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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.
Learning Objectives: 10 - Harcourt Brace & Company
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 individual—an 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 procedures—NPV, 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: 4 OF 58 DAYS (50-minute periods)
Harcourt Brace & Company Lecture Suggestions: 10 -
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 project—one 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.
Chapter 11: The Basics of Capital Budgeting Answers and Solutions 268
Solutions to End-of-Chapter Problems
11-1 Financial calculator solution: Input CF 0 = -52125, CF1-8 = 12000, I/YR = 12, and then solve for NPV = $7,486.68.
11-2 Financial calculator solution: Input CF 0 = -52125, CF (^) 1-8 = 12000, and then solve for IRR = 16%
11-3 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,
13,
15,
16,
18,
21,
23,
26, 52,125 MIRR = 13.89% 147,
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)
269 Answers and Solutions Chapter 11: The Basics of Capital Budgeting
Using a financial calculator, enter N = 5; PV = -6000; PMT = 0; FV = 13220.21; and solve for MIRRA = I/YR = 17.12%.
271 Answers and Solutions 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, Cumulative CF: -6,000 -4,000 -2,000 0 2,000 4,
Regular Payback (^) A = 3 years.
Discounted payback calculation: 0 1 2 3 4 5 | | | | | | -6,000 2,000 2,000 2,000 2,000 2, Discounted CF: -6,000 1,754.391,538.941,349.941,184.161,038. Cumulative CF: -6,000 -4,245.61 -2,706.67 -1,356.73 -172. 7 866.
Discounted Payback (^) A = 4 + $172.57/$1,038.74 = 4.17 years.
Project B: CF 0 = -18000; CF1-5 = 5600; I/YR = 14.
Solve for NPVB = $1,255.25. IRR (^) B = 16.80%.
MIRR calculation: 0 1 2 3 4 5 | | | | | | -18,000 5,600 5,600 5,600 5,600 5, 6,384. 7,277. 8,296. 9,458. 37,016.
Using a financial calculator, enter N = 5; PV = -18000; PMT = 0; FV = 37016.59; and solve for MIRRB = I/YR = 15.51%.
Payback calculation: 0 1 2 3 4 5 | | | | | | -18,000 5,600 5,600 5,600 5,600 5, Cumulative CF: -18,000 -12,400 -6,800 -1,200 4,400 10,
Regular Payback (^) B = 3 + $1,200/$5,600 = 3.21 years.
Chapter 11: The Basics of Capital Budgeting Answers and Solutions 272
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
Using a financial calculator, enter the data as follows: CF 0 = -240; CF1-5 = 80; I/YR = 17. Solve 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 0 = -280; CF1-5 = 84; I/YR = 17. Solve 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 0 = -400; CF (^) 1-3 = 55; CF (^) 4-5 = 225; I/YR = 10. Solve for NPV = $30.16.
Project B: Using a financial calculator, enter the following data: CF 0 = -600; CF1-2 = 300; CF3-4 = 50; CF 5 = 49; I/YR = 10. Solve for NPV = $22.80.
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 NPVA = $30.16 compared to NPVB = $22.80.
11-11 Project S: Using a financial calculator, enter the following data: CF 0 = -15000; CF1- = 4500; I/YR = 14. NPVS = $448.86.
Project L: Using a financial calculator, enter the following data: CF 0 = -37500; CF1- = 11100; I/YR = 14. NPVL = $607.20.
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 L since NPV (^) L =
Chapter 11: The Basics of Capital Budgeting Answers and Solutions 274
$607.20 compared to NPVS = $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 0 = -1000; CF 1 = 900; CF 2 = 250; CF (^) 3-4 = 10; I/YR = 10. Solve for NPV (^) S = $39.14; IRR (^) S = 13.49%.
Project L: CF 0 = -1000; CF 1 = 0; CF 2 = 250; CF 3 = 400; CF 4 = 800; I/YR = 10. Solve for NPVL = $53.55; IRRL = 11.74%.
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 (^) L = 11.74%.
11-13 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 | | | | |
-1,000 100 300 400 700.
1,000 13.59% = MIRRX 1,664.
$1,000 = $1,664.81/(1 + MIRRX ) 4.
Project Y: 0 1 2 3 4 | | | | | -1,000 1,000 100 50 50.
1,404. 1,000 13.10% = MIRRY 1,636.
$1,000 = $1,636.37/(1 + MIRRY) 4.
Thus, since MIRR (^) X > MIRRY, Project X should be chosen.
Alternate step: You could calculate the NPVs, see that Project X has the higher NPV, and just calculate MIRRX.
NPVX = $58.02 and NPVY = $39.94.
11-14 a. HCC: Using a financial calculator, enter the following data: CF 0 = -600000; CF1- = -50000; I/YR = 7. Solve for NPV = -$805,009.87.
275 Answers and Solutions Chapter 11: The Basics of Capital Budgeting
b. Using a financial calculator, calculate each plan’s NPVs at different discount rates (as shown in the table below) and graph the NPV profiles.
Discount Rate NPV Plan A NPV Plan B 0% $88,000,000 $42,400, 5 39,758,146 21,897, 10 14,486,808 11,156, 15.03 0 4,997, 20 -8,834,690 1,245, 22.26 -11,765,254 0
The crossover rate is somewhere between 11% and 12%.
c. The NPV method implicitly assumes that the opportunity exists to reinvest the cash flows generated by a project at the WACC, while use of the IRR method implies the opportunity to reinvest at the IRR. The firm will invest in all independent projects with an NPV > $0. As cash flows come in from these projects, the firm will either pay them out to investors, or use them as a substitute for outside capital which, in this case, costs 10%. Thus, since these cash flows are expected to save the firm 10%, this is their opportunity cost reinvestment rate. The IRR method assumes reinvestment at the internal rate of return itself, which is an incorrect assumption, given a constant expected future cost of capital, and ready access to capital markets.
11-17 a. Using a financial calculator and entering each project’s cash flows into the cash flow registers and entering I/YR = 12, you would calculate each project’s NPV. At WACC = 12%, Project A has the greater NPV, specifically $200.41 as compared to Project B’s NPV of $145.93.
b. Using a financial calculator and entering each project’s cash flows into the cash flow registers, you would calculate each project’s IRR. IRRA = 18.1%; IRR (^) B = 24.0%.
c. Here is the MIRR for Project A when WACC = 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.
MIRR is the discount rate that 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/YR = MIRR (^) A = 15.10%.
Here is the MIRR for Project B when WACC = 12%: PV costs = $405.
TV inflows = $134(1.12) 6 + $134(1.12) 5 + $134(1.12) 4 + $
277 Answers and Solutions Chapter 11: The Basics of Capital Budgeting
(1.12)^3 + $134(1.12)^2 + $134(1.12)
MIRR is the discount rate that forces the TV of $1,217.93 in 7 years to equal $405.
Using a financial calculator enter the following inputs: N = 7; PV = -405; PMT = 0; and FV = 1217.93. Then, solve for I/YR = MIRR (^) B = 17.03%.
d. WACC = 12% criteria: Project A Project B NPV $200.41 $145. IRR 18.1% 24.0% MIRR 15.1% 17.03%
The correct decision is that Project A should be chosen because NPV (^) A > NPV (^) B.
At WACC = 18%, using your financial calculator enter the cash flows for each project, enter I/YR = WACC = 18, and then solve for each Project’s NPV.
NPVA = $2.66; NPVB = $63.68.
At WACC = 18%, NPVB > NPVA so Project B would be chosen.
Chapter 11: The Basics of Capital Budgeting Answers and Solutions 278
11-18 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.
WACC = 12% annual (1% per month).
a. 0 1 2 59 60 | | | F 0 B 7F 0 B 7F 0 B 7 | | -2,000 -2,000 -2,000 -2,
PV cost of old lease: N = 60; I/YR = 1; PMT = -2000; FV = 0; PV =? PV = - $89,910.08.
0 1 9 10 59 60 | | F 0 B 7F 0 B 7F 0 B 7 | | F 0 B 7F 0 B 7F 0 B 7 | | 0 0 -2,600 -2,600 -2,
PV cost of new lease: CF 0 = 0, CF (^) 1-9 = 0; CF (^) 10-60 = -2600; I/YR = 1. NPV = - $94,611.45.
Sharon should not accept the new lease because the present value of its cost is $94,611.45 – $89,910.08 = $4,701.37 greater than the old lease.
b. At t = 9 the FV of the original lease’s cost = -$89,910.08(1.01) 9 = -$98,333.33. Since lease payments for months 0-9 would be zero, we can calculate the lease payments during the remaining 51 months as follows: N = 51; I/YR = 1; PV = 98333.33; and FV = 0. Solve for PMT = -$2,470.80.
Check: 0 1 9 10 59 60 | | F 0 B 7F 0 B 7F 0 B 7 | | F 0 B 7F 0 B 7F 0 B 7 | | 0 0 -2,470.80 -2,470.80-2,470.
PV cost of new lease: CF 0 = 0; CF1-9 = 0; CF (^) 10-60 = -2470.80; I/YR = 1. NPV = - $89,909.99.
Except for rounding; the PV cost of this lease equals the PV cost of the old lease.
c. Period Old Lease New Lease F 0 4 4Lease 0 0 0 0 1-9 -2,000 0 -2, 10-60 -2,000 -2,600 600
CF 0 = 0; CF (^) 1-9 = -2000; CF (^) 10-60 = 600; IRR =? IRR = 1.9113%. This is the periodic rate. To obtain the nominal cost of capital, multiply by 12: 12(0.019113) = 22.94%.
Check: Old lease terms: N = 60; I/YR = 1.9113; PMT = -2000; FV = 0; PV =? PV = -$71,039.17.
Chapter 11: The Basics of Capital Budgeting Answers and Solutions 280
New lease terms: CF 0 = 0; CF1-9 = 0; CF10-60 = -2600; I/YR = 1.9113; NPV =? NPV = -$71,038.98.
Except for rounding differences; the costs are the same.
11-19 a. The project’s expected cash flows are as follows (in millions of dollars):
Time Net Cash Flow 0 ($ 2.0) 1 13. 2 (12.0)
We can construct the following NPV profile: NPV (Millionsof Dollars)
0
-0.
-1. 0 100 200 300 400 500
WACC(%)
NPV (Millionsof Dollars)
0
-0.
-1. 0 100 200 300 400 500
WACC(%)
WACC NPV
b. If WACC = 10%, reject the project since NPV < $0. Its NPV at WACC = 10% is equal to 0 0 1 E $99,174. But if WACC = 20%, accept the project because NPV > $0. Its NPV at WACC = 20% is $500,000.
c. Other possible projects with multiple rates of return could be nuclear power plants where disposal of radioactive wastes is required at the end of the project’s life.
d. MIRR @ WACC = 10%:
281 Answers and Solutions Chapter 11: The Basics of Capital Budgeting
Calculate the project’s MIRR:
| | | F 0 B 7F 0 B 7F 0 B 7 | |
1,000 10.93% = MIRR TV = 2,820.
FV of inflows: With a financial calculator, input N = 10, I/YR = 10, PV = 0, and PMT = 0 0 1 E 176.98 to obtain FV = $2,820.61. Then input N = 10, PV = -1000, PMT = 0, and FV = 2820.61 to obtain I/YR = MIRR = 10.93%.
11-22 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 these two values. In this instance, the MIRR is given, but a cash outflow is missing and must be solved for. Therefore, if the terminal future value of the cash inflows is found, it can be entered into a financial calculator, along with the number of years the project lasts and the MIRR, 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 be the present value of the missing cash outflow in Year 2.
Cash Inflows Compounding Rate FV in Year 5 @ 10% CF 1 =$202 F 0 B 4(1.10) 4 $ 295. CF 3 = 196 F 0 B 4(1.10) 2 237. CF 4 = 350 F 0 B 41.10 385. CF 5 = 451 F 0 B 41.00 451. $1,368.
Using the financial calculator to solve for the present value of cash outflows: N = 5; I/YR = 14.14; PV = ?; PMT = 0; FV = 1368.
The total present value of cash outflows is $706.62, and since the outflow 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.
283 Answers and Solutions Chapter 11: The Basics of Capital Budgeting
Comprehensive/Spreadsheet Problem
Note to Instructors: The solution to this problem is not provided to students at the back of their text. Instructors can access the Excel file on the textbook’s Web site or the Instructor’s Resource CD.
11-23 a. Project A:
Using a financial calculator, enter the following data: CF 0 = -30; CF 1 = 5; CF 2 = 10; CF 3 = 15; CF 4 = 20; I/YR = 10; and solve for NPV (^) A = $7.74; IRRA = 19.19%.
Calculate MIRRA at WACC = 10%:
Step 1:Calculate the NPV of the uneven cash flow stream, so its FV can then be calculated. With a financial calculator, enter the cash flow stream into the cash flow registers, then enter I/YR = 10, and solve for NPV = $37.739.
Step 2:Calculate the FV of the cash flow stream as follows: Enter N = 4, I/YR = 10, PV = -37.739, and PMT = 0 to solve for FV = $55.255.
Step 3:Calculate MIRRA as follows:
Enter N = 4, PV = -30, PMT = 0, and FV = 55.255 to solve for I/YR = 16.50%.
Payback A (cash flows in millions): Annual Period Cash Flows Cumulative 0 ($30) ($30) 1 5 (25) 2 10 (15) 3 15 0 4 20 20
PaybackA = 3 years.
Discounted Payback A (cash flows in millions): Annual Discounted @10% Cumulative Period Cash Flows Cash Flows Cash Flows 0 ($30) ($30.00) ($30.00) 1 5 4.55 (25.45) 2 10 8.26 (17.19) 3 15 11.27 (5.92) 4 20 13.66 7.
Discounted Payback (^) A = 3 + $5.92/$13.66 = 3.43 years.
Project B:
Chapter 11: The Basics of Capital Budgeting Comprehensive/Spreadsheet Problem 284
