0Corporate Finance Ross Westerfield Jaffe Sixth Edition7Chapter SevenNet Present Value and Capital BudgetingPrepared byGady JacobyUniversity of ManitobaandSebouh AintablianAmerican University of Beirut
1Chapter Outline 7.1 Incremental Cash Flows 7.2 The Majestic Mulch and Compost Company: An Example7.3 Inflation and Capital Budgeting7.4 Investments of Unequal Lives: The Equivalent Annual Cost Method7.5 Summary and Conclusions
3Cash Flows—Not Accounting Earnings Consider depreciation expense.You never write a cheque made out to “depreciation.”Much of the work in evaluating a project lies in taking accounting numbers and generating cash flows.
4Incremental Cash Flows Sunk costs are not relevantJust because “we have come this far” does not mean that we should continue to throw good money after bad.Opportunity costs do matter. Just because a project has a positive NPV does not mean that it should also have automatic acceptance. Specifically if another project with a higher NPV would have to be passed up we should not proceed.Side effects matter.Erosion and cannibalism are both bad things. If our new product causes existing customers to demand less of current products, we need to recognize that.When I was an undergrad at the University of Missouri-Rolla, a good friend of mine abandoned college three credit hours shy of graduation. Really. Entreaties from his friends and parents regarding how far he had come and how hard he had worked could not change Louis’ mind. That was all a sunk cost to Louis. He already had a job and didn’t value the degree as much as the incremental work of an easy three-hour required class called ET-10 engineering drafting. Fifteen years later, he still has a good job, a great wife and two charming daughters. Louis taught me a lot about sunk costs.
5Estimating Cash Flows Cash Flows from Operations Recall that: Operating Cash Flow = EBIT – Taxes + DepreciationNet Capital SpendingDon’t forget salvage value (after tax, of course).Changes in Net Working CapitalRecall that when the project winds down, we enjoy a return of net working capital.
6Interest ExpenseLater chapters will deal with the impact that the amount of debt that a firm has in its capital structure has on firm value.For now, it’s enough to assume that the firm’s level of debt (hence interest expense) is independent of the project at hand.
77.2 The Majestic Mulch and Compost Company (MMCC): An Example Costs of test marketing (already spent): $250,000.The proposed factory site (which we own) has no resale value.Cost of the tool making machine: $800,000 (CCA calculations are based on a class 8, 20-percent rate).Production (in units) by year during 8-year life of the machine: 6,000, 9,000, 12,000, 13,000, 12,000, 10,000, 8,000, and 6,000.Price during first year is $100; price increases 2-percent per year thereafter.Production costs during first year are $64 per unit and increase at the annual inflation rate of 5-percent per year thereafter.Fixed production costs are $50,000 each year.Working capital: initially $40,000, then 15-percent of sales at the end of each year. Falls to $0 by the project’s end.See the text for the details of the case.
8The Worksheet for Cash Flows of the MMCC (All cash flows occur at the end of the year.)Recall that production (in units) by year during 8-year life of the machine is given by: (6,000, 9,000, 12,000, 13,000, 12,000, 10,000, 8,000, 6,000).Price during first year is $100 and increases 2% per year thereafter.Sales revenue in year 5 = 12,000×[$100×(1.02)4] = $1,298,919.
9The Worksheet for Cash Flows of the MMCC (continued) (All cash flows occur at the end of the year.)Again, production (in units) by year during 8-year life of the machine is given by: (6,000, 9,000, 12,000, 13,000, 12,000, 10,000, 8,000, 6,000).Variable costs during first year (per unit) are $64 and (increase 5% per year thereafter). Fixed costs are $50,000 each year.Production costs in year 2 = 12,000×[$64×(1.05)4] + 50,000= $983,509.
10The Worksheet for Cash Flows of the MMCC (continued) (All cash flows occur at the end of the year.)Annual CCACCA calculations are based on a class 8, 20% rate (shown at right)The machine cost $800,000.CCA charge in year 5 =$368,640×(.20) = $73,728.
11The Worksheet for Cash Flows of the MMCC (continued) (All cash flows occur at the end of the year.)
12The Worksheet for Cash Flows of the MMCC (continued) (All cash flows occur at the end of the year.)
13Incremental After Tax Cash Flows (IATCF) of the MMCC (All cash flows occur at the end of the year.)If the project’sdiscount rate isabove 15.07%,it should not beaccepted (sinceNPV > 0).$500,135$188,042$2,280($137,896)IRR %
147.3 Inflation and Capital Budgeting Inflation is an important fact of economic life and must be considered in capital budgeting.Consider the relationship between interest rates and inflation, often referred to as the Fisher relationship:(1 + Nominal Rate) = (1 + Real Rate) × (1 + Inflation Rate)For low rates of inflation, this is often approximated asReal Rate Nominal Rate – Inflation RateWhile the nominal rate in the U.S. has fluctuated with inflation, most of the time the real rate has exhibited far less variance than the nominal rate.When accounting for inflation in capital budgeting, one must compare real cash flows discounted at real rates or nominal cash flows discounted at nominal rates.
15Example of Capital Budgeting under Inflation Canadian Electronics Inc. (CEI) has an investment opportunity to produce a new stereo colour TV.The required investment on January 1 of this year is $32 million. CCA calculations are based on a class 8, 20% rate. The firm is in the 34% tax bracket.This investment will have no resale value at the end of the project (in four years).The price of the product on January 1 will be $400 per unit. The price will stay constant in real terms.Labour costs will be $15 per hour on January 1. The will increase at 2% per year in real terms.Energy costs will be $5 per TV; they will increase 3% per year in real terms.The inflation rate is 5%.Revenues are received and costs are paid at year-end.
16Example of Capital Budgeting under Inflation Year 1Year 2Year 3Year 4Physical Production (units)100,000200,000150,000Labour Input (hours)2,000,000Energy input, physical unitsThe riskless nominal discount rate is 4%.The real discount rate for costs and revenues is 8%. Calculate the NPV.
17Present Value of the Tax Shield on CCA The PV of CCA tax shield is a perpetuity, with an adjustment forthe 1st year 50-percent rulethe sale of the asset at the time when the project is terminatedThe PV of CCA tax shield is given by:S = Min[resale value of assets, original price of assets]C = original price of the assetsd = depreciation rate that applies to the asset classd = discount raten = the time when assets are sold
18Example of Capital Budgeting under Inflation The depreciation tax shield is a risk-free nominal cash flow, and is therefore discounted at the nominal riskless rate.Cost of investment today: C = $32,000,000Project life: n = 4 yearsClass 8 depreciation rate: d = 20%Asset resale value: S = 0Finally: k = 0.04 and TC = 0.34The PV of CCA tax shield is given by:
19Example of Capital Budgeting under Inflation Risky Real Cash FlowsPrice: $400 per unit with zero real price increaseLabour: $15 per hour with 2% real wage increaseEnergy: $5 per unit with 3% real energy cost increaseYear 1 After-tax Real Risky Cash Flows:After-tax revenues =$400 × 100,000 × (1-.34) = $26,400,000After-tax labour costs =$15 × 2,000,000 × 1.02 × (1-.34) = $20,196,000After-tax energy costs =$5 × 2,00,000 × 1.03 × (1-.34) = $679,800After-tax net operating CF =$26,400,000 - $20,196,000 - $679,800 =$5,524,200
20Example of Capital Budgeting under Inflation Year One After-tax revenues = $400 × 100,000 × (1-.34) = $26,400,000Year One After-tax labour costs = $15 × 2,000,000 × 1.02 × (1-.34) = $20,196,000Year One After-tax energy costs = $5 × 2,00,000 × 1.03 × (1-.34) = $679,800Year One After-tax net operating CF =$5,524,200$5,524, $31,499,886 $31,066,882 $17,425,007The cash flows in years 2,3, and 4 are easily verified.-$32,000,000
21Example of Capital Budgeting under Inflation The project NPV can now be computed as the sum of the PV of the cost, the PV of the risky cash flows discounted at the risky rate, and the PV of the risk-free CCA tax shield cash flows discounted at the risk-free discount rate.NPV = -$32,000,000 + $69,590,868 + $8,892,308 = $46,483,176
227.4 Investments of Unequal Lives: The Equivalent Annual Cost Method There are times when application of the NPV rule can lead to the wrong decision. Consider a factory that must have an air cleaner. The equipment is mandated by law, so there is no “doing without.”There are two choices:The “Cadillac cleaner” costs $4,000 today, has annual operating costs of $100 and lasts for 10 years.The “cheaper cleaner” costs $1,000 today, has annual operating costs of $500 and lasts for five years.Which one should we choose?
237.4 Investments of Unequal Lives: The Equivalent Annual Cost Method At first glance, the cheap cleaner has the lower NPV (r = 10%):This overlooks the fact that the Cadillac cleaner lasts twice as long.When we incorporate that, the Cadillac cleaner is actually cheaper.
247.4 Investments of Unequal Lives: The Equivalent Annual Cost Method The Cadillac cleaner time line of cash flows:-$4,000 –The “cheaper cleaner” time line of cash flows over 10 years:-$1,000 – ,
25Investments of Unequal Lives Replacement ChainRepeat the projects forever, find the PV of that perpetuity.Assumption: Both projects can and will be repeated.Matching CycleRepeat projects until they begin and end at the same time—like we just did with the air cleaners.Compute NPV for the “repeated projects.”The Equivalent Annual Cost Method
26Investments of Unequal Lives: EAC The Equivalent Annual Cost MethodApplicable to a much more robust set of circumstances than replacement chain or matching cycle.The Equivalent Annual Cost is the value of the level payment annuity that has the same PV as our original set of cash flows.NPV = EAC × ArTFor example, the EAC for the Cadillac air cleaner is $750.98To find ArT, just make PMT = $1 in your financial calculator, set T and r, and solve for PVThe EAC for the cheaper air cleaner is $ which confirms our earlier decision to reject it.
27Example of Replacement Projects Consider a Belgian Dentist’s office; he needs an autoclave to sterilize his instruments. He has an old one that is in use, but the maintenance costs are rising and so he is considering replacing this indispensable piece of equipment.New AutoclaveCost = $3,000 today,Maintenance cost = $20 per yearResale value after 6 years = $1,200NPV of new autoclave (at r = 10%):The often-cited investor who wants to keep his affairs private is described as “a Belgian Dentist”.EAC of new autoclave = -$553.29
28Example of Replacement Projects Existing AutoclaveYearMaintenanceResaleTotal Annual Cost620Total Cost for year 4 = (700 × 1.10 – 600) = $620Total Cost for year 5 = (600 × 1.10 – 500) = $660660435Total Cost for year 2 = (850 × 1.10 – 775) = $435478Total Cost for year 3 = (775 × 1.10 – 700) = $478Total Cost for year 1 = (900 × 1.10 – 850) = $340340Note that the total cost of keeping an autoclave for the first year includes the $200 maintenance cost as well as the opportunity cost of the foregone future value of the $900 we didn’t get from selling it in year 0 less the $850 we have if we still own it at year 1.
29Example of Replacement Projects New AutoclaveEAC of new autoclave = -$553.29Existing AutoclaveYearMaintenanceResaleTotal Annual Cost340435478620660We should keep the old autoclave until it’s cheaper to buy a new one.Replace the autoclave after year 3: at that point the new one will cost $ for the next year’s autoclaving and the old one will cost $620 for one more year.
307.5 Summary and Conclusions Capital budgeting must be placed on an incremental basis.Sunk costs are ignoredOpportunity costs and side effects matterInflation must be handled consistentlyDiscount real flows at real ratesDiscount nominal flows at nominal ratesWhen a firm must choose between two machines of unequal lives:the firm can apply either the matching cycle approachor the equivalent annual cost approach