    –$    28,400   
1         12,400   
2         15,400   
3         11,400   
________________________________________
 
If the required return is 15 percent, what is the IRR for this project? (Do not round intermediate calculations and enter your answer as a percent rounded to 2 decimal places, e.g., 32.16.)

Should the firm accept the project?

•   
No
•   
Yes
Explanation
Note: Intermediate answers are shown below as rounded, but the full answer was used to complete the calculation.

The IRR is the interest rate that makes the NPV of the project equal to zero. So, the equation that defines the IRR for this project is:

0 = –$28,400 + $12,400/(1 + IRR) + $15,400/(1 + IRR)2 + $11,400/(1 + IRR)3

Using a spreadsheet, financial calculator, or trial and error to find the root of the equation, we find that:

IRR = 18.24%

Since the IRR is greater than the required return, we would accept the project.
 
Calculator Solution:

CFo	–$28,400
C01	$12,400
F01	1
C02	$15,400
F02	1
C03	$11,400
F03	1
IRR CPT
18.24%

Thank you!

An investment project provides cash inflows of $675 per year for eight years.

Problem 9-2 Calculating Payback [LO2]
An investment project provides cash inflows of $675 per year for eight years.
a.    What is the project payback period if the initial cost is $1,850? (Enter 0 if the project never pays back. Round your answer to 2 decimal places, e.g., 32.16.)

b.    What is the project payback period if the initial cost is $3,600? (Enter 0 if the project never pays back. Round your answer to 2 decimal places, e.g., 32.16.)
c.    What is the project payback period if the initial cost is $5,500? (Enter 0 if the project never pays back. 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.

To calculate the payback period, we need to find the time that the project requires to recover its initial investment. The cash flows in this problem are an annuity, so the calculation is simpler. If the initial cost is $1,850, the payback period is:

Payback = 2 + ($500/$675) = 2.74 years
 
There is a shortcut to calculate the payback period when the future cash flows are an annuity. Just divide the initial cost by the annual cash flow. For the $3,600 cost, the payback period is:

Payback = $3,600/$675 = 5.33 years
 
The payback period for an initial cost of $5,500 is a little trickier. Notice that the total cash inflows after eight years will be:

Total cash inflows = 8($675) = $5,400

If the initial cost is $5,500, the project never pays back. Notice that if you use the shortcut for annuity cash flows, you get:

Payback = $5,500/$675 = 8.15 years

This answer does not make sense since the cash flows stop after eight years, so again, we must conclude the payback period is never.

The Jackson-Timberlake Wardrobe Co. just paid a dividend of $1.55 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 14 percent on the company's stock.

Problem 8-1 Stock Values [LO1]
The Jackson-Timberlake Wardrobe Co. just paid a dividend of $1.55 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 14 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 7 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 = $1.55(1.06)/(.14 − .06)
P0 = $20.54

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 = $1.55(1.06)4/(.14 − .06)
P3 = $24.46

We can do the same thing to find the dividend in Year 8, which gives us the price in Year 7, so:

P7 = D7(1 + g)/(R − g) = D0(1 + g)8/(R − g)
P7 = $1.55(1.06)8/(.14 − .06)
P7 = $30.88

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 =$20.54(1 + .06)3
P3 = $24.46

And the stock price in 7 years will be:

P7 = P0(1 + g)7
P7 = $20.54(1 + .06)7
P7 = $30.88

The Perfect Rose Co. has earnings of $1.95 per share. The benchmark PE for the company is 12.

Problem 8-12 Stock Valuation and PE [LO2]
The Perfect Rose Co. has earnings of $1.95 per share. The benchmark PE for the company is 12.
a.    What stock price would you consider appropriate? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

b.    What if the benchmark PE were 15? (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.

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 12, we find:

P = 12($1.95)
P = $23.40

And with a PE ratio of 15, we find:

P = 15($1.95)
P = $29.25

Red, Inc., Yellow Corp., and Blue Company each will pay a dividend of $2.60 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.

Problem 8-9 Stock Valuation and Required Return [LO1]
Red, Inc., Yellow Corp., and Blue Company each will pay a dividend of $2.60 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? (Do not round intermediate calculations and round your answers 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.

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 = $2.60/(.06 − .04) = $130.00
Yellow stock price = $2.60/(.09 − .04) = $52.00
Blue stock price = $2.60/(.12 − .04) = $32.50

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.

Grateful Eight Co. is expected to maintain a constant 6.8 percent growth rate in its dividends indefinitely. If the company has a dividend yield of 8.6 percent, what is the required return on the company’s stock?

Problem 8-5 Stock Valuation [LO1]
Grateful Eight Co. is expected to maintain a constant 6.8 percent growth rate in its dividends indefinitely. If the company has a dividend yield of 8.6 percent, what is the required return on the company’s stock? (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 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 = .086 + .068
R = .1540, or 15.40%

The Jackson-Timberlake Wardrobe Co. just paid a dividend of $1.55 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 14 percent on the company's stock.

Problem 8-1 Stock Values [LO1]

The Jackson-Timberlake Wardrobe Co. just paid a dividend of $1.55 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 14 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 7 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 = $1.55(1.06)/(.14 − .06)
P0 = $20.54

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 = $1.55(1.06)4/(.14 − .06)
P3 = $24.46

We can do the same thing to find the dividend in Year 8, which gives us the price in Year 7, so:

P7 = D7(1 + g)/(R − g) = D0(1 + g)8/(R − g)
P7 = $1.55(1.06)8/(.14 − .06)
P7 = $30.88

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 =$20.54(1 + .06)3
P3 = $24.46

And the stock price in 7 years will be:

P7 = P0(1 + g)7
P7 = $20.54(1 + .06)7
P7 = $30.88

Thank You!