What’s next?What’s next?

Capital BudgetingCapital Budgeting: involves making : involves making decisions about real asset investments.decisions about real asset investments. Chapter 7: Net Present Value and Other Chapter 7: Net Present Value and Other

Investment CriteriaInvestment Criteria Chapter 8: Estimating cash flows for a potential Chapter 8: Estimating cash flows for a potential

investment.investment. Chapter 12: Estimating a required rate of Chapter 12: Estimating a required rate of

return for a potential investment = opportunity return for a potential investment = opportunity cost of capital. (need chapters 10 & 11 to help cost of capital. (need chapters 10 & 11 to help us with chapter 12)us with chapter 12)

Chapter 7Chapter 7

Net Present Value & Other Net Present Value & Other Investment CriteriaInvestment Criteria

Topic OverviewTopic Overview Project TypesProject Types Capital Budgeting Decision CriteriaCapital Budgeting Decision Criteria

Net Present Value (NPV)Net Present Value (NPV) Payback Period Payback Period Internal Rate of Return (IRR) Internal Rate of Return (IRR) Profitability Index (PI)Profitability Index (PI)

Equivalent Annual Cost and Equivalent Equivalent Annual Cost and Equivalent Annual AnnuityAnnual Annuity

Capital RationingCapital Rationing

Learning ObjectivesLearning Objectives

Understand how to calculate and Understand how to calculate and use capital budgeting decision use capital budgeting decision techniques: Payback, NPV, IRR, & PI.techniques: Payback, NPV, IRR, & PI.

Understand the advantages and Understand the advantages and disadvantages of each technique.disadvantages of each technique.

Understand which project to select Understand which project to select when there is a ranking conflict when there is a ranking conflict between NPV and IRR. between NPV and IRR.

Think about this as we Think about this as we cover Chapter 7 Investment cover Chapter 7 Investment

Criteria.Criteria. Which of the following investment Which of the following investment

opportunities would you prefer?opportunities would you prefer? #1) Give me $1 now and I’ll give you #1) Give me $1 now and I’ll give you

$2 at the end of class.$2 at the end of class. #2) Give me $100 now and I’ll give #2) Give me $100 now and I’ll give

you $150 at the end of class.you $150 at the end of class.

Project TypesProject Types Independent Projects – don’t affect acceptance Independent Projects – don’t affect acceptance

of other projectsof other projects Mutually Exclusive Projects – interact with other Mutually Exclusive Projects – interact with other

projects or accomplish the same objectiveprojects or accomplish the same objective

Normal Projects -only one sign change in Normal Projects -only one sign change in sequence of cash flowssequence of cash flows

Non-normal Projects - multiple sign changes in Non-normal Projects - multiple sign changes in cash flow series.cash flow series.

Our Case StudyOur Case Study

We want to help Marge Simpson, Inc. analyze We want to help Marge Simpson, Inc. analyze the following business opportunities by using the following business opportunities by using the following cash flow information. Assume the following cash flow information. Assume Marge's opportunity cost of capital is 12%.Marge's opportunity cost of capital is 12%.

Time Falafel-Full How 'Bout A Pretzel?

0 (20,000) (20,000) 1 15,000 2,000 2 15,000 2,500 3 13,000 3,000 4 3,000 50,000

Net Present ValueNet Present Value

Net Present Value - Present value of cash flows minus initial investments.

Opportunity Cost of Capital - Expected rate of return given up by investing in a project

Net Present ValueNet Present Value

NPV = PV - required investmentNPV = PV - required investment

NPV CC

rt

t

0 1( )

NPV CC

r

C

r

C

rt

t

01

12

21 1 1( ) ( )...

( )

Net Present ValueNet Present Value

TerminologyTerminologyC = Cash FlowC = Cash Flowt = time period of the investmentt = time period of the investmentr = “opportunity cost of capital”r = “opportunity cost of capital”

The Cash Flow could be positive or The Cash Flow could be positive or negative at any time period.negative at any time period.

Net Present ValueNet Present Value

Net Present Value RuleNet Present Value Rule

Managers increase shareholders’ Managers increase shareholders’ wealth by accepting all projects that wealth by accepting all projects that are worth more than they cost. are worth more than they cost.

Therefore, they should accept all Therefore, they should accept all projects with a positive net present projects with a positive net present value.value.

Marge’s NPVs: r = 12%Marge’s NPVs: r = 12%

Calculator Steps. Falafel-Full: CF0 = -20,000, C01 = Calculator Steps. Falafel-Full: CF0 = -20,000, C01 = 15,000, F01 = 2, C02 = 13,000, F02 = 1, C03 = 3,000. 15,000, F01 = 2, C02 = 13,000, F02 = 1, C03 = 3,000. NPV: I = 12, CPT NPV = 16,510NPV: I = 12, CPT NPV = 16,510

Pretzel: CF0 = -20,000, C01 = 2,000, F01=1, C02 = Pretzel: CF0 = -20,000, C01 = 2,000, F01=1, C02 = 2,500, F02=1, C03 = 3,000, F03=1, C04 = 50,000. NPV: 2,500, F02=1, C03 = 3,000, F03=1, C04 = 50,000. NPV: I = 12, CPT NPV = 17,690I = 12, CPT NPV = 17,690

Time Falafel-Full PV(CF) How 'Bout A Pretzel? PV(CF)

0 (20,000) (20,000) (20,000) (20,000) 1 15,000 13,393 2,000 1,786 2 15,000 11,958 2,500 1,993 3 13,000 9,253 3,000 2,135 4 3,000 1,907 50,000 31,776

NPV 16,510 17,690

Excel and NPV: Why Excel and NPV: Why Microsoft deserves its legal Microsoft deserves its legal

troubles.troubles. Excel’s NPV function is goofed up. =NPV(r, Excel’s NPV function is goofed up. =NPV(r,

range of cash flows)range of cash flows) Assumes first cash flow in range occurs at Assumes first cash flow in range occurs at

t = 1.t = 1. See spreadsheet.See spreadsheet. Solution to this spreadsheet problem: Solution to this spreadsheet problem:

exclude initial cost (t = 0 cash flow) from exclude initial cost (t = 0 cash flow) from NPV cell range and add initial cost (if NPV cell range and add initial cost (if already negative) to the NPV function.already negative) to the NPV function.

Marge’s NPV DecisionMarge’s NPV Decision

If projects are independent, If projects are independent, Marge should select both.Marge should select both. Both have positive NPV.Both have positive NPV.

If the projects are mutually If the projects are mutually exclusive, select How ‘Bout A exclusive, select How ‘Bout A Pretzel?Pretzel? Pretzel NPV > Falafel NPV.Pretzel NPV > Falafel NPV.

Payback Period (PB)Payback Period (PB) Measures how long it takes to Measures how long it takes to

recovers a project’s cost.recovers a project’s cost. Easy to calculate and a good Easy to calculate and a good

measure of a project’s risk and measure of a project’s risk and liquidity.liquidity.

Decision Rule: Accept if PB < some Decision Rule: Accept if PB < some maximum period of time.maximum period of time.

Marge’s Payback (Assume Marge’s Payback (Assume Marge’s max is 2 years)Marge’s max is 2 years)

Falafel PB = less than 2 yearsFalafel PB = less than 2 years Pretzel PB = less than 4 yearsPretzel PB = less than 4 years Marge should choose Falafel using Marge should choose Falafel using

Payback Period.Payback Period.

Time Falafel-Full Cumulative CF How 'Bout A Pretzel? Cumulative CF

0 (20,000) (20,000) (20,000) (20,000) 1 15,000 (5,000) 2,000 (18,000) 2 15,000 10,000 2,500 (15,500) 3 13,000 23,000 3,000 (12,500) 4 3,000 26,000 50,000 37,500

Problems with PaybackProblems with Payback

Ignores time value of money!Ignores time value of money! Ignores cash flows beyond payback Ignores cash flows beyond payback

period.period. Not a good investment decision Not a good investment decision

technique.technique.

Internal Rate of Return (IRR)Internal Rate of Return (IRR)

Internal Rate of Return is a project’s expected Internal Rate of Return is a project’s expected rate of return on its investment.rate of return on its investment.

IRR is the interest rate where the PV of the IRR is the interest rate where the PV of the project’s cash flows equals its cost.project’s cash flows equals its cost.

In other words, the IRR is the rate where a In other words, the IRR is the rate where a project’s NPV = 0.project’s NPV = 0.

∑∑CFCFtt/(1 + IRR)/(1 + IRR)tt = Cost = Cost Decision Rule: Accept if IRR > r Decision Rule: Accept if IRR > r

(opportunity cost of capital).(opportunity cost of capital). Non-normal projects have multiple IRRs. Don’t Non-normal projects have multiple IRRs. Don’t

use IRR to decide on non-normal projects.use IRR to decide on non-normal projects.

Marge’s IRRsMarge’s IRRs

Best to use calculator. Calculator Steps. Best to use calculator. Calculator Steps. Falafel-Full: CF0 = -20,000, C01 = 15,000, F01 = 2, C02 = Falafel-Full: CF0 = -20,000, C01 = 15,000, F01 = 2, C02 =

13,000, F02 = 1, C03 = 3,000. Press IRR, then CPT: IRR = 13,000, F02 = 1, C03 = 3,000. Press IRR, then CPT: IRR = 54.7%54.7%

Pretzel: CF0 = -20,000, C01 = 2,000, F01=1, C02 = 2,500, Pretzel: CF0 = -20,000, C01 = 2,000, F01=1, C02 = 2,500, F02=1, C03 = 3,000, F03=1, C04 = 50,000. Press IRR, then F02=1, C03 = 3,000, F03=1, C04 = 50,000. Press IRR, then CPT: IRR = 33.3%CPT: IRR = 33.3%

r = 12%. If independent projects: select both, IRRs > r = 12%. If independent projects: select both, IRRs > 12%. Mutually exclusive: select Falafel; higher IRR.12%. Mutually exclusive: select Falafel; higher IRR.

Time Falafel-Full How 'Bout A Pretzel?

0 (20,000) (20,000) 1 15,000 2,000 2 15,000 2,500 3 13,000 3,000 4 3,000 50,000

Comparison of NPV & IRRComparison of NPV & IRR

For normal independent projects, all For normal independent projects, all three methods give same three methods give same accept/reject decision.accept/reject decision. NPV > 0 yields IRR > r in order to NPV > 0 yields IRR > r in order to

lower NPV to 0.lower NPV to 0. However, these methods can rank However, these methods can rank

mutually exclusive projects mutually exclusive projects differently.differently.

What to do, then?What to do, then?

NPV ProfilesNPV Profiles

A graph which shows a project’s NPV at different A graph which shows a project’s NPV at different interest rates (opportunity cost of capital).interest rates (opportunity cost of capital).

Can illustrate ranking conflicts between NPV and Can illustrate ranking conflicts between NPV and IRR.IRR.

Below is a table of NPVs for Marge’s projects.Below is a table of NPVs for Marge’s projects.

r Falafel-Full How 'Bout A Pretzel?0% 26,000 37,500 5% 21,589 27,899

10% 17,849 20,289 12% 16,510 17,690 15% 14,649 14,190 25% 9,485 5,216 35% 5,529 (874) 55% (68) (8,201)

Marge’s ProjectsMarge’s Projects

Marge's NPV Profiles

-20,000

-10,000

0

10,000

20,000

30,000

40,000

0% 10% 20% 30% 40% 50% 60%

Cost of Capital (r)

NPV

Falafel-Full

How 'Bout APretzel?

IRR(P) IRR(F)

Determining NPV/IRR Determining NPV/IRR Conflict RangeConflict Range

For each year, subtract one project’s cash For each year, subtract one project’s cash flows from the other.flows from the other.

If there is a change of signs of these cash If there is a change of signs of these cash flow differences, a ranking conflict exists.flow differences, a ranking conflict exists.

Find IRR of these cash flow differences to Find IRR of these cash flow differences to find rate where the two projects have the find rate where the two projects have the same NPV = crossover rate.same NPV = crossover rate.

At a cost of capital less than this crossover At a cost of capital less than this crossover rate, a ranking conflict between NPV and rate, a ranking conflict between NPV and IRR exists.IRR exists.

Time Falafel-Full How 'Bout A Pretzel? Falafel - Pretzel0 (20,000) (20,000) - CF01 15,000 2,000 13,000 C012 15,000 2,500 12,500 C023 13,000 3,000 10,000 C034 3,000 50,000 (47,000) C04

IRR = Crossover Rate 14.1%

Marge’s crossover rateMarge’s crossover rate

At a cost of capital less than 14.1%, Pretzel has higher NPV but lower IRR At a cost of capital less than 14.1%, Pretzel has higher NPV but lower IRR = Ranking Conflict.= Ranking Conflict.

At cost of capital greater than 14.1%, Falafel has the higher NPV and IRR.At cost of capital greater than 14.1%, Falafel has the higher NPV and IRR. Why? Cash flow timing differences in this case.Why? Cash flow timing differences in this case. Other cause: initial cost differences, but not here.Other cause: initial cost differences, but not here.

Marge's NPV Profiles

-20,000

-10,000

0

10,000

20,000

30,000

40,000

0% 10% 20% 30% 40% 50% 60%

Cost of Capital (k)

NPV

Falafel-Full

How 'Bout APretzel?

IRR(P) IRR(F)

Reconciling NPV/IRR Reconciling NPV/IRR Ranking ConflictsRanking Conflicts

Shareholder Wealth MaximizationShareholder Wealth Maximization:: Want to add more value to the firm than Want to add more value to the firm than

less.less. Result: Choose project with Result: Choose project with

highest NPV when NPV/IRR highest NPV when NPV/IRR ranking conflict exists for ranking conflict exists for mutually exclusive projects.mutually exclusive projects.

Also, IRR has the multiple IRR problem Also, IRR has the multiple IRR problem for non-normal projectsfor non-normal projects like the like the following.following.

Acme, Inc. Rocket-Powered Acme, Inc. Rocket-Powered Roller Blade ProjectRoller Blade Project

Acme is considering the following project which Acme is considering the following project which would market these roller blades to coyotes would market these roller blades to coyotes trying to catch road runners. Acme expects a trying to catch road runners. Acme expects a cash inflow in the year 1, but an outflow in the 2cash inflow in the year 1, but an outflow in the 2ndnd (last) year of the project due to liability claims (last) year of the project due to liability claims from injured cartoon coyotes. Acme’s opportunity from injured cartoon coyotes. Acme’s opportunity cost of capital is 13%.cost of capital is 13%.

YearYear 00 11 22

Cash Flow Cash Flow (5)(5) 3030 (30)(30)

NPV = -1.95NPV = -1.95IRR = 26.8%IRR = 26.8%

Rocket-Powered Roller Rocket-Powered Roller Blade NPV ProfileBlade NPV Profile

-6

-1

4

0% 50% 100% 150% 200% 250% 300% 350% 400% 450% 500% 550%NPV

At Acme’s 13% opportunity cost of capital, the project has a At Acme’s 13% opportunity cost of capital, the project has a negative NPV even though the IRRs is greater than 13%.negative NPV even though the IRRs is greater than 13%.

Because of this conflict, don’t use IRR to make decisions for Because of this conflict, don’t use IRR to make decisions for non-normal projects! (or look for a first IRR that is less than non-normal projects! (or look for a first IRR that is less than cost of capital)cost of capital)

Comparing Projects with Comparing Projects with unequal livesunequal lives

To replace the Budweiser sign that the ferret dropped in the To replace the Budweiser sign that the ferret dropped in the frog pond, Louie the Lizard is evaluating two new signs. Louie frog pond, Louie the Lizard is evaluating two new signs. Louie must purchase and care for a replacement sign indefinitely. must purchase and care for a replacement sign indefinitely. Here are the annual costs for the two replacement signs.Here are the annual costs for the two replacement signs.

Which sign should Louie choose given an opportunity cost of Which sign should Louie choose given an opportunity cost of capital of 11%?capital of 11%?

YearYear Frying FrogsFrying Frogs Lizards Leaping over FrogsLizards Leaping over Frogs00 4,0004,000 6,0006,00011 1,0001,000 90090022 1,0001,000 70070033 70070044 700700

  

Equivalent Annual CostEquivalent Annual Cost

Equivalent Annual CostEquivalent Annual Cost - The cost per - The cost per period with the same present value period with the same present value as the cost of buying and operating a as the cost of buying and operating a machine.machine.

Equivalent annual cost =present value of costs

annuity factor

Louie The Lizard’s Decision, Louie The Lizard’s Decision, r = 11%r = 11%

YearYear Frying FrogsFrying Frogs Lizards Leaping over FrogsLizards Leaping over Frogs00 4,0004,000 6,0006,00011 1,0001,000 90090022 1,0001,000 70070033 70070044 700700 Frying Frogs (FF) PV of costs = 5713Frying Frogs (FF) PV of costs = 5713 Lizards Leaping (LL) PV of costs = 8352Lizards Leaping (LL) PV of costs = 8352 FF EAC: 5713=PV, 11=I/Y, 2=N, 0=FV, CPT PMT = 3336FF EAC: 5713=PV, 11=I/Y, 2=N, 0=FV, CPT PMT = 3336 LL EAC: 8352=PV, 11=I/Y, 4=N, 0=FV, CPT PMT = 2692LL EAC: 8352=PV, 11=I/Y, 4=N, 0=FV, CPT PMT = 2692 Louie should choose the Lizards Leaping over Frogs sign Louie should choose the Lizards Leaping over Frogs sign

because of its lower cost on an annual basis.because of its lower cost on an annual basis.

Comparing Projects (NPV>0) Comparing Projects (NPV>0) with unequal lives: Equivalent with unequal lives: Equivalent Annual AnnuityAnnual Annuity Burns Power is considering the following Burns Power is considering the following

mutually exclusive projects in order to mutually exclusive projects in order to increase power consumption in Springfield increase power consumption in Springfield indefinitely. Which project should be selected indefinitely. Which project should be selected if Burns Power’s opportunity cost of capital is if Burns Power’s opportunity cost of capital is 10%?10%?

YearYear 00 11 22 33

Sun-BlockerSun-Blocker (50)(50) 6060 6060

Fog-MakerFog-Maker (30)(30) 4040 40404040

Find NPV and Equivalent Find NPV and Equivalent Annual AnnuityAnnual Annuity

NPV of Sun-Blocker = $54.1 mNPV of Sun-Blocker = $54.1 m NPV of Fog-Maker = $69.5 mNPV of Fog-Maker = $69.5 m Sun-Blocker EAA: -54.1=PV, 10=I/Y, 2=N, Sun-Blocker EAA: -54.1=PV, 10=I/Y, 2=N,

0=FV, CPT PMT = $31.2m 0=FV, CPT PMT = $31.2m Fog-Maker EAA: -69.5=PV, 10=I/Y, 3=N, 0=FV, Fog-Maker EAA: -69.5=PV, 10=I/Y, 3=N, 0=FV,

CPT PMT = $27.9mCPT PMT = $27.9m Burns should choose the Sun-Blocker because it Burns should choose the Sun-Blocker because it

would add the most value on an annual basis. would add the most value on an annual basis.

factorannuity

luepresent vanet =annuity annual Equivalent

Investment TimingInvestment Timing

Sometimes you have the ability to Sometimes you have the ability to defer an investment and select a time defer an investment and select a time that is more ideal at which to make the that is more ideal at which to make the investment decision. A common investment decision. A common example involves a tree farm. You example involves a tree farm. You may defer the harvesting of trees. By may defer the harvesting of trees. By doing so, you defer the receipt of the doing so, you defer the receipt of the cash flow, yet increase the cash flow.cash flow, yet increase the cash flow.

Investment Timing: #31, pg Investment Timing: #31, pg 207 of textbook207 of textbook

Can purchase a scanner today for $400 Can purchase a scanner today for $400 that would provide $60 in annual benefits that would provide $60 in annual benefits for 10 years. However, scanner prices are for 10 years. However, scanner prices are expected to decrease 20% per year.expected to decrease 20% per year.

Should you purchase the scanner today or Should you purchase the scanner today or wait if your discount rate is 10%?wait if your discount rate is 10%?

PV of annual benefits: 60=PMT, 10=N, PV of annual benefits: 60=PMT, 10=N, 10=I/Y, 0=FV, CPT PV = $36910=I/Y, 0=FV, CPT PV = $369

NPV = $369 – Expected Scanner CostNPV = $369 – Expected Scanner Cost

Investment Timing Example Investment Timing Example (cont.): r = 10%(cont.): r = 10%

YearYear CostCost PV BenefitsPV Benefits NPV at PurchaseNPV at Purchase NPV TodayNPV Today

00 400400 369369 -31-31 -31-31

11 320320 369369 4949 4545

22 256256 369369 113113 9393

33 205205 369369 164164 123123

44 164164 369369 205205 140140

55 131131 369369 238238 148148

66 105105 369369 264264 149149

77 84 84 369369 285285 146146To maximize value, you should wait 6 years to buy To maximize value, you should wait 6 years to buy the scanner.the scanner.

Capital RationingCapital Rationing

Capital RationingCapital Rationing - Limit set on the amount - Limit set on the amount of funds available for investment.of funds available for investment.

Soft RationingSoft Rationing - Limits on available funds - Limits on available funds imposed by management.imposed by management.

Hard RationingHard Rationing - Limits on available funds - Limits on available funds imposed by the unavailability of funds in imposed by the unavailability of funds in the capital market.the capital market.

Profitability Index (PI)Profitability Index (PI) The ratio of the net present value of a project’s The ratio of the net present value of a project’s

cash flows to its cost.cash flows to its cost. PI = NPV/CostPI = NPV/Cost Decision Rule: Accept if PI > 0Decision Rule: Accept if PI > 0 PI can be used to rank projects under capital PI can be used to rank projects under capital

rationing conditions. Accept highest PI projects rationing conditions. Accept highest PI projects under the capital constraint to maximize NPV.under the capital constraint to maximize NPV.

CAUTION: PI can rank mutually exclusive CAUTION: PI can rank mutually exclusive projects that have different initial costs projects that have different initial costs differently than NPV.differently than NPV.

Summary of Capital Summary of Capital Budgeting MethodsBudgeting Methods

Want a method the uses the time value Want a method the uses the time value of money with all project cash flows: NPV, of money with all project cash flows: NPV, PI, IRR.PI, IRR.

IRR can give erroneous decision for non-IRR can give erroneous decision for non-normal projects.normal projects.

Overall, NPV is the best and preferred Overall, NPV is the best and preferred method.method.

However, under capital rationing (budget However, under capital rationing (budget restraint), ranking projects by PI can be restraint), ranking projects by PI can be useful in helping to maximize NPV under useful in helping to maximize NPV under capital constraint.capital constraint.