CHAPTER 12
Cash Flow Estimation and Risk Analysis Relevant cash flows Incorporating inflation Types of risk
FIN 1439 – SUMMER 2003
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.
FIN 1439 – SUMMER 2003
Sales: 100,000 units/year @ $2. Variable cost = 60% of sales. Tax rate = 40%. WACC = 10%.
FIN 1439 – SUMMER 2003
Set up, without numbers, a time line for the project’s cash flows.
0 Initial Costs (CF0) 1 OCF1 2 OCF2 3 OCF3 4 OCF4 + Terminal CF NCF1 NCF2
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NCF0
NCF3
NCF4
Investment at t = 0: Equipment -$200
Installation & Shipping
Increase in inventories Increase in A/P Net CF0
-40
-25 5 -$260
DNOWC = $25 – $5 = $20.
FIN 1439 – SUMMER 2003
What’s the annual depreciation?
Year Rate x Basis Depreciation
1 2 3 4
0.33 0.45 0.15 0.07 1.00
$240 240 240 240
$ 79 108 36 17 $240
Due to 1/2-year convention, a 3-year asset is depreciated over 4 years.
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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
FIN 1439 – SUMMER 2003
Net Terminal CF at t = 4: Recovery of NOWC Salvage Value Tax on SV (40%) Net termination CF $20 25 -10 $35
Q. Q.
Always a tax on SV? Ever a positive tax number? How is NOWC recovered?
FIN 1439 – SUMMER 2003
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.
FIN 1439 – SUMMER 2003
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.
FIN 1439 – SUMMER 2003
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.
FIN 1439 – SUMMER 2003
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.
FIN 1439 – SUMMER 2003
Here are all the project’s net CFs (in thousands) on a time line:
0
k = 10%
1
2
3
4 54.7 35.0 89.7
-260
79.7
91.2 62.4 Terminal CF
Enter CFs in CF register, and I = 10%.
NPV = -$4.03 IRR = 9.3%
FIN 1439 – SUMMER 2003
What’s the project’s MIRR?
0 -260 1 79.7 2 91.2
10% 10% MIRR = ?
3 62.4
10%
4 89.7 68.6 110.4 106.1 374.8
-260
Can we solve using a calculator?
FIN 1439 – SUMMER 2003
Yes.
CF0 CF1 CF2 CF3 CF4 I
= = = = = =
0 79.7 91.2 62.4 89.7 10
NPV = 255.97
INPUTS
OUTPUT 4
N
10
I/YR
-255.97
PV
0
PMT FV
TV = FV = 374.8
FIN 1439 – SUMMER 2003
Use the FV = TV of inputs to find MIRR
INPUTS OUTPUT
4
N I/YR
-260
PV
0
PMT
374.8
FV
9.6
MIRR = 9.6%. Since MIRR < k = 10%, reject the project.
FIN 1439 – SUMMER 2003
What’s the payback period?
0 -260 1 79.7 2 91.2 3 62.4 4 89.7
Cumulative:
-260 -180.3 -89.1 -26.7 63.0 Payback = 3 + 26.7/89.7 = 3.3 years.
FIN 1439 – SUMMER 2003
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.
FIN 1439 – SUMMER 2003
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.
FIN 1439 – SUMMER 2003
Q. If E(INFL) = 5%, is NPV biased?
CFt Re v t Cost t A. YES. NPV . t t 1 k 1 t 0 k
n
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.
FIN 1439 – SUMMER 2003
Consider project with 5% inflation. Investment remains same, $260. Terminal CF remains same, $35. Operating cash flows:
1 Revenues $210 Op. cost 60% -126 Depr’n -79 Oper. inc. (BT) 5 Tax, 40% 2 Oper. inc. (AT) 3 Add Depr’n 79 Op. CF 82 2 $220 -132 -108 -20 -8 -12 108 96 3 $232 -139 -36 57 23 34 36 70 4 $243 -146 -17 80 32 48 17 65
FIN 1439 – SUMMER 2003
Here are all the project’s net CFs (in thousands) when inflation is considered.
0 1 2 3 4 65.0 35.0 100.0
k = 10%
-260
82.1
96.1 70.0 Terminal CF
Enter CFs in CF register, and I = 10%.
NPV = $15.0 Project should be accepted. IRR = 12.6%
FIN 1439 – SUMMER 2003
What are the three types of project risk that are normally considered? Stand-alone risk Corporate risk
Market risk
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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.
FIN 1439 – SUMMER 2003
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.
FIN 1439 – SUMMER 2003
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.
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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.
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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.
FIN 1439 – SUMMER 2003
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.
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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.
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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.
FIN 1439 – SUMMER 2003
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 Worst Base Best Probability 0.25 0.50 0.25
FIN 1439 – SUMMER 2003
Unit sales 75,000 100,000 125,000
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 Worst Base Best
Probability 0.25 0.50 0.25
NPV ($27.8) $15.0 $57.8
FIN 1439 – SUMMER 2003
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.
FIN 1439 – SUMMER 2003
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.
FIN 1439 – SUMMER 2003
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.
FIN 1439 – SUMMER 2003
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.
FIN 1439 – SUMMER 2003
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 standalone risk), the NPV of the project is -$2.2 .
FIN 1439 – SUMMER 2003
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.
FIN 1439 – SUMMER 2003