# Net present values, investment requirements, discount rates.

1. You just won the lottery and want to put some money away for your child's college education. College will cost $65,000 in 18 years. You can earn 8% compounded annually. How much do you need to invest?

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2. You just won the lottery. You and your heirs will receive $25,000 per year forever, beginning one year from now. What is the present value of your winnings at an 8% discount rate? Answer:

3. You are suppose to receive $2,000 five years from now. At an interest rate of 6%, what is that $2,000 worth today? Answer: =

4. What is the future value in 10 years of $1,000 payments received at the beginning of each year for the next 10 years? Assume an interest rate of 5.625%. Answer: =

5. In order to help you through college, your parents just deposited $25,000 into a back account paying 8% interest. Starting next year, you plan to withdraw equal amounts for the account at the end of each of the next four years. What is the most you can withdraw annually? Answer: =

6. What is the market value of a bond that will pay a total of forty semiannual coupons of $50 each over the remainder of its life? Assume the bond has a $1,000 face value and an 8% yield to maturity (YTM).

Answer: =

Answer =

Price of the Bond

7. J&J, Inc. just issued a bond with a $1,000 face value and a coupon rate of 7%. If the bond has a life of 30 years, pays annual coupons and the YTM is 6.8%, what will the bond sell for? =

8. What would you pay for a bond that pays an annual coupon of $35, has a face value of $1,000, matures in 7 years, and has a yield to maturity (YTM) of 8%?

Answer: =

Answer: =

Price of Bond =

9. What would you pay for a share of ABC Corporation stock today if the next dividend will be $2 per share, your required return on equity investments is 12%, and the stock is expected to be worth $110 one year from now?

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10. What would you pay today for a stock that is expected to make a $1.50 dividend in one year if the expected dividend growth rate is 3% and you require a 16% return on your investment? Answer:

11. A project costs $475 and has cash flows of $100 for the first three years and $75 in each of the project's last five years. What is the payback period of the project?

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12 What is the NPV of a project that is expected to pay $10,000 a year for 7 years if the initial investment is $40,000 and the required return is 15%?

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13. Calculate the NPV of the following project using a discount rate of 12%.

YR0 = -$500; YR1 = -$50; YR2 = $50; YR3 = $200; YR4 = $400; YR5 = $400

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14. A project has an initial investment of $10,000, with $3,500 annual inflows for each of the subsequent four (4) years. If the required return is 15%, what is the Net Present Value (NPV)? Answer:

15. What is the IRR of an investment that costs $77,700 and pays $27,500 a year for 4 years? ?

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16. Suppose a project costs $300 and produces cash flow of $100 over each of the following six years. What is the IRR of this project?

Answer: =

17. A firm's stock has a required return of 10%. The stock's dividend yield is 6%. What dividend did the firm just pay if the current stock price is $40?

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18. Topstone Industries' preferred stock pays an annual dividend of $4.00 per share. When issued, the shares sold for their par value of $100 per share. What is the cost of preferred stock if the current price is $125.00?

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19. Why do you think debt offerings are more common than equity offerings and typically much larger as well?

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20. A number of publicly traded firms pay no dividends yet investors are willing to buy shares in these firms? Does this violate our basic principle of stock valuation? Explain.

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#### Solution Preview

19 Why do you think debt offerings are more common than equity offerings and typically much larger as well?

This decision is related to long term financing decision. Long term financing decision is about determining firm's optimum capital structure. A firm's optimal capital structure is that mixture of debt and equity than minimizes its weighted average cost of capital (WACC).

Since the after-tax cost of debt is lower than equity for many corporations,iIt turns out that, debt reduces a company's tax liability because interest payments are deductible expenses. Hence debt offerings are more than the equity offerings as they are cheaper.

One caution:

Higher amounts of debt raise the ...

#### Solution Summary

The solution answers many questions on investments, discount rates, present values, and bond pricing.

Cash Flow Problems

1. The payback period is the length of time it takes an investment to generate sufficient cash flows to enable the project to:

A. produce a positive annual cash flow.

B. produce a positive cash flow from assets.

C. offset its fixed expenses.

D. offset its total expenses.

E. recoup its initial cost.

2. The average net income of a project divided by the project's average book value is referred to as the project's:

A. required return.

B. market rate of return.

C. internal rate of return.

D. average accounting return.

E. discounted rate of return.

3. Which one of the following defines the internal rate of return for a project?

A. Discount rate that creates a zero cash flow from assets

B. Discount rate which results in a zero net present value for the project

C. Discount rate which results in a net present value equal to the project's initial cost

D. Rate of return required by the project's investors

E. The project's current market rate of return

4. Which one of the following can be defined as a benefit-cost ratio?

A. Net present value

B. Internal rate of return

C. Profitability index

D. Accounting rate of return

E. Modified internal rate of return

5. Which one of the following indicates that a project is expected to create value for its owners?

A. Profitability index less than 1.0

B. Payback period greater than the requirement

C. Positive net present value

D. Positive average accounting rate of return

E. Internal rate of return that is less than the requirement

6. The net present value:

A. decreases as the required rate of return increases.

B. is equal to the initial investment when the internal rate of return is equal to the required return.

C. method of analysis cannot be applied to mutually exclusive projects.

D. is directly related to the discount rate.

E. is unaffected by the timing of an investment's cash flows.

7. Which one of the following is generally considered to be the best form of analysis if you have to select a single method to analyze a variety of investment opportunities?

A. Payback

B. Profitability index

C. Accounting rate of return

D. Internal rate of return

E. Net present value

8. Which one of the following indicates that a project should be rejected?

A. Average accounting return that exceeds the requirement

B. Payback period that is shorter than the requirement period

C. Positive net present value

D. Profitability index less than 1.0

E. Internal rate of return that exceeds the required return

9. Which one of the following indicators offers the best assurance that a project will produce value for its owners?

A. PI equal to zero

B. Negative rate of return

C. Positive AAR

D. Positive IRR

E. Positive NPV

10. Which one of the following statements is correct?

A. A longer payback period is preferred over a shorter payback period.

B. The payback rule states that you should accept a project if the payback period is less than one year.

C. The payback period ignores the time value of money.

D. The payback rule is biased in favor of long-term projects.

E. The payback period considers the timing and amount of all of a project's cash flows.

11. You were recently hired by a firm as a project analyst. The owner of the firm is unfamiliar with financial analysis and only wants to know what the expected dollar return is per dollar spent on a given project. Which financial method of analysis will provide the information that the owner requests?

A. Internal rate of return

B. Modified internal rate of return

C. Net present value

D. Profitability index

E. Payback

12. Mary has just been asked to analyze an investment to determine if it is acceptable. Unfortunately, she is not being given sufficient time to analyze the project using various methods. She must select one method of analysis and provide an answer based solely on that method. Which method do you suggest she use in this situation?

A. Internal rate of return

B. Payback

C. Average accounting rate of return

D. Net present value

E. Profitability index

13. Which one of the following is specifically designed to compute the rate of return on a project that has unconventional cash flows?

A. Average accounting return

B. Profitability index

C. Internal rate of return

D. Indexed rate of return

E. Modified internal rate of return

14. The average accounting return:

A. measures profitability rather than cash flow.

B. discounts all values to today's dollars.

C. is expressed as a percentage of an investment's current market value.

D. will equal the required return when the net present value equals zero.

E. is used more often by CFOs than the internal rate of return.

15. The reinvestment approach to the modified internal rate of return:

A. individually discounts each separate cash flow back to the present.

B. reinvests all the cash flows, including the initial cash flow, to the end of the project.

C. discounts all negative cash flows to the present and compounds all positive cash flows to the end of the project.

D. discounts all negative cash flows back to the present and combines them with the initial cost.

E. compounds all of the cash flows, except for the initial cash flow, to the end of the project.

16. Which one of the following is true if the managers of a firm only accept projects that have a profitability index greater than 1.5?

A. The firm should increase in value each time the firm accepts a new project.

B. The firm is most likely steadily losing value.

C. The price of the firm's stock should remain constant.

D. The net present value of each new project is zero.

E. The internal rate of return on each new project is zero.

17. What is the net present value of a project with the following cash flows if the discount rate is 14 percent?

A. $742.50

B. $801.68

C. $823.92

D. $899.46

E. $901.15

18. A project has the following cash flows. What is the payback period?

A. 2.48 years

B. 2.59 years

C. 2.96 years

D. 3.21 years

E. 3.43 years

19. An investment has an initial cost of $410,000 and will generate the net income amounts shown below. This investment will be depreciated straight line to zero over the 4-year life of the project. Should this project be accepted based on the average accounting rate of return if the required rate is 16 percent? Why or why not?

A. Yes; because the AAR is equal to 16 percent

B. Yes; because the AAR is greater than 16 percent

C. Yes; because the AAR is less than 16 percent

D. No; because the AAR is greater than 16 percent

E. No; because the AAR is less than 16 percent

20. Which one of the following methods of analysis is most appropriate to use when two investments are mutually exclusive?

A. Internal rate of return

B. Profitability index

C. Net present value

D. Modified internal rate of return

E. Average accounting return