Managerial Finance Chapter 10 solutions by Gitman 14 Edition
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The document details various capital budgeting problems and solutions, focusing on payback periods, net present value (NPV), and internal rate of return (IRR) assessments for multiple projects. It provides specific calculations and recommendations for decision-making based on payback periods, NPV, and IRR, highlighting which projects are acceptable or preferable based on defined criteria. Additionally, it discusses the importance of using a financial calculator for NPV and IRR calculations in the analysis process.
![CAPITAL BUDGETING PROBLEMS: CHAPTER 10
P10-14. IRR—Mutually exclusive projects
LG 4; Intermediate
IRR is found by solving:
Most financial calculators have an ―IRR‖ key, allowing easy computation of the internal rate of return. The numerical
inputs are described below for eachproject.
Project A
CF0 $90,000; CF1 $20,000; CF2 $25,000; CF3 $30,000; CF4 $35,000; CF5 $40,000
Solve for IRR 17.43%
If the firm’s cost of capital is below 17%, the project would be acceptable.
Project B
CF0 $490,000; CF1 $150,000; CF2 $150,000; CF3 $150,000; CF4 $150,000
[or, CF0 $490,000; CF1 $150,000, F1 4]
Solve forIRR 8.62%
The firm’s maximum cost of capital for project acceptability would be 8.62%.
Project C
CF0 $20,000; CF1 $7500; CF2 $7500; CF3 $7500; CF4 $7500; CF5 $7500
[or, CF0 $20,000; CF1 $7500; F1 5]
Solve for IRR 25.41%
The firm’s maximum cost of capital for project acceptability would be 25.41%.
Project D
CF0 $240,000; CF1 $120,000; CF2 $100,000; CF3 $80,000; CF4 $60,000
Solve for IRR 21.16%
The firm’s maximum cost of capital for project acceptability would be 21% (21.16%).
P10-15. IRR—Mutually exclusive projects
LG 4; Intermediate
a. and b.
Project X
$0
CF0 -$500,000; CF1 $100,000; CF2 $120,000; CF3 $150,000; CF4 $190,000
CF5 $250,000
Solve for IRR 15.67; since IRR cost of capital, accept.
Project Y
$0
n
$0
t 1
CFt
(1 IRR)t
initial investment
$100,000 $120,000 $150,000 $190,000
(1 IRR)1
(1 IRR)2
(1 IRR)3
(1 IRR)4
$250,000
(1 IRR)5
$500,000
$140,000 $120,000 $95,000 $70,000
(1 IRR)1
(1 IRR)2
(1 IRR)3
(1 IRR)4
$50,000
(1 IRR)5
$325,000](https://image.slidesharecdn.com/chapter10solutions-converted-191021020402/85/Managerial-Finance-Chapter-10-solutions-by-Gitman-14-Edition-10-320.jpg)
Managerial Finance Chapter 10 solutions by Gitman 14 Edition
- 1. CAPITAL BUDGETING PROBLEMS: CHAPTER 10 Answers to Warm-Up Exercises E10-1. Payback period Answer: The payback period for Project Hydrogen is 4.29 years. The payback period for Project Helium is5.75 years. Both projects are acceptable because their payback periods are less than Elysian Fields’ maximum payback period criterion of 6years. E10-2. NPV Answer: Year Cash Inflow Present Value 1 $400,000 $ 377,358.49 2 375,000 333,748.67 3 300,000 251,885.78 4 350,000 277,232.78 5 200,000 149,451.63 Total $1,389,677.35 NPV $1,389,677.35 $1,250,000 $139,677.35 Herky Foods should acquire the new wrapping machine.
- 2. CAPITAL BUDGETING PROBLEMS: CHAPTER 10 E10-3: NPV comparison of twoprojects Answer: Project Kelvin Presentvalueofexpenses –$45,000 Presentvalueofcashinflows 51,542 (PMT $20,000, N 3,I 8,Solvefor PV) NPV $ 6,542 Project Thompson Presentvalueofexpenses $275,000 Presentvalueofcashinflows 277,373 (PMT $60,000,N 6, I 8,Solvefor PV) NPV $ 2,373 BasedonNPVanalysis,AxisCorporation should chooseanoverhaulofthe existingsystem. E10-4: IRR Answer: You may use a financial calculator to determine the IRR of each project. Choose the project with the higher IRR. Project T-Shirt PV 15,000, N 4, PMT 8,000 Solve for I IRR 39.08% Project Board Shorts PV 25,000, N 5, PMT 12,000 Solve for I IRR 38.62% Based on IRR analysis, Billabong Tech should choose project T-Shirt. E10-5: NPV Answer: Note: The IRR for Project Terra is 10.68% while that of Project Firma is 10.21%. Furthermore, when the discount rate is zero, the sum of Project Terra’s cash flows exceed that ofProjectFirma.Hence,atanydiscountratethat producesapositive NPV,ProjectTerra provides the higher net present value.
- 3. CAPITAL BUDGETING PROBLEMS: CHAPTER 10 Solutions to Problems Note to instructor: Inmostproblemsinvolving the IRRcalculation, afinancialcalculatorhasbeenused. Answers to NPV-based questions in the first ten problems provide detailed analysis of the present value ofindividual cashflows.Thereafter,financial calculatorworksheetkeystrokesareprovided.Most students will probably employ calculator functionality to facilitate their problem solution in this chapter and throughout the course. P10-1. Payback period LG 2; Basic a. $42,000 $7,000 6 years b. Thecompanyshouldaccepttheproject,since6 8. P10-2. Payback comparisons LG 2; Intermediate a. Machine1:$14,000 $3,000 4 years, 8months Machine2:$21,000 $4,000 5 years, 3months b. Only Machine 1has apayback faster than 5years andis acceptable. c. Thefirmwillacceptthefirstmachinebecausethepaybackperiodof4years,8monthsis lessthan the 5-year maximum payback required byNova Products. d. Machine2hasreturnsthatlast20yearswhile Machine1hasonly 7yearsofreturns. Paybackcannotconsiderthis difference;itignoresallcashinflowsbeyondthepaybackperiod.Inthiscase,thetotalcashflowfromMachine1is $59,000($80,000 $21,000) less than Machine 2.
- 4. CAPITAL BUDGETING PROBLEMS: CHAPTER 10 P10-3. Choosing between two projects with acceptable payback periods LG 2; Intermediate a. Project A Project B Year Cash Inflows Investment Balance Year Cash Inflows Investment Balance 0 $100,000 0 $100,000 1 $10,000 90,000 1 40,000 60,000 2 20,000 70,000 2 30,000 30,000 3 30,000 40,000 3 20,000 10,000 4 40,000 0 4 10,000 0 5 20,000 5 20,000 Both Project A and Project B have payback periods of exactly 4 years. b. Basedontheminimumpaybackacceptancecriteriaof4yearssetbyJohnShell,both projects should be accepted. However, since they are mutually exclusive projects, John should accept Project B. c. ProjectBispreferredoverAbecausethelargercashflowsareintheearlyyearsofthe project. The quicker cashinflows occur, the greater their value. P10-4. Personal finance: Long-term investment decisions, payback period LG 4 a. and b. Project A Project B Year Annual Cash Flow Cumulative Cash Flow Annual Cash Flow Cumulative Cash Flow 0 $(9,000) $(9,000) $(9,000) $(9,000) 1 2,00 (6,800) 1,500 (7,500) 2 2,500 (4,300) 1,500 (6,000) 3 2,500 (1,800) 1,500 (4,500) 4 2,000 3,500 (1,000) 5 1,800 4,000 Total Cash Flow 11,000 12,000 Payback Period 3 1,800/2,000 3.9 years 4 1,000/4,000 4.25years c. ThepaybackmethodwouldselectProjectAsinceitspaybackof3.9yearsislowerthan Project B’s payback of 4.25 years. d. One weakness of the payback method isthat itdisregards expected future cash flows as in the case of Project B.
- 5. CAPITAL BUDGETING PROBLEMS: CHAPTER 10 P10-5. NPV LG 3; Basic NPV PVn Initial investment a. N 20, I 14%, PMT $2,000 Solve for PV $13,246.26 NPV $13,246.26 $10,000 NPV $3,246.26 Accept project b. N 20, I 14%, PMT $3,000 Solve for PV 19,869.39 NPV $19,869.39 $25,000 NPV $5,130.61 Reject c. N 20, I 14%, PMT $5,000 Solve for PV $33,115.65 NPV $33,115.65 $30,000 NPV $33,115.65 NPV $3,115 Accept P10-6. NPV for varying cost of capital LG 3; Basic a. 10% N 8, I 10%, PMT $5000 Solve forPV $26,674.63 NPV PVn Initial investment NPV $26,674.63 $24,000 NPV $2,674.63 Accept; positive NPV b. 12% N 8, I 12%, PMT $5,000 Solve forPV $24,838.20 NPV PVn Initial investment NPV $24,838.20 $24,000 NPV $838.20 Accept; positive NPV
- 6. CAPITAL BUDGETING PROBLEMS: CHAPTER 10 c. 14% N 8, I 14%, PMT $5,000 Solve forPV $23,194.32 NPV PVn Initial investment NPV $23,194.32 $24,000 NPV -$805.68 Reject; negative NPV P10-7. NPV—independent projects LG 3; Intermediate Project A N 10, I 14%, PMT $4,000 Solve for PV $20,864.46 NPV $20,864.46 $26,000 NPV $5,135.54 Reject Project B—PVofCash Inflows CF0 -$500,000; CF1 $100,000; CF2 $120,000; CF3 $140,000; CF4 $160,000; CF5 $180,000; CF6 $200,000 SetI 14% Solve for NPV $53,887.93 Accept Project C—PVof Cash Inflows CF0 -$170,000; CF1 $20,000; CF2 $19,000; CF3 $18,000; CF4 $17,000; CF5 $16,000; CF6 $15,000; CF7 $14,000; CF8 $13,000; CF9 $12,000; CF10 $11,000, Set I 14% Solve for NPV -$83,668.24 Reject Project D N 8, I 14%, PMT $230,000 Solve for PV $1,066,939 NPV PVn Initial investment NPV $1,066,939 $950,000 NPV $116,939 Accept Project E—PVof Cash Inflows CF0 -$80,000; CF1 $0; CF2 $0; CF3 $0; CF4 $20,000; CF5 $30,000; CF6 $0; CF7 $50,000; CF8 $60,000; CF9$70,000 SetI 14% Solve for NPV $9,963.63 Accept
- 7. CAPITAL BUDGETING PROBLEMS: CHAPTER 10 P10-8. NPV LG 3; Challenge a. N 5, I 9%, PMT $385,000 Solve for PV $1,497,515.74 The immediate payment of $1,500,000 is not preferred because it has a higher present value than does the annuity. b. N 5, I 9%, PV $1,500,000 Solve for PMT $385,638.69 c. PresentvalueAnnuity Due PVordinary annuity (1 discount rate) $1,497,515.74 (1.09) $1,632,292 Calculator solution: $1,632,292 Changing the annuity to a beginning-of-the-period annuity due would cause Simes Innovations toprefertomakea $1,500,000one-timepaymentbecausethepresentvalueoftheannuity due is greater than the $1,500,000 lump- sum option. d. No,thecashflowsfromtheprojectwillnotinfluencethedecisiononhowtofundthe project. The investment andfinancing decisions are separate. P10-9. NPV and maximum return LG 3; Challenge a. N 4, I 10%, PMT $4,000 Solve forPV $12,679.46 NPV PV Initial investment NPV $12,679.46 $13,000 NPV –$320.54 Reject this project due to its negative NPV. b. N 4, PV -$13,000, PMT $4,000 Solve for I 8.86% 8.86% is the maximum required returnthatthe firm could have forthe project to be acceptable. Since the firm’s required return is10% the cost of capital is greater than the expected return and the project is rejected. P10-10. NPV—mutually exclusive projects LG 3; Intermediate a. and b. Press A CF0 -$85,000; CF1 $18,000; F1 8 SetI 15% Solve for NPV -$4,228.21 Reject
- 8. CAPITAL BUDGETING PROBLEMS: CHAPTER 10 Press B CF0 -$60,000; CF1 $12,000; CF2 $14,000; CF3 $16,000; CF4 $18,000; CF5 $20,000; CF6 $25,000 SetI 15% Solve for NPV $2,584.34 Accept Press C CF0 -$130,000; CF1 $50,000; CF2 $30,000; CF3 $20,000; CF4 $20,000; CF5 $20,000; CF6 $30,000; CF7 $40,000; CF8 $50,000 SetI 15% Solve for NPV $15,043.89 Accept c. Ranking—using NPV ascriterion Rank Press NPV 1 C $15,043.89 2 B 2,584.34 3 A 4,228.21 d. Profitability Indexes Profitability Index PresentValueCashInflows Investment PressA:$80,771 $85,000 0.95 PressB: $62,588 $60,000 1.04 Press C: $145,070 $130,000 1.12 e. The profitability index measure indicates that Press C is the best, then Press B, then Press A (whichisunacceptable). Thisisthe samerankingaswasgeneratedbythe NPVrule. P10-11. Personal finance: Long-term investment decisions, NPV method LG 3 Key information: Cost of MBA program $100,000 Annual incremental benefit $20,000 Time frame (years) 40 Opportunity cost 6.0% Calculator Worksheet Keystrokes: CF0 100,000 CF1 20,000 F1 40 Set I 6% Solve for NPV $200,926 The financial benefits outweigh the cost of the MBA program.
- 9. CAPITAL BUDGETING PROBLEMS: CHAPTER 10 P10-12. Payback and NPV LG 2, 3; Intermediate a. Project Payback Period A $40,000 $13,000 3.08 years B 3 ($10,000 $16,000) 3.63 years C 2 ($5,000 $13,000) 2.38 years Project C, with the shortest payback period, is preferred. b. Worksheet keystrokes Year Project A Project B Project C 0 $40,000 $40,000 $40,000 1 13,000 7,000 19,000 2 13,000 10,000 16,000 3 13,000 13,000 13,000 4 13,000 16,000 10,000 5 13,000 19,000 7,000 Solve for NPV $2,565.82 $322.53 $5,454.17 Accept Reject Accept Project C is preferred using the NPV as a decision criterion. c. Atacostof16%, ProjectChasthehighest NPV.BecauseofProjectC’s cashflow characteristics, high early-year cash inflows, ithas the lowest payback period and the highest NPV. P10-13. NPV and EVA LG 3; Intermediate a. NPV $2,500,000 $240,000 0.09 $166,667 b. Annual EVA $240,000 –($2,500,000 x0.09) $15,000 c. Overall EVA $15,000 0.09 $166,667 In this case, NPV and EVA give exactly the same answer.
- 10. CAPITAL BUDGETING PROBLEMS: CHAPTER 10 P10-14. IRR—Mutually exclusive projects LG 4; Intermediate IRR is found by solving: Most financial calculators have an ―IRR‖ key, allowing easy computation of the internal rate of return. The numerical inputs are described below for eachproject. Project A CF0 $90,000; CF1 $20,000; CF2 $25,000; CF3 $30,000; CF4 $35,000; CF5 $40,000 Solve for IRR 17.43% If the firm’s cost of capital is below 17%, the project would be acceptable. Project B CF0 $490,000; CF1 $150,000; CF2 $150,000; CF3 $150,000; CF4 $150,000 [or, CF0 $490,000; CF1 $150,000, F1 4] Solve forIRR 8.62% The firm’s maximum cost of capital for project acceptability would be 8.62%. Project C CF0 $20,000; CF1 $7500; CF2 $7500; CF3 $7500; CF4 $7500; CF5 $7500 [or, CF0 $20,000; CF1 $7500; F1 5] Solve for IRR 25.41% The firm’s maximum cost of capital for project acceptability would be 25.41%. Project D CF0 $240,000; CF1 $120,000; CF2 $100,000; CF3 $80,000; CF4 $60,000 Solve for IRR 21.16% The firm’s maximum cost of capital for project acceptability would be 21% (21.16%). P10-15. IRR—Mutually exclusive projects LG 4; Intermediate a. and b. Project X $0 CF0 -$500,000; CF1 $100,000; CF2 $120,000; CF3 $150,000; CF4 $190,000 CF5 $250,000 Solve for IRR 15.67; since IRR cost of capital, accept. Project Y $0 n $0 t 1 CFt (1 IRR)t initial investment $100,000 $120,000 $150,000 $190,000 (1 IRR)1 (1 IRR)2 (1 IRR)3 (1 IRR)4 $250,000 (1 IRR)5 $500,000 $140,000 $120,000 $95,000 $70,000 (1 IRR)1 (1 IRR)2 (1 IRR)3 (1 IRR)4 $50,000 (1 IRR)5 $325,000
- 11. CAPITAL BUDGETING PROBLEMS: CHAPTER 10 CF0 $325,000; CF1 $140,000; CF2 $120,000; CF3 $95,000; CF4 $70,000 CF5 $50,000 Solve for IRR 17.29%; since IRR cost of capital, accept. c. ProjectY, withthe higher IRR, ispreferred,although both are acceptable. P10-16. Personal Finance: Long-term investment decisions, IRR method LG 4; Intermediate IRRistherateofreturnatwhichNPVequalszeroComputer inputs and output: N 5, PV $25,000, PMT $6,000 Solve forIRR 6.40% Required rate of return: 7.5% Decision: Reject investment opportunity P10-17.IRR,investmentlife,andcashinflows LG 4; Challenge a. N 10, PV -$61,450, PMT $10,000 Solve for I 10.0% The IRR cost of capital; reject the project. b. I 15%, PV $61,450, PMT $10,000 Solve for N 18.23 years The project would have to run a little over 8 more years to make the project acceptable with the 15% cost ofcapital. c. N 10, I 15%, PV $61,450 Solve for PMT $12,244.04 P10-18. NPV and IRR LG 3, 4; Intermediate a. N 7, I 10%, PMT $4,000 Solve forPV $19,473.68 NPV PV Initial investment NPV $19,472 $18,250 NPV $1,223.68 b. N 7, PV $18,250, PMT $4,000 Solve for I 12.01% c. TheprojectshouldbeacceptedsincetheNPV 0andthe IRR the cost of capital.
- 12. CAPITAL BUDGETING PROBLEMS: CHAPTER 10 P10-19. NPV, with rankings LG 3, 4; Intermediate a. NPVA $45,665.50 (N 3, I 15, PMT $20,000) $50,000 NPVA -$4,335.50 Or, using NPV keystrokes CF0 $50,000; CF1 $20,000; CF2 $20,000; CF3 $20,000 SetI 15% NPVA $4,335.50 Reject NPVB Key strokes CF0 $100,000; CF1 $35,000; CF2 $50,000; CF3 $50,000 SetI 15% Solve for NPV $1,117.78 Accept NPVC Key strokes CF0 $80,000; CF1 $20,000; CF2 $40,000; CF3 $60,000 SetI 15% Solve for NPV $7,088.02 Accept NPVD Key strokes CF0 $180,000; CF1 $100,000; CF2 $80,000; CF3 $60,000 SetI 15% Solve for NPV $6,898.99 Accept b. Rank Press NPV 1 C $7,088.02 2 D 6,898.99 3 B 1,117.78 4 A 4335.50 c. Using the calculator, the IRRs of the projects are: Project IRR A 9.70% B 15.63% C 19.44% D 17.51% SincethelowestIRRis9.7%,alloftheprojectswouldbeacceptableifthecostofcapitalwas 9.7%. Note: SinceProjectAwastheonlyrejectedprojectfromthefourprojects,allthatwas neededtofind the minimum acceptable costofcapital wastofind theIRR ofA.
- 13. CAPITAL BUDGETING PROBLEMS: CHAPTER 10 P10-20. All techniques, conflicting rankings LG 2, 3, 4: Intermediate a. Project A Project B Year Cash Inflows Investment Balance Year Cash Inflows Investment Balance 0 $150,000 0 $150,000 1 $45,000 105,000 1 $75,000 75,000 2 45,000 60,000 2 60,000 15,000 3 45,000 15,000 3 30,000 15,000 4 45,000 30,000 4 30,000 0 5 45,000 30,000 6 45,000 30,000 Payback A $150,000 $45,000 3.33years 3 years 4months PaybackB 2years $15,000 $30,000 years 2.5years 2 years 6months b. Atadiscountrateofzero,dollarshavethesamevaluethroughtimeandallthatisneededisa summation of the cash flows across time. NPVA ($45,000 6)-$150,000 $270,000 $150,000 $120,000 NPVB $75,000 $60,000 $120,000 $150,000 $105,000 c. NPVA: CF0 $150,000; CF1 $45,000; F1 6 SetI 9% Solve for NPVA $51,886.34 NPVB: CF0 $150,000; CF1 $75,000; CF2 $60,000; CF3 $120,000 SetI 9% Solve for NPV $51,112.36 Accept d. IRRA: CF0 $150,000; CF1 $45,000; F1 6 Solve forIRR 19.91% IRRB: CF0 $150,000; CF1 $75,000; CF2 $60,000; CF3 $120,000 Solve for IRR 22.71%
- 14. CAPITAL BUDGETING PROBLEMS: CHAPTER 10 e. Rank Project Payback NPV IRR A 2 1 2 B 1 2 1 TheprojectthatshouldbeselectedisA.TheconflictbetweenNPVandIRRisduepartially to the reinvestment rate assumption. The assumed reinvestment rate of Project B is22.71%, theproject’sIRR.Thereinvestmentrate assumptionofAis9%,thefirm’scostofcapital.On a practicallevelProjectBmaybe selecteddue to management’spreferenceformakingdecisionsbasedonpercentagereturnsandtheirdesiretoreceiveareturnofcash quickly. P10-21. Payback, NPV, and IRR LG 2, 3, 4; Intermediate a. Payback period Balanceafter3years:$95,000 $20,000 $25,000 $30,000 $20,000 3 ($20,000 $35,000) 3.57 years b. NPV computation CF0 $95,000; CF1 $20,000; CF2 $25,000; CF3 $30,000; CF4 $35,000 CF5 $40,000 SetI 12% Solve for NPV $9,080.60 c. $0 CF0 $95,000; CF1 $20,000; CF2 $25,000; CF3 $30,000; CF4 $35,000 CF5 $40,000 Solve for IRR 15.36% d. NPV $9,080; sinceNPV 0; accept IRR 15%; since IRR 12% cost ofcapital; accept The project should be implemented since it meets the decision criteria for both NPV and IRR. P10-22. NPV, IRR, and NPV profiles LG 3, 4, 5; Challenge a. and b. Project A CF0 $130,000; CF1 $25,000; CF2 $35,000; CF3 $45,000 CF4 $50,000; CF5 $55,000 SetI 12% NPVA $15,237.71 Based on the NPV the project is acceptable since the NPV is greater than zero. Solve for IRRA 16.06% $20,000 $25,000 $30,000 $35,000 (1 IRR)1 (1 IRR)2 (1 IRR)3 (1 IRR)4 $40,000 (1 IRR)5 $95,000
- 15. CAPITAL BUDGETING PROBLEMS: CHAPTER 10 BasedontheIRRtheprojectisacceptablesincetheIRRof16%isgreaterthanthe12%cost of capital.
- 16. CAPITAL BUDGETING PROBLEMS: CHAPTER 10 Project B CF0 $85,000; CF1 $40,000; CF2 $35,000; CF3 $30,000 CF4 $10,000; CF5 $5,000 SetI 12% NPVB $9,161.79 Based on the NPV the project is acceptable since the NPV is greater than zero. Solve for IRRB 17.75% BasedontheIRRtheprojectisacceptablesincetheIRRof17.75%isgreaterthanthe12% cost of capital. c. Data for NPV Profiles NPV Discount Rate A B 0% $80,000 $35,000 12% $15,238 $9,161 15% — $ 4,177 16% 0 — 18% — 0 d. The net present value profile indicates that there are conflicting rankings at a discount rate lessthantheintersection point ofthetwoprofiles(approximately15%).Theconflictin rankingsiscausedbytherelativecashflowpattern ofthetwoprojects.Atdiscountrates above approximately 15%, Project B is preferable; below approximately 15%, Project A is better.BasedonThomasCompany’s12%costofcapital,ProjectAshouldbechosen. e. ProjectAhasanincreasingcashflowfromYear1throughYear5,whereasProjectBhasa decreasingcashflow fromYear1throughYear5.Cashflowsmovinginoppositedirections oftencauseconflictingrankings.TheIRR methodreinvestsProjectB’slargerearlycashflows at the higher IRR rate, not the 12% cost of capital.
- 17. CAPITAL BUDGETING PROBLEMS: CHAPTER 10 P10-23. All techniques—decision among mutually exclusive investments LG 2, 3, 4, 5, 6; Challenge Project A B C Cash inflows (years 1 5) $20,000 $ 31,500 $ 32,500 a. Payback* 3 years 3.2 years 3.4 years b. NPV* $10,345 $ 10,793 $ 4,310 c. IRR* 19.86% 17.33% 14.59% * Supporting calculations shown below: a. Payback Period: Project A: $60,000 $20,000 3 years Project B: $100,000 $31,500 3.2 years Project C: $110,000 $32,500 3.4 years b. NPV Project A CF0 $60,000; CF1 $20,000; F1 5 SetI 13% Solve for NPVA $10,344.63 Project B CF0 $100,000; CF1 $31,500; F1 5 SetI 13% Solve for NPVB $10,792.78 Project C CF0 $110,000; CF1 $32,500; F1 5 SetI 13% Solve forNPVC $4,310.02 c. IRR Project A CF0 $60,000; CF1 $20,000; F1 5 Solve for IRRA 19.86% Project B CF0 $100,000; CF1 $31,500; F1 5 Solve for IRRB 17.34% Project C CF0 $110,000; CF1 $32,500; F1 5 Solve for IRRC 14.59%
- 18. CAPITAL BUDGETING PROBLEMS: CHAPTER 10 d. Data for NPV Profiles NPV Discount Rate A B C 0% $40,000 $57,500 $52,500 13% $10,340 10,793 4,310 15% — — 0 17% — 0 — 20% 0 — — ThedifferenceinthemagnitudeofthecashflowforeachprojectcausestheNPVtocompare favorably or unfavorably, depending on the discount rate. e. EventhoughArankshigherinPaybackandIRR,financialtheoristswould arguethatBis superiorsinceithasthe highestNPV.AdoptingBadds$448.15moretothevalueofthefirm than does adopting A. P10-24. All techniques with NPV profile—mutually exclusive projects LG 2, 3, 4, 5, 6; Challenge a. Project A Payback period Year1 Year2 Year3 $60,000 Year4 $20,000 Initial investment $80,000 Payback 3years ($20,000 30,000) Payback 3.67 years
- 19. CAPITAL BUDGETING PROBLEMS: CHAPTER 10 Project B Payback period $50,000 $15,000 3.33 years b. Project A CF0 $80,000; CF1 $15,000; CF2 $20,000; CF3 $25,000; CF4 $30,000; CF5 $35,000 SetI 13% Solve for NPVA $3,659.68 Project B CF0 $50,000; CF1 $15,000; F1 5 SetI 13% Solve for NPVB $2,758.47 c. Project A CF0 $80,000; CF1 $15,000; CF2 $20,000; CF3 $25,000; CF4 $30,000; CF5 $35,000 Solve for IRRA 14.61% Project B CF0 $50,000; CF1 $15,000; F1 5 Solve for IRRB 15.24% d.
- 20. CAPITAL BUDGETING PROBLEMS: CHAPTER 10 Data for NPV Profiles NPV Discount Rate A B 0% $45,000 $25,000 13% $3,655 2,755 14.6% 0 — 15.2% — 0 Intersection—approximately 14% Ifcostofcapitalisabove14%,conflictingrankingsoccur. The calculator solution is 13.87%. e. Bothprojectsareacceptable.Bothhavesimilarpaybackperiods,positive NPVs,and equivalent IRRs that are greater than the cost of capital. Although Project B has a slightly higherIRR,theratesareveryclose.Since ProjectAhasahigherNPV,acceptProjectA. P10-25. Integrative—Multiple IRRs LG 6; Basic a. Firsttheprojectdoesnothaveaninitial cashoutflow.Ithasaninflow,sothepaybackis immediate.However, therearecashoutflowsinlateryears.After2years,theproject’soutflows are greater than its inflows, but that reverses in year 3. The oscillating cash flows (positive-negative-positive-negative-positive) make it difficult to even think about how the payback period should be defined. b. CF0 $200,000, CF1 920,000, CF2 $1,592,000, CF3 $1,205,200, CF4 $343,200 SetI 0%; Solve forNPV $0.00 SetI 5%; Solve forNPV $15.43 SetI 10%; Solve for NPV $0.00 SetI 15%; Solve for NPV $6.43 SetI 20%; Solve for NPV $0.00 SetI 25%; Solve for NPV $7.68 SetI 30%; Solve for NPV $0.00 SetI 35%, Solve forNPV $39.51 c. TherearemultipleIRRsbecausethereareseveraldiscountratesatwhichtheNPViszero. d. ItwouldbedifficulttousetheIRRapproachtoanswerthisquestionbecauseitisnotclearwhichIRRshould be comparedtoeachcostofcapital.Forinstance,at5%,the NPVis negative, so the project would be rejected. However, at a higher 15% discount rate the NPV is positive and the project would be accepted. e. ItisbestsimplytouseNPVinacasewheretherearemultipleIRRsduetothechanging signs of the cash flows.
- 21. CAPITAL BUDGETING PROBLEMS: CHAPTER 10 P10-26. Integrative—Conflicting Rankings LG 3, 4, 5; Intermediate a. Plant Expansion CF0 $3,500,000, CF1 1,500,000, CF2 $2,000,000, CF3 $2,500,000, CF4 $2,750,000 SetI 20%; Solve for NPV $1,911,844.14 Solve for IRR 43.70% CF1 1,500,000, CF2 $2,000,000, CF3 $2,500,000, CF4 $2,750,000 SetI 20%; Solve for NPV $5,411,844.14 (ThisisthePVofthecashinflows) PI $5,411,844.14 $3,500,000 1.55 Product Introduction CF0 $500,000, CF1 250,000, CF2 $350,000, CF3 $375,000, CF4 $425,000 SetI 20%; Solve for NPV $373,360.34 Solve for IRR 52.33% CF1 250,000, CF2 $350,000, CF3 $375,000, CF4 $425,000 SetI 20%; Solve for NPV $873,360.34 (ThisisthePVofthecashinflows) PI $873,360.34 $500,000 1.75 b. Rank Project NPV IRR PI Plant Expansion 1 2 2 Product Introduction 2 1 1 c. The NPV is higher for the plant expansion, but both the IRR and the PI are higher for the product introduction project. The rankingsdo not agree because the plant expansion has a muchlargerscale.TheNPVrecognizesthatitis bettertoacceptalowerreturnonalarger projecthere.TheIRRandPImethodssimplymeasuretherateofreturnon theprojectand not its scale (and therefore not how much money in total the firm makes from each project). d. Because the NPV of the plant expansion project is higher, the firm’s shareholders would be betteroffifthe firm pursuedthatproject,eventhough ithasalowerrateofreturn. P10-27. Ethics problem LG 1, 6; Intermediate ExpensesarealmostsuretoincreaseforGap.Thestockpricewouldalmostsurelydeclineinthe immediate future, as cash expenses rise relative to cash revenues. In the long run, Gap may be able to attract and retain better employees (as does Chick- fil-A, interestingly enough, by being closed on Sundays), new human rights and environmentally conscious customers, and new investor demand from the burgeoning sociallyresponsible investingmutualfunds. This long-run effectis not assured, and we are again reminded that it’s not merely shareholder wealth maximization we’re after—butmaximizing shareholderwealthsubjecttoethicalconstraints.Infact,ifGapwasunwilling to renegotiate worker conditions, Calvert Group (and others) might sell Gap shares and thereby decrease shareholder wealth.