第七章 净现值和资本预算

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1. Chapter Outline7.1 Incremental Cash Flows 7.2 The Baldwin 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
2. 7.1 Incremental Cash FlowsCash 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.
3. Cash Flows—Not Accounting Earnings.Consider depreciation expense. You never write a check made out to “depreciation”. Much of the work in evaluating a project lies in taking accounting numbers and generating cash flows.
4. Incremental Cash FlowsSunk 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 that 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.
5. Estimating Cash FlowsCash 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.
6. Interest 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.
7. 7.2 The Baldwin Company: An Example Costs of test marketing (already spent): $250,000. Current market value of proposed factory site (which we own): $150,000. Cost of bowling ball machine: $100,000 (depreciated according to ACRS 5-year life). Increase in net working capital: $10,000. Production (in units) by year during 5-year life of the machine: 5,000, 8,000, 12,000, 10,000, 6,000. Price during first year is $20; price increases 2% per year thereafter. Production costs during first year are $10 per unit and increase 10% per year thereafter. Annual inflation rate: 5% Working Capital: initially $10,000 changes with sales.
8. The Worksheet for Cash Flows of the Baldwin Company Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Investments: (1) Bowling ball machine –100.00 21.76* (2) Accumulated 20.00 52.00 71.20 82.72 94.24 depreciation (3) Adjusted basis of 80.00 48.00 28.80 17.28 5.76 machine after depreciation (end of year) (4) Opportunity cost –150.00 150.00(warehouse) (5) Net working capital 10.00 10.00 16.32 24.97 21.22 0 (end of year) (6) Change in net –10.00 –6.32 –8.65 3.75 21.22 working capital (7) Total cash flow of –260.00 –6.32 –8.65 3.75 192.98 investment[(1) + (4) + (6)] * We assume that the ending market value of the capital investment at year 5 is $30,000. Capital gain is the difference between ending market value and adjusted basis of the machine. The adjusted basis is the original purchase price of the machine less depreciation. The capital gain is $24,240 (= $30,000 – $5,760). We will assume the incremental corporate tax for Baldwin on this project is 34 percent. Capital gains are now taxed at the ordinary income rate, so the capital gains tax due is $8,240 [0.34  ($30,000 – $5,760)]. The after-tax salvage value is $30,000 – [0.34  ($30,000 – $5,760)] = 21,760. ($ thousands) (All cash flows occur at the end of the year.)
9. The Worksheet for Cash Flows of the Baldwin CompanyAt the end of the project, the warehouse is unencumbered, so we can sell it if we want to.($ thousands) (All cash flows occur at the end of the year.) Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Investments: (1) Bowling ball machine –100.00 21.76* (2) Accumulated 20.00 52.00 71.20 82.72 94.24 depreciation (3) Adjusted basis of 80.00 48.00 28.80 17.28 5.76 machine after depreciation (end of year) (4) Opportunity cost –150.00 150.00(warehouse) (5) Net working capital 10.00 10.00 16.32 24.97 21.22 0 (end of year) (6) Change in net –10.00 –6.32 –8.65 3.75 21.22 working capital (7) Total cash flow of –260.00 –6.32 –8.65 3.75 192.98 investment[(1) + (4) + (6)]
10. The Worksheet for Cash Flows of the Baldwin Company (continued) Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Income: (8) Sales Revenues 100.00 163.00 249.72 212.20 129.90 ($ thousands) (All cash flows occur at the end of the year.)Recall that production (in units) by year during 5-year life of the machine is given by: (5,000, 8,000, 12,000, 10,000, 6,000). Price during first year is $20 and increases 2% per year thereafter. Sales revenue in year 3 = 12,000×[$20×(1.02)2] = 12,000×$20.81 = $249,720.
11. The Worksheet for Cash Flows of the Baldwin Company (continued) Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Income: (8) Sales Revenues 100.00 163.00 249.72 212.20 129.90 (9) Operating costs 50.00 88.00 145.20 133.10 87.84 ($ thousands) (All cash flows occur at the end of the year.)Again, production (in units) by year during 5-year life of the machine is given by: (5,000, 8,000, 12,000, 10,000, 6,000). Production costs during first year (per unit) are $10 and (increase 10% per year thereafter). Production costs in year 2 = 8,000×[$10×(1.10)1] = $88,000
12. The Worksheet for Cash Flows of the Baldwin Company (continued) Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Income: (8) Sales Revenues 100.00 163.00 249.72 212.20 129.90 (9) Operating costs 50.00 88.00 145.20 133.10 87.84 (10) Depreciation 20.00 32.00 19.20 11.52 11.52($ thousands) (All cash flows occur at the end of the year.)Depreciation is calculated using the Accelerated Cost Recovery System (shown at right) Our cost basis is $100,000 Depreciation charge in year 4 = $100,000×(.1152) = $11,520. Year ACRS % 1 20.00% 2 32.00% 3 19.20% 4 11.52% 5 11.52% 6 5.76% Total 100.00%
13. The Worksheet for Cash Flows of the Baldwin Company (continued) Year 0 Year 1 Year 2 Year 3 Year 4 Year 5 Income: (8) Sales Revenues 100.00 163.00 249.72 212.20 129.90 (9) Operating costs 50.00 88.00 145.20 133.10 87.84 (10) Depreciation 20.00 32.00 19.20 11.52 11.52 (11) Income before taxes 30.00 43.20 85.32 67.58 30.54 [(8) – (9) - (10)] (12) Tax at 34 percent 10.20 14.69 29.01 22.98 10.38 (13) Net Income 19.80 28.51 56.31 44.60 20.16 ($ thousands) (All cash flows occur at the end of the year.)
14. Incremental After Tax Cash Flows of the Baldwin Company Year 0Year 1 Year 2 Year 3 Year 4 Year 5 (1) Sales Revenues $100.00 $163.00 $249.72 $212.20 $129.90 (2) Operating costs -50.00 -88.00 -145.20 133.10 -87.84 (3) Taxes -10.20 -14.69 -29.01 -22.98 -10.38 (4) OCF (1) – (2) - (3) 39.80 60.51 75.51 56.12 31.68 (5) Total CF of Investment –260. –6.32 –8.65 3.75 192.98 (6) IATCF [(4) + (5)] –260. 39.80 54.19 66.86 59.87 224.66
15. 7.3 Inflation and Capital BudgetingInflation 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.
16. Example of Capital Budgeting under Inflation Sony International has an investment opportunity to produce a new stereo color TV. The required investment on January 1 of this year is $32 million. The firm will depreciate the investment to zero using the straight-line method. The firm is in the 34% tax bracket. The price of the product on January 1 will be $400 per unit. The price will stay constant in real terms. Labor 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.
17. Example of Capital Budgeting under InflationThe riskless nominal discount rate is 4%. The real discount rate for costs and revenues is 8%. Calculate the NPV. Year 1 Year 2 Year 3 Year 4 Physical Production (units) 100,000 200,000 200,000 150,000 Labor Input (hours) 2,000,000 2,000,000 2,000,000 2,000,000 Energy input, physical units 200,000 200,000 200,000 200,000
18. Example of Capital Budgeting under InflationThe depreciation tax shield is a risk-free nominal cash flow, and is therefore discounted at the nominal riskless rate. Cost of investment today = $32,000,000 Project life = 4 years Annual depreciation expense: Depreciation tax shield = $8,000,000 × .34 = $2,720,000
19. Example of Capital Budgeting under InflationRisky Real Cash Flows Price: $400 per unit with zero real price increase Labor: $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 labor 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
20. Example of Capital Budgeting under Inflation$5,524,200 $31,499,886 $31,066,882 $17,425,007-$32,000,0000 1 2 3 4Year One After-tax revenues = $400 × 100,000 × (1-.34) = $26,400,000 Year One After-tax labor 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
21. 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 cash flows discounted at the risk-free discount rate. NPV = -$32,000,000 + $69,590,868 + $9,873,315 = $47,464,183
22. Investments of Unequal LivesThe Equivalent Annual Cost Method 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”.
23. 7.4 Investments of Unequal Lives: The Equivalent Annual Cost MethodThere are times when application of the NPV rule can lead to the wrong decision. Consider a factory which 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 5 years. Which one should we choose?
24. 7.4 Investments of Unequal Lives: The Equivalent Annual Cost MethodAt 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.
25. 7.4 Investments of Unequal Lives: The Equivalent Annual Cost MethodThe Cadillac cleaner time line of cash flows:-$4,000 –100 -100 -100 -100 -100 -100 -100 -100 -100 -1000 1 2 3 4 5 6 7 8 9 10-$1,000 –500 -500 -500 -500 -1,500 -500 -500 -500 -500 -5000 1 2 3 4 5 6 7 8 9 10The “cheaper cleaner” time line of cash flows over ten years:
26. Investments of Unequal Lives: EACThe 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 The EAC for the cheaper air cleaner is $763.80 which confirms our earlier decision to reject it.
27. 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 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%): EAC of new autoclave = -$553.29
28. Example of Replacement Projects Existing Autoclave Year 0 1 2 3 4 5 Maintenance 0 200 275 325 450 500 Resale 900 850 775 700 600 500 Total Annual Cost Total Cost for year 1 = (900 × 1.10 – 850) + 200 = $340340435Total Cost for year 2 = (850 × 1.10 – 775) + 275 = $435478 Total Cost for year 3 = (775 × 1.10 – 700) + 325 = $478620Total Cost for year 4 = (700 × 1.10 – 600) + 450 = $620Total Cost for year 5 = (600 × 1.10 – 500) + 500 = $660660Note 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.
29. Example of Replacement Projects 340435478620660New Autoclave EAC of new autoclave = -$553.29 Existing Autoclave Year 0 1 2 3 4 5 Maintenance 0 200 275 325 450 500 Resale 900 850 775 700 600 500 Total Annual Cost 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 $553.29 for the next year’s autoclaving and the old one will cost $620 for one more year.
30. 7.5 Summary and ConclusionsCapital 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.