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1)You have just started your summer internship, and your boss asks you to review a recent analysis that was done to compare three alternative proposals to enhance the firm’s manufacturing facility. You find that the prior analysis ranked the proposals according to their IRR, and recommended the highest IRR option, Proposal A. You are concerned and decide to redo the analysis using NPV to determine whether this recommendation was appropriate. But while you are confident the IRRs were computed correctly, it seems that some of the underlying data regarding the cash flows that were estimated for each proposal was not included in the report. For Proposal B, you cannot find information regarding the total initial investment that was required in Year 0. And for Proposal C, you cannot find the data regarding additional salvage value that will be recovered in Year 3. Here is the information you have (in $ millions):

Proposal |
IRR |
Year 0 |
Year 1 |
Year 2 |
Year 3 |

A |
60.0% | −$100 | $30 | $153 | $88 |

B |
57.6% | ? | $0 | $206 | $95 |

C |
51.2% | −$100 | $37 | $0 | $204+? |

Suppose the appropriate cost of capital for each alternative is 10%. Using this information, determine the NPV of each proposal. Which project should the firm choose? Why is ranking the projects by their IRR not valid in this situation?

Fill in the missing values ($ millions).

(Round to two decimal places.)

Proposal |
IRR |
Year 0 |
Year 1 |
Year 2 |
Year 3 |

A |
60.0% | −$100 | $30 | $153 | $88 |

B |
57.6% | $——- | $0 | $206 | $95 |

C |
51.2% | −$100 | $37 | $0 | $………. |

Suppose the appropriate cost of capital for each alternative is 10%. Using this information, determine theNPV of each proposal.

The NPV for proposal A is $———– million. (Round to two decimal places.)

The NPV for proposal B is $———– million. (Round to two decimal places.)

The NPV for proposal C is $———- million. (Round to two decimal places.)

Which project should the firm choose?

The firm should choose

▼

project A

project B

project C

.

(Select from the drop-down menu.)

Why is ranking the projects by their IRR not valid in this situation? (Select the best choice below.)

A.

Ranking the projects by their IRR is not valid in this situation because the projects have different NPVs and different patterns of cash flows over time.

B.

Ranking the projects by their IRR is not valid in this situation because the projects have different scales and different patterns of cash flows over time.

C.

Ranking the projects by their IRR is not valid in this situation because the projects have different scales and different project lifecycles.

D.Ranking the projects by their IRR is not valid in this situation because the projects have different discount rates and different patterns of cash flows over time.

2) You own a coal mining company and are considering opening a new mine. The mine itself will cost $118 million to open. If this money is spent immediately, the mine will generate $20 million for the next 10 years. After that, the coal will run out and the site must be cleaned and maintained at environmental standards. The cleaning and maintenance are expected to cost $1.9 million per year in perpetuity. What does the IRR rule say about whether you should accept this opportunity?

(*Hint*:

Consider the number of sign changes in the cash flows.) If the cost of capital is

8.2%, what does the NPV rule say?

What does the IRR rule say about whether you should accept this opportunity? (Select the best choice below.)

A.Reject the opportunity because the IRR is lower than the 8.2% cost of capital.

B.Accept the opportunity because the IRR is greater than the cost of capital.

C.There are two IRRs, so you cannot use the IRR as a criterion for accepting the opportunity.

D.The IRR is 9.37%, so accept the opportunity.If the cost of capital is 8.2%,

what does the NPV rule say? (Select the best choice below.)

A.Since the NPV is less than zero comma reject theopportunity.

B.Since the NPV is greater than or equal to zero comma accept the opportunity.Since the NPV is greater than or equal to zero, accept the opportunity.

C.The NPV rule cannot be used because there are two IRRs.

D.The NPV rule cannot be used because there is no IRR.

3)FastTrack Bikes, Inc. is thinking of developing a new composite road bike. Development will take six years and the cost is $177,000

per year. Once in production, the bike is expected to make $265,500 per year for 10 years. Assume the cost of capital is 10%.

- Calculate the NPV of this investmentopportunity, assuming all cash flows occur at the end of each year. Should the company make theinvestment?
- By how much must the cost of capital estimate deviate to change thedecision?

(*Hint*:

Use Excel to calculate the IRR.)

- What is the NPV of the investment if the cost of capital is 14%?

**Note**:

Assume that all cash flows occur at the end of the appropriate year and that the inflows do not start until year 7.

- Calculate the NPV of this investmentopportunity, assuming all cash flows occur at the end of each year. Should the company make theinvestment?

The present value of the costs is $———-.(Round to the nearest dollar.)

The present value of the benefits is

$———. (Round to the nearest dollar.)

The net present value is $……….. (Round to the nearest dollar.)

(Select from the drop-down menus.)

You should

▼

accept

reject

the investment because the NPV is

positive

negative

** **

- By how much must the cost of capital estimate deviate to change thedecision? (Hint: Use Excel to calculate theIRR.)

To change the decision, the deviation would need to be ———%.(Round to two decimal places.)

** **

- What is the NPV of the investment if the cost of capital is 14%?

The present value of the costs is $——–. (Round to the nearest dollar.)

The present value of the benefits is $——–. (Round to the nearest dollar.)

The NPV will be $……….. (Round to the nearest dollar.)

4)You are considering investing in a start up company. The founder asked you for $290,000

today and you expect to get$980,000in 14years. Given the riskiness of the investment opportunity, your cost of capital is 29%. What is the NPV of the investment opportunity? Should you undertake the investment opportunity? Calculate the IRR and use it to determine the maximum deviation allowable in the cost of capital estimate to leave the decision unchanged.

What is the NPV of the investment opportunity?

The NPV of the investment is $———-. (Round to the nearest dollar.)

Should you undertake the investment opportunity?

Since the NPV is ( negative –positive ) choose the correct answer, you should (not take,take) choose the correct answer

Calculate the IRR and use it to determine the maximum deviation allowable in the cost of capital estimate to leave the decision unchanged.

The IRR is ——–%.(Round to two decimal places.)

The maximum deviation allowable in the cost of capital is ………%.(Round to two decimal places.)

5)

You work for an outdoor play structure manufacturing company and are trying to decide between the following two projects:

Year-End Cash Flows ($ thousands) |
||||

Project |
0 |
1 |
2 |
IRR |

Playhouse (minor project) | −26 | 18 | 19 | 26.8% |

Fort (majorpoject) | −77 | 40 | 51 | 11.4% |

You can undertake only one project. If your cost of capital is 9%, use the incremental IRR rule to make the correct decision.

The incremental IRR is ———%.(Round to two decimal places.)

With the incremental IRR at 3.66%and the cost of capital of 9%,you should undertake the ( playhouse project—fort project) (Select the right chose.)

6) You are considering making a movie. The movie is expected to cost $10.3million upfront and take a year to make. After that, it is expected to make $4.1million in the first year it is released (end of year 2) and $2.1million for the following four years (end of years 3 through 6) . What is the payback period of this investment? If you require a payback period of two years, will you make the movie? Does the movie have positive NPV if the cost of capital is 10.1%?

What is the payback period of this investment?

The payback period is ———years. (Round up to nearest integer.)

Based on the payback period requirement, would you make this movie?Yes or No (Selectone )

Does the movie have positive NPV if the cost of capital is 10.1%?

The NPV is $——— million. (Round to three decimal places.)

The movie has a ( negative – positive )NPV.(Select one .)

7) Consider two investment projects, which both require an upfront investment of $10million, and both of which pay a constant positive amount each year for the next 11years. Under what conditions can you rank these projects by comparing their IRRs?

. Select the best choice below.)

A.There are no conditions under which you can use the IRR to rank projects.

B.Ranking by IRR will work in this case so long as the projects’ cash flows do not decrease from year to year.

C.Ranking by IRR will work in this case so long as the projects’ cash flows do not increase from year to year.

D.Ranking by IRR will work in this case so long as the projects have the same risk.

8)You are considering investing in a new gold mine in South Africa. Gold in South Africa is buried very deep, so the mine will require an initial investment of $270million. Once this investment is made, the mine is expected to produce revenues of $28million per year for the next 20 years. It will cost $10

million per year to operate the mine. After 20 years, the gold will be depleted. The mine must then be stabilized on an ongoing basis, which will cost $4.9million per year in perpetuity. Calculate the IRR of this investment.(*Hint*:Plot the NPV as a function of the discount rate.)

(Select the best choice below.)

A.No positive IRR exists since the NPV, calculated as a function of various discount rates, never equals or exceeds zero.

B.The IRR is about 11%.

C.The IRR is infinite as a result of the perpetuity.

D.There are multiple IRRs.

9)You are considering an investment in a clothes distributer. The company needs $102,000today and expects to repay you $128,000in a year from now. What is the IRR of this investment opportunity? Given the riskiness of the investment opportunity, your cost of capital is 14%. What does the IRR rule say about whether you should invest?

What is the IRR of this investment opportunity?

The IRR of this investment opportunity is ———–%.(Round to one decimal place.)

Given the riskiness of the investment opportunity, your cost of capital is 14%. What does the IRR rule say about whether you should invest?

The IRR rule says that you:(should be indifferent – should not invest- should invest)Select from the drop-down menu.)

10)You are considering constructing a new plant in a remote wilderness area to process the ore from a planned mining operation. You anticipate that the plant will take a year to build and cost $97 million upfront. Once built, it will generate cash flows of

$18 million at the end of every year over the life of the plant. The plant will be useless 20

years after its completion once the mine runs out of ore. At that point you expect to pay

$263 million to shut the plant down and restore the area to its pristine state. Using a cost of capital of

13%:

- What is the NPV of theproject?
- Is using the IRR rule reliable for thisproject? Explain.
- What are the IRRs of thisproject?

- What is the NPV of theproject?

The NPV of the project is $——- million. (Round to one decimal place.)

** **

- Is using the IRR rule reliable for thisproject? Explain. (Select the best choicebelow.)

A.No, the IRR rule is not reliable, because the project has a negative net present value.

B.Yes, the IRR rule is reliable, because the project has a negative net present value.

C.No, the IRR rule is not reliable, because the project has a negative cash flow that comes after the positive ones.

D.Yes, the IRR rule is reliable, because the project has a negative cash flow that comes after the positive ones.

- What are the IRRs of thisproject?

The IRRs of this project in ASCENDING order are ………%and ………..%.(Round to two decimal places.)

11)Professor Wendy Smith has been offered the following deal: A law firm would like to retain her for an upfront payment of $52,000. In return, for the next year, the firm would have access to eight hours of her time every month. Smith’s rate is $551per hour, and her opportunity cost of capital is 15%

(equivalent annual rate, EAR). What is the IRR (annual)? What does the IRR rule advise regarding this opportunity? What is the NPV? What does the NPV rule say about this opportunity?

What is the IRR (annual)?

The IRR (annual)is ……….%.(Round to two decimal places.)

What does the IRR rule advise regarding this opportunity? (Select from the drop-down menu.)

Smith’s cost of capital is 15%,so according to the IRR rule, she should ( accept – turn down)this opportunity.

What is the NPV?

The NPV is $——–. (Round to the nearest cent.)

What does the NPV rule say about this opportunity? (Select from the drop-down menus.)

the NPV is ( negative – positive), so the correct decision is to ( accept -turn down)the deal.

12) You are considering opening a new plant. The plant will cost $101.3

million upfront and will take one year to build. After that, it is expected to produce profits of $29.1

million at the end of every year of production. The cash flows are expected to last forever. Calculate the NPV of this investment opportunity if your cost of capital is 6.2%.

Should you make the investment? Calculate the IRR. Does the IRR rule agree with the NPV rule?

Calculate the NPV of this investment opportunity if your cost of capital is 6.2%.

The NPV of this investment opportunity is $………million. (Round to one decimal place.)

Should you make the investment? (Select the best choice below.)

A.Yes, because the NPV is positive.

B.No, because the NPV is less than zero.

C.No, because the NPV is not greater than the initial costs.

D.Yes, because the project will generate cash flows forever.

Calculate the IRR.

The IRR of the project is ………%.(Round to two decimal places.)

Does the IRR rule agree with the NPV rule? (Select the best choice below.)

A.Since the IRR exceeds the 6.2% discount rate, the IRR rule gives a different answer than the NPV rule.

B.Since the IRR is less than the 6.2% discount rate, the IRR rule gives the same answer as the NPV rule.

C.Since the IRR is less than the 6.2% discount rate, the IRR rule gives a different answer than the NPV rule.

D.Since the IRR exceeds the 6.2% discount rate, the IRR rule gives the same answer as the NPV rule.

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