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**Corporate Finance Ross Westerfield Jaffe**

Sixth Edition 7 Chapter Seven Net Present Value and Capital Budgeting Prepared by Gady Jacoby University of Manitoba and Sebouh Aintablian American University of Beirut

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**Chapter Outline 7.1 Incremental Cash Flows**

7.2 The Majestic Mulch and Compost Company: An Example 7.3 Inflation and Capital Budgeting 7.4 Investments of Unequal Lives: The Equivalent Annual Cost Method 7.5 Summary and Conclusions

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**7.1 Incremental Cash Flows**

Cash flows matter—not accounting earnings. Sunk costs don’t matter. Incremental cash flows matter. Opportunity costs matter. Side effects like cannibalism and erosion matter. Taxes matter: we want incremental after-tax cash flows. Inflation matters.

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**Cash 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.

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**Incremental Cash Flows**

Sunk costs are not relevant Just 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.

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**Estimating Cash Flows Cash Flows from Operations Recall that:**

Operating Cash Flow = EBIT – Taxes + Depreciation Net Capital Spending Don’t forget salvage value (after tax, of course). Changes in Net Working Capital Recall that when the project winds down, we enjoy a return of net working capital.

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Interest Expense Later 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.

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**7.2 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.

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**The 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.

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**The 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.

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**The Worksheet for Cash Flows of the MMCC (continued)**

(All cash flows occur at the end of the year.) Annual CCA CCA 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.

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**The Worksheet for Cash Flows of the MMCC (continued)**

(All cash flows occur at the end of the year.)

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**The Worksheet for Cash Flows of the MMCC (continued)**

(All cash flows occur at the end of the year.)

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**Incremental After Tax Cash Flows (IATCF) of the MMCC**

(All cash flows occur at the end of the year.) If the project’s discount rate is above 15.07%, it should not be accepted (since NPV > 0). $500,135 $188,042 $2,280 ($137,896) IRR %

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**7.3 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 as Real Rate Nominal Rate – Inflation Rate While 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.

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**Example 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.

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**Example of Capital Budgeting under Inflation**

Year 1 Year 2 Year 3 Year 4 Physical Production (units) 100,000 200,000 150,000 Labour Input (hours) 2,000,000 Energy input, physical units The riskless nominal discount rate is 4%. The real discount rate for costs and revenues is 8%. Calculate the NPV.

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**Present Value of the Tax Shield on CCA**

The PV of CCA tax shield is a perpetuity, with an adjustment for the 1st year 50-percent rule the sale of the asset at the time when the project is terminated The PV of CCA tax shield is given by: S = Min[resale value of assets, original price of assets] C = original price of the assets d = depreciation rate that applies to the asset class d = discount rate n = the time when assets are sold

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**Example 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 = $32,000,000 Project life: n = 4 years Class 8 depreciation rate: d = 20% Asset resale value: S = 0 Finally: k = 0.04 and TC = 0.34 The PV of CCA tax shield is given by:

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**Example of Capital Budgeting under Inflation**

Risky Real Cash Flows Price: $400 per unit with zero real price increase Labour: $15 per hour with 2% real wage increase Energy: $5 per unit with 3% real energy cost increase Year 1 After-tax Real Risky Cash Flows: After-tax revenues = $400 × 100,000 × (1-.34) = $26,400,000 After-tax labour costs = $15 × 2,000,000 × 1.02 × (1-.34) = $20,196,000 After-tax energy costs = $5 × 2,00,000 × 1.03 × (1-.34) = $679,800 After-tax net operating CF = $26,400,000 - $20,196,000 - $679,800 =$5,524,200

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**Example of Capital Budgeting under Inflation**

Year One After-tax revenues = $400 × 100,000 × (1-.34) = $26,400,000 Year One After-tax labour costs = $15 × 2,000,000 × 1.02 × (1-.34) = $20,196,000 Year One After-tax energy costs = $5 × 2,00,000 × 1.03 × (1-.34) = $679,800 Year One After-tax net operating CF =$5,524,200 $5,524, $31,499,886 $31,066,882 $17,425,007 The cash flows in years 2,3, and 4 are easily verified. -$32,000,000

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**Example 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

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**7.4 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?

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**7.4 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.

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**7.4 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 – ,

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**Investments of Unequal Lives**

Replacement Chain Repeat the projects forever, find the PV of that perpetuity. Assumption: Both projects can and will be repeated. Matching Cycle Repeat 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

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**Investments of Unequal Lives: EAC**

The Equivalent Annual Cost Method Applicable 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 × ArT For example, the EAC for the Cadillac air cleaner is $750.98 To find ArT, just make PMT = $1 in your financial calculator, set T and r, and solve for PV The EAC for the cheaper air cleaner is $ which confirms our earlier decision to reject it.

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**Example 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 Autoclave Cost = $3,000 today, Maintenance cost = $20 per year Resale value after 6 years = $1,200 NPV 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

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**Example of Replacement Projects**

Existing Autoclave Year Maintenance Resale Total Annual Cost 620 Total Cost for year 4 = (700 × 1.10 – 600) = $620 Total Cost for year 5 = (600 × 1.10 – 500) = $660 660 435 Total Cost for year 2 = (850 × 1.10 – 775) = $435 478 Total Cost for year 3 = (775 × 1.10 – 700) = $478 Total Cost for year 1 = (900 × 1.10 – 850) = $340 340 Note 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.

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**Example of Replacement Projects**

New Autoclave EAC of new autoclave = -$553.29 Existing Autoclave Year Maintenance Resale Total Annual Cost 340 435 478 620 660 We 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.

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**7.5 Summary and Conclusions**

Capital budgeting must be placed on an incremental basis. Sunk costs are ignored Opportunity costs and side effects matter Inflation must be handled consistently Discount real flows at real rates Discount nominal flows at nominal rates When a firm must choose between two machines of unequal lives: the firm can apply either the matching cycle approach or the equivalent annual cost approach

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