SOLUTION MANUAL FINANCIAL MANAGEMENT 14TH EDITION BRIGHAM

SOLUTION MANUAL FINANCIAL MANAGEMENT 14TH EDITION BRIGHAM

Chapter 10
The Basics of Capital Budgeting: Evaluating Cash Flows
ANSWERS TO END-OF-CHAPTER QUESTIONS

10-1 a. Capital budgeting is the whole process of analyzing projects and deciding whether they should be included in the capital budget. This process is of fundamental importance to the success or failure of the firm as the fixed asset investment decisions chart the course of a company for many years into the future. The payback, or payback period, is the number of years it takes a firm to recover its project investment. Payback may be calculated with either raw cash flows (regular payback) or discounted cash flows (discounted payback). In either case, payback does not capture a project’s entire cash flow stream and is thus not the preferred evaluation method. Note, however, that the payback does measure a project’s liquidity, and hence many firms use it as a risk measure.

b. Mutually exclusive projects cannot be performed at the same time. We can choose either Project 1 or Project 2, or we can reject both, but we cannot accept both projects. Independent projects can be accepted or rejected individually.

c. The net present value (NPV) and internal rate of return (IRR) techniques are discounted cash flow (DCF) evaluation techniques. These are called DCF methods because they explicitly recognize the time value of money. NPV is the present value of the project’s expected future cash flows (both inflows and outflows), discounted at the appropriate cost of capital. NPV is a direct measure of the value of the project to shareholders. The internal rate of return (IRR) is the discount rate that equates the present value of the expected future cash inflows and outflows. IRR measures the rate of return on a project, but it assumes that all cash flows can be reinvested at the IRR rate. The profitability index is the ratio of the present value of future cash flows to the project’s initial cost. It shows the relative profitability of any project. A profitability index greater than 1 is equivalent to a positive NPV project.

d. The modified internal rate of return (MIRR) assumes that cash flows from all projects are reinvested at the cost of capital as opposed to the project’s own IRR. This makes the modified internal rate of return a better indicator of a project’s true profitability.

e. An NPV profile is the plot of a project’s NPV versus its cost of capital. The crossover rate is the cost of capital at which the NPV profiles for two projects intersect indicating that at that point their NPVs are equal.

f. Capital projects with nonnormal cash flows have a large cash outflow either sometime during or at the end of their lives. A common problem encountered when evaluating projects with nonnormal cash flows is multiple IRRs. A project has normal cash flows if one or more cash outflows (costs) are followed by a series of cash inflows.

g. The mathematics of the NPV method imply that project cash flows are reinvested at the cost of capital while the IRR method assumes reinvestment at the IRR. Since project cash flows can be replaced by new external capital that costs r, the proper reinvestment rate assumption is the cost of capital, and thus the best capital budget decision rule is NPV.

h. A replacement chain is a method of comparing mutually exclu¬sive projects that have unequal lives. Each project is replicated such that they will both terminate in a common year. If projects with lives of 3 years and 5 years are being evaluated, the 3-year project would be replicated 5 times and the 5-year project replicated 3 times; thus, both projects would terminate in 15 years. Not all projects maximize their NPV if operated over their engineering lives and therefore it may be best to terminate a project prior to its potential life. The economic life is the number of years a project should be operated to maximize its NPV, and is often less than the maximum potential life. Capital rationing occurs when a firm’s management limits its capital expenditures to an amount less than would be required to fund the optimal capital budget. The equivalent annual annuity method is an alternative method of comparing mutually exclusive projects that have unequal lives. This method converts the annual cash flows under the alternative investments into a constant cash flow stream whose NPV is equal to the NPV of the initial stream.

10-2 Projects requiring greater investments or that have greater risk should be given detailed analysis the capital budgeting process.

10-3 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.

10-4 This question is related to Question 10-3 and the same rationale applies. With regard to the second part of the question, the answer is no; the IRR rankings are constant and independent of the firm’s cost of capital.

10-5 Generally, the failure to employ common-life analysis in such situations will bias the NPV against the shorter project because it “gets no credit” for profits beyond its initial life, even though it could possibly be “renewed” and thus provide additional NPV.

SOLUTIONS TO END-OF-CHAPTER PROBLEMS

10-1 NPV = -$40,000 + $9,000[(1/I) – (1/(I × (1 + I)N)]
= -$40,000 + $9,000[(1/0.11) – (1/(0.11 × (1 + 0.11)7)]
= $2,409.77.

Financial calculator solution: Input CF0 = -40000, CF1-7 = 9000, I/YR = 11, and then solve for NPV = $2,409.77.

10-2 Financial calculator solution: Input CF0 = -40000, CF1-8 = 9000, and then solve for IRR = 12.84%.

10-3 MIRR: PV Costs = $40000.

FV Inflows:

PV FV
0 1 2 3 4 5 6 7
| | | | | | | |
9,000 9,000 9,000 9,000 9,000 9,000 9,000
9,900
11,089
12,309
13,663
15,166
16,834
40,000 MIRR= 11.93% 88,049

Financial calculator: Obtain the FVA by inputting N = 7, I/YR = 11, PV = 0, PMT = 9000, and then solve for FV = $87,049. The MIRR can be obtained by inputting N = 7, PV = -40000, PMT = 0, FV = 88049, and then solving for I/YR = 11.93%.

10-4 PV = $9,000[(1/I) – (1/(I × (1 + I)N)]
= $9,000[(1/0.11) – (1/(0.11 × (1 + 0.11)7)]
= $42,410.

Financial calculator: Find present value of future cash flows by inputting N = 7, I/YR = 11, PMT = -9000, FV = 0, then solve for PV = $42,409.

PI = PV of future cash flows/Initial cost
= $42,409/$40,000 = 1.06.

10-5 Since the cash flows are a constant $9,000, calculate the payback period as: $40,000/$9,000 = 4.44, so the payback is about 4 years.

10-6 The project’s discounted payback period is calculated as follows:

Year
Annual CF Discounted CF (@11%) Cumulative Discounted CF
0 -40,000 -40,000.00
1 9,000 8,108.11 (31,891.89)
2 9,000 7,304.60 (24,587.29)
3 9,000 6,580.72 (18,006.57)
4 9,000 5,928.58 (12,077.99)
5 9,000 5,341.06 (6,736.93)
6 9,000 4,811.77 (1,925.16)
7 9,000 4,334.93 2,409.77

The discounted payback period is 6 + years, or 6.44 years.

10-7 a. Project A: Using a financial calculator, enter the following:
CF0 = -15000000
CF1 = 5000000
CF2 = 10000000
CF3 = 20000000

I/YR = 10; NPV = $12,836,213.
Change I/YR = 10 to I/YR = 5; NPV = $16,108,952.
Change I/YR = 5 to I/YR = 15; NPV = $10,059,587.

Project B: Using a financial calculator, enter the following:
CF0 = -15000000
CF1 = 20000000
CF2 = 10000000
CF3 = 6000000

I/YR = 10; NPV = $15,954,170.
Change I/YR = 10 to I/YR = 5; NPV = $18,300,939.
Change I/YR = 5 to I/YR = 15; NPV = $13,897,838.

b. Using the data for Project A, enter the cash flows into a financial calculator and solve for IRRA = 43.97%. The IRR is independent of the WACC, so IRR doesn’t change when the WACC changes.

Using the data for Project B, enter the cash flows into a financial calculator and solve for IRRB = 82.03%. Again, the IRR is independent of the WACC, so IRR doesn’t change when the WACC changes.

10-8 Truck:
NPV = -$17,100 + $5,100(PVIFA14%,5)
= -$17,100 + $5,100(3.4331) = -$17,100 + $17,509
= $409. (Accept)

Financial calculator: Input the appropriate cash flows into the cash flow register, input I/YR = 14, and then solve for NPV = $409.

Financial calculator: Input the appropriate cash flows into the cash flow register and then solve for IRR = 14.99% ≈ 15%.

MIRR: PV Costs = $17,100.

FV Inflows:
PV FV
0 1 2 3 4 5
| | | | | |
5,100 5,100 5,100 5,100 5,100
5,814
6,628
7,556
8,614
17,100 MIRR = 14.54% (Accept) 33,712

Financial calculator: Obtain the FVA by inputting N = 5, I/YR = 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, and then solving for I/YR = 14.54%.

Pulley:
NPV = -$22,430 + $7,500(3.4331) = -$22,430 + $25,748
= $3,318. (Accept)

Financial calculator: Input the appropriate cash flows into the cash flow register, input I/YR = 14, and then solve for NPV = $3,318.

Financial calculator: Input the appropriate cash flows into the cash flow register and then solve for IRR = 20%.

MIRR: PV Costs = $22,430.

FV Inflows:
PV FV
0 1 2 3 4 5
| | | | | |
7,500 7,500 7,500 7,500 7,500
8,550
9,747
11,112
12,667
22,430 MIRR = 17.19% (Accept) 49,576

Financial calculator: Obtain the FVA by inputting N = 5, I/YR = 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, and then solving for I/YR = 17.19%.

10-9 Electric-powered:
NPVE = -$22,000 + $6,290[(1/i) – (1/(i × (1 + i)n)]
= -$22,000 + $6,290[(1/0.12) – (1/(0.12 × (1 + 0.12)6)]
= -$22,000 + $6,290(4.1114) = -$22,000 + $25,861 = $3,861.

Financial calculator: Input the appropriate cash flows into the cash flow register, input I/YR = 12, and then solve for NPV = $3,861.

Financial calculator: Input the appropriate cash flows into the cash flow register and then solve for IRR = 18%.

Gas-powered:
NPVG = -$17,500 + $5,000[(1/i) – (1/(i × (1 + i)n)]
= -$17,500 + $5,000[(1/0.12) – (1/(0.12 × (1 + 0.12)6)]
= -$17,500 + $5,000(4.1114) = -$17,500 + $20,557 = $3,057.

Financial calculator: Input the appropriate cash flows into the cash flow register, input I/YR = 12, and then solve for NPV = $3,057.

Financial calculator: Input the appropriate cash flows into the cash flow register and then solve for IRR = 17.97% ≈ 18%.

The firm should purchase the electric-powered forklift because it has a higher NPV than the gas-powered forklift. The company gets a high rate of return (18% > r = 12%) on a larger investment.

10-10 Financial calculator solution, NPV:

Project S

Inputs 5 12 3000 0

 

Output = -10,814.33

NPVS = $10,814.33 – $10,000 = $814.33.

Project L

Inputs 5 12 7400 0

 

Output = -26,675.34

NPVL = $26,675.34 – $25,000 = $1,675.34.

Financial calculator solution, IRR:
Input CF0 = -10000, CF1 = 3000, Nj = 5, IRRS = ? IRRS = 15.24%.
Input CF0 = -25000, CF1 = 7400, Nj = 5, IRRL = ? IRRL = 14.67%.

Financial calculator solution, MIRR:
Project S