basics of capital budgeting

CHAPTER 10

CHAPTER 11THE BASICS OF CAPITAL BUDGETING

(Difficulty Levels: Easy, Easy/Medium, Medium, Medium/Hard, and Hard)

PART I New and Revised Carryover Problems and QuestionsMultiple Choice: Problems

NPV (constant cash flows; 3 years)Answer: a EASY

.Thomson Electric Systems is considering a project that has the following cash flow and WACC data. What is the project's NPV? Note that a project's projected NPV can be negative, in which case it will be rejected.

WACC = 10%

Year:

0 1

2

3

Cash flows:-$1,000$500

$500

$500

a.$243.43b.$251.23c.$268.91d.$272.46e.$289.53NPV (constant cash flows; 4 years)Answer: c EASY

.Blanchford Enterprises is considering a project that has the following cash flow and WACC data. What is the project's NPV? Note that a project's projected NPV can be negative, in which case it will be rejected.

WACC = 10%

Year:

0 1

2

3

4


$475

$475

$475

a.$482.16b.$496.38c.$505.69d.$519.05e.$524.72NPV (constant cash flows; 5 years)Answer: e EASY

.Tapley Dental Associates is considering a project that has the following cash flow and WACC data. What is the project's NPV? Note that a project's projected NPV can be negative, in which case it will be rejected.

WACC = 10%

Year:

0 1

2

3

4

5


$300

$300

$300

$300

a.$116.73b.$123.15c.$128.47d.$131.96e.$137.24IRR (constant cash flows; 3 years)Answer: b EASY

.Blanchford Enterprises 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:

0 1

2

3


$450

$450

a.16.20%b.16.65%

c.17.10%d.17.55%e.18.00%IRR (constant cash flows; 4 years)Answer: d EASY

.Blanchford Enterprises 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:

0 1

2

3

4


$400

$400

$400

a.17.76%b.19.17%c.20.56%d.21.86%

e.23.01%IRR (constant cash flows; 5 years)Answer: a EASY

.Smithfield Foods 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:

0 1

2

3

4

5


$350

$350

$350

$350

a.22.11%b.22.74%c.23.58%d.24.14%e.24.93%Payback (constant cash flows; 3 years)Answer: c EASY

.Blanchford Enterprises is considering a project that has the following cash flow data. What is the project's payback?

Year:

0 1

2

3


$500

$500

a.1.50 yearsb.1.75 yearsc.2.00 years

d.2.25 yearse.2.50 yearsPayback (nonconstant cash flows; 5 years)Answer: e EASY/MEDIUM

.Tapley Dental Associates is considering a project that has the following cash flow data. What is the project's payback?

Year:

0 1

2

3

4

5


$310

$320

$330

$340

a.2.11 yearsb.2.50 yearsc.2.71 yearsd.3.05 yearse.3.21 years

NPV (uneven cash flows; 3 years)Answer: a EASY/MEDIUM

.Edison Electric Systems is considering a project that has the following cash flow and WACC data. What is the project's NPV? Note that a project's projected NPV can be negative, in which case it will be rejected.

WACC = 10%

Year:

0 1

2

3


$460

$470

a.$142.37b.$151.59c.$166.51d.$173.26e.$189.94NPV (uneven cash flows; 3 years)Answer: c EASY/MEDIUM

.Rockmont Recreation Inc. is considering a project that has the following cash flow and WACC data. What is the project's NPV? Note that a project's projected NPV can be negative, in which case it will be rejected.

WACC = 10%

Year:

0 1

2

3


$440

$430

a.$ 88.84b.$ 92.25c.$ 95.79

d.$ 98.49e.$102.63NPV (uneven cash flows; 4 years)Answer: e EASY/MEDIUM

.Ryngaert Medical Enterprises is considering a project that has the following cash flow and WACC data. What is the project's NPV? Note that a project's projected NPV can be negative, in which case it will be rejected.

WACC = 10%

Year:

0 1

2

3

4


$405

$410

$415

a.$241.24b.$255.83c.$268.54d.$274.78e.$289.84

NPV (uneven cash flows; 5 years)Answer: b EASY/MEDIUM

.Richards Enterprises is considering a project that has the following cash flow and WACC data. What is the project's NPV? Note that a project's projected NPV can be negative, in which case it will be rejected.

WACC = 10%

Year:

0 1

2

3

4

5


$395

$390

$385

$380

a.$478.74b.$482.01

c.$495.05d.$507.98e.$517.93IRR (uneven cash flows; 3 years)Answer: d EASY/MEDIUM

.Edison Electric Systems 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:

0 1

2

3


$470

$490

a.16.73%b.17.44%c.18.89%d.19.05%

e.20.37%IRR (uneven cash flows; 4 years)Answer: a EASY/MEDIUM

.Rockmont Recreation Inc. 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:

0 1

2

3

4


$230

$210

$190a.-5.15%b.-3.44%c.-1.17%d. 2.25%e. 3.72%IRR (uneven cash flows; 5 years)Answer: c EASY/MEDIUM

.Sam's Stores Enterprises 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.

WACC = 10%

Year:

0 1

2

3

4

5


$295

$290

$285

$280

a.12.00%b.13.00%c.14.00%

d.15.00%e.16.00%Discounted payback (constant cash flows; 3 years)Answer: b MEDIUM

.Blanchford Enterprises is considering a project that has the following cash flow and WACC data. What is the project's discounted payback?

WACC = 10%

Year:

0 1

2

3


$500

$500

a.2.01 yearsb.2.35 years

c.2.65 yearsd.2.84 yearse.3.17 yearsDiscounted payback (nonconstant cash flows; 4 years)Answer: d MEDIUM

.Reynolds Bikes is considering a project that has the following cash flow and WACC data. What is the project's discounted payback?

WACC = 10%

Year:

0 1

2

3

4


$485

$445

$405

a.1.66 yearsb.1.82 yearsc.2.03 yearsd.2.36 years

e.2.41 yearsMIRR (uneven cash flows; 3 years)Answer: e MEDIUM

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

WACC = 10%

Year:

0 1

2

3


$370

$390

a.4.90%b.5.18%c.5.72%d.6.23%e.6.87%

MIRR (uneven cash flows; 4 years)Answer: b MEDIUM

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

WACC = 10%

Year:

0 1

2

3

4

Cash flows:-$900$300

$320

$340

$360

a.13.33%b.14.01%

c.15.69%d.16.35%e.17.18%NPV vs IRR (constant cash flows; 3 years)Answer: d MEDIUM

.Last month, Wong Systems Inc. decided to accept the project whose cash flows are shown below. However, before actually starting the project, the Federal Reserve took actions that changed interest rates and Wong's WACC. By how much did the change in the WACC affect the project's forecasted NPV? Assume that the Fed action will not affect the cash flows, and note that a project's projected NPV can be negative, in which case it should be rejected.

Old WACC = 10%

New WACC = 5%

Year:

0 1

2

3


$500

$500

a.$ 88.67b.$ 92.16c.$104.93d.$118.19e.$124.18NPV vs IRR (nonconstant cash flows; 3 years)Answer: a MEDIUM

.The Federal Reserve recently shifted its monetary policy, causing Lasik Vision's WACC to change. Lasik had recently analyzed the project whose cash flows are shown below. However, the CFO wants to reconsider this and all other proposed projects in view of the Fed action. How much did the changed WACC cause the forecasted NPV to change? Assume that the Fed action will not affect the cash flows, and note that a project's projected NPV can be negative, in which case it should be rejected.

Old WACC = 10%

New WACC = 8%

Year:

0 1

2

3


$520

$540

a.$47.44

b.$59.45c.$68.57d.$74.16e.$84.16NPV vs IRR (size differences)Answer: c MEDIUM/HARD

.Pettway Inc. is considering Projects S and L, whose cash flows are shown below. These projects are mutually exclusive, equally risky, and not repeatable. If the decision is made by choosing the project with the higher IRR, how much value will be forgone? Note that under some conditions choosing projects on the basis of the IRR will cause $0.00 value to be lost.

WACC = 12%

Year:

0 1

2

3

4

CFS:

-$1,025$375

$380

$385

$390

CFL:

-$2,153$750

$759

$768

$777

a.$15.57b.$21.49c.$27.52d.$33.69e.$37.39NPV vs IRR (different timing patterns)Answer: e MEDIUM/HARD

.Porter & Co. is considering Projects S and L, whose cash flows are shown below. These projects are mutually exclusive, equally risky, and not repeatable. If the decision is made by choosing the project with the higher IRR, how much value will be forgone? Note that under some conditions choosing projects on the basis of the IRR will cause $0.00 value to be lost.

WACC = 10%

Year:

0 1

2

3

4

CFS:

-$1,025$650

$450

$250

$ 50

CFL:

-$1,025$100

$300

$500

$700

a.-$6.93b.-$2.26c. $0.00d. $3.31e. $7.82NPV vs IRR (different timing patterns)Answer: a MEDIUM/HARD

.Ritter Dental Equipment is considering Projects S and L, whose cash flows are shown below. These projects are mutually exclusive, equally risky, and are not repeatable. If the decision is made by choosing the project with the higher IRR, how much value will be forgone? Note that under some conditions choosing projects on the basis of the IRR will cause $0.00 value to be lost.

WACC = 10.5%

Year:

0 1

2

3

4

CFS:

-$1,050$650

$650

CFL:

-$1,050$400

$400

$400

$400

a.$ 0.00b.$133.77

c.$197.48d.$246.81e.$305.54NPV vs MIRR (size differences)Answer: d MEDIUM/HARD

.Precision Products is considering Projects S and L, whose cash flows are shown below. These projects are mutually exclusive, equally risky, and not repeatable. If the decision is made by choosing the project with the higher MIRR, how much value will be forgone? Note that under some conditions choosing projects on the basis of the MIRR will cause $0.00 value to be lost.

WACC = 10%

Year:

0 1

2

3

4

CFS:

-$1,000$375

$375

$375

$375

CFL:

-$2,010$725

$725

$725

$725

a.$ 78.67b.$ 85.64c.$ 90.39d.$ 99.45

e.$107.38NPV vs paybackAnswer: d MEDIUM/HARD

.Pettway Inc. is considering Projects S and L, whose cash flows are shown below. These projects are mutually exclusive, equally risky, and not repeatable. If the decision is made by choosing the project with the shorter payback, some value may be forgone. How much value will be lost in this instance? Note that under some conditions choosing projects on the basis of the shorter payback will not cause value to be lost.

WACC = 13%

Year:

0 1

2

3

4

CFS:

-$1,000$400

$400

$400

$400

CFL:

-$2,100$800

$800

$800

$800a.$55.16b.$66.42c.$78.79d.$89.79e.$96.16NPV vs IRRAnswer: a HARD

.Ross Inc.'s CFO thinks the company should rely primarily on the NPV method, but the president prefers the IRR, so decisions are based on the IRR. The CFO wants you to show the president that at times decisions based on the IRR result in a reduction in the company's value relative to its value if the NPV criterion were used. The CFO then asked you to analyze two projects that the company is now considering, S and L, whose cash flows are shown below. These projects are mutually exclusive, equally risky, and not repeatable. If the decision is made by choosing the project with the higher IRR, how much value will Ross be forgoing? Note that at times the project with the higher IRR will also have the higher NPV, and in these cases no value will by lost by relying on the IRR.

WACC = 10%

Year:

0 1

2

3

4

CFS:

-$1,025$650

$650

CFL:

-$1,025$400

$400

$400

$400

a.$ 0.00

b.$125.47c.$139.85

d.$143.96e.$157.01NPV and paybackAnswer: e HARD

.You must find the payback for a project, and you have misplaced some of the information that you were given. You know that the project will generate positive cash flows of $60,000 per year at the end of each of the next 5 years, that its NPV is $75,000, and that the companys WACC is 10%. What is the projects regular payback? Hint: You must first find the project's cost, then use it to find the payback.

a.2.11 yearsb.2.27 years c.2.38 yearsd.2.45 yearse.2.54 years

Multiple Choice: Conceptual

Note to Professors: We designated most of these questions as being MEDIUM or HARD. However, their difficulty as seen by students will depend on (1) what was discussed in class and (2) how long students have to answer the questions. If time is not an issue, then many of the questions should be classified as one notch easier than our designation. So, consider the amount of time students have when selecting questions for an exam.

Also, it is EXTREMELY HELPFUL for students to draw an NPV profile when answering a number of the questions. We recommend pointing this out in class. Drawing these profiles takes time, but it is a necessary step for many people if they are to answer the questions correctly. This is true even for students who understand the concepts.Ranking methodsAnswer: b EASY

.Assume a project has normal cash flows. All else equal, which of the following statements is CORRECT?

a.The projects IRR increases as the WACC declines.

b.The projects NPV increases as the WACC declines.

c.The projects MIRR is unaffected by changes in the WACC.

d.The projects regular payback increases as the WACC declines.

e.The projects discounted payback increases as the WACC declines.

Ranking methodsAnswer: d EASY

.Which of the following statements is CORRECT?

a.The internal rate of return method (IRR) is generally regarded by academics as being the best single method for evaluating capital budgeting projects.

b.The payback method is generally regarded by academics as being the best single method for evaluating capital budgeting projects.

c.The discounted payback method is generally regarded by academics as being the best single method for evaluating capital budgeting projects.

d.The net present value method (NPV) is generally regarded by academics as being the best single method for evaluating capital budgeting projects.

e.The modified internal rate of return method (MIRR) is generally regarded by academics as being the best single method for evaluating capital budgeting projects.

Ranking methods: paybackAnswer: d EASY


a.The regular payback method recognizes all cash flows over a projects life.

b.The discounted payback method recognizes all cash flows over a projects life, and it also adjusts these cash flows to account for the time value of money.

c.The regular payback method was, years ago, widely used, but virtually no companies even calculate the payback today.

d.The regular payback is useful as an indicator of a projects liquidity because it gives managers an idea of how long it will take to recover the funds invested in a project.

e.The regular payback does not consider cash flows beyond the payback year, but discounted payback overcomes this defect.

Ranking methods: IRRAnswer: e EASY


a.One defect of the IRR method is that it does not take account of cash flows over a projects full life.

b.One defect of the IRR method is that it does not take account of the time value of money.

c.One defect of the IRR method is that it does consider the time value of money.

d.One defect of the IRR method is that it values a dollar received today the same as a dollar that will not be received until some time in the future.

e.One defect of the IRR method is that it assumes that the cash flows to be received from a project can be reinvested at the IRR itself, and that assumption is often not valid.

Normal vs. nonnormal cash flowsAnswer: e EASY


a.If a project has normal cash flows, then its IRR must be positive.

b.If a project has normal cash flows, then its MIRR must be positive.

c.If a project has normal cash flows, then it will have exactly two real IRRs.

d.The definition of normal cash flows is that the cash flow stream has one or more negative cash flows followed by a stream of positive cash flows and then one negative cash flow at the end of the projects life.

e.If a project has normal cash flows, then it can have only one real IRR, whereas a project with nonnormal cash flows might have more than one real IRR.

Normal vs. nonnormal cash flowsAnswer: a EASY


a.Projects with normal cash flows can have only one real IRR.

b.Projects with normal cash flows can have two or more real IRRs.

c.Projects with normal cash flows must have two changes in the sign of the cash flows, e.g., from negative to positive to negative. If there are more sign changes, then the cash flow stream is nonnormal.

d.The multiple IRR problem can arise if a projects cash flows are normal.

e.Projects with nonnormal cash flows are almost never encountered in the real world.

NPVAnswer: c EASY

.Which of the following statements is CORRECT? Assume that the project being considered has normal cash flows, with one outflow followed by a series of inflows.

a.A projects NPV is found by compounding the cash inflows at the IRR to find the terminal value (TV), then discounting the TV at the WACC.

b.The lower the WACC used to calculate it, the lower the calculated NPV will be.

c.If a projects NPV is less than zero, then its IRR must be less than the WACC.

d.If a projects NPV is greater than zero, then its IRR must be less than zero.

e.The NPV of a relatively low risk project should be found using a relatively high WACC.

PaybackAnswer: b EASY


a.The longer a projects payback period, the more desirable the project is normally considered to be by this criterion.

b.One drawback of the payback criterion for evaluating projects is that this method does not properly account for the time value of money.

c.If a projects payback is positive, then the project should be rejected because it must have a negative NPV.

d.The regular payback ignores cash flows beyond the payback period, but the discounted payback method overcomes this problem.

e.If a company uses the same requirement to evaluate all projects, say it requires a payback of 4 years or less, then the company will tend to reject projects with relatively short lives and accept long-lived projects, and this will cause its risk to increase over time.

PaybackAnswer: b EASY


a.The shorter a projects payback period, the less desirable the project is normally considered to be by this criterion.

b.One drawback of the payback criterion for evaluating projects is that this method does not take account of cash flows beyond the payback period.

c.If a projects payback is positive, then the project should be accepted because it must have a positive NPV.

d.The regular payback ignores cash flows beyond the payback period, but the discounted payback method overcomes this problem.

e.One drawback of the discounted payback is that this method does not consider the time value of money, while the regular payback overcomes this drawback.IRRAnswer: d EASY


a.A projects regular IRR is found by compounding the cash inflows at the WACC to find the terminal value (TV), then discounting this TV at the WACC.

b.A projects regular IRR is found by discounting the cash inflows at the WACC to find the present value (PV), then compounding this PV to find the IRR.

c.If a projects IRR is greater than the WACC, then its NPV must be negative.

d.To find a projects IRR, we must solve for the discount rate that causes the PV of the inflows to equal the PV of the projects costs.

e.To find a projects IRR, we must find a discount rate that is equal to the WACC.

IRRAnswer: d EASY


a.A projects regular IRR is found by compounding the initial cost at the WACC to find the terminal value (TV), then discounting the TV at the WACC.

b.A projects regular IRR is found by compounding the cash inflows at the WACC to find the present value (PV), then discounting to find the IRR.

c.If a projects IRR is less than the WACC, then its NPV will be positive.

d.A projects IRR is the discount rate that causes the PV of the inflows to equal the projects cost.

e.If a projects IRR is positive, then its NPV must also be positive.

Ranking methods: NPVAnswer: e MEDIUM


a.The NPV method was once the favorite of academics and business executives, but today most authorities regard the MIRR as being the best indicator of a projects profitability.

b.If the cost of capital is reduced, this reduces a projects NPV.

c.The NPV method is regarded by most academics as being the best indicator of a projects profitability, hence academics recommend that firms use only this one method.

d.A projects NPV depends on the total amount of cash flows the project produces, but because the cash flows are discounted at the WACC, it does not matter if the cash flows occur early or late in the projects life.

e.The NPV and IRR methods may give different recommendations regarding which of two mutually exclusive projects should be accepted, but they always give the same recommendation regarding the acceptability of a normal, independent project.

Ranking methods: NPVAnswer: b MEDIUM


a.One advantage of the NPV over the IRR method is that NPV takes account of cash flows over a projects full life whereas IRR does not.

b.One advantage of the NPV over the IRR is that NPV assumes that cash flows will be reinvested at the WACC whereas IRR assumes that cash flows are reinvested at the IRR, and the NPVs assumption is generally more likely to be appropriate.

c.One advantage of the NPV over the MIRR method is that NPV takes account of cash flows over a projects full life whereas MIRR does not.

d.One advantage of the NPV over the MIRR method is that NPV discounts cash flows whereas the MIRR is based on undiscounted cash flows.

e.Since cash flows under the IRR and MIRR are both discounted at the same rate (the WACC), these two methods always rank mutually exclusive projects in the same order.

NPV profilesAnswer: d EASY/MEDIUM


a.An NPV profile graph shows how a projects payback varies as the cost of capital changes.

b.An NPV profile graph for a project normally shows a positive (upward) slope as the life of the project increases.

c.An NPV profile graph is designed to give decision makers an idea about how a projects risk varies with its life.

d.An NPV profile graph is designed to give decision makers an idea about how a projects contribution to the firms value varies with the cost of capital.

e.We cannot draw a projects NPV profile unless we know the appropriate WACC for use in evaluating the projects NPV.

Ranking conflictsAnswer: a MEDIUM


a.The NPV method assumes that cash flows will be reinvested at the WACC, while the IRR method assumes reinvestment at the IRR.

b.The NPV method assumes that cash flows will be reinvested at the risk-free rate, while the IRR method assumes reinvestment at the IRR.

c.The NPV method assumes that cash flows will be reinvested at the WACC, while the IRR method assumes reinvestment at the risk-free rate.

d.The NPV method does not consider all relevant cash flows, particularly, cash flows beyond the payback period.

e.The IRR method does not consider all relevant cash flows, particularly, cash flows beyond the payback period.

Payback periodAnswer: d MEDIUM

.The regular payback method has a number of disadvantages. Which of the following 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 projects liquidity.

e.Does not directly account for differences in risk among projects.

NPVAnswer: b MEDIUM


a.A projects NPV is generally found by compounding the cash inflows at the WACC to find the terminal value (TV), then discounting the TV at the IRR to find its PV.

b.The higher the WACC used to calculate the NPV, the lower the calculated NPV will be.

c.If a projects NPV is greater than zero, then its IRR must be less than the WACC.

d.If a projects NPV is greater than zero, then its IRR must be less than zero.

e.The NPVs of relatively risky projects should be found using relatively low WACCs.

NPV and IRRAnswer: e MEDIUM


a.If Project A has a higher IRR than Project B, then Project A must have the lower NPV.

b.If Project A has a higher IRR than Project B, then Project A must also have a higher NPV.

c.The IRR calculation implicitly assumes that all cash flows are reinvested at the WACC.

d.The IRR calculation implicitly assumes that cash flows are withdrawn from the business rather than being reinvested in the business.

e.If a project has normal cash flows and its IRR exceeds its WACC, then the projects NPV must be positive.

NPV profilesAnswer: a MEDIUM

.Projects A and B have identical expected lives and identical initial cash outflows (costs). However, most of one projects cash flows come in the early years, while most of the other projects cash flows occur in the later years. The two NPV profiles are given below:

Which of the following statements is CORRECT?

a.More of Project As cash flows occur in the later years.

b.More of Project Bs cash flows occur in the later years.

c.We must have information on the cost of capital in order to determine which project has the larger early cash flows.

d.The NPV profile graph is inconsistent with the statement made in the problem.

e.The crossover rate, i.e., the rate at which Projects A and B have the same NPV, is greater than either projects IRR.

NPV profilesAnswer: b MEDIUM

.Projects S and L each have an initial cost of $10,000, followed by a series of positive cash inflows. Project Ss undiscounted net cash flows total to $20,000, while Ls total undiscounted flows are $30,000. At a WACC of 10%, the two projects have identical NPVs. Which projects NPV is more sensitive to changes in the WACC?

a.Project S.

b.Project L.

c.Both projects are equally sensitive to changes in the WACC since their NPVs are equal at all costs of capital.

d.Neither project is sensitive to changes in the discount rate, since both have NPV profiles that are horizontal.

e.The solution cannot be determined because the problem gives us no information that can be used to determine the projects relative IRRs.

NPV, IRR, and MIRRAnswer: a MEDIUM


a.If a project with normal cash flows has an IRR greater than the WACC, the project must have a positive NPV.

b.If Project As IRR exceeds Project Bs, then A must have the higher NPV.

c.A projects MIRR can never exceed its IRR.

d.If a project with normal cash flows has an IRR less than the WACC, the project must have a positive NPV.

e.If the NPV is negative, the IRR must also be negative.

NPV, IRR, and MIRRAnswer: c MEDIUM


a.The MIRR and NPV decision criteria never conflict.

b.The IRR method can never be subject to the multiple IRR problem, while the MIRR method can be.

c.One reason why some people prefer the MIRR method to the IRR method is that the MIRR is based on a more reasonable assumption about reinvestment rates than the IRR method.

d.The higher the WACC, the lower the discounted payback period.

e.The MIRR method assumes that cash flows are reinvested at the crossover rate.

Miscellaneous conceptsAnswer: a MEDIUM


a.The IRR method appeals to some managers because it gives an estimate of the rate of return on projects rather than a dollar amount like the NPV method provides.

b.The discounted payback method eliminates all of the problems associated with the payback method.

c.When evaluating independent projects, the NPV and IRR methods often yield conflicting results.

d.To find the MIRR, we discount the TV at the IRR.

e.A projects NPV profile must intersect the x-axis at the projects WACC.

Miscellaneous conceptsAnswer: a MEDIUM

.Projects C and D are mutually exclusive and have normal cash flows. Project C has a higher NPV if the WACC is less than 12%, whereas Project D has a higher NPV if the WACC exceeds 12%. Which of the following statements is CORRECT?

a.Project D has a higher IRR.

b.Project D is probably larger in scale than Project C.

c.Project C probably has a faster payback.

d.Project C has a higher IRR.

e.The crossover rate between the two projects is below 12%.

NPV, IRR, and MIRRAnswer: c MEDIUM


a.For independent projects, the NPV, IRR, MIRR, and discounted payback (using a payback requirement of 3 or less years) methods always lead to the same accept/reject decisions for a given project.

b.For mutually exclusive projects, the NPV and MIRR methods never conflict, but their results could conflict with the discounted payback and the regular IRR methods.

c.Multiple IRRs can exist, but not multiple MIRRs. This is one reason for favoring the MIRR over the IRR.

d.If a firm uses the discounted payback method with a required payback of 4 years, then it will accept more projects than if it used as its cutoff criterion a regular payback of 4 years.

e.The percentage difference between the MIRR and the IRR is equal to the projects WACC.

NPV, IRR, and MIRRAnswer: e MEDIUM


a.For a project with normal cash flows, any change in the WACC will change both the NPV and the IRR.

b.To find the MIRR, we first compound cash flows at the regular IRR to find the TV, and then we discount the TV at the WACC to find the PV.

c.The NPV and IRR methods both assume cash flows can be reinvested at the WACC. However, the MIRR method assumes reinvestment at the MIRR itself.

d.If two projects have the same cost, and if their NPV profiles cross, then the project with the higher IRR probably has more of its cash flows coming in the later years.

e.If two projects have the same cost, and if their NPV profiles cross, then the project with the lower IRR probably has more of its cash flows coming in the later years.

Multiple IRRs Answer: d MEDIUM


a.For a project to have more than one IRR, then both IRRs must be greater than the WACC.

b.If two projects are mutually exclusive, then they are likely to have multiple IRRs.

c.If a project is independent, then it cannot have multiple IRRs.

d.Multiple IRRs can only occur if the signs of the cash flows change more than once.

e.If a project has two IRRs, then the one that is closest to the vertical axis is the one that should be accepted.

NPV profiles Answer: a MEDIUM/HARD

.Projects S and L are equally risky, mutually exclusive projects with normal cash flows. Project S has an IRR of 15%, while Project Ls IRR is 12%. The two projects have the same NPV when the WACC is 7%. Which of the following statements is CORRECT?

a.If the WACC is 10%, both projects will have positive NPVs.

b.If the WACC is 6%, Project S will have the higher NPV.

c.If the WACC is 13%, Project S will have the lower NPV.

d.If the WACC is 10%, both projects will have a negative NPV.

e.Project Ss NPV is more sensitive to changes in WACC than Project Ls.

NPV profilesAnswer: e MEDIUM/HARD

.Sacramento Paper is considering two equally risky, mutually exclusive projects, and both projects have normal cash flows. Project A has an IRR of 11%, while Project B has an IRR of 14%. When the WACC is 8%, the projects have the same NPV. Given this information, which of the following statements is CORRECT?

a. If the WACC is 13%, Project As NPV will be higher than Project Bs.

b. If the WACC is 9%, Project As NPV will be higher than Project Bs.

c. If the WACC is 6%, Project Bs NPV will be higher than Project As.

d. If the WACC goes over 14%, Project As IRR will exceed Project Bs.

e. If the WACC is 9%, Project Bs NPV will be higher than Project As.

NPV profilesAnswer: b MEDIUM/HARD

.You are considering two mutually exclusive, equally risky, projects. Both projects have IRRs that exceed the WACC that is used to evaluate both of them. Which of the following statements is CORRECT? Assume that the projects being considered have normal cash flows, with one outflow followed by a series of inflows.

a.If the two projects NPV profiles do not cross, then there will be a sharp conflict as to which one should be selected.

b.If the cost of capital is greater than the crossover rate, then the IRR and the NPV criteria will not result in a conflict between the projects. One project will rank higher by both criteria.

c.If the cost of capital is less than the crossover rate, then the IRR and the NPV criteria will not result in a conflict between the projects. One project will rank higher by both criteria.

d.For a conflict to exist between NPV and IRR, the initial investment cost of one project must exceed the cost of the other.

e.For a conflict to exist between NPV and IRR, one project must have an increasing stream of cash flows over time while the other has a decreasing stream. If both sets of cash flows are increasing or decreasing, then it would be impossible for a conflict to exist, even if one project is larger than the other.

NPV profilesAnswer: b MEDIUM/HARD

.Project Xs IRR is 19%, and Project Ys IRR is 17%. The projects have the same risk and the same lives, and their cash flows are constant over their lives. If the WACC is 10%, Project Y has a higher NPV than Project X. Given this information, which of the following statements is CORRECT?

a.The crossover rate between the two projects must be less than 10%.

b.The crossover rate between the two projects must be greater than 10%.

c.If the WACC is 8%, Project X will have the higher NPV.

d.If the WACC is 18%, Project Y will have the higher NPV.

e.Project X is larger in the sense that it has the higher initial cost.

NPV profilesAnswer: e HARD

.Assume that Projects S and L both have normal cash flows, and those cash flows are not affected by the WACC used to evaluate them. Moreover, the projects have the same risk, hence both are evaluated with the same WACC, 10%. However, Project S has a higher IRR than Project L. Which of the following statements is CORRECT?

a.Project S must have a higher NPV than Project L.

b.If Project S has a positive NPV, Project L must also have a positive NPV.

c.If the WACC falls, each projects IRR will increase.

d.If the WACC increases, each projects IRR will decrease.

e.If Projects S and L have the same NPV at the current WACC, 10%, then Project L, the one with the lower IRR, would have a higher NPV if the WACC used to evaluate the projects declined.

NPV profilesAnswer: c HARD

.Which of the following statements is CORRECT? Assume that all projects being considered have normal cash flows and are equally risky.

a.If a projects IRR is equal to its WACC, then under all reasonable conditions, the projects NPV must be negative.

b.If a projects IRR is equal to its WACC, then under all reasonable conditions, the projects IRR must be negative.c.If a projects IRR is equal to its WACC, then under all reasonable conditions, the projects NPV must be zero.d.There is no necessary relationship between a projects IRR, its WACC, and its NPV.

e.When evaluating mutually exclusive projects, those projects with relatively long lives will tend to have relatively high NPVs when the cost of capital is relatively high.

NPV profilesAnswer: d HARD

.A company is choosing between two projects. The larger project has an initial cost of $100,000, annual cash flows of $30,000 for 5 years, and an IRR of 15.24%. The smaller project has an initial cost of $50,000, annual cash flows of $16,000 for 5 years, and an IRR of 16.63%. The projects are equally risky. Which of the following statements is CORRECT?

a.Since the smaller project has the higher IRR, the two projects NPV profiles cannot cross, and the smaller project will look better based on the NPV at all positive values of WACC.

b.Since the smaller project has the higher IRR, the two projects NPV profiles will cross, and the larger project will look better based on the NPV at all positive values of WACC.

c.If the company uses the NPV method, it will tend to favor smaller, shorter-term projects over larger, longer-term projects, regardless of how high or low the WACC is.

d.Since the smaller project has the higher IRR but the larger project has the higher NPV at a zero discount rate, the two projects NPV profiles will cross, and the larger project will have the higher NPV if the WACC is less than the crossover rate.

e.Since the smaller project has the higher IRR and the larger NPV at a zero discount rate, the two projects NPV profiles will cross, and the larger smaller project will look better if the WACC is less than the crossover rate.

MIRRAnswer: c HARD


a.A projects MIRR is always greater than its regular IRR.

b.A projects MIRR is always less than its regular IRR.

c.If a projects IRR is greater than its WACC, then the MIRR will be less than the IRR.

d.If a projects IRR is greater than its WACC, then the MIRR will be greater than the IRR.

e.To find a projects MIRR, we compound cash inflows at the IRR and then discount the terminal value at the WACC.

MIRRAnswer: e HARD

.Which of the following statements is CORRECT? Assume that the project being considered has normal cash flows, with one cash outflow at t = 0 followed by a series of positive cash flows.

a.A projects MIRR is always greater than its regular IRR.

b.A projects MIRR is always less than its regular IRR.

c.If a projects IRR is greater than its WACC, then its MIRR will be greater than the IRR.

d.To find a projects MIRR, we compound cash inflows at the regular IRR and then find the discount rate that causes the PV of the terminal value to equal the initial cost.

e.To find a projects MIRR, the textbook recommends compounding cash inflows at the WACC and then finding the discount rate that causes the PV of the terminal value to equal the initial cost.

NPV and project selectionAnswer: c HARD

.Moynihan Motors has a WACC of 10%. The firm is considering two normal, equally risky, but mutually exclusive projects. Project A has an IRR of 15%, while Project B has an IRR of 20%. Which of the following statements is CORRECT?

a.Both projects have a negative NPV.

b.Since the projects are mutually exclusive, the firm should always select Project B.

c.If the crossover rate is 8%, Project B will have a higher NPV than Project A.d.Only one project has a positive NPV.

e.If the crossover rate is 8%, Project A will have a higher NPV than Project B.Choosing among mutually exclusive projectsAnswer: c HARD

.Projects A and B are mutually exclusive and have normal cash flows. Project A has an IRR of 15% and Project B has an IRR of 20%. Also, the companys WACC is 12%, and at that rate Project A has the higher NPV. Which of the following statements is CORRECT?

a.The crossover rate for the two projects must be less than 12%.

b.Assuming the timing pattern of the two projects cash flows is the same, Project B probably has a higher cost (and larger scale).

c.Assuming the two projects have the same scale, Project B probably has a faster payback than Project A.

d.The crossover rate for the two projects must be 12%.

e.Since B has the higher IRR, then it must also have the higher NPV if the crossover rate is less than the WACC of 12%.

Multiple IRRsAnswer: c HARD

.You are on the staff of Collier Company. The CFO believes project acceptance should be based on the NPV, but Bob Collier, the president, insists that no project can be accepted unless its IRR exceeds the projects risk-adjusted WACC. Now you must make a recommendation on a project that has a cost of $15,000 and two cash flows. $110,000 at the end of Year 1 and -$100,000 at the end of Year 2. The president and the CFO both agree that the appropriate WACC for this project is 10%. At 10%, the NPV is $2,355.37, but you find two IRRs, one at 6.33% and one at 527%, and a MIRR of 11.32%. Which of the following statements best describes your optimal recommendation, i.e., the analysis and recommendation that is best for the company and least likely to get you in trouble with either the CFO or the president?

a.You should recommend that the project be rejected because its NPV is negative and its IRR is less than the WACC.

b.You should recommend that the project be rejected because, although its NPV is positive, it has an IRR that is less than the WACC.

c.You should recommend that the project be accepted because (1) its NPV is positive and (2) although it has two IRRs, in this case it would be better to focus on the MIRR, which exceeds the WACC. You should explain this to the president and tell him that that the firms value will increase if the project is accepted.d.You should recommend that the project be rejected because (1) although its NPV is positive and (2) it has two IRRs, one of which is less than the WACC, which indicates that the firms value will decline if the project is accepted.

e.You should recommend that the project be rejected because, although its NPV is positive, its MIRR is less than the WACC, and that indicates that the firms value will decline if it is accepted.PART II Questions and Problems from Prior Test Bank not used in Part I

Multiple Choice: Problems

MEDIUM (#69 through #81)Payback periodAnswer: b

.The Seattle Corporation has an investment opportunity that will yield cash flows of $30,000 per year in Years 1 through 4, $35,000 per year in Years 5 through 9, and $40,000 in Year 10. This investment will cost $150,000 today, and the firms WACC is 10%. What is the payback period for this investment?

a.5.23 years

b.4.86 years

c.4.00 years

d.6.12 years

e.4.35 years

Payback periodAnswer: c

.Michigan Mattress Company is considering the purchase of land and the construction of a new plant. The land, which would be bought immediately (at t = 0), has a cost of $100,000 and the building, which would be erected at the end of the first year (t = 1), would cost $500,000. It is estimated that the firms after-tax cash flow will be increased by $100,000 starting at the end of the second year, and that this incremental cash flow would increase by 10% annually over the next 10 years. What is the approximate payback period?

a. 2 years

b. 4 years

c. 6 years

d. 8 years

e.10 years

Discounted paybackAnswer: e

.Coughlin Motors is considering a project with the following expected cash flows:

Project

Year Cash Flow

0-$700 million

1200 million

2370 million

3225 million

4700 million

If, the projects WACC is 10%, what is the projects discounted payback?

a.3.15 years

b.4.09 years

c.1.62 years

d.2.58 years

e.3.09 years

Discounted paybackAnswer: d

.A project has the following cash flows:

Project

YearCash Flow

0-$3,000

1 1,000

2 1,000

3 1,000

4 1,000

If its WACC is 10%, what is the projects discounted payback period?

a.3.00 years

b.3.30 years

c.3.52 years

d.3.75 years

e.4.75 years

NPVAnswer: a

.As the capital budgeting director for Denver Corporation, you are evaluating two mutually exclusive projects with the following net cash flows:

Project X Project Z

Year Cash Flow Cash Flow 0 -$100,000 -$100,000

1 50,000 10,000

2 40,000 30,000

3 30,000 40,000

4 10,000 60,000

If Denvers WACC is 15%, which project would you choose?

a.Neither project.

b.Project X, since it has the higher IRR.

c.Project Z, since it has the higher NPV.

d.Project X, since it has the higher NPV.

e.Project Z, since it has the higher IRR.

NPVAnswer: a

.Two mutually exclusive projects have the following projected cash flows:

Project A Project B

Year Cash Flow Cash Flow 0 -$50,000 -$50,000

1 15,625 0

2 15,625 0

3 15,625 0

4 15,625 0

5 15,625 99,500

If the required rate of return on these projects is 10%, which would be chosen and why?

a.Project B because it has the higher NPV.

b.Project B because it has the higher IRR.

c.Project A because it has the higher NPV.

d.Project A because it has the higher IRR.

e.Neither, because both have IRRs less than the cost of capital.

IRRAnswer: c

.The capital budgeting director of Sparrow Corporation is evaluating a project that costs $200,000, is expected to last for 10 years and produces after-tax cash flows, including depreciation, of $44,503 per year. If the firms WACC is 14% and its tax rate is 40%, what is the projects IRR?

a. 8%

b.14%

c.18%

d.-5%

e.12%

IRRAnswer: c

.An insurance firm agrees to pay you $3,310 at the end of 20 years if you pay premiums of $100 per year at the end of each year for 20 years. Find the internal rate of return to the nearest whole percentage point.

a. 9%

b. 7%

c. 5%

d. 3%

e.11%

IRR, payback, and missing cash flowAnswer: d

.Oak Furnishings is considering a project that has an up-front cost and a series of positive cash flows. The projects estimated cash flows are summarized below:

Project

Year Cash Flow

0

?

1

$500 million

2

300 million

3

400 million

4

600 million

The project has a regular payback of 2.25 years. What is the projects internal rate of return (IRR)?

a. 23.1%

b.143.9%

c. 17.7%

d. 33.5%

e. 41.0%

IRR and mutually exclusive projectsAnswer: d

.A company is analyzing two mutually exclusive projects, S and L, whose cash flows are shown below:

Years0

123

|

|||

S-1,1001,00035050

L-1,10003001,500

The companys WACC is 12%. What is the regular IRR of the better project, that is, the project that maximizes the firms stock price?

a.12.00%

b.15.53%

c.18.62%

d.19.08%

e.20.46%

NPV and IRRAnswer: b

.The cash flows for two non-repeatable, mutually exclusive projects are shown below. If your firms WACC is 10%, how much value is sacrificed if your firm selects the project with the higher IRR?

Project S: 0 1 2 3

| | | |

-1,000 500 500 500

Project L: 0 1 2 3 4 5

| | | | | |

-2,000 668.76 668.76 668.76 668.76 668.76

a.$243.43

b.$291.70

c.$332.50

d.$481.15

e.$535.13

NPV and IRRAnswer: e

.A firm is analyzing two mutually exclusive projects with the following cash flows:

Project A

Project B

Year

Cash Flow

Cash Flow 0

-$50,000

-$30,000

1

10,000

6,000

2

15,000

12,000

3

40,000

18,000

4

20,000

12,000

If the companys WACC is 10%, what is the NPV of the project with the highest IRR?

a.$ 7,090

b.$ 8,360

c.$11,450

d.$12,510

e.$15,200

NPV, IRR, and paybackAnswer: d

.Braun Industries is considering an investment project that has the following cash flows:

YearCash Flow 0-$1,000

1

400

2300

3500

4400

The companys WACC is 10%. What is the projects payback, IRR, and NPV?

a.Payback = 2.4, IRR = 10.00%, NPV = $600.

b.Payback = 2.4, IRR = 21.22%, NPV = $260.

c.Payback = 2.6, IRR = 21.22%, NPV = $300.

d.Payback = 2.6, IRR = 21.22%, NPV = $260.

e.Payback = 2.6, IRR = 24.12%, NPV = $300.

MEDIUM/HARD (#82 through #98)Payback periodAnswer: c

.Haig Aircraft is considering a project that has an up-front cost paid today at t = 0. The project will generate positive cash flows of $60,000 a year at the end of each of the next five years. The projects NPV is $75,000 and the companys WACC is 10%. What is the projects regular payback?

a.3.22 years

b.1.56 years

c.2.54 years

d.2.35 years

e.4.16 years


.Davis Corporation has an investment policy that requires acceptable projects to recover all costs within 3 years. The corporation uses the discounted payback method to assess potential projects and uses a WACC of 10%. The cash flows for two independent projects are shown below:

Project A

Project B

Year

Cash Flow

Cash Flow

0

-$100,000

-$80,000

1

40,000

50,000

2

40,000

20,000

3

40,000

30,000

4

30,000

0

In which investment project(s) should the company invest?

a.Project A only.

b.Neither Project A nor Project B.

c.Project A and Project B.

d.Project B only.

NPVAnswer: d

.The Seattle Corporation has an investment opportunity that will yield cash flows of $30,000 per year in Years 1 through 4, $35,000 per year in Years 5 through 9, and $40,000 in Year 10. This investment will cost $150,000 today, and the firms WACC is 10%. What is the NPV of this investment?

a.$135,984

b.$ 18,023

c.$219,045

d.$ 51,138

e.$ 92,146

NPVAnswer: b

.You are considering the purchase of an investment that would pay you $5,000 per year for Years 1-5, $3,000 per year for Years 6-8, and $2,000 per year for Years 9 and 10. If you require a 14% rate of return, and the cash flows occur at the end of each year, then how much should you be willing to pay for this investment?

a.$15,819.27

b.$21,937.26

c.$32,415.85

d.$38,000.00

e.$52,815.71

NPV

Answer: d

.Brown Grocery is considering a project that has an up-front cost of $X. The project will generate a positive cash flow of $75,000 at the end of each of the next 20 years. The project has a WACC of 10% and an IRR of 12%. What is the projects NPV?

a.$1,250,000

b.$ 638,517

c.$ 560,208

d.$ 78,309

e.$ 250,000

NPV, payback, and missing cash flowAnswer: b

.Shannon Industries is considering a project that has the following cash flows:

Project

Year

Cash Flow 0

?

1

$2,000

2

3,000

3

3,000

4

1,500

The project has a payback of 2.5 years, and its WACC 12%. What is the projects NPV?

a.$ 577.68

b.$ 765.91

c.$1,049.80

d.$2,761.32

e.$3,765.91

IRRAnswer: d

.Genuine Products Inc. requires a new machine. Two companies have submitted bids, and you have been assigned the task of choosing one of the machines. Cash flow analysis indicates the following:

Machine AMachine B

YearCash FlowCash Flow

0

-$2,000-$2,000

1

0832

2

0832

3

0832

4

3,877832

What is the IRR for each machine?

a.IRRA = 16%; IRRB = 20%

b.IRRA = 24%; IRRB = 20%

c.IRRA = 18%; IRRB = 16%

d.IRRA = 18%; IRRB = 24%

e.IRRA = 24%; IRRB = 26%

IRRAnswer: c

.Whitney Crane Inc. has the following independent investment opportunities for the coming year:

Annual ADVANCE \r2

ADVANCE \r2Life

Project Cost Cash Inflows (Years) IRR A $10,000 $11,800 1

B 5,000 3,075 2 15

C 12,000 5,696 3

D 3,000 1,009 4 13

The IRRs for Projects A and C, respectively, are:

a.16% and 14%

b.18% and 10%

c.18% and 20%

d.18% and 13%

e.16% and 13%

IRRAnswer: e

.A project has the following net cash flows:

Project

YearCash Flow 0 -$ X

1 150

2 200

3 250

4 400

5 100

At the projects WACC of 10%, the project has an NPV of $124.78. What is the projects IRR?

a.10.00%

b.12.62%

c.13.49%

d.15.62%

e.16.38%

NPV and IRRAnswer: a

.A company is analyzing two mutually exclusive projects, S and L, whose cash flows are shown below:

Years 0 1 2 3 4

S -1,100 900 350 50 10

L -1,100 0 300 500 850

The companys WACC is 12%, and it can get an unlimited amount of capital at that cost. What is the regular IRR (not MIRR) of the better project?

a.13.09%

b.12.00%

c.17.46%

d.13.88%

e.12.53%

IRR, payback, and missing cash flowAnswer: c

.Hadl.com is considering the following two projects:

Project 1Project 2


0-$100 ?

1 30 40

2 50 80

3 40 60

4 50 60

The two projects have the same payback. What is Project 2s internal rate of return (IRR)?

a.44.27%

b.23.40%

c.20.85%

d.14.73%

e.17.64%

MIRRAnswer: d

.Alyeska Salmon Inc is considering a new automated production line project. The project has a cost of $275,000 and is expected to provide after-tax annual cash flows of $73,306 for eight years. The firms management prefers using the modified IRR approach. The firms WACC is 12%. What is the projects MIRR?

a.15.0%

b.14.0%

c.12.0%

d.16.0%

e.17.0%

MIRRAnswer: e

.Martin Manufacturers is considering a five-year investment that costs $100,000. The investment will produce cash flows of $25,000 each year for the first two years, $50,000 a year for each of the remaining three years. The company has a WACC of 12%. What is the MIRR of the investment?

a.12.10%

b.14.33%

c.16.00%

d.18.25%

e.19.45%

MIRRAnswer: d

.A company is considering a project with the following cash flows:

Project

Year

Cash Flow 0

-$100,000

1

50,000

2

50,000

3

50,000

4

-10,000

The projects WACC is estimated to be 10%. What is the MIRR?

a.11.25%

b.11.56%

c.13.28%

d.14.25%

e.20.34%

MIRRAnswer: e

.Capitol City Transfer Company is considering building a new terminal that will require expenditures of $1 million immediately (at t = 0) and another $1 million at the end of Year 1 (t = 1). It will then receive net cash flows of $0.5 million at the end of Years 2-5, and it expects to sell the property and net $1 million at the end of Year 6. All cash inflows and outflows are after taxes. The companys WACC is 12%, and it uses the MIRR criterion for capital budgeting decisions. What is the projects MIRR?

a.11.9%

b.12.0%

c.11.4%

d.11.5%

e.11.7%

MIRR

Answer: e

.Arrington Motors is considering a project with the following cash flows:

Time periodCash Flows0 -$200

1 +120

2 -50

3 +700

The project has a WACC of 12%. What is the projects MIRR?

a.68.47%

b.51.49%

c.48.58%

d.37.22%

e.52.49%

MIRRAnswer: e

.Ditka Diners is considering a project with the following expected cash flows (in millions of dollars):

Project

YearCash Flow

0-$300

1 -100

2 70

3 125

4 700

The projects WACC is 10%. What is the projects MIRR?

a.36.95%

b.18.13%

c.27.35%

d.26.48%

e.23.93%

HARD (#99 through #110)

MIRR and missing cash flowAnswer: d

.Belanger Construction is considering a project with the following subsequent cash flows:

Project

YearCash Flow

0 ?

1$400

2 500

3 200

The projects payback is 1.5 years, and it has a WACC of 10%. What is the projects MIRR?

a.10.00%

b.19.65%

c.21.54%

d.23.82%

e.14.75%

MIRR, payback, and missing cash flowAnswer: d

.Tyrell Corporation is considering a project with the following cash flows (in millions of dollars):

Project

YearCash Flow

0

?

1

$1.0

2

1.5

3

2.0

4

2.5

The project has a payback of exactly 2.0 years. The projects WACC is 12%. What is the projects MIRR?

a.12.50%

b.28.54%

c.15.57%

d.33.86%

e.38.12%

Mutually exclusive projectsAnswer: b

.Two mutually exclusive projects have the following projected cash flows:

Project A Project B

YearCash FlowCash Flow 0-$100,000-$100,000

1 39,500 0 2 39,500 0 3 39,500 133,000Based only on the information given, which of the two projects would be preferred, and why?

a.Project A, because it has a higher NPV.

b.Project B, because it has a higher IRR.

c.Indifferent, because the projects have equal IRRs.

d.Include both in the capital budget, since the sum of the cash inflows exceeds the initial investment in both cases.

e.Choose neither, since their NPVs are negative.

Before-tax cash flowsAnswer: b

.Scott Corporations new project calls for an investment of $10,000. It has an estimated life of 10 years and an IRR of 15%. If cash flows are evenly distributed and the tax rate is 40%, what is the annual before-tax cash flow each year? (Assume depreciation is a negligible amount.)

a.$1,993

b.$3,321

c.$1,500

d.$4,983

e.$5,019

NPVAnswer: c

.Returns on the market and Takeda Companys stock during the last 3 years are shown below:

YearMarketTakeda 1 -12% -14%

2 23 31

3 16 10

The risk-free rate is 7%, and the market risk premium is 5%. Takeda is considering a project whose market beta was found by adding 0.2 to the companys overall corporate beta. Takeda is 100% equity financed, all of which comes from retained earnings. The project has a cost of $100 million, and it is expected to provide cash flows of $20 million per year at the end of Years 1 through 5 and then $30 million per year at the end of Years 6 through 10. What is the projects NPV (in millions of dollars)?

a.$20.89

b.$22.55

c.$23.11

d.$25.76

e.$28.12

NPVAnswer: c

.Returns on the market and Company Ys stock during the last 3 years are shown below:

YearMarketCompany Y1-24% -22%

2 10 13

3 22 36

The risk-free rate is 5 percent, and the required return on the market is 11 percent. You are considering a low-risk project whose market beta is 0.5 less than the companys overall corporate beta. You finance only with equity, all of which comes from retained earnings. The project has a cost of $500 million, and it is expected to provide cash flows of $100 million per year at the end of Years 1 through 5 and then $50 million per year at the end of Years 6 through 10. What is the projects NPV (in millions of dollars)?

a.$ 7.10

b.$ 9.26

c.$10.42

d.$12.10

e.$15.75

MIRR and NPVAnswer: c

.Two mutually exclusive projects, X and Y, have the following cash flows:

Project X Project Y

Year Cash Flow Cash Flow

0 -$2,000 -$2,000

1 200 2,000

2 600 200

3 800 100

4 1,400 75

The projects are equally risky, and your firms WACC is 12%. You must make a recommendation, and it must be based on the modified IRR (MIRR). What is the MIRR of the better project?

a.12.00%

b.11.46%

c.13.59%

d.12.89%

e.15.73%

MIRR and missing cash flowAnswer: b

.Project C has the following net cash flows:

Project C

YearCash Flow

0 -$500

1 200

2 -X

3 300

4 500

Note that the cash flow, X, at t = 2 is an outflow (that is, X < 0). Project C has a WACC of 10% and an MIRR of 12%. What is the projects cash outflow at t = 2?

a.-$196.65

b.-$237.95

c.-$246.68

d.-$262.92

e.-$318.13

MIRR and missing cash flowAnswer: b

.Diefenbaker Inc. is considering a project with the following cash flows:

Project

YearCash Flow

0?

1$100,000

2200,000

3200,000

4-100,000

The project has a payback of 2.0 years and a WACC of 10%. What is the projects MIRR?

a. 5.74%

b.12.74%

c.13.34%

d.16.37%

e.17.67%

MIRRAnswer: e

.Taylor Technologies has a target capital structure that consists of 40% debt and 60% equity. The equity will be financed with retained earnings. The companys bonds have a yield to maturity of 10%. The companys stock has a beta = 1.1. The risk-free rate is 6%, the market risk premium is 5%, and the tax rate is 30%. The company is considering a project with the following cash flows:

Project A

Year

Cash Flow 0

-$50,000

1

35,000

2

43,000

3

60,000

4

-40,000

What is the projects MIRR?

a. 6.76%

b. 9.26%

c.10.78%

d.16.14%

e.20.52%

MIRRAnswer: b

.Houston Inc. is considering building a new refrigerated warehouse that will cost $7,000,000 at t = 0 and is expected to have operating cash flows of $500,000 at the end of each of the next 20 years. However, repairs that will cost $1,000,000 must be incurred at the end of the 10th year. Thus, at the end of Year 10 there will be a $500,000 operating cash inflow and an outflow of -$1,000,000 for repairs. If Houstons WACC is 12%, what is the projects MIRR?

a. 7.75%

b. 8.17%

c. 9.81%

d.11.45%

e.12.33%PV of cash flowsAnswer: c

.A specialty shop in a local mall currently has a lease that calls for payments of $1,000 at the end of each of the next 60 months. The landlord has offered a new 5-year lease that calls for zero rent for 6 months, then rental payments of $1,050 at the end of each month for the next 54 months. Sallys cost of capital is 11%. By what absolute dollar amount would accepting the new lease change Sallys theoretical net worth?

a.$2,810.09

b.$3,243.24

c.$3,803.06

d.$4,299.87

e.$4,681.76

Multiple part:

(The following information applies to the next five problems.)

Woodgate Inc. is considering a project with the following after-tax operating cash flows (in millions of dollars):

Project

Year

Cash Flow 0

-$300

1

125

2

75

3

200

4

100

The project has a WACC of 10%.

Payback periodAnswer: b

.What is the projects payback period?

a.2.00 years

b.2.50 years

c.2.65 years

d.2.83 years

e.3.00 years


.What is the projects discounted payback period?

a.2.00 years

b.2.50 years

c.2.65 years

d.2.83 years

e.3.00 years

IRRAnswer: d

.What is the projects IRR?

a.10.00%

b.16.83%

c.19.12%

d.23.42%

e.26.32%

NPVAnswer: c

.What is the projects NPV?

a.$ 25.88 million

b.$ 40.91 million

c.$ 94.18 million

d.$137.56 million

e.$198.73 million

MIRRAnswer: c

.What is the projects MIRR?

a. 7.64%

b.10.53%

c.17.77%

d.19.12%

e.27.64%

(The following information applies to the following three problems.)

Project A has a WACC of 10% and the following cash flows:

Project A

YearCash Flow 0 -$300

1 100

2 150

3 200

4 50

NPVAnswer: d

.What is Project As NPV?

a.$ 21.32

b.$ 66.26

c.$ 83.00

d.$ 99.29

e.$112.31

IRRAnswer: d

.What is Project As IRR?

a.13.44%

b.16.16%

c.18.92%

d.24.79%

e.26.54%

MIRRAnswer: e

.What is Project As MIRR?

a. 7.40%

b.12.15%

c.14.49%

d.15.54%

e.18.15%

(The following information applies to the next two problems.)

Company A is considering a project with the following cash flows:

Project

YearCash Flow 0 -$5,000

1 5,000

2 3,000

3 -1,000

The project has a WACC of 10%.

NPVAnswer: b

.What is the projects NPV?

a.$1,157

b.$1,273

c.$1,818

d.$2,000

e.$2,776

MIRRAnswer: c

.What is the projects MIRR?

a.16.6%

b.17.0%

c.17.6%

d.18.0%

e.18.6%

(The following information applies to the next two problems.)

Company B is considering a project with the following cash flows:

Project

YearCash Flow 0 - X

1 175

2 175

3 300

Missing cash flow, payback period, and NPVAnswer: a

.Assume that the project has a regular payback period of 2 years and a WACC of 10%. What is the projects NPV?

a.$179.11

b.$204.11

c.$229.11

d.$254.11

e.$279.11

Missing cash flow, IRR, and NPVAnswer: c

.Now instead of making an assumption about the payback period, assume that the project has an IRR of 15%. Given this assumption, what would be the projects NPV, if the WACC equals 12%?

a.$ 0.00

b.$18.08

c.$27.54

d.$37.30

e.$47.36

(The following information applies to the next three problems.)

Bell Corporation is considering two mutually exclusive projects, Project A and Project B. The projects have the following cash flows:

Project AProject B


0-500-500

1 150 300

2 200 300

3 250 350

4 100-300

Both projects have WACCs of 10%.

NPVAnswer: d

.What is Project As NPV?

a.30.12

b.34.86

c.46.13

d.57.78

e.62.01

IRRAnswer: a

.What is Project As IRR?

a.15.32%

b.15.82%

c.16.04%

d.16.68%

e.17.01%

MIRRAnswer: b

.What is Project Bs MIRR?

a.12.05%

b.12.95%

c.13.37%

d.14.01%

e.14.88%

CHAPTER 11ANSWERS AND SOLUTIONS

r (%)

B

A

NPV

($)

r = 10%

r = 10%

r = 12%

.NPV (constant cash flows; 3 years)Answer: a EASY

.NPV (constant cash flows; 4 years)Answer: c EASY

.NPV (constant cash flows; 5 years)Answer: e EASY

.IRR (constant cash flows; 3 years)Answer: b EASY

.IRR (constant cash flows; 4 years)Answer: d EASY

.IRR (constant cash flows; 5 years)Answer: a EASY

.Payback (constant cash flows; 3 years)Answer: c EASY

.Payback (nonconstant cash flows; 5 years)Answer: e EASY/MEDIUM

.NPV (uneven cash flows; 3 years)Answer: a EASY/MEDIUM

.NPV (uneven cash flows; 3 years)Answer: c EASY/MEDIUM

.NPV (uneven cash flows; 4 years)Answer: e EASY/MEDIUM

.NPV (uneven cash flows; 5 years)Answer: b EASY/MEDIUM

.IRR (uneven cash flows; 3 years)Answer: d EASY/MEDIUM

.IRR (uneven cash flows; 4 years)Answer: a EASY/MEDIUM

.IRR (uneven cash flows; 5 years)Answer: c EASY/MEDIUM

.Discounted payback (constant cash flows; 3 years)Answer: b MEDIUM

.Discounted payback (nonconstant cash flows; 4 years)Answer: d MEDIUM

.MIRR (uneven cash flows; 3 years)Answer: e MEDIUM

.MIRR (uneven cash flows; 4 years)Answer: b MEDIUM

.NPV vs IRR (constant cash flows; 3 years)Answer: d MEDIUM

.NPV vs IRR (nonconstant cash flows; 3 years)Answer: a MEDIUM

.NPV vs IRR (size differences)Answer: c MEDIUM/HARD

.NPV vs IRR (different timing patterns)Answer: e MEDIUM/HARD

.NPV vs IRR (different timing patterns)Answer: a MEDIUM/HARD

.NPV vs MIRR (size differences)Answer: d MEDIUM/HARD

.NPV vs paybackAnswer: d MEDIUM/HARD

.NPV vs IRRAnswer: a HARD

.NPV and paybackAnswer: e HARD

.Ranking methodsAnswer: b EASY

Statement b is true, because a projects NPV increases as the WACC declines.

.Ranking methodsAnswer: d EASY

Statement d is true. Academics prefer NPV because it indicates the amount by which a project increases the firms value.

.Ranking methods: paybackAnswer: d EASY

Statement d is true. The payback does indicate how long it should take to recover the investment, hence it is a measure of liquidity.

.Ranking methods: IRRAnswer: e EASY

The IRR assumes reinvestment at the IRR, and that is generally not as valid as assuming reinvestment at the WACC, as with the NPV.

.Normal vs. nonnormal cash flowsAnswer: e EASY

.Normal vs. nonnormal cash flowsAnswer: a EASY

.NPVAnswer: c EASY

.PaybackAnswer: b EASY

.PaybackAnswer: b EASY

.IRRAnswer: d EASY

.IRRAnswer: d EASY

.Ranking methods: NPVAnswer: e MEDIUM

Statement e is correct. The others are all false. If you draw an NPV profile for one project, you will see that if the WACC is less than the IRR, the NPV must be positive.

.Ranking methods: NPVAnswer: b MEDIUM

Statement b is correct, and the others are all false. Cash flows from a project can be used to replace funds that would be raised in the market at the WACC, so the WACC is the opportunity cost for reinvested cash flows. Since the NPV assumes reinvestment at the WACC while the IRR assumes reinvestment at the IRR, NPV is generally the better method.

.NPV profilesAnswer: d EASY/MEDIUM

.Ranking conflictsAnswer: a MEDIUM

.Payback periodAnswer: d MEDIUM

.NPVAnswer: b MEDIUM

.NPV and IRRAnswer: e MEDIUM

.NPV profilesAnswer: a MEDIUM

Statement a is true and the other statements are all false. Distant cash flows are more severely penalized by high discount rates, so if the NPV profile line has a steep slope, this indicates that its cash flows occur relatively late.

.NPV profilesAnswer: b MEDIUM

Statement b is true, while the other statements are all false. Project L must have the longer life, and since distant cash flows are impacted more by changes in the discount rate, its NPV profile must be steeper.

.NPV, IRR, and MIRRAnswer: a MEDIUM

.NPV, IRR, and MIRRAnswer: c MEDIUM

.Miscellaneous conceptsAnswer: a MEDIUM

.Miscellaneous conceptsAnswer: a MEDIUM

.NPV, IRR, and MIRRAnswer: c MEDIUM

.NPV, IRR, and MIRRAnswer: e MEDIUM

.Multiple IRRsAnswer: d MEDIUM

.NPV profiles Answer: a MEDIUM/HARD

EMBED Word.Picture.8

Statement a is true, because both projects have an IRR greater than the WACC and thus will have a positive NPV. Statement b is false, because at 6%, the WACC is less than the crossover rate and Project L has a higher NPV than S. Statement c is false, because at 13% the WACC is greater than the crossover rate and L would have a higher NPV than S. Statement d is false, because of reasons mentioned for statement a. Statement e is false, because Project Ss NPV profile is flatter, which means Project Ls NPV is more sensitive to changes in WACC.

.NPV profilesAnswer: e MEDIUM/HARD


Statement e is true, while the other statements are all false.

.NPV profilesAnswer: b MEDIUM/HARD


Statement a is false, because if the profiles do not cross, then one will dominate the other, with a higher IRR and a higher NPV at every discount rate. Statement b is true. Statement c is false. Statement d is false because a conflict can result from difference in the timing of the cash flows. Statement e is false because scale differences can result in profile crossovers and thus conflicts.

.NPV profilesAnswer: b MEDIUM/HARD


As we can see from the graph, statement b is true, but the other statements are all false.

.NPV profilesAnswer: e HARD

Refer to the NPV profile below. Statement a is false, because you do not know which project has the higher NPV unless you know the WACC. Statement b is false, because if the WACC is greater than IRRL but less than IRRS then Project S will have a positive NPV and Project Ls NPV will be negative. Statements c and d are false, because IRR is independent of WACC. Statement e is true, because Project S has the higher IRR, so Project Ls NPV profile is above Project Ss when the WACC is below the crossover.


.NPV profilesAnswer: c HARD


Recall that the very definition of the IRR is the discount rate at which the NPV is zero. Therefore, statement c is true, while all the other statements are false.

.NPV profilesAnswer: d HARD

EMBED Excel.Chart.8 \s

Statement d true, but all the other statements are false.

.MIRRAnswer: c HARD

Recall that if the IRR is equal to the WACC, then the MIRR and the IRR will be equal, but if the IRR is greater than the WACC, the MIRR will be less than the IRR, and vice versa if the IRR is less than the WACC. This situation exists because the MIRR is found by compounding at the WACC while the IRR is found by compounding at the IRR. In other words, if we compound the inflows at the IRR to find the TV, we will get a larger TV than if we compound at the WACC. Then, the rates that cause the PVs of those TVs to equal the cost are the IRR and the MIRR, respectively.

As a result, statement c is correctif the IRR exceeds the WACC, the IRR will exceed the MIRR. The other statements are all false.

.MIRRAnswer: e HARD

.NPV and project selectionAnswer: c HARD

Statement c is true, while the other statements are all false. If we draw an NPV profile graph, we would see that A must have the steeper slope. If the crossover is at 8%, and the WACC is at 10%, then B will have the higher NPV.

.Choosing among mutually exclusive projectsAnswer: c HARD

.Multiple IRRsAnswer: c HARD

Statement c is true, while the other statements are all false. One could calculate the two IRRs and the MIRR, but the data in the problem are correct, so this is not necessary.

.Payback periodAnswer: b

EMBED Word.Document.6 \s

The project will completely recover the initial investment after $30/$35 = 0.86 of Year 5:

Payback = 4 + EMBED Equation.2 = 4.86 years.

.Payback periodAnswer: c

EMBED Word.Document.8 \s

Payback = 5 + EMBED Equation.2 = 5.928 years 6 years.

.Discounted paybackAnswer: e

The PV of the outflows is -$700 million. To find the discounted payback you need to keep adding cash flows until the cumulative PVs of the cash inflows equal the PV of the outflow:

Discounted

Year Cash Flow Cash Flow @ 10%Cumulative PV

0-$700 million-$700.0000-$700.0000

1200 million181.8182-518.1818

2370 million305.7851-212.3967

3225 million169.0458-43.3509

4700 million478.1094434.7585

The payback occurs somewhere in Year 4. To find out exactly where, we calculate $43.3509/$478.1094 = 0.0907 through the year. Therefore, the discounted payback is 3.091 years.

.Discounted paybackAnswer: d

Discounted


0 -$3,000 -$3,000.00 -$3,000.00

1 1,000 909.09 -2,090.91

2 1,000 826.45 -1,264.46

3 1,000 751.31 -513.15

4 1,000 683.01 169.86

After Year 3, you can see that you wont need all of Year 4 cash flows to break even. To find the portion that you need, calculate $513.15/$683.01 = 0.75. Therefore, the discounted payback is 3.75 years.

.NPVAnswer: a

Financial calculator solution (in thousands):

Project X: Inputs: CF0 = -100; CF1 = 50; CF2 = 40; CF3 = 30;

CF4 = 10; I/YR = 15.

Output: NPVX = -0.833 = -$833.

Project Z: Inputs: CF0 = -100; CF1 = 10; CF2 = 30; CF3 = 40;

CF4 = 60; I/YR = 15.

Output: NPVZ = -8.014 = -$8,014.

At a WACC of 15%, both projects have negative NPVs and should be rejected.

.NPVAnswer: a

Financial calculator solution:

Project A: Inputs: CF0 = -50000; CF1 = 15625; Nj = 5; I/YR = 10.

Output: NPV = $9,231.04.

Project B: Inputs: CF0 = -50000; CF1 = 0; Nj = 4; CF2 = 99500; I/YR = 10.

Output: NPV = $11,781.67.

NPVB > NPVA; $11,781.67 > $9,231.04; Choose Project B.

.IRRAnswer: c


Inputs: CF0 = -200000; CF1 = 44503; Nj = 10. Output: IRR = 18%.

.IRRAnswer: c


Inputs: CF0 = 0; CF1 = -100; Nj = 19; CF2 = 3210. Output: IRR = 5.0%.

.IRR, payback, and missing cash flowAnswer: d

Step 1:Determine the cash outflow at t = 0:

The payback is 2.25 years, so the cash flow will be:

CF0= -[CF1 + CF2 + 0.25(CF3)]

= -[$500 + $300 + 0.25($400)]

= -$900.

Step 2:Calculate the IRR:

CF0 = -900; CF1 = 500; CF2 = 300; CF3 = 400; CF4 = 600; and then solve for IRR = 33.49% ( 33.5%.

.IRR and mutually exclusive projectsAnswer: d

Because the two projects are mutually exclusive, the project with the higher positive NPV is the better project.

Project S

Inputs: CF0 = -1100; CF1 = 1000; CF2 = 350; CF3 = 50; I/YR = 12.

Outputs: NPV = $107.46; IRR = 20.46%.

Project L

Inputs: CF0 = -1100; CF1 = 0; CF2 = 300; CF3 = 1500; I/YR = 12.

Outputs: NPV = $206.83; IRR = 19.08%.

Project L is the better project because it has the higher NPV; its IRR = 19.08%.

.NPV and IRRAnswer: b

Project S: Inputs: CF0 = -1000; CF1 = 500; Nj = 3; I/YR = 10.

Outputs: $243.43; IRR = 23.38%.

Project L: Inputs: CF0 = -2000; CF1 = 668.76; Nj = 5; I/YR = 10.

Outputs: $535.13; IRR = 20%.

Value sacrificed: $535.13 - $243.43 = $291.70.

.NPV and IRRAnswer: e


Project A:Inputs: CF0 = -50000; CF1 = 10000; CF2 = 15000; CF3 = 40000; CF4 = 20000; I/YR = 10.

Outputs: NPV = $15,200.46 $15,200; IRR = 21.38%.

Project B:Inputs: CF0 = -30000; CF1 = 6000; CF2 = 12000; CF3 = 18000; CF4 = 12000; I/YR = 10.

Outputs: NPV = $7,091.73 $7,092; IRR = 19.28%.

Project A has the highest IRR, so the answer is $15,200.

.NPV, IRR, and paybackAnswer: d

Payback = 2 + $300/$500 = 2.6 years.

Using the cash flow register, calculate the NPV and IRR as follows:

Inputs: CF0 = -1000; CF1 = 400; CF2 = 300; CF3 = 500; CF4 = 400; I/YR = 10.

Outputs: NPV = $260.43 $260; IRR = 21.22%.

.Payback periodAnswer: c

Step 1:Calculate the PV of the cash flows:

Inputs: N = 5; I/YR = 10; PMT = 60000; FV =0.

Output: PV = -$227,447.21. PV of cash flows = $227,447.21 $227,447.

Step 2:Calculate the Year 0 outflow:

The outflow at t = 0 is X where $227,447 - X = $75,000. X or CF0 = -$152,447.

Step 3:Calculate the regular payback:

Year CF Cumulative CF

0-$152,447 -$152,447

1 60,000 -92,447

2 60,000 -32,447

3 60,000 27,553

4 60,000 87,553

5 60,000 147,553

So the payback is 2 + EMBED Equation.3 = 2.54 years.

.Discounted paybackAnswer: d

Project A:

Discounted


0-$100,000-$100,000.00-$100,000.00

1 40,000 36,363.64 -63,636.36

2 40,000 33,057.85 -30,578.51

3 40,000 30,052.59 -525.92

4 30,000 20,490.49 19,964.57

Project As discounted payback period exceeds 3 years, so it would not be accepted.

Project B:

Discounted


0 -$80,000 -$80,000.00 -$80,000.00

1 50,000 45,454.55 -34,545.45

2 20,000 16,528.93 -18,016.52

3 30,000 22,539.44 4,522.92

4 0 0 4,522.92

You can see that in Year 3 the cumulative cash flow becomes positive so the projects payback period is less than 3 years.

.NPVAnswer: d


Inputs: CF0 = -150; CF1 = 30; Nj = 4; CF2 = 35; Nj = 5; CF3 = 40; I/YR = 10.

Output: NPV = $51.13824 = $51,138.24 $51,138.

.NPVAnswer: b


Inputs: CF0 = 0; CF1 = 5; Nj = 5; CF2 = 3; Nj = 3; CF3 = 2; Nj = 2; I/YR = 14.

Output: NPV = 21.93726 = $21,937.26.

.NPVAnswer: d

First, find the value of X (the up-front cash flow in this project). IRR is the rate at which you need to reinvest the cash flows for NPV to equal $0. In this case, the IRR is 12%, so if you invest all the projects cash flows at 12%, you should have an NPV of zero.

Step 1:Calculate the value of the initial cash flow by solving for NPV at a WACC of 12%:

You dont have CF0, so use 0 as the placeholder. Enter the following data as inputs in your calculator: CF0 = 0; CF1 = 75000; Nj = 20; and I/YR = 12. Then solve for NPV = $560,208.27.

This is the NPV when the initial cash flow is missing. The NPV with the cash flow must be $0, so that initial cash flow must be $560,208.27.

Step 2:Calculate the projects NPV at its WACC of 10%:

Enter the following data as inputs in your calculator: CF0 = -560208.27; CF1 = 75000; Nj = 20; and I/YR = 10. Then solve for NPV = $78,309.01 ( $78,309.

.NPV, payback, and missing cash flowAnswer: b

First, find the missing t = 0 cash flow. If payback = 2.5 years, this implies t = 0 cash flow must be -$2,000 - $3,000 + (0.5)$3,000 = -$6,500.

NPV = -$6,500 + EMBED Equation.3 + EMBED Equation.3 + EMBED Equation.3 + EMBED Equation.3

= $765.91.


Inputs: CF0 = -6500; CF1 = 2000; Nj = 3000; CF2 = 1500; I/YR = 12.

Output: NPV = $765.91.

.IRRAnswer: d


Machine A: Inputs: CF0 = -2000; CF1 = 0; Nj = 3; CF2 = 3877.

Output: IRR = 17.996% 18%.

Machine B: Inputs: CF0 = -2000; CF1 = 832; Nj = 4.

Output: IRR = 24.01% 24%.

.IRRAnswer: c


Project A:Inputs: N = 1; PV = -10000; PMT = 0; FV = 11800.

Output: I/YR = 18% = IRRA.

Project C:Inputs: N = 3; PV = -12000; PMT = 5696; FV = 0.

Output: I/YR = 19.99% 20% = IRRC.

.IRRAnswer: e

Using

basics of capital budgeting

Documents

irr constant cash flows

projects npv

following cash flow

payback constant cash

projects irr

years npv uneven cash

wacc data

projects payback