Lecture Fourteen Cash Flow Estimation and Other Topics in Capital Budgeting

1. Lecture FourteenCash Flow Estimation and Other Topics in Capital Budgeting • Relevant cash flows • Working capital in capital budgeting • Unequal project lives • Inflation

2. Proposed Project • Cost: $200,000 + $10,000 shipping + $30,000 installation. Depreciable cost: $240,000. • Inventories will rise by $25,000 and payables by $5,000. • Economic life = 4 years. • Salvage value = $25,000. • MACRS 3-year class.

3. Sales: 100,000 units/yr @ $2. • Variable cost = 60% of sales. • Tax rate = 40%. • WACC = 10%.

4. Set up, without numbers, a time line for the project’s cash flows. 0 1 2 3 4 Initial Costs OCF1 OCF2 OCF3 OCF4 + (CF0) Terminal CF NCF0 NCF1 NCF2 NCF3 NCF4

5. Investment at t = 0: Equipment -$200 Installation & Shipping -40 Increase in inventories -25 Increase in A/P 5 Net CF0 -$260 DNWC = $25 - $5 = $20.

6. Modified Accelerated Cost Recovery System (MACRS)Major Classes and Asset Lives for MACRS

7. Recovery Allowance Percentage for Personal Property (MACRS)

8. What’s the annual depreciation? Year Rate x Basis Depreciation 1 0.33 $240 $ 79 2 0.45 240 108 3 0.15 240 36 4 0.07 240 17 1.00 $240 Due to 1/2-year convention, a 3-year asset is depreciated over 4 years.

9. Computing the Cash Inflow from Operations

11. 0 1 2 3 4 5 6 7 8 12% -82,500 22,800 26,760 22,470 20,160 19,830 18,180 16,200 16,200

12. 11 - 7 Operating cash flows: 1 2 3 4 Revenues $200 $200 $200 $200 Op. Cost, 60% -120 -120 -120 -120 Depreciation -79 -108 -36 -17 Oper. inc. (BT) 1 -28 44 63 Tax, 40% -- -11 18 25 1 -17 26 38 Oper. inc. (AT) Add. Depr’n 79 108 36 17 Op. CF 80 91 62 55

13. 11 - 8 Net Terminal CF at t = 4: Recovery of NWC $20 Salvage Value 25 Tax on SV (40%) -10 Net termination CF $35 Q. Always a tax on SV? Ever a positive tax number? Q. How is NWC recovered?

14. 11 - 9 Should CFs include interest expense? Dividends? • No. The cost of capital is accounted for by discounting at the 10% WACC, so deducting interest and dividends would be “double counting” financing costs.

15. 11 - 10 Suppose $50,000 had been spent last year to improve the building. Should this cost be included in the analysis? No. This is a sunk cost.Analyze incremental investment.

16. 11 - 11 Suppose the plant could be leased out for $25,000 a year. Would this affect the analysis? • Yes. Accepting the project means foregoing the $25,000. This is an opportunity cost, and it should be charged to the project. • A.T. opportunity cost = $25,000(1 - T) = $25,000(0.6) = $15,000 annual cost.

17. 11 - 12 If the new product line would decrease sales of the firm’s other lines, would this affect the analysis? • Yes. The effect on other projects’ CFs is an “externality.” • Net CF loss per year on other lines would be a cost to this project. • Externalities can be positive or negative, i.e., complements or substitutes.

18. 11 - 13 Here are all the project’s net CFs (in thousands) on a time line: 0 1 2 3 4 k = 10% -260 79.7 91.2 62.4 54.7 Terminal CF 35.0 89.7 Enter CFs in CF register, and I = 10%. NPV = -$4.03 IRR = 9.3%

19. 11 - 14 What’s the project’s MIRR? 0 1 2 3 4 -260 79.7 91.2 62.4 89.7 10% 68.6 10% 110.4 10% 106.1 MIRR = ? 374.8 -260 Can we solve using a calculator?

20. N I/YR PV PMT FV 11 - 15 Yes. CF0 = 0 CF1 = 79.7 CF2 = 91.2 CF3 = 62.4 CF4 = 89.7 I = 10 NPV = 255.97 INPUTS 4 10 -255.97 0 TV = FV = 374.8 OUTPUT

21. N I/YR PV PMT FV 11 - 16 Use the FV = TV of inputs to find MIRR INPUTS 4 -260 0 374.8 9.6 OUTPUT MIRR = 9.6%. Since MIRR < k = 10%, reject the project.

22. 11 - 17 What’s the payback period? 0 1 2 3 4 -260 79.7 91.2 62.4 89.7 Cumulative: -260 -180.3 -89.1 -26.7 63.0 Payback = 3 + 26.7/89.7 = 3.3 years.

23. 11 - 18 If this were a replacement rather than a new project, would the analysis change? Yes. The old equipment would be sold, and the incremental CFs would be the changes from the old to the new situation.

24. 11 - 19 • The relevant depreciation would be the change with the new equipment. • Also, if the firm sold the old machine now, it would not receive the SV at the end of the machine’s life. This is an opportunity cost for the replacement project.

25. 11 - 20 Q. If E(INFL) = 5%, is NPV biased? A. YES. k = k* + IP + DRP + LP + MRP. Inflation is in denominator but not in numerator, so downward bias to NPV. Should build inflation into CF forecasts.

26. 11 - 21 Consider project with 5% inflation. Investment remains same, $260. Terminal CF remains same, $35. Operating cash flows: 1 2 3 4 Revenues $210 $220 $232 $243 Op. cost 60% -126 -132 -139 -146 Depr’n -79 -108 -36 -17 Oper. inc. (BT) 5 -20 57 80 Tax, 40% 2 -8 23 32 Oper. inc. (AT) 3 -12 34 48 Add Depr’n 79 108 36 17 Op. CF 82 96 70 65

27. NPV = $15.0 IRR = 12.6% 11 - 22 Here are all the project’s net CFs (in thousands) when inflation is considered. 0 1 2 3 4 k = 10% -260 82.1 96.1 70.0 65.0 Terminal CF 35.0 100.0 Enter CFs in CF register, and I = 10%. Project should be accepted.

28. 11 - 23 S and L are mutually exclusive and will be repeated. k = 10%. Which is better? Expected Net CFs Year Project S Project L ($100,000) 0 ($100,000) 60,000 1 33,500 60,000 2 33,500 -- 3 33,500 -- 4 33,500

29. 11 - 24 S L CF -100,000 -100,000 0 CF 60,000 33,500 1 N 2 4 j I 10 10 NPV 4,132 6,190 Q. NPVL > NPVS. Is L better? A. Can’t say. Need replacement chain analysis.

30. 11 - 25 • Note that Project S could be repeated after 2 years to generate additional profits. • Use replacement chain to calculate extended NPVS to a common life. • Since S has a 2-year life and L has a 4-year life, the common life is 4 years.

31. 11 - 26 L: 0 1 2 3 4 10% -100,000 33,500 33,500 33,500 33,500 NPVL = $6,190 (already to Year 4) S: 0 1 2 3 4 10% -100,000 60,000 60,000 60,000 60,000 -100,000 -40,000 NPVS = $7,547 (on extended basis)

32. 1 11 - 27 Equivalent Annual Annuity (EAA) That annuity PMT whose PV equals the project’s NPV. S: 2 0 10% 10% EAAS EAAS PV1 PV2 4,132 = Previously determined NPVS.

33. N I/YR PV PMT FV N I/YR PV PMT FV 11 - 28 Project S (EAA): INPUTS 2 10 -4132 0 EAAS = 2380.82 OUTPUT Project L (EAA): INPUTS 4 10 -6190 0 EAAL = 1952.76 OUTPUT The higher annuity is better.

34. 11 - 29 • The project, in effect, provides an annuity of EAA. • EAAS > EAAL , so pick S. • Replacement chains and EAA always lead to the same decision.

35. 2 3 60,000 -105,000 -45,000 11 - 30 If the cost to repeat S in two years rises to $105,000, which would be best? 4 0 1 10% -100,000 60,000 60,000 60,000 NPVS = 3,415 < NPVL = 6,190. Now choose L.

36. 11-11 The Erley Equipment Company purchased a machine 5 years ago at a cost of $100,000. The machine had an expected life of 10 years at the time of purchase, and an expected salvage value of $10,000 at the end of 10 years. It is being depreciated by the straight line method toward a salvage value of $10,000, or by $9,000 per year. A new machine can be purchased for $150,000, including installation costs. During its 5-year life, it will reduce cash operating expenses by $50,000 per year. Sales are not expected to change. At the end of its useful life, the machine is estimated to be worthless. MACRS depreciation will be used, and the machine will be depreciated over its 3-year class life rather than its 5-year economic life. (See Table 11A-2 for MACRS recovery allowance percentages.) The old machine can be sold today for $65,000. The firm’s tax rate is 35 percent. The appropriate discount rate is 16 percent. a) If the machine is purchased, what is the amount of the initial cash flow at Year 0? b) What incremental operating cash flows will occur at the end of Years 1 through 5 as a result of replacing the old machine? c) What incremental terminal cash flow will occur at the end of Year 5 if the new machine is purchased? d) What is the NPV of this project? Should Erley replace the old machine?

38. 0 1 2 3 4 5 16% (88,500) 46,675 52,975 37,225 33,025 29,350 (10,000) 19,350