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1 Capital Budgeting Techniques How do firms make decisions about whether to invest in costly, long-lived assets? How does a firm make a choice between two acceptable investments when only one can be purchased? How are different capital budgeting techniques related? Which capital budgeting methods do firms actually use?

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2 Capital Budgeting Introduction to Capital Budgeting Payback Period—traditional and discounted Net Present Value (NPV) Internal Rate of Return (IRR) Modified IRR Comparison of NPV and IRR NPV/IRR Ranking Conflicts/Cautions

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3 Capital Budgeting Capital Budgeting Basics and Techniques r—firm’s required rate of return CF—cash flows generated by an investment GivenCompute Capital Budgeting—cash flows and risk r—firm’s required rate of return CF—cash flows generated by an investment

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4 Capital Budgeting Basics Importance of capital budgeting decisions long-term effect—capital, or long-term funds, raised by the firms are used to invest in assets that enable the firm to generate revenues several years into the future. timing of a decision is important—decisions impact the firm for several years. Generating ideas for capital budgeting employees, customers, suppliers, and so forth based on needs and experiences of the firm and these groups

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5 Capital Budgeting Basics Project classifications—replacement decisions versus expansion decisions replacement decision—intended to maintain existing levels of operations expansion decision—a decision concerning whether the firm should expand operations Project classifications—independent projects versus mutually exclusive projects independent project—accepting one independent project does not affect the acceptance of any other project mutually exclusive projects—only one project can be purchased

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6 Capital Budgeting Basics— Capital Budgeting Versus Asset Valuation Value of an asset = PV of the cash flows the asset is expected to generate during its life: An asset is an acceptable investment if the cost of the asset is less than its value: Acceptable if: PV of CFs > Cost

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7 Capital Budgeting Techniques Payback period Net present value Internal rate of return

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8 Capital Budgeting Techniques Illustrative Investment 0(7,000) 12,000 21,000 35,000 43,000 r = 15% YearCash Flow,

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9 Capital Budgeting Example Cash Flow Time Line 2,0001,0005,0003,000 10234 (7,000.00) 15% 1,739.13 756.14 3,287.58 1,715.26 498.11 = PV = 7,498.11

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10 Capital Budgeting Techniques Payback Period Number of years it takes to recapture the initial investment. YearCash FlowCumulative CF 0$(7,000)$(7,000) 12,000 (5,000) 21,000 (4,000) 35,000 1,000 43,000 4,000 } 2

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11 Capital Budgeting Techniques Payback Period YearCash FlowCumulative CF 0$(7,000)$(7,000) 12,000 (5,000) 21,000 (4,000) 35,000 1,000 43,000 4,000 } 2

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12 Capital Budgeting Techniques Payback Period Accept the project if Payback, PB < some number of years established by the firm PB = 2.8 years is acceptable if the firm has established a maximum payback of 4.0 years

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13 Capital Budgeting Techniques Payback Period Advantages: Simple Cash flows are used Provides an indication of the liquidity of a project Disadvantages: Does not use time value of money concepts Cash flows beyond the payback period are ignored

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14 Capital Budgeting Techniques Payback Period YearCash FlowCumulative CF 0$(7,000)$(7,000) 12,000 (5,000) 21,000 (4,000) 35,000 1,000 43,000 4,000 } PB = 2.80 yrs YearCash FlowCumulative CF 0$(7,000)$(7,000) 12,000 (5,000) 21,000 (4,000) 35,000 1,000 43,000 4,000 51,000,0001,004,000

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15 Capital Budgeting Net Present Value (NPV) NPV = present value of future cash flows less the initial investment An investment is acceptable if NPV > 0 n 0t t t r)(1 CF n n 2 2 1 1 0 r)(1 CF r)(1 CF r)(1 CF NPV

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16 Capital Budgeting—NPV $498.11 (1.15) $3,000 (1.15) $5,000 (1.15) $1,000 (1.15) $2,000 $7,000NPV 4321 $1,715.26 $3,287.58 $756.14 $1,739.13$7,000 NPV = $498.11 > 0, so the project is acceptable

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17 10234 2,0001,0005,0003,000(7,000.00) 15% 1,739.13 756.14 3,287.58 1,715.26 498.11 = NPV Capital Budgeting Example Cash Flow Time Line

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18 Capital Budgeting—NPV Advantages: Cash flows rather than profits are analyzed Recognizes the time value of money Acceptance criterion is consistent with the goal of maximizing value Disadvantage: Detailed, accurate long-term forecasts are required to evaluate a project’s acceptance

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19 Solving for NPV Numerical (equation) solution Financial Calculator solution Spreadsheet solution

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20 Solving for NPV Numerical Solution $498.11 $1,715.26 $3,287.58 $756.14 $1,739.13$7,000 (1.15) $3,00 (1.15) $5,000 (1.15) $1,000 (1.15) $2,000 $7,000NPV 4321

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21 Solving for NPV Financial Calculator Solution Input the following into the cash flow register: CF 0 =-7,000 CF 1 =2,000 CF 2 =1,000 CF 3 =5,000 CF 4 =3,000 Input I = 15 Compute NPV = 498.12

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22 Capital Budgeting Discounted Payback Period Payback period computed using the present values of the future cash flows. 0$(7,000)$(7,000.00)$(7,000.00) 12,000 1,739.13(5,260.87) 21,000 756.14(4,504.73) 35,000 3,287.58(1,217.14) 43,000 1,715.26 498.12 } PB disc = 3.71 Cumulative YearCash FlowPV of CF @15% PV of CF A project is acceptable if PB disc < project’s life

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23 Capital Budgeting Internal Rate of Return (IRR) If NPV>0, project’s return > r Example: Initial investment = $7,000.00 PV of future cash flows = $7,498.12 NPV = $498.12 r = 15% IRR > 15% If IRR = project’s rate of return IRR = the rate of return that causes the NPV of the project to equal zero, or where the present value of the future cash flows equals the initial investment.

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24 Capital Budgeting Internal Rate of Return (IRR) n n 2 2 1 1 0 IRR)(1 CF IRR)(1 CF IRR)(1 CF n n 2 2 1 1 0 0 IRR)(1 CF IRR)(1 CF IRR)(1 CF NPV A project is acceptable if its IRR > r

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25 Capital Budgeting Internal Rate of Return (IRR) 4321 IRR)(1 $3,000 IRR)(1 $5,000 IRR)(1 $1,000 IRR)(1 $2,000 $7,000 4321 0 IRR)(1 3,000 IRR)(1 5,000 IRR)(1 1,000 IRR)(1 2,000 7,000NPV

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26 Internal Rate of Return (IRR) Cash Flow Time Line 10234 2,0001,0005,0003,000(7,000) IRR = ? 0 = NPV of PVs = 7,000

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27 Capital Budgeting—IRR Advantages: Cash flows rather than profits are analyzed Recognizes the time value of money Acceptance criterion is consistent with the goal of maximizing value Disadvantages: Detailed, accurate long-term forecasts are required to evaluate a project’s acceptance Difficult to solve for IRR without a financial calculator or spreadsheet

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28 Solving for IRR Numerical Solution Using the trial-and-error method plug in values for IRR until the left and right side of the following equation become equal. 4321 IRR)(1 $3,000 IRR)(1 $5,000 IRR)(1 $1,000 IRR)(1 $2,000 $7,000

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29 Solving for IRR Numerical Solution Rate of Return NPV 15%498.12 16327.46 17162.72 183.62 19(150.08) } 18

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30 Solving for IRR Financial Calculator Solution Input the following into the cash flow register: CF 0 =-7,000 CF 1 =2,000 CF 2 =1,000 CF 3 =5,000 CF 4 =3,000 Compute IRR = 18.02%

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31 NPV versus IRR When NPV > 0, a project is acceptable because the firm will increase its value, which means the firm earns a return greater than its required rate of return (r) if it invests in the project. When IRR > r, a project is acceptable because the firm will earn a return greater than its required rate of return (r) if it invests in the project. When NPV > 0, IRR > r for a project—that is, if a project is acceptable using NPV, it is also acceptable using IRR.

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32 Accept/Reject Decisions Using NPV, Discounted Payback, and IRR Technique Evaluation Result Acceptable? NPVNPV> 0 IRRIRR>r Discounted PBPB disc < project’s life YES

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33 NPV Profile A graph that shows the NPVs of a project at various required rates of return. Rate of Return NPV 15%498.12 16327.46 17162.72 183.62 19(150.08) 20(298.61) 21(442.20)

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34 NPV Profile IRR = 18.02% ($2,000) ($1,000) $0 $1,000 $2,000 $3,000 $4,000 $5,000 5%10%15%20% 25% NPV r NPV > 0 NPV < 0

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35 Capital Budgeting Techniques Illustrative Projects A & B 0(7,000.00) 12,000.00 21,000.00 35,000.00 43,000.00 r = 15% Cash Flow, Year Project A 0 12,000.00 21,000.00 35,000.00 43,000.00 Trad PB =2.80 NPV =498.12 IRR =18.02% (8,000.00) 6,000.00 3,000.00 1,000.00 500.00 Project B 1.67 429.22 19.03%

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36 NPV Profiles for Projects A & B -2000 -1000 0 1000 2000 3000 4000 5000 5%10%15% 20%25% NPV r IRR B = 19.03 IRR A = 18.02 Crossover = 16.15 Project A Project B

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37 NPV Profile—Projects A & B NPV B 429.22 318.71 210.94 105.82 3.26 (96.84) (194.55) NPV B 429.22 318.71 210.94 105.82 3.26 (96.84) (194.55) Rate of Return NPV A 15%498.12 16327.46 17162.72 183.62 19(150.08) 20(298.61) 21(442.20) Rate of Return NPV A 15%498.12 16327.46 17162.72 183.62 19(150.08) 20(298.61) 21(442.20) Rate of Return 15% 16 17 18 19 20 21

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38 Capital Budgeting Techniques Illustrative Projects A & B 0(7,000)(8,000) 12,0006,000 21,0003,000 35,0001,000 43,000500 Cash Flow, Year Project AProject B CF A - CF B 1,000 (4,000) (2,000) 4,000 2,500 IRR of (CF A – CF B ) Cash Flow Stream = 16.15% At r = 16.15%, NPV A = NPV B = 302.37

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39 NPV/IRR Ranking Conflicts Asset AAsset B Traditional PB2.80 yrs1.67 yrs Discounted PB3.71 yrs2.78 yrs NPV$498.12$429.22 IRR18.02%19.03% Which asset(s) should be purchased? Asset A, because it has the higher NPV. Asset A Traditional PB2.80 yrs Discounted PB3.71 yrs NPV$498.12 IRR18.02% Asset AAsset B Traditional PB2.80 yrs1.67 yrs Discounted PB3.71 yrs2.78 yrs NPV$498.12$429.22 IRR18.02%19.03%

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40 NPV/IRR Ranking Conflicts Ranking conflicts result from: Cash flow timing differences Size differences Unequal lives Reinvestment rate assumptions NPV—reinvest at the firm’s required rate of return IRR—reinvest at the project’s internal rate of return, IRR

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41 Multiple IRRs Conventional cash flow pattern—cash outflow(s) occurs at the beginning of the project’s life, followed by a series of cash inflows. Unconventional cash flow pattern—cash outflow(s) occurs during the life of the project, after cash inflows have been generated. An IRR solution occurs when a cash flow pattern is interrupted; if a cash flow pattern is interrupted more than once, then more than one IRR solution exists.

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42 Multiple IRRs—Example YearCash Flow 0(15,000) 140,150 2(13,210) 3(16,495) IRR 1 = 22.5% IRR 2 = 92.0%

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43 Modified Internal Rate of Return (MIRR) Generally solves the ranking conflict and the multiple IRR problem

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44 MIRR—Example YearProject AProject B 0(7,000)(8,000) 12,0006,000 21,0003,000 35,0001,000 43,000500 Discounted PB3.71 yrs2.78 yrs NPV$498.12$429.22 IRR18.02%19.03%

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45 MIRR—Example YearProject AProject B 0(7,000)(8,000) 12,0006,000 21,0003,000 35,0001,000 43,000500 Project A—calculator solution: N = 4, PV = -7,000, PMT = 0, FV = 13,114.25; I/Y = 16.99 = MIRR A Project B—calculator solution: N = 4, PV = -8,000, PMT = 0, FV = 14,742.75; I/Y = 16.51 = MIRR B Project A—calculator solution: N = 4, PV = -7,000, PMT = 0, FV = 13,114.25; I/Y = 16.99 = MIRR A

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46 Capital Budgeting—The Answers How do firms make decisions about whether to invest in costly, long-lived assets? Firms use decision-making methods that are based on fundamental valuation concepts How does a firm make a choice between two acceptable investments when only one can be purchased? The decision should be consistent with the goal of maximizing the value of the firm

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47 How are different capital budgeting techniques related? All techniques except traditional payback period (PB) are based on time value of money Which capital budgeting methods do firms actually use? Most firms rely heavily on NPV and IRR to make investment decisions Capital Budgeting—The Answers

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