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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%.

1. Calculate the NPV of this investment​opportunity, assuming all cash flows occur at the end of each year. Should the company make the​investment?
2. By how much must the cost of capital estimate deviate to change the​decision?

​(Hint​:

Use Excel to calculate the​ IRR.)

1. 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.

1. Calculate the NPV of this investment​opportunity, assuming all cash flows occur at the end of each year. Should the company make the​investment?

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.)

You should

accept

reject

the investment because the NPV is

positive

negative

1. By how much must the cost of capital estimate deviate to change the​decision? (Hint: Use Excel to calculate the​IRR.)

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

1. 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.

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%​:

1. What is the NPV of the​project?
2. Is using the IRR rule reliable for this​project? Explain.
3. What are the IRRs of this​project?

1. What is the NPV of the​project?

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

1. Is using the IRR rule reliable for this​project? Explain.  ​(Select the best choice​below.)

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.

1. What are the IRRs of this​project?

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.)

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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