1. 12 - 1 Copyright © 2001 by Harcourt, Inc.All rights reserved. CHAPTER 12 Cash Flow Estimation and Risk Analysis Relevant cash flows Incorporating inflation Types of risk

2. 12 - 2 Copyright © 2001 by Harcourt, Inc.All rights reserved. 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. Sales: 100,000 units/year @ $2. Variable cost = 60% of sales. Tax rate = 40%. WACC = 10%.

3. 12 - 3 Copyright © 2001 by Harcourt, Inc.All rights reserved. Set up, without numbers, a time line for the project’s cash flows. 01234 OCF 1 OCF 2 OCF 3 OCF 4 Initial Costs (CF 0 ) + Terminal CF NCF 0 NCF 1 NCF 2 NCF 3 NCF 4

4. 12 - 4 Copyright © 2001 by Harcourt, Inc.All rights reserved. Equipment-$200 Installation & Shipping-40 Increase in inventories-25 Increase in A/P5 Net CF 0 -$260  NOWC = $25 – $5 = $20. Investment at t = 0:

5. 12 - 5 Copyright © 2001 by Harcourt, Inc.All rights reserved. What’s the annual depreciation? Due to 1/2-year convention, a 3-year asset is depreciated over 4 years. YearRatexBasisDepreciation 10.33$240$ 79 20.45240108 30.1524036 40.07240 17 1.00$240

6. 12 - 6 Copyright © 2001 by Harcourt, Inc.All rights reserved. Operating cash flows: 1234 Revenues$200 Op. Cost, 60%-120 Depreciation-79-108-36-17 Oper. inc. (BT)1-284463 Tax, 40%---111825 1-172638 Add. Depr’n791083617 Op. CF80916255 Oper. inc. (AT)

7. 12 - 7 Copyright © 2001 by Harcourt, Inc.All rights reserved. Net Terminal CF at t = 4: Salvage Value 25 Tax on SV (40%)-10 Recovery of NOWC$20 Net termination CF$35 Q.Always a tax on SV? Ever a positive tax number? Q.How is NOWC recovered?

8. 12 - 8 Copyright © 2001 by Harcourt, Inc.All rights reserved. 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.

9. 12 - 9 Copyright © 2001 by Harcourt, Inc.All rights reserved. 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.

10. 12 - 10 Copyright © 2001 by Harcourt, Inc.All rights reserved. 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.

11. 12 - 11 Copyright © 2001 by Harcourt, Inc.All rights reserved. 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.

12. 12 - 12 Copyright © 2001 by Harcourt, Inc.All rights reserved. Here are all the project’s net CFs (in thousands) on a time line: Enter CFs in CF register, and I = 10%. NPV = -$4.03 IRR = 9.3% k = 10% 0 79.7 1 91.2 2 62.4 3 54.7 4 -260 Terminal CF35.0 89.7

13. 12 - 13 Copyright © 2001 by Harcourt, Inc.All rights reserved. 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.

14. 12 - 14 Copyright © 2001 by Harcourt, Inc.All rights reserved. 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)5-205780 Tax, 40% 2 -8 23 32 Oper. inc. (AT)3-123448 Add Depr’n 79 108 36 17 Op. CF 82 96 70 65

15. 12 - 15 Copyright © 2001 by Harcourt, Inc.All rights reserved. Here are all the project’s net CFs (in thousands) when inflation is considered. Enter CFs in CF register, and I = 10%. NPV = $14.95 IRR = 12.59% k = 10% 0 82.1 1 96.1 2 70.0 3 65.0 4 -260 Terminal CF 35.0 100.0 Project should be accepted.

16. 12 - 16 Copyright © 2001 by Harcourt, Inc.All rights reserved. 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.

17. 12 - 17 Copyright © 2001 by Harcourt, Inc.All rights reserved. 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.

18. 12 - 18 Copyright © 2001 by Harcourt, Inc.All rights reserved. What’s the payback period? 0 79.7 1 91.2 2 62.4 3 89.7 4 -260 Cumulative: -26.7-260-89.1-180.363.0 Payback = 3 + 26.7/89.7 = 3.3 years.

19. 12 - 19 Copyright © 2001 by Harcourt, Inc.All rights reserved. MIRR = ? 10% What’s the project’s MIRR? Can we solve using a calculator? 0 79.7 1 91.2 2 62.4 3 89.7 4 -260 374.8 -260 68.6 110.4 10% 106.1

20. 12 - 20 Copyright © 2001 by Harcourt, Inc.All rights reserved. What are the three types of project risk that are normally considered? Stand-alone risk Corporate risk Market risk

21. 12 - 21 Copyright © 2001 by Harcourt, Inc.All rights reserved. What is stand-alone risk? The project’s total risk if it were operated independently. Usually measured by standard deviation (or coefficient of variation). Though it ignores the firm’s diversification among projects and investor’s diversification among firms.

22. 12 - 22 Copyright © 2001 by Harcourt, Inc.All rights reserved. What is corporate risk? The project’s risk giving consideration to the firm’s other projects, i.e., diversification within the firm. Corporate risk is a function of the project’s NPV and standard deviation and its correlation with the returns on other projects in the firm.

23. 12 - 23 Copyright © 2001 by Harcourt, Inc.All rights reserved. What is market risk? The project’s risk to a well-diversified investor. Theoretically, it is measured by the project’s beta and it considers both corporate and stockholder diversification.

24. 12 - 24 Copyright © 2001 by Harcourt, Inc.All rights reserved. Which type of risk is most relevant? Market risk is the most relevant risk for capital projects, because management’s primary goal is shareholder wealth maximization. However, since total risk affects creditors, customers, suppliers, and employees, it should not be completely ignored.

25. 12 - 25 Copyright © 2001 by Harcourt, Inc.All rights reserved. Are the three types of risk generally highly correlated? Yes. Since most projects the firm undertakes are in its core business, stand-alone risk is likely to be highly correlated with its corporate risk, which in turn is likely to be highly correlated with its market risk.

26. 12 - 26 Copyright © 2001 by Harcourt, Inc.All rights reserved. What is sensitivity analysis? Sensitivity analysis measures the effect of changes in a variable on the project’s NPV. To perform a sensitivity analysis, all variables are fixed at their expected values, except for the variable in question which is allowed to fluctuate. The resulting changes in NPV are noted.

27. 12 - 27 Copyright © 2001 by Harcourt, Inc.All rights reserved. What are the primary advantages and disadvantages of sensitivity analysis? ADVANTAGE: Sensitivity analysis identifies variables that may have the greatest potential impact on profitability. This allows management to focus on those variables that are most important.

28. 12 - 28 Copyright © 2001 by Harcourt, Inc.All rights reserved. DISADVANTAGES: Sensitivity analysis does not reflect the effects of diversification. Sensitivity analysis does not incorporate any information about the possible magnitudes of the forecast errors.

29. 12 - 29 Copyright © 2001 by Harcourt, Inc.All rights reserved. Best 0.25 125,000 Perform a scenario analysis of the project, based on changes in the sales forecast. Assume that we are confident of all the variables that affect the cash flows, except unit sales. We expect unit sales to adhere to the following profile: CaseProbabilityUnit sales Base 0.50 100,000 Worst 0.25 75,000

30. 12 - 30 Copyright © 2001 by Harcourt, Inc.All rights reserved. If cash costs are to remain 60% of revenues, and all other factors are constant, we can solve for project NPV under each scenario. Best 0.25 $57.8 CaseProbability NPV Base 0.50 $15.0 Worst 0.25 ($27.8)

31. 12 - 31 Copyright © 2001 by Harcourt, Inc.All rights reserved. E(NPV)=.25(-$27.8)+.5($15.0)+.25($57.8) E(NPV)= $15.0. Use these scenarios, with their given probabilities, to find the project’s expected NPV,  NPV, and CV NPV.  NPV = [.25(-$27.8-$15.0) 2 +.5($15.0-$15.0) 2 +.25($57.8-$15.0) 2 ] 1/2  NPV = $30.3. CV NPV = $30.3 /$15.0 = 2.0.

32. 12 - 32 Copyright © 2001 by Harcourt, Inc.All rights reserved. The firm’s average projects have coefficients of variation ranging from 1.25 to 1.75. Would this project be of high, average, or low risk? The project’s CV of 2.0 would suggest that it would be classified as high risk.

33. 12 - 33 Copyright © 2001 by Harcourt, Inc.All rights reserved. Is this project likely to be correlated with the firm’s business? How would it contribute to the firm’s overall risk? We would expect a positive correlation with the firm’s aggregate cash flows. As long as this correlation is not perfectly positive (i.e., r  1), we would expect it to contribute to the lowering of the firm’s total risk.

34. 12 - 34 Copyright © 2001 by Harcourt, Inc.All rights reserved. The project’s corporate risk would not be directly affected. However, when combined with the project’s high stand-alone risk, correlation with the economy would suggest that market risk (beta) is high. If the project had a high correlation with the economy, how would corporate and market risk be affected?

35. 12 - 35 Copyright © 2001 by Harcourt, Inc.All rights reserved. Reevaluating this project at a 13% cost of capital (due to high stand- alone risk), the NPV of the project is -$2.2. If the firm uses a +/-3% risk adjustment for the cost of capital, should the project be accepted?

36. 12 - 36 Copyright © 2001 by Harcourt, Inc.All rights reserved. A risk analysis technique in which probable future events are simulated on a computer, generating estimated rates of return and risk indexes. What is Monte Carlo simulation?