1. CHAPTER 12 Cash Flow Estimation and Risk Analysis
Relevant cash flows
Incorporating inflation
Types of risk

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 $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.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
DNOWC = $25 – $5 = $20.

6. 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.

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
Oper. inc. (AT) 1
-17 26 38
Add. Depr’n 79
108 36 17
Op. CF 80 91 62 55

8. Net Terminal CF at t = 4:
Recovery of NOWC
$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 NOWC recovered?

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.

10. Suppose $50,000 had been spent last year to improve the building
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.

11. Suppose the plant could be leased out for $25,000 a year
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.

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.

13. Here are all the project’s net CFs (in thousands) on a time line: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%

14. What’s the project’s MIRR?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?

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

16. Use the FV = TV of inputs to find MIRR
9.6 N
I/YR PV
PMT FV
OUTPUT
MIRR = 9.6%. Since MIRR < k = 10%, reject the project.

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

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.

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.

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.

21. Consider project with 5% inflation. Investment remains same, $260
Consider project with 5% inflation. Investment remains same, $260. Terminal CF remains same, $35.
Operating cash flows:
Revenues $210 $220 $232 $243
Op. cost 60%
Depr’n
Oper. inc. (BT)
Tax, 40%
Oper. inc. (AT)
Add Depr’n
Op. CF

22. Enter CFs in CF register, and I = 10%.
Here are all the project’s net CFs (in thousands) when inflation is considered. 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%.
NPV = $15.0
IRR = 12.6%
Project should be accepted.

23. What are the three types of project risk that are normally considered?
Stand-alone risk
Corporate risk
Market risk

24. 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.

25. 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.

26. 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.

27. 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.

28. 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.

29. 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.

30. What are the primary advantages and disadvantages of sensitivity analysis?
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.

31. 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.

32. 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:
Case Probability Unit sales
Worst ,000
Base ,000
Best ,000

33. If cash costs are to remain 60% of revenues, and all other factors are constant, we can solve for project NPV under each scenario.
Case Probability NPV
Worst ($27.8)
Base $15.0
Best $57.8

34. Use these scenarios, with their given probabilities, to find the project’s expected NPV, NPV, and CVNPV.
E(NPV)=.25(-$27.8)+.5($15.0)+.25($57.8)
E(NPV)= $15.0.
NPV = [.25(-$27.8-$15.0)2 + .5($15.0-$15.0)2
+ .25($57.8-$15.0)2]1/2
NPV = $30.3.
CVNPV = $30.3 /$15.0 = 2.0.

35. The firm’s average projects have coefficients of variation ranging from 1.25 to 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.

36. Is this project likely to be correlated with the firm’s business
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.

37. If the project had a high correlation with the economy, how would corporate and market risk be affected?
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.

38. If the firm uses a +/-3% risk adjustment for the cost of capital, should the project be accepted?
Reevaluating this project at a 13% cost of capital (due to high stand-alone risk), the NPV of the project is -$2.2 .

39. What is Monte Carlo simulation?
A risk analysis technique in which probable future events are simulated on a computer, generating estimated rates of return and risk indexes.