Financial managment Solution Manual:The Basics of Capital Budgeting

After reading this chapter, students should be able to: • Define capital budgeting, explain why it is important, and state how project proposals are generally classified. • List the steps involved in evaluating a capital budgeting project. • Calculate payback period, discounted payback period, Net Present Value (NPV), and Internal Rate of Return (IRR) for a given project and evaluate each method. • Define NPV profiles, and explain the rationale behind the NPV and IRR methods, their reinvestment rate assumptions, and which method is better when evaluating independent versus mutually exclusive projects. • Briefly explain the problem of multiple IRRs and when this situation could occur. • Calculate the Modified Internal Rate of Return (MIRR) for a given project and evaluate this method. • Identify at least one relevant piece of information provided to decision makers for each capital budgeting decision method discussed in the chapter. • Identify and explain the purposes of the post-audit in the capital budgeting process. • Identify a number of different types of decisions that use the capital budgeting techniques developed in this chapter.

After reading this chapter, students should be able to:

 Define capital budgeting, explain why it is important, and state how

project proposals are generally classified

 List the steps involved in evaluating a capital budgeting project

 Calculate payback period, discounted payback period, Net Present Value

(NPV), and Internal Rate of Return (IRR) for a given project andevaluate each method

 Define NPV profiles, and explain the rationale behind the NPV and IRR

methods, their reinvestment rate assumptions, and which method is betterwhen evaluating independent versus mutually exclusive projects

 Briefly explain the problem of multiple IRRs and when this situation

could occur

 Calculate the Modified Internal Rate of Return (MIRR) for a given

project and evaluate this method

 Identify at least one relevant piece of information provided to decision

makers for each capital budgeting decision method discussed in thechapter

 Identify and explain the purposes of the post-audit in the capital

budgeting process

 Identify a number of different types of decisions that use the capital

budgeting techniques developed in this chapter

Chapter 10 The Basics of Capital Budgeting

LEARNING OBJECTIVES

This is a relatively straight-forward chapter, and, for the most part, it is adirect application of the time value concepts first discussed in Chapter 6.

We point out that capital budgeting is to a company what buying stocks orbonds is to an individual an investment decision, when the company wants toknow if the expected value of the cash flows is greater than the cost of theproject, and whether or not the expected rate of return on the project exceedsthe cost of the funds required to take on the project We cover the standardcapital budgeting procedures payback, discounted payback, NPV, IRR, and MIRR

At this point, students who have not yet mastered time value conceptsand how to use their calculator efficiently get another chance to catch on.Students who have mastered those tools and concepts have fun, because they cansee what is happening and the usefulness of what they are learning

The details of what we cover, and the way we cover it, can be seen by

scanning Blueprints, Chapter 10 For other suggestions about the lecture,

please see the “Lecture Suggestions” in Chapter 2, where we describe how weconduct our classes

DAYS ON CHAPTER: 3 OF 58 DAYS (50-minute periods)

LECTURE SUGGESTIONS

10-1 Project classification schemes can be used to indicate how much analysis

is required to evaluate a given project, the level of the executive whomust approve the project, and the cost of capital that should be used tocalculate the project’s NPV Thus, classification schemes can increasethe efficiency of the capital budgeting process

10-2 The NPV is obtained by discounting future cash flows, and the

discounting process actually compounds the interest rate over time.Thus, an increase in the discount rate has a much greater impact on acash flow in Year 5 than on a cash flow in Year 1

10-3 This question is related to Question 10-2 and the same rationale

applies With regard to the second part of the question, the answer isno; the IRR rankings are constant and independent of the firm’s cost ofcapital

10-4 The NPV and IRR methods both involve compound interest, and the

mathematics of discounting requires an assumption about reinvestmentrates The NPV method assumes reinvestment at the cost of capital,while the IRR method assumes reinvestment at the IRR MIRR is amodified version of IRR that assumes reinvestment at the cost ofcapital

10-5 The statement is true The NPV and IRR methods result in conflicts only

if mutually exclusive projects are being considered since the NPV ispositive if and only if the IRR is greater than the cost of capital Ifthe assumptions were changed so that the firm had mutually exclusiveprojects, then the IRR and NPV methods could lead to differentconclusions A change in the cost of capital or in the cash flowstreams would not lead to conflicts if the projects were independent.Therefore, the IRR method can be used in lieu of the NPV if the projectsbeing considered are independent

10-6 Yes, if the cash position of the firm is poor and if it has limited

access to additional outside financing it might be better off to choose

a machine with a rapid payback But even here, the relationship betweenpresent value and cost would be a better decision tool

10-7 a In general, the answer is no The objective of management should be

to maximize value, and as we point out in subsequent chapters, stockvalues are determined by both earnings and growth The NPVcalculation automatically takes this into account, and if the NPV of

a long-term project exceeds that of a short-term project, the higherfuture growth from the long-term project must be more than enough tocompensate for the lower earnings in early years

ANSWERS TO END-OF-CHAPTER QUESTIONS

b If the same $100 million had been spent on a short-term project onewith a faster payback reported profits would have been higher for aperiod of years This is, of course, another reason why firmssometimes use the payback method.

10-8 Mutually exclusive projects are a set of projects in which only one of

the projects can be accepted For example, the installation of aconveyor-belt system in a warehouse and the purchase of a fleet offorklifts for the same warehouse would be mutually exclusive projects accepting one implies rejection of the other When choosing betweenmutually exclusive projects, managers should rank the projects based onthe NPV decision rule The mutually exclusive project with the highestpositive NPV should be chosen The NPV decision rule properly ranks theprojects because it assumes the appropriate reinvestment rate is thecost of capital

10-9 Project X should be chosen over Project Y Since the two projects are

mutually exclusive, only one project can be accepted The decision rulethat should be used is NPV Since Project X has the higher NPV, itshould be chosen The cost of capital used in the NPV analysisappropriately includes risk

10-1 $52,125/$12,000 = 4.3438, so the payback is about 4 years.

10-2 Financial Calculator Solution: Input CF0 = -52125, CF1-8 = 12000, I =

12, and then solve for NPV = $7,486.68

10-3 Financial Calculator Solution: Input CF0 = -52125, CF1-8 = 12000, and

then solve for IRR = 16%

10-4 Project K’s discounted payback period is calculated as follows:

19.8

$5,42

11

$2,788

years, or 6.51 years

Alternatively, since the annual cash flows are the same, one can divide

$12,000 by 1.12 (the discount rate = 12%) to arrive at CF1 and thencontinue to divide by 1.12 seven more times to obtain the discountedcash flows (Column 3 values) The remainder of the analysis would bethe same

10-5 MIRR: PV Costs = $52,125

FV Inflows:

PV FV

0 1 2 3 4 5 6 7 8 | | | | | | | | | 12,000 12,000 12,000 12,000 12,000 12,000 12,000 12,000 13,440 15,053 16,859 18,882 21,148

13.89% 147,596

Financial Calculator Solution: Obtain the FVA by inputting N = 8, I =

12, PV = 0, PMT = 12000, and then solve for FV = $147,596 The MIRR can

be obtained by inputting N = 8, PV = -52125, PMT = 0, FV = 147596, andthen solving for I = 13.89%

7,556

8,614

17,100 MIRR = 14.54% (Accept) 33,712

Financial Calculator Solution: Obtain the FVA by inputting N = 5, I =

14, PV = 0, PMT = 5100, and then solve for FV = $33,712 The MIRR can

be obtained by inputting N = 5, PV = -17100, PMT = 0, FV = 33712, andthen solving for I = MIRR = 14.54%

Financial Calculator Solution: Obtain the FVA by inputting N = 5, I =

14, PV = 0, PMT = 7500, and then solve for FV = $49,576 The MIRR can

be obtained by inputting N = 5, PV = -22430, PMT = 0, FV = 49576, andthen solving for I = 17.19%

10-8 Using a financial calculator:

10-9 a The IRRs of the two alternatives are undefined To calculate an IRR,

the cash flow stream must include both cash inflows and outflows

b The PV of costs for the conveyor system is -$556,717, while the PV ofcosts for the forklift system is -$493,407 Thus, the forkliftsystem is expected to be -$493,407 - (-$556,717) = $63,310 lesscostly than the conveyor system, and hence the forklifts should beused

Thus, since MIRRX > MIRRY, Project X should be chosen

Alternate step: You could calculate NPVs, see that Project X has thehigher NPV, and just calculate MIRRX

NPVX = $58.02 and NPVY = $39.94

10-11 Input the appropriate cash flows into the cash flow register, and then

calculate NPV at 10 percent and the IRR of each of the projects:

| |    |-1,000 PMT PMTWith a financial calculator, input N = 10, I = 12, PV = -1000,and FV = 0 to obtain PMT = $176.98.

Step 2: Calculate the project’s MIRR:

-1,000 176.98 176.98 176.98 176.98

194.68 379.37

417 31

FV of inflows: With a financial calculator, input N = 10, I =

10, PV = 0, and PMT = -176.98 to obtain FV = $2,820.61 Theninput

c Environmental effects could be added by estimating penalties or anyother cash outflows that might be imposed on the firm to help returnthe land to its previous state (if possible) These outflows could

be so large as to cause the project to have a negative NPV, in whichcase the project should not be undertaken

10-14 a Year Sales Royalties Marketing Net

NPV = $60,000/(1.11) + $39,000/(1.11) + $21,000/(1.11) - $20,000 = $81,062.35.

Using a financial calculator, input CF0 = -20000; CF1 = 60000, CF2 =

39000, CF3 = 21000, and then solve for IRR = 261.90%

b Finance theory dictates that this investment should be accepted.However, ask your students “Does this service encourage cheating?”

If yes, does a businessperson have a social responsibility not tomake this service available?

10-15 Facts: 5 years remaining on lease; rent = $2,000/month; 60 payments

left, payment at end of month

New lease terms: $0/month for 9 months; $2,600/month for 51 months.Cost of capital = 12% annual (1% per month)

CF0 = 0; CF1-9 = 0; CF10-60 = 2600; I = 1.9113; NPV = ? NPV =

-$71,038.98

Except for rounding differences; the costs are the same

10-16 a The payback periods for Projects A and B are calculated as follows:

c Finding net present values, use a financial calculator and enter thefollowing data:

By the NPV criterion, Project A is preferred to Project B

d Finding the IRR, use a financial calculator and enter the following:Project A Project B

According to the MIRR criterion, Project A is the superior project.10-17 Since the IRR is the cost of capital at which the NPV of a project

equals zero, the projects inflows can be evaluated at the IRR and thepresent value of these inflows must equal the initial investment

Using a financial calculator enter the following:

Therefore, the initial investment for this project is $65,002.11 Using

a calculator, the project's NPV can now be solved

10-18 The MIRR can be solved with a financial calculator by finding the

terminal future value of the cash inflows and the initial present value

of cash outflows, and solving for the discount rate that equates thesetwo values In this instance, the MIRR is given, but a cash outflow ismissing and must be solved for Therefore, if the terminal future value

of the cash inflows is found, it can be entered into a financialcalculator, along with the number of years the project lasts and theMIRR, to solve for the initial present value of the cash outflows One

of these cash outflows occurs in Year 0 and the remaining value must bethe present value of the missing cash outflow in Year 2

Cash inflows Compounding Rate FV in Year 5 @ 10%

for Year 0 is $500, the present value of the Year 2 cash outflow is

$206.62 Therefore, the missing cash outflow for Year 2 is $206.62 ×(1.1)2

= $250.01

10-19 a At k = 12%, Project A has the greater NPV, specifically $200.41 as

compared to Project B’s NPV of $145.93 Thus, Project A would beselected At k = 18%, Project B has an NPV of $63.68 which is higherthan Project A’s NPV of $2.66 Thus, choose Project B if k = 18%.b

20 0

10 0 -100 -2 00 -300

5 10 15 20 25 30

Cost of Capital (%)

NPV ($)

Project A

Project B

IR R B = 16.7%

Projects A and B are mutually exclusive, thus, only one of theprojects can be chosen As long as the cost of capital is greaterthan the crossover rate, both the NPV and IRR methods will lead tothe same project selection However, if the cost of capital is lessthan the crossover rate the two methods lead to different projectselections a conflict exists When a conflict exists the NPV methodmust be used

Because of the sign changes and the size of the cash flows, Project

 has multiple IRRs Thus, a calculator’s IRR function will not work.One could use the trial and error method of entering different discountrates until NPV = $0 However, an HP can be “tricked” into giving theroots After you have keyed Project Delta’s cash flows into the cashflow registers of an HP-10B, you will see an “Error-Soln” message Nowenter 10  STO  IRR/YR and the 14.53 percent IRR is found Thenenter 100  STO  IRR/YR to obtain IRR = 456.22% Similarly, Excelcan also be used

e Here is the MIRR for Project A when k = 12%:

PV costs = $300 + $387/(1.12)1 + $193/(1.12)2

+ $100/(1.12)3 + $180/(1.12)7 = $952.00

TV inflows = $600(1.12)3 + $600(1.12)2 + $850(1.12)1 = $2,547.60.Now, MIRR is that discount rate which forces the TV of $2,547.60 in

7 years to equal $952.00

Using a financial calculator enter the following inputs: N = 7, PV =-952, PMT = 0, and FV = 2547.60 Then solve for I = MIRRA = 15.10%.Similarly, MIRRB = 17.03%

At k = 18%,

MIRRA = 18.05%

MIRRB = 20.49%

10-20 a

The crossover rate is approximately 16 percent If the cost ofcapital is less than the crossover rate, then Plan B should beaccepted; if the cost of capital is greater than the crossover rate,then Plan A is preferred At the crossover rate, the two projects’NPVs are equal Thus, other criteria such as the IRR must be used toevaluate the projects The exact crossover rate is calculated as16.07 percent, the IRR of Project , the difference between the cashflow streams of the two projects.

b Yes Assuming (1) equal risk among projects, and (2) that the cost

of capital is a constant and does not vary with the amount of capitalraised, the firm would take on all available projects with returnsgreater than its 12 percent cost of capital If the firm hadinvested in all available projects with returns greater than 12percent, then its best alternative would be to repay capital Thus,the cost of capital is the correct reinvestment rate for evaluating aproject’s cash flows

10-21 a Using a financial calculator, we get:

c The NPV method implicitly assumes that the opportunity exists toreinvest the cash flows generated by a project at the cost ofcapital, while use of the IRR method implies the opportunity toreinvest at the IRR The firm will invest in all independentprojects with an NPV > $0 As cash flows come in from these

NPV

(Millions of Dollars)

20 40 60 80

projects, the firm will either pay them out to investors, or use them

as a substitute for outside capital which, in this case, costs 10percent Thus, since these cash flows are expected to save the firm

10 percent, this is their opportunity cost reinvestment rate

The IRR method assumes reinvestment at the internal rate of returnitself, which is an incorrect assumption, given a constant expectedfuture cost of capital, and ready access to capital markets

10-22 a The project’s expected cash flows are as follows (in millions of

0 10 0 200 30 0 40 0 50 0 k (%)

c Other possible projects with multiple rates of return could benuclear power plants where disposal of radioactive wastes is required

at the end of the project’s life