1 chapter 6: capital budgeting: the basics copyright © prentice hall inc. 1999. author: nick bagley...

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Chapter 6: Capital Chapter 6: Capital Budgeting: The BasicsBudgeting: The Basics

Copyright © Prentice Hall Inc. 1999. Author: Nick Bagley

ObjectiveExplain Capital Budgeting

Develop Criteria

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Chapter 6 ContentsChapter 6 Contents

• 1 The Nature of Project 1 The Nature of Project AnalysisAnalysis

• 2 Where do Investment 2 Where do Investment Ideas come from?Ideas come from?

• 3 The NPV Investment Rule3 The NPV Investment Rule

• 4 Estimating a Project’s 4 Estimating a Project’s Cash FlowsCash Flows

• 5 Cost of Capital5 Cost of Capital

• 6 Sensitivity Analysis6 Sensitivity Analysis

• 7 Analyzing Cost-7 Analyzing Cost-Reducing ProjectsReducing Projects

• 8 Projects with Different 8 Projects with Different LivesLives

• 9 Ranking Mutually 9 Ranking Mutually Exclusive ProjectsExclusive Projects

• 10 Inflation & Capital 10 Inflation & Capital BudgetingBudgeting

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ObjectivesObjectives

• To show how to use discounted cash To show how to use discounted cash flow analysis to make decisions flow analysis to make decisions such as:such as:– Whether to enter a new line of Whether to enter a new line of

businessbusiness

– Whether to invest in equipment to Whether to invest in equipment to reduce costsreduce costs

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IntroductionIntroduction

• Recall the objective of a firmRecall the objective of a firm– Maximization of the market value of Maximization of the market value of

shareholders’ equityshareholders’ equity• The theory of how to do this was The theory of how to do this was

provided in the prior two chaptersprovided in the prior two chapters

– Compute the net present value of the Compute the net present value of the project’s expected cash flows, and project’s expected cash flows, and undertake only those with positive NPVundertake only those with positive NPV

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6.1 The Nature of Project 6.1 The Nature of Project AnalysisAnalysis

• Basic unit of analysisBasic unit of analysis– the individual investment projectthe individual investment project

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Procedural OutlineProcedural Outline

• Form ideas on how to increase Form ideas on how to increase shareholders’ equityshareholders’ equity

• Plan how to implement the ideasPlan how to implement the ideas

• Gather information on timing and Gather information on timing and magnitude of costs and benefitsmagnitude of costs and benefits

• Apply NPV criterionApply NPV criterion

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Generating a forecast Generating a forecast

• Information is often biased towards its Information is often biased towards its provider’s goal (agency problem)provider’s goal (agency problem)

• There are many ways to implement a goal There are many ways to implement a goal

• Some information is not fully quantifiableSome information is not fully quantifiable

• Impact on shareholder wealth difficult to Impact on shareholder wealth difficult to evaluate when cash flows are riskyevaluate when cash flows are risky

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The Nature of Project The Nature of Project AnalysisAnalysis

• We will postpone discussion of risky We will postpone discussion of risky cash flows to avoid the complex issue cash flows to avoid the complex issue of how they affect shareholder wealthof how they affect shareholder wealth

• The criterion used The criterion used – find the present value of all future cash find the present value of all future cash

flows, and subtract the initial investment flows, and subtract the initial investment to obtain the net present value (NPV)to obtain the net present value (NPV)

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6.2 Where do Investment 6.2 Where do Investment Ideas Come From?Ideas Come From?

– monitor existing & potential customers monitor existing & potential customers needsneeds

– monitor existing & potential technological monitor existing & potential technological capacity of the firmcapacity of the firm

– monitor the competition’s marketing, monitor the competition’s marketing, investment, patents, and technical investment, patents, and technical recruitingrecruiting

– monitor production & distribution functions monitor production & distribution functions for revenue enhancement / cost savingsfor revenue enhancement / cost savings

– reward employees for innovative ideasreward employees for innovative ideas

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6.3 Net Present Value 6.3 Net Present Value RuleRule

• A project’s net present value isA project’s net present value is– the amount by which the project is the amount by which the project is

expected to increase the wealth of the expected to increase the wealth of the firm’s current shareholdersfirm’s current shareholders

• As a criterionAs a criterion– Invest in proposed projects with Invest in proposed projects with

positive NPVpositive NPV

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IllustrationIllustration

• The following tables show the The following tables show the computation of NPVcomputation of NPV– To show the affect of the discount rate, To show the affect of the discount rate,

three tables are shown based on three tables are shown based on different ratesdifferent rates

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NPV of a Project

Discout 10%

Year Flow PV Cum_PV0 -1000 -1000 -10001 450 409 -5912 350 289 -3023 250 188 -1144 150 102 -115 50 31 20

NPV 20 Do Project DCF Payback

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NPV of a Project

Discout 15%

Year Flow PV Cum_PV0 -1000 -1000 -10001 450 391 -6092 350 265 -3443 250 164 -1804 150 86 -945 50 25 -69

NPV -69

Don’t Do Project

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NPV of a Project

Discout 11.04%

Year Flow PV Cum_PV0 -1000 -1000 -10001 450 405 -5952 350 284 -3113 250 183 -1284 150 99 -305 50 30 0

NPV 0 Indifferent

Internal Rate of Return

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Common ErrorCommon Error

• It is a common mistake to start the It is a common mistake to start the investment in year 1 rather than investment in year 1 rather than year 0 (when this was not intended)year 0 (when this was not intended)– Now is time 0Now is time 0

– Like a child, a project is not one-year Like a child, a project is not one-year old until a year has passedold until a year has passed

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SummarySummary

• The discount rate The discount rate – in the first scenario it was assumed to in the first scenario it was assumed to

be 10%, and the resulting NPV was $20be 10%, and the resulting NPV was $20

– In the second scenario it was assumed In the second scenario it was assumed to be 15%, and the NPV was -$69to be 15%, and the NPV was -$69

– In the third scenario, the discount rate In the third scenario, the discount rate that resulted in a zero NPV was found that resulted in a zero NPV was found

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NPV as a Function of Discount Rate

-200

-150

-100

-50

0

50

100

150

200

250

0% 5% 10% 15% 20%

Discount Rate

NP

V

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6.4 Depreciation and Cash 6.4 Depreciation and Cash FlowsFlows

• It is important to remember that It is important to remember that when making financial decisions when making financial decisions only timed only timed cash flowscash flows are used are used– depreciation is an expense, but is depreciation is an expense, but is notnot a a

cash expense, and must be cash expense, and must be excludedexcluded

– the tax benefit of depreciation, the tax benefit of depreciation, however, is a cash flow, and must be however, is a cash flow, and must be includedincluded

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Working Capital & Cash Working Capital & Cash FlowsFlows

• Some cash flows do not occur on Some cash flows do not occur on the income statement, but involve the income statement, but involve timingtiming– working capital additions and working capital additions and

reductions are cash flowsreductions are cash flows

– at the end of a project, the sum of the at the end of a project, the sum of the nominal changes in working capital is nominal changes in working capital is zerozero

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Accruals & DeferralsAccruals & Deferrals

• Take extra care if you are provided Take extra care if you are provided with net income information by an with net income information by an accountantaccountant– the flows forming net income may includethe flows forming net income may include

• accrualsaccruals

• deferralsdeferrals

– these are typically small, and may some-these are typically small, and may some-times be ignoredtimes be ignored

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Incremental Cash FlowsIncremental Cash Flows

• Only the incremental cash flows should Only the incremental cash flows should form part of an investment decisionform part of an investment decision– Evaluate the projected cash flows, by Evaluate the projected cash flows, by

(category and) timing, both with and (category and) timing, both with and without the project, and find the differencewithout the project, and find the difference

– This difference is a collection of timed cash This difference is a collection of timed cash flows, and this is what affects the wealth of flows, and this is what affects the wealth of the shareholdersthe shareholders

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Illustration: CannibalismIllustration: Cannibalism

• A proposed project will generate A proposed project will generate $10,000 in revenue, but will causes $10,000 in revenue, but will causes another product line to lose $3,000 another product line to lose $3,000 in revenuesin revenues

• The incremental cash flow is only The incremental cash flow is only $7,000$7,000

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Illustration: Prior Illustration: Prior ExpensesExpenses

• R&D expenses are $10,000 to-date for R&D expenses are $10,000 to-date for your project, and you plan to spend your project, and you plan to spend another $20,000, making $30,000 in allanother $20,000, making $30,000 in all– The $10,000 is a sunk cost. The decision The $10,000 is a sunk cost. The decision

whether to undertake the project will not whether to undertake the project will not change this expenditurechange this expenditure

– Only the $20,000 is an incremental cost, Only the $20,000 is an incremental cost, and the $10,000 should be excludedand the $10,000 should be excluded

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Sunk CostsSunk Costs

• Shareholders are interested in the timing Shareholders are interested in the timing and magnitude of cash flowsand magnitude of cash flows

– From an investor’s vantage, a project gives From an investor’s vantage, a project gives rise to an alternative cash flowrise to an alternative cash flow

– If If (alternative cash flows) - (original cash (alternative cash flows) - (original cash flows)flows) is valuable to shareholders, do project is valuable to shareholders, do project

– A sunk cost has no impact on future cash A sunk cost has no impact on future cash flows: it is irrelevant to shareholdersflows: it is irrelevant to shareholders

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Illustration: Underutilized Illustration: Underutilized ResourcesResources

• A project uses an existing (non-cancelable) A project uses an existing (non-cancelable) leased warehouse with a remaining life of leased warehouse with a remaining life of 20 years, and total annual rent of $100,00020 years, and total annual rent of $100,000

• The warehouse is projected to remain 50% The warehouse is projected to remain 50% utilized, unless your project is undertakenutilized, unless your project is undertaken

• The lease prohibits sub-leasing The lease prohibits sub-leasing

• The current project is making a loss The current project is making a loss

• Your project will use 25% of the warehouseYour project will use 25% of the warehouse

• What should the project be charged?What should the project be charged?

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Proposed Solution 1Proposed Solution 1

• The original project currently using The original project currently using the warehouse is making a loss:the warehouse is making a loss:– ““Charge the full $100,000 /year so the Charge the full $100,000 /year so the

company can recover the very real company can recover the very real warehousing costs.”warehousing costs.”

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• Half the warehouse is available:Half the warehouse is available:– ““The project should be charged the full The project should be charged the full

$50,000 /year if it needs to use it. A $50,000 /year if it needs to use it. A portion of the warehousing costs will portion of the warehousing costs will not be charged-out otherwise.”not be charged-out otherwise.”

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• The project should be charged for The project should be charged for its share of the its share of the usedused space: space:– ““Charge $33,333 /year.”Charge $33,333 /year.”

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• The project is going to use only 25% The project is going to use only 25% of the space.of the space.– ““Charge $25,000 /year.”Charge $25,000 /year.”

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• The charge should be proportioned The charge should be proportioned according to revenues generated by according to revenues generated by each project--that is fair, isn’t it?each project--that is fair, isn’t it?– ““The old project’s revenues = The old project’s revenues =

$9,000,000, and the new project has $9,000,000, and the new project has projected revenues = $1,000,000, so projected revenues = $1,000,000, so the charge is 10%, or $10,000/year.”the charge is 10%, or $10,000/year.”

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• There is a suitable new (smaller) There is a suitable new (smaller) warehouse available on the market warehouse available on the market for $27,000 /year. for $27,000 /year. – ““Charge the project the market rate of Charge the project the market rate of

the space, $27,000.”the space, $27,000.”

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• The original lease was entered into The original lease was entered into when warehouse space was cheap, when warehouse space was cheap, but now space is twice what it was:but now space is twice what it was:– ““The market value of the leased The market value of the leased

warehouse is now $200,000, and the warehouse is now $200,000, and the project should take its proper share of project should take its proper share of that amount.”that amount.”

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• This is a new project, so give it a This is a new project, so give it a sporting chance:sporting chance:– ““The project should be charged The project should be charged

nothing.”nothing.”

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Warehouse IllustrationWarehouse Illustration

• The solution in this case is proposed The solution in this case is proposed solution # 8, (but for another reason): solution # 8, (but for another reason): The project should be charged The project should be charged nothingnothing– The warehouse expenditure will occur The warehouse expenditure will occur

whether the project is done or not. It is whether the project is done or not. It is therefore therefore not an incremental cash flownot an incremental cash flow

– With different facts (alternative usage or With different facts (alternative usage or lease re-negotiation) the answer would be lease re-negotiation) the answer would be differentdifferent

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6.5 The Cost of Capital6.5 The Cost of Capital

• When determining the cost of capitalWhen determining the cost of capital– the risk of the project is, in general, the risk of the project is, in general,

different from the risk of existing projectsdifferent from the risk of existing projects

– only the market-related risk is relevantonly the market-related risk is relevant

– only the risk from a project’s cash flows is only the risk from a project’s cash flows is relevant (not that of financing instruments)relevant (not that of financing instruments)

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Computing the Average Computing the Average Cost of Capital of a Cost of Capital of a CorporationCorporation

• Determine the return to security Determine the return to security holders of each class of security issuedholders of each class of security issued

• Determine the market value of each Determine the market value of each class of the company’s securities, and class of the company’s securities, and compute the weight of eachcompute the weight of each

• After adjusting for tax, compute the After adjusting for tax, compute the weighted sum of returnsweighted sum of returns

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Average Cost of Capital: Average Cost of Capital: Example with 3-SecuritiesExample with 3-Securities

• LetLet• kkee be the return on equity be the return on equity

• kkdd be the return on debt be the return on debt

• kkpp be the return on preferred be the return on preferred

• VVee be the market value of issued equity be the market value of issued equity

• VVdd be the Market value of issued bonds be the Market value of issued bonds

• VVpp be the market value of issued preferred be the market value of issued preferred

• t be the tax ratet be the tax rate

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Average Cost of Capital: Average Cost of Capital: Example with 3-SecuritiesExample with 3-Securities

• k = kk = kee * V * Vee + k + kpp * V * Vpp + k + kdd * V * Vdd* (1 - * (1 -

t)t)

• The average cost of capital is also The average cost of capital is also the cost of capital for each of the the cost of capital for each of the firms business divisions weighted firms business divisions weighted according to their market valueaccording to their market value

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6.6 Sensitivity Analysis 6.6 Sensitivity Analysis Using SpreadsheetsUsing Spreadsheets

• Will the project still be economical if Will the project still be economical if some of the underlying variables some of the underlying variables are inaccurate?are inaccurate?– Spreadsheets are an excellent tool for Spreadsheets are an excellent tool for

exploring the influence of estimation exploring the influence of estimation errors on financial decisionserrors on financial decisions

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Base CaseBase Case

• The following is an embedded Excel The following is an embedded Excel worksheet for the cash flow of a firmworksheet for the cash flow of a firm– It is generally a good practice to divide the It is generally a good practice to divide the

worksheet into two segments, one worksheet into two segments, one containing only data, and the other containing only data, and the other containing only formulaecontaining only formulae

– This practice increases flexibility & reduces This practice increases flexibility & reduces the chance of errorthe chance of error

– It is also a good practice to name variables It is also a good practice to name variables using Insert:Name:Create in Excelusing Insert:Name:Create in Excel

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Tax rate 40.00%Unit sales in year 1 $4,000Sales growth rate 0.00%Unit price $5,000Unit Price Growth 0.00%Fixed Start 3,100,000Fixed Growth 0.00%Variable pcent 75.00%Depreciation schedule 400,000 NPV = 1236Start working capt 2,200,000Investment schedule 2,800,000Capital movements sch 0Dividend 1,000,000Working Cap Sch 2,200,000

Year 0 1 2 3 4 5 6 7CF ForecastSales revenue 20,000 20,000 20,000 20,000 20,000 20,000 20,000ExpensesFixed Costs (cash) 3,100 3,100 3,100 3,100 3,100 3,100 3,100Variable costs 15,000 15,000 15,000 15,000 15,000 15,000 15,000Depreciation 400 400 400 400 400 400 400Operating Profit 1,500 1,500 1,500 1,500 1,500 1,500 1,500Taxes 600 600 600 600 600 600 600Net Profit 900 900 900 900 900 900 900Operating CF 1,300 1,300 1,300 1,300 1,300 1,300 1,300Working cap move 2200 -2,200Investment in P&E 2,800 0 0 0 0 0 0Invest CF 5,000 0 0 0 0 0 0 -2,200Net CF -5,000 1,300 1,300 1,300 1,300 1,300 1,300 3,500PV(NCF) -5000 1130 983 855 743 646 562 1316

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A Modified Scenario A Modified Scenario

– In this case the cash is piling up (Watch In this case the cash is piling up (Watch out for IRS penalties in this case!)out for IRS penalties in this case!)

– The assumption is now made that sales The assumption is now made that sales units grow by +2%, unit prices by -3%, units grow by +2%, unit prices by -3%, and fixed costs by +8% (No, Victor: Fixed and fixed costs by +8% (No, Victor: Fixed costs may vary with time. Yes, Valerie: costs may vary with time. Yes, Valerie: Fixed costs do not vary with sales.)Fixed costs do not vary with sales.)

– Assume a dividend of $1,000,000/yearAssume a dividend of $1,000,000/year

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Assumptions (Table in $'000)Cost of capital 15.00%Tax rate 40.00%Unit sales in year 1 $4,000Sales growth rate 2.00%Unit price $5,000Unit Price Growth -3.00%Fixed Start 3,100,000Fixed Growth 8.00%Variable pcent 75.00%Depreciation schedule 400,000 NPV = -797Start working capt 2,200,000Investment schedule 2,800,000Capital movements sch 0Dividend 1,000,000Working Cap Sch 2,200,000

Year 0 1 2 3 4 5 6 7CF ForecastSales revenue 20,000 19,788 19,578 19,371 19,165 18,962 18,761ExpensesFixed Costs (cash) 3,100 3,348 3,616 3,905 4,218 4,555 4,919Variable costs 15,000 14,841 14,684 14,528 14,374 14,222 14,071Depreciation 400 400 400 400 400 400 400Operating Profit 1,500 1,199 879 538 174 -214 -629Taxes 600 480 351 215 70 -86 -252Net Profit 900 719 527 323 104 -129 -377Operating CF 1,300 1,119 927 723 504 271 23Working cap move 2200 -2,200Investment in P&E 2,800 0 0 0 0 0 0Invest CF 5,000 0 0 0 0 0 0 -2,200Net CF -5,000 1,300 1,119 927 723 504 271 2,223PV(NCF) -5000 1130 846 610 413 251 117 836

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Additional Scenarios Additional Scenarios

• The following graphs are variations The following graphs are variations of from the basic model constructed of from the basic model constructed by changing one variable at a time:by changing one variable at a time:

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Assumptions (Table in $'000)Cost of capital 25.00%Tax rate 40.00%Unit sales in year 1 $4,000Sales growth rate 0.00%Unit price $5,000Unit Price Growth 0.00%Fixed Start 3,100,000Fixed Growth 0.00%Variable pcent 75.00%Depreciation schedule 400,000 NPV = -429Start working capt 2,200,000Investment schedule 2,800,000Capital movements sch 0Dividend 1,000,000Working Cap Sch 2,200,000


Was 15%

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Assumptions (Table in $'000)Cost of capital 15.00%Tax rate 30.00%Unit sales in year 1 $4,000Sales growth rate 0.00%Unit price $5,000Unit Price Growth 0.00%Fixed Start 3,100,000Fixed Growth 0.00%Variable pcent 75.00%Depreciation schedule 400,000 NPV = 1860Start working capt 2,200,000Investment schedule 2,800,000Capital movements sch 0Dividend 1,000,000Working Cap Sch 2,200,000

Year 0 1 2 3 4 5 6 7CF ForecastSales revenue 20,000 20,000 20,000 20,000 20,000 20,000 20,000ExpensesFixed Costs (cash) 3,100 3,100 3,100 3,100 3,100 3,100 3,100Variable costs 15,000 15,000 15,000 15,000 15,000 15,000 15,000Depreciation 400 400 400 400 400 400 400Operating Profit 1,500 1,500 1,500 1,500 1,500 1,500 1,500Taxes 450 450 450 450 450 450 450Net Profit 1,050 1,050 1,050 1,050 1,050 1,050 1,050Operating CF 1,450 1,450 1,450 1,450 1,450 1,450 1,450Working cap move 2200 -2,200Investment in P&E 2,800 0 0 0 0 0 0Invest CF 5,000 0 0 0 0 0 0 -2,200Net CF -5,000 1,450 1,450 1,450 1,450 1,450 1,450 3,650PV(NCF) -5000 1261 1096 953 829 721 627 1372

Was 40%

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Year 0 1 2 3 4 5 6 7CF ForecastSales revenue 20,000 21,000 22,050 23,153 24,310 25,526 26,802ExpensesFixed Costs (cash) 3,100 3,100 3,100 3,100 3,100 3,100 3,100Variable costs 15,000 15,750 16,538 17,364 18,233 19,144 20,101Depreciation 400 400 400 400 400 400 400Operating Profit 1,500 1,750 2,013 2,288 2,578 2,881 3,200Taxes 600 700 805 915 1,031 1,153 1,280Net Profit 900 1,050 1,208 1,373 1,547 1,729 1,920Operating CF 1,300 1,450 1,608 1,773 1,947 2,129 2,320Working cap move 2200 -2,200Investment in P&E 2,800 0 0 0 0 0 0Invest CF 5,000 0 0 0 0 0 0 -2,200Net CF -5,000 1,300 1,450 1,608 1,773 1,947 2,129 4,520PV(NCF) -5000 1130 1096 1057 1014 968 920 1699

Was 0%

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Assumptions (Table in $'000)Cost of capital 15.00%Tax rate 40.00%Unit sales in year 1 $4,000Sales growth rate 0.00%Unit price $5,000Unit Price Growth 0.00%Fixed Start 3,100,000Fixed Growth 0.00%Variable pcent 85.00%Depreciation schedule 400,000 NPV = -3757Start working capt 2,200,000Investment schedule 2,800,000Capital movements sch 0Dividend 1,000,000Working Cap Sch 2,200,000

Year 0 1 2 3 4 5 6 7CF ForecastSales revenue 20,000 20,000 20,000 20,000 20,000 20,000 20,000ExpensesFixed Costs (cash) 3,100 3,100 3,100 3,100 3,100 3,100 3,100Variable costs 17,000 17,000 17,000 17,000 17,000 17,000 17,000Depreciation 400 400 400 400 400 400 400Operating Profit -500 -500 -500 -500 -500 -500 -500Taxes -200 -200 -200 -200 -200 -200 -200Net Profit -300 -300 -300 -300 -300 -300 -300Operating CF 100 100 100 100 100 100 100Working cap move 2200 -2,200Investment in P&E 2,800 0 0 0 0 0 0Invest CF 5,000 0 0 0 0 0 0 -2,200Net CF -5,000 100 100 100 100 100 100 2,300PV(NCF) -5000 87 76 66 57 50 43 865

Was 75%

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Was $3,100,000

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ConsequencesConsequences

– Notice that the reduced long-term Notice that the reduced long-term viability of the product, together with viability of the product, together with the dividend for demands, will cause:the dividend for demands, will cause:

– a cash flow crisis early in year 5, a cash flow crisis early in year 5,

– negative accounting profits in year 6, negative accounting profits in year 6,

– and a serious negative operating cash and a serious negative operating cash flow in year 8 when the tax benefits of flow in year 8 when the tax benefits of depreciation are finally consumed.depreciation are finally consumed.

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GraphsGraphs

– Graphs are a useful supplement to Graphs are a useful supplement to spreadsheets as they may illustrate spreadsheets as they may illustrate behavior of the model to continuing behavior of the model to continuing changes in a selected independent changes in a selected independent variablevariable

– The following graphs explore a modelThe following graphs explore a model

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Table 6.4 Project Sensitivity to Sales Table 6.4 Project Sensitivity to Sales VolumeVolume

Sales Units Net CF Operations NPV Project2000 200000 50050223000 550000 18847083604 1003009 04000 1300000 12356075000 2050000 43559226000 2800000 7476237

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NPV v. Discount Rate

$3,000

$2,000

$1,000

$0

$1,000

$2,000

$3,000

$4,000

$5,000

$6,000

$7,000

0% 5% 10% 15% 20% 25% 30% 35% 40% 45% 50%

Rate

NP

V $

000

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Sensitivity of Project to Sale Volume

$500,000

$0

$500,000

$1,000,000

$1,500,000

$2,000,000

$2,500,000

$3,000,000

$2,000 $2,500 $3,000 $3,500 $4,000 $4,500 $5,000 $5,500 $6,000

Sales (Units)

Net

CF

fro

m O

per

atio

ns

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NPV Project

$6,000,000

$4,000,000

$2,000,000

$0

$2,000,000

$4,000,000

$6,000,000

$8,000,000

$10,000,000

2000 2500 3000 3500 4000 4500 5000 5500 6000

Sales (Units)

NP

V

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Spreadsheet Planning Spreadsheet Planning Conclusions:Conclusions:• Spreadsheets permit management to Spreadsheets permit management to

explore perturbations caused by explore perturbations caused by randomness in the model’s inputsrandomness in the model’s inputs– This should lead to management This should lead to management

correctly prioritizing time to the variables correctly prioritizing time to the variables of the modelof the model

– Management will recognize dangers Management will recognize dangers sooner, and will create contingency plans sooner, and will create contingency plans to avoid their worst consequences to avoid their worst consequences

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6.7 Break-Even and 6.7 Break-Even and Indifference PointsIndifference Points

• Break-even point is number of sales Break-even point is number of sales resulting in a NPV = 0resulting in a NPV = 0

• IRR is discount rate resulting in NPV = 0IRR is discount rate resulting in NPV = 0

• Price B/E is unit price resulting in NPV= 0Price B/E is unit price resulting in NPV= 0

• Payback period is the project life Payback period is the project life resulting in NPV = 0resulting in NPV = 0

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6.8 Projects with Different 6.8 Projects with Different LivesLives

• When do you replace a sales car?When do you replace a sales car?– As a car agesAs a car ages

• its resale price decreasesits resale price decreases

• the annual repair bills increasethe annual repair bills increase

• sales people become discontentedsales people become discontented– people who live in their cars demand reliabilitypeople who live in their cars demand reliability– customers are influenced by sales people’s carscustomers are influenced by sales people’s cars– a nice car is part of their unofficial remunerationa nice car is part of their unofficial remuneration

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Data CollectionData Collection

• A car uses about the same amount A car uses about the same amount of oil, gasoline, cleaning, tire usage, of oil, gasoline, cleaning, tire usage, et cetera, no matter how old it iset cetera, no matter how old it is– This data need not be collected, This data need not be collected,

because we are interested only in because we are interested only in incrementalincremental cash flows cash flows• assume that the degree of tires wear is assume that the degree of tires wear is

compensated by a credit on salecompensated by a credit on sale

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• In order to simplify this example, it In order to simplify this example, it will be assumed that all cash flows will be assumed that all cash flows are in are in realreal terms terms

• Assumed that the required rate of Assumed that the required rate of return on cars is a real 10% (Excited return on cars is a real 10% (Excited already?)already?)

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• Sales people use the Bdella Sedan. Sales people use the Bdella Sedan.

• The market prices for new and used The market prices for new and used Bdellas is given on the next slideBdellas is given on the next slide

• The expected annual maintenance The expected annual maintenance charges by year are also givencharges by year are also given

• Intangible losses have been listedIntangible losses have been listed

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Schedule of Bdella Price & Maint

Age Price Maint Intang0 20,000 01 16,000 0 1,0002 12,800 1,000 8003 10,240 1,100 04 8,192 1,210 -5005 4,096 1,331 -6006 2,048 1,464 -8407 1,024 1,611 -1,1768 512 1,772 -1,6469 256 1,949 -2,305

10 128 2,144 -3,227

Discount 5.00%

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Car ReplacementCar Replacement

• First compute the NPV of First compute the NPV of – purchasing in year 0, and selling in year 1,purchasing in year 0, and selling in year 1,

– purchasing in year 0, and selling in year 2, purchasing in year 0, and selling in year 2,

– … …

– purchasing in year 0, and selling in year purchasing in year 0, and selling in year 1010

• These figures are shown in col. PV_ProjThese figures are shown in col. PV_Proj

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Age Price Maint Intang PV_Price PV_Maint PV_Intang PV_Proj0 20,000 0 20,0001 16,000 0 1,000 15,238 0 952 -3,8102 12,800 1,000 800 11,610 907 726 -7,6193 10,240 1,100 0 8,846 950 0 -11,3344 8,192 1,210 -500 6,740 995 -411 -14,8465 4,096 1,331 -600 3,209 1,043 -470 -19,8906 2,048 1,464 -840 1,528 1,093 -627 -23,2907 1,024 1,611 -1,176 728 1,145 -836 -26,0718 512 1,772 -1,646 347 1,199 -1,114 -28,7669 256 1,949 -2,305 165 1,256 -1,486 -31,689

10 128 2,144 -3,227 79 1,316 -1,981 -35,073

Discount 5.00%

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InterpretationInterpretation

• We see that the incremental cost of We see that the incremental cost of replacing the car every year is $3810, replacing the car every year is $3810, replacing it every two years is $7,619… replacing it every two years is $7,619…

• You are not yet tempted to select You are not yet tempted to select “replace every year” because this “replace every year” because this option does not provide a Bdella Sedan option does not provide a Bdella Sedan after the 1st year, while replace after 2-after the 1st year, while replace after 2-years doesyears does

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Additional AnalysisAdditional Analysis

• The analysis so far does not provide The analysis so far does not provide for a replacement car. for a replacement car.

• The simplest way to do this is to The simplest way to do this is to replace each project with an identical replace each project with an identical project foreverproject forever

• We have the perpetuity equation for We have the perpetuity equation for thisthis

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Additional AnalysisAdditional Analysis

• Take the two year problem as an Take the two year problem as an exampleexample

• The NPV is discounted to year 0, the The NPV is discounted to year 0, the 1st replacement NPV is discounted to 1st replacement NPV is discounted to year 2, the 2nd to year 4, … for everyear 2, the 2nd to year 4, … for ever

• This is a perpetuity due, with interest This is a perpetuity due, with interest (1.05)(1.05)22 - 1 = 10.25% - 1 = 10.25%

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Age Price Maint Intang PV_Price PV_Maint PV_Intang PV_Proj Rate PV_Infinity Ann_Equ0 20,000 0 20,0001 16,000 0 1,000 15,238 0 952 -3,810 5.00% -80,000 -3,8102 12,800 1,000 800 11,610 907 726 -7,619 10.25% -81,951 -3,9023 10,240 1,100 0 8,846 950 0 -11,334 15.76% -83,236 -3,9644 8,192 1,210 -500 6,740 995 -411 -14,846 21.55% -83,738 -3,9885 4,096 1,331 -600 3,209 1,043 -470 -19,890 27.63% -91,881 -4,3756 2,048 1,464 -840 1,528 1,093 -627 -23,290 34.01% -91,771 -4,3707 1,024 1,611 -1,176 728 1,145 -836 -26,071 40.71% -90,112 -4,2918 512 1,772 -1,646 347 1,199 -1,114 -28,766 47.75% -89,013 -4,2399 256 1,949 -2,305 165 1,256 -1,486 -31,689 55.13% -89,167 -4,246

10 128 2,144 -3,227 79 1,316 -1,981 -35,073 62.89% -90,841 -4,326

Discount 5.00%

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ConclusionConclusion

• Replacing the car every year is the Replacing the car every year is the best scenario, but, watch out for an best scenario, but, watch out for an agency problem. Without the agency problem. Without the intangibles the answer is to keep intangibles the answer is to keep the car as long as possiblethe car as long as possible

• The Bdella Sedan is like a Volvo on The Bdella Sedan is like a Volvo on Geritol: it doesn't know when to dieGeritol: it doesn't know when to die

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6.9 Ranking Mutually 6.9 Ranking Mutually Exclusive ProjectsExclusive Projects

• Using the NPV method, you are unlikely Using the NPV method, you are unlikely to encounter any serious problemsto encounter any serious problems– Some managers, particularly those with an Some managers, particularly those with an

engineering background, prefer to use the engineering background, prefer to use the IRR methodIRR method• The IRR method may be The IRR method may be mademade to give the to give the

correct answer, but this requires correct answer, but this requires considerable skill. Avoid it (unless your boss considerable skill. Avoid it (unless your boss engineer)engineer)

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6.10 Inflation and Capital 6.10 Inflation and Capital BudgetingBudgeting

• When computing NPVWhen computing NPV– Use the nominal cost of capital to Use the nominal cost of capital to

discount nominal cash flowsdiscount nominal cash flows• (Nominal cash flows are rarely constant)(Nominal cash flows are rarely constant)

– Use the real cost of capital to discount Use the real cost of capital to discount real cash flowsreal cash flows

1 chapter 6: capital budgeting: the basics copyright © prentice hall inc. 1999. author: nick bagley...

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