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ch12 The Basics of Capital Budgeting (solutions_nss_nc_11)

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ch12 The Basics of Capital Budgeting (solutions_nss_nc_11)

    Chapter 11

    The Basics of Capital Budgeting

    Learning Objectives

After reading this chapter, students should be able to:

    ; Define capital budgeting, explain why it is important, differentiate between security valuation and

    capital budgeting, and state how project proposals are generally classified.

    ; Calculate net present value (NPV) and internal rate of return (IRR) for a given project and evaluate

    each method.

    ; Define NPV profiles, the crossover rate, 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. ; Calculate both the payback and discounted payback periods for a given project and evaluate each

    method.

    ; Identify at least one relevant piece of information provided to decision makers for each capital

    budgeting decision method discussed in the chapter.

    ; Identify a number of different types of decisions that use the capital budgeting techniques developed in

    this chapter.

    ; Identify and explain the purposes of the post-audit in the capital budgeting process.

Chapter 11: The Basics of Capital Budgeting Learning Objectives 265

    Lecture Suggestions

    This is a relatively straight-forward chapter, and, for the most part, it is a direct application of the time value concepts first discussed in Chapter 2. We point out that capital budgeting is to a company what buying stocks or bonds is to an individualan investment decision, when the company wants to know if the

    expected value of the cash flows is greater than the cost of the project, and whether or not the expected rate of return on the project exceeds the cost of the funds required to do the project. We cover the standard capital budgeting proceduresNPV, IRR, MIRR, payback and discounted payback.

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

    What we cover, and the way we cover it, can be seen by scanning the slides and Integrated Case solution for Chapter 11, which appears at the end of this chapter solution. For other suggestions about the lecture, please see the ―Lecture Suggestions‖ in Chapter 2, where we describe how we conduct our classes.

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

266 Lecture Suggestions Chapter 11: The Basics of Capital Budgeting

    Answers to End-of-Chapter Questions

    11-1 Project classification schemes can be used to indicate how much analysis is required to evaluate a

    given project, the level of the executive who must approve the project, and the cost of capital that

    should be used to calculate the project’s NPV. Thus, classification schemes can increase the

    efficiency of the capital budgeting process.

    11-2 The regular payback method has three main flaws: (1) Dollars received in different years are all

    given the same weight. (2) Cash flows beyond the payback year are given no consideration

    whatever, regardless of how large they might be. (3) Unlike the NPV, which tells us by how much

    the project should increase shareholder wealth, and the IRR, which tells us how much a project

    yields over the cost of capital, the payback merely tells us when we get our investment back. The

    discounted payback corrects the first flaw, but the other two flaws still remain.

    11-3 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 a cash flow in Year 5 than on a cash flow in Year 1.

    11-4 Mutually exclusive projects are a set of projects in which only one of the projects can be accepted.

    For example, the installation of a conveyor-belt system in a warehouse and the purchase of a fleet

    of forklifts for the same warehouse would be mutually exclusive projectsaccepting one implies

    rejection of the other. When choosing between mutually exclusive projects, managers should rank

    the projects based on the NPV decision rule. The mutually exclusive project with the highest

    positive NPV should be chosen. The NPV decision rule properly ranks the projects because it

    assumes the appropriate reinvestment rate is the cost of capital.

    11-5 The first question is related to Question 11-3 and the same rationale applies. A high cost of capital

    favors a shorter-term project. If the cost of capital declined, it would lead firms to invest more in

    long-term projects. With regard to the last question, the answer is no; the IRR rankings are

    constant and independent of the firm’s cost of capital.

    11-6 The statement is true. The NPV and IRR methods result in conflicts only if mutually exclusive

    projects are being considered since the NPV is positive if and only if the IRR is greater than the cost

    of capital. If the assumptions were changed so that the firm had mutually exclusive projects, then

    the IRR and NPV methods could lead to different conclusions. A change in the cost of capital or in

    the cash flow streams would not lead to conflicts if the projects were independent. Therefore, the

    IRR method can be used in lieu of the NPV if the projects being considered are independent.

    11-7 Payback provides information on how long funds will be tied up in a project. The shorter the

    payback, other things held constant, the greater the project’s liquidity. This factor is often

    important for smaller firms that don’t have ready access to the capital markets. Also, cash flows

    expected in the distant future are generally riskier than near-term cash flows, so the payback can

    be used as a risk indicator.

    11-8 Project X should be chosen over Project Y. Since the two projects are mutually exclusive, only one

    project can be accepted. The decision rule that should be used is NPV. Since Project X has the

    higher NPV, it should be chosen. The cost of capital used in the NPV analysis appropriately

    includes risk.

Chapter 11: The Basics of Capital Budgeting Integrated Case 267

    11-9 The NPV method assumes reinvestment at the cost of capital, while the IRR method assumes reinvestment at the IRR. MIRR is a modified version of IRR that assumes reinvestment at the cost of capital.

    The NPV method assumes that the rate of return that the firm can invest differential cash flows it would receive if it chose a smaller project is the cost of capital. With NPV we are calculating present values and the interest rate or discount rate is the cost of capital. When we find the IRR we are discounting at the rate that causes NPV to equal zero, which means that the IRR method assumes that cash flows can be reinvested at the IRR (the project’s rate of return). With MIRR, since positive cash flows are compounded at the cost of capital and negative cash flows are discounted at the cost of capital, the MIRR assumes that the cash flows are reinvested at the cost of capital.

    11-10 a. In general, the answer is no. The objective of management should be to maximize value, and

    as we point out in subsequent chapters, stock values are determined by both earnings and

    growth. The NPV calculation automatically takes this into account, and if the NPV of a long-

    term project exceeds that of a short-term project, the higher future growth from the long-term

    project must be more than enough to compensate for the lower earnings in early years.

b. If the same $100 million had been spent on a short-term projectone with a faster payback

    reported profits would have been higher for a period of years. This is, of course, another

    reason why firms sometimes use the payback method.

    268 Integrated Case Chapter 11: The Basics of Capital Budgeting

    Solutions to End-of-Chapter Problems

11-1 Financial calculator solution: Input CF = -52125, CF = 12000, I/YR = 12, and then solve for 01-8

    NPV = $7,486.68.

11-2 Financial calculator solution: Input CF = -52125, CF = 12000, and then solve for IRR = 16%. 01-8

11-3 MIRR: PV costs = $52,125.

    FV inflows:

     PV FV

     0 1 2 3 4 5 6 7 8 12% | | | | | | | | |

     12,000 12,000 12,000 12,000 12,000 12,000 12,000 12,000 1.12 13,440 2 (1.12) 15,053 3 (1.12) 16,859 4 (1.12) 18,882 5 (1.12) 21,148 6 (1.12) 23,686 7 (1.12) 26,528

    52,125 MIRR = 13.89% 147,596

    Financial calculator solution: Obtain the FVA by inputting N = 8, I/YR = 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, and then solving for I/YR = 13.89%.

11-4 Since the cash flows are a constant $12,000, calculate the payback period as: $52,125/$12,000 =

    4.3438, so the payback is about 4 years.

    11-5 Project K’s discounted payback period is calculated as follows:

     Annual Discounted @12%

     Period Cash Flows Cash Flows Cumulative

     0 ($52,125) ($52,125.00) ($52,125.00)

     1 12,000 10,714.29 (41,410.71)

     2 12,000 9,566.33 (31,844.38)

     3 12,000 8,541.36 (23,303.02)

     4 12,000 7,626.22 (15,676.80)

     5 12,000 6,809.12 (8,867.68)

     6 12,000 6,079.57 (2,788.11)

     7 12,000 5,428.19 2,640.08

     8 12,000 4,846.60 7,486.68

    $2,788.11The discounted payback period is 6 + years, or 6.51 years. $5,428.19

    Chapter 11: The Basics of Capital Budgeting Integrated Case 269

    11-6 a. Project A: Using a financial calculator, enter the following:

     = -25, CF = 5, CF = 10, CF = 17, I/YR = 5; NPV = $3.52. CF0123

    Change I/YR = 5 to I/YR = 10; NPV = $0.58.

    Change I/YR = 10 to I/YR = 15; NPV = -$1.91.

    Project B: Using a financial calculator, enter the following:

    CF = -20, CF = 10, CF = 9, CF = 6, I/YR = 5; NPV = $2.87. 0123

    Change I/YR = 5 to I/YR = 10; NPV = $1.04.

    Change I/YR = 10 to I/YR = 15; NPV = -$0.55.

b. Using the data for Project A, enter the cash flows into a financial calculator and solve for IRR A

    = 11.10%. The IRR is independent of the WACC, so it doesn’t change when the WACC changes.

    Using the data for Project B, enter the cash flows into a financial calculator and solve for IRR B

    = 13.18%. Again, the IRR is independent of the WACC, so it doesn’t change when the WACC

    changes.

c. At a WACC = 5%, NPV> NPV so choose Project A. A B

     At a WACC = 10%, NPV > NPV so choose Project B. BA

    At a WACC = 15%, both NPVs are less than zero, so neither project would be chosen.

    11-7 a. Project A:

    CF = -6000; CF = 2000; I/YR = 14. 01-5

    Solve for NPV = $866.16. IRR = 19.86%. AA

    MIRR calculation:

     0 1 2 3 4 5

     | | | | | |

     -6,000 2,000 2,000 2,000 2,000 2,000 1.14 2,280.00 2 (1.14) 2,599.20 3 (1.14) 2,963.09 4 (1.14) 3,377.92

     13,220.21

    Using a financial calculator, enter N = 5; PV = -6000; PMT = 0; FV = 13220.21; and solve for

    MIRR = I/YR = 17.12%. A

    270 Integrated Case Chapter 11: The Basics of Capital Budgeting

Payback calculation:

     0 1 2 3 4 5

     | | | | | |

     -6,000 2,000 2,000 2,000 2,000 2,000 Cumulative CF: -6,000 -4,000 -2,000 0 2,000 4,000

     = 3 years. Regular PaybackA

Discounted payback calculation:

     0 1 2 3 4 5

     | | | | | |

     -6,000 2,000 2,000 2,000 2,000 2,000 Discounted CF: -6,000 1,754.39 1,538.94 1,349.94 1,184.16 1,038.74

    Cumulative CF: -6,000 -4,245.61 -2,706.67 -1,356.73 -172.57 866.17

Discounted Payback = 4 + $172.57/$1,038.74 = 4.17 years. A

Project B:

    CF = -18000; CF = 5600; I/YR = 14. 01-5

Solve for NPV = $1,255.25. IRR = 16.80%. BB

MIRR calculation:

     0 1 2 3 4 5

     | | | | | |

     -18,000 5,600 5,600 5,600 5,600 5,600

     1.14 6,384.00 2 (1.14) 7,277.76 3 (1.14) 8,296.65 4 (1.14) 9,458.18

     37,016.59

Using a financial calculator, enter N = 5; PV = -18000; PMT = 0; FV = 37016.59; and solve for

    MIRR = I/YR = 15.51%. B

Payback calculation:

     0 1 2 3 4 5

     | | | | | |

     -18,000 5,600 5,600 5,600 5,600 5,600 Cumulative CF: -18,000 -12,400 -6,800 -1,200 4,400 10,000

Regular Payback = 3 + $1,200/$5,600 = 3.21 years. B

    Chapter 11: The Basics of Capital Budgeting Integrated Case 271

Discounted payback calculation:

     0 1 2 3 4 5

     | | | | | |

     -18,000 5,600 5,600 5,600 5,600 5,600

    Discounted CF: -18,000 4,912.28 4,309.02 3,779.84 3,315.65 2,908.46 Cumulative CF: -18,000 -13,087.72 -8,778.70 -4,998.86 -1,683.21 1,225.25

     = 4 + $1,683.21/$2,908.46 = 4.58 years. Discounted PaybackB

Summary of capital budgeting rules results:

     Project A Project B

    NPV $866.16 $1,225.25

    IRR 19.86% 16.80%

    MIRR 17.12% 15.51%

    Payback 3.0 years 3.21 years

    Discounted payback 4.17 years 4.58 years

    b. If the projects are independent, both projects would be accepted since both of their NPVs are positive.

    c. If the projects are mutually exclusive then only one project can be accepted, so the project with the highest positive NPV is chosen. Accept Project B.

    d. The conflict between NPV and IRR occurs due to the difference in the size of the projects. Project B is 3 times larger than Project A.

    11-8 a. No mitigation analysis (in millions of dollars):

     0 1 2 3 4 5 12% | | | | | |

     -60 20 20 20 20 20

Using a financial calculator, enter the data as follows: CF = -60; CF = 20; I/YR = 12. Solve 01-5

    for NPV = $12.10 million and IRR = 19.86%.

With mitigation analysis (in millions of dollars):

     0 1 2 3 4 5 12% | | | | | |

     -70 21 21 21 21 21

Using a financial calculator, enter the data as follows: CF = -70; CF = 21; I/YR = 12. Solve 01-5

    for NPV = $5.70 million and IRR = 15.24%.

b. The environmental effects if not mitigated could result in additional loss of cash flows and/or

    fines and penalties due to ill will among customers, community, etc. Therefore, even though the mine is legal without mitigation, the company needs to make sure that they have anticipated all costs in the ―no mitigation‖ analysis from not doing the environmental mitigation.

    272 Integrated Case Chapter 11: The Basics of Capital Budgeting

    c. Even when mitigation is considered the project has a positive NPV, so it should be undertaken.

    The question becomes whether you mitigate or don’t mitigate for environmental problems.

    Under the assumption that all costs have been considered, the company would not mitigate for

    the environmental impact of the project since its NPV is $12.10 million vs. $5.70 million when

    mitigation costs are included in the analysis.

    11-9 a. No mitigation analysis (in millions of dollars):

     0 1 2 3 4 5

     | | | | | |

     -240 80 80 80 80 80

     = -240; CF= 80; I/YR = 17. Solve Using a financial calculator, enter the data as follows: CF01-5

    for NPV = $15.95 million and IRR = 19.86%.

    With mitigation analysis (in millions of dollars):

     0 1 2 3 4 5

     | | | | | |

     -280 84 84 84 84 84

    Using a financial calculator, enter the data as follows: CF = -280; CF= 84; I/YR = 17. Solve 01-5

    for NPV = -$11.25 million and IRR = 15.24%.

    b. If the utility mitigates for the environmental effects, the project is not acceptable. However,

    before the company chooses to do the project without mitigation, it needs to make sure that

    any costs of ―ill will‖ for not mitigating for the environmental effects have been considered in

    that analysis.

    c. Again, the project should be undertaken only if they do not mitigate for the environmental

    effects. However, they want to make sure that they’ve done the analysis properly due to any

    ―ill will‖ and additional ―costs‖ that might result from undertaking the project without concern

    for the environmental impacts.

    11-10 Project A: Using a financial calculator, enter the following data: CF = -400; CF = 55; CF = 01-34-5

    225; I/YR = 10. Solve for NPV = $30.16.

Project B: Using a financial calculator, enter the following data: CF = -600; CF = 300; CF = 01-23-4

    50; CF = 49; I/YR = 10. Solve for NPV = $22.80. 5

    The decision rule for mutually exclusive projects is to accept the project with the highest positive NPV. In this situation, the firm would accept Project A since NPV = $30.16 compared to NPV = AB

    $22.80.

    11-11 Project S: Using a financial calculator, enter the following data: CF = -15000; CF = 4500; I/YR 01-5

    = 14. NPV = $448.86. S

    Project L: Using a financial calculator, enter the following data: CF = -37500; CF = 11100; I/YR 01-5

    = 14. NPV = $607.20. L

    Chapter 11: The Basics of Capital Budgeting Integrated Case 273

    The decision rule for mutually exclusive projects is to accept the project with the highest positive

     = $607.20 compared to NPV = NPV. In this situation, the firm would accept Project L since NPVLS

    $448.86.

    11-12 Input the appropriate cash flows into the cash flow register, and then calculate NPV at 10% and the IRR of each of the projects:

    Project S: CF = -1000; CF = 900; CF = 250; CF = 10; I/YR = 10. Solve for NPV = $39.14; 0123-4S

    IRR = 13.49%. S

    Project L: CF = -1000; CF = 0; CF = 250; CF = 400; CF = 800; I/YR = 10. Solve for NPV = 01234L

    $53.55; IRR = 11.74%. L

    Since Project L has the higher NPV, it is the better project, even though its IRR is less than Project S’s IRR. The IRR of the better project is IRR = 11.74%. L

    12-13 Because both projects are the same size you can just calculate each project’s MIRR and choose the project with the higher MIRR.

Project X: 0 1 2 3 4 12% | | | | |

     -1,000 100 300 400 700.00 1.12 448.00 2 (1.12) 376.32 3 (1.12) 140.49

     1,000 13.59% = MIRR 1,664.81 X 4$1,000 = $1,664.81/(1 + MIRR). X

    Project Y: 0 1 2 3 4 12% | | | | |

     -1,000 1,000 100 50 50.00 1.12 56.00 2 (1.12) 125.44 3 (1.12) 1,404.93

     1,000 13.10% = MIRR 1,636.37 Y 4$1,000 = $1,636.37/(1 + MIRR). Y

    Thus, since MIRR > MIRR, Project X should be chosen. XY

    Alternate step: You could calculate the NPVs, see that Project X has the higher NPV, and just calculate MIRR. X

    NPV = $58.02 and NPV = $39.94. XY

    11-14 a. HCC: Using a financial calculator, enter the following data: CF = -600000; CF = -50000; 01-5

    I/YR = 7. Solve for NPV = -$805,009.87.

    LCC: Using a financial calculator, enter the following data: CF = -100000; CF = -175000; 01-5

    I/YR = 7. Solve for NPV = -$817,534.55.

    274 Integrated Case Chapter 11: The Basics of Capital Budgeting

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