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# Present and Future value, NPV, IRR, Profitability index, Ranking of projects

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Question 1: Future value of annuity problem.
You deposit \$8,000 into a retirement account at the end of the next 12 years earning 10% interest, what is the future value of your retirement after 12 years?
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Question 2:
Part 1)
Using a 4.4% discount rate, calculate the Net Present Value, Payback, Profitability Index and IRR for each of the investment projects below (note, the inflows are for each year). Based on your calculations rank the projects and support you answer.
Project 1:
Initial Invest = \$505,000, Cash inflows of \$105,000 for years 1-5 and \$50,000 for years 6-10
Project 2:
Initial Invest = \$1,100,000, Cash inflows of \$420,000 for years 1-3, \$0 for years 4-7 and \$250,000 for years 8-10.
Project 3:
Initial Invest = \$840,000, Cash inflows of \$300,000 for years 1-5, \$0 for years 6-9 and \$100,000 for year 10.
(Part 2)
Assuming a budget of \$1,200,000 what are your recommendations for the three projects in the above problem. Explain.
Assuming a budget of \$2,000,000 what are your recommendations for the above problem? Explain.
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Question 3: Risk & Return and the CAPM.
Based on the following information, calculate the required return based on the CAPM:
Risk Free Rate = 3.75%
Market Return =10%
Beta = 1.32
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Question 4: Present value of annuity problem.
You will receive \$2,000 at the end of the next 12 years, assuming a 6% discount rate, what is the present value of the cash flows?

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#### Solution Summary

This solution provides calculations in Excel for future value, preset value, required return, and various other financial questions.

\$2.19

## Capital Budgeting and Cost of Capital

1. A project has an up-front cost of \$100,000. The project's WACC is 12 percent and its net present value is \$10,000. Which of the following statements is most correct?

a. The project should be rejected since its return is less than the WACC.
b. The project's internal rate of return is greater than 12 percent.
c. The project's modified internal rate of return is less than 12 percent
d. All of the above answers are correct.
e. None of the above answers is correct.

2. The regular payback method has a number of disadvantages, some of which are listed below. Which of these items is not a disadvantage of this method?
a. Lack of an objective, market-determined benchmark for making decisions
b. Ignores cash flows beyond the payback period.
c. Does not directly account for the time value of money.
d. Does not provide any indication regarding a project's liquidity.
e. Does not directly account for differences in risk among projects.

3. Assume that you plan to buy a share of XYZ stock today and to hold it for 2 years. Your expectations are that you will not receive a dividend at the end of Year 1, but you will receive a dividend of \$9.25 at the end of Year 2. In addition, you expect to sell the stock for \$150 at the end of Year 2.

Question: If your expected rate of return is 16 percent, how much should you be willing to pay for this stock today?

4. Which of the following statements is correct?
a. The characteristics line is the regression line that results from plotting the returns on a particular stock versus the returns on a stock from a different industry.
b. The distance of the plot points from the characteristics line is a measure of the stock's discounted value risk.
c. "Characteristics line" is another name for the Security Market Line.
d. The distance of the plot points from the characteristics line is a measure of the stock's market risk.
e. The slope of the characteristic line is the stock's standard deviation.

5. A share of common stock has just paid a dividend of \$2. If the expected long-run growth rate for this stock is 5%, and if investors required rate of return is 10.5%, what is the stock price?

a.\$35.39
b.\$38.80
c.\$37.23
d.\$38.18
\$39.14

6. Gary Wells Inc. plans to issue perpetual preferred stock with an annual dividend of \$6.50 per share. If the required return on this preferred stock is 6.5%, at what price should the stock sell?

a. \$90.37
b. \$92.69
c. \$95.06
d. \$97.50
e. \$100.00

7. You were hired as a consultant to Kroncke Company, whose target capital structure is 40% debt, 10% preferred, and 50% common equity. The after-tax cost of debt is 6%, the cost of preferred is 7.5%, and the cost of retained earnings is 13.25%. The firm will not be issuing any new stock. What is its WACC?

a. 9.48%
b. 9.78%
c. 10.07%
d. 10.37%
e. 10.68%

8. The Bingo Corporation is in the process of determining which of the following two projects that they may invest in. The details are provided below:
Project Cost of Capital Life of project Annual cash flow Initial cost Salvage Value

A 12% 20 Years \$350,000 \$1,250,000 \$250,000

B 12% 20 Years \$400,000 \$1,400,000 \$110,000

a. What is the payback period?
b. What is the net present value of the two projects?

c. What is the internal rate of return of the two projects?
d. What is the profitability index?
e. Which of the two projects would you choose and which criteria would you use?

9. Sorenson Stores is considering a project that has the following cash flows:

Year Cash Flows (end of period)

1 \$2,000

2 \$3,000

3 \$3,000

4 \$1,500

The project has a payback of 2.5 years, and the firm's cost of capital is 12%. What is the project's NPV?

a. \$577.68
b. \$765.91
c. \$1,049.80
d. \$2,761.32
e. \$3,765.91

10. Thompson Stores is considering a project that has the following cash flow data. What is the project's IRR? Note that a project's projected IRR can be less than the WACC (and even negative), in which case it will be rejected.

Year Cash Flow
0 (\$1,000)
1 \$300
2 \$295
3 \$290
4 \$285
5 \$270

a. 11.16%
b. 12.40%
c. 13.78%
d. 15.16%
e. 16.68%

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