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CHAPTER 12Cash Flow Estimation and

Risk Analysis

Relevant cash flowsIncorporating inflationTypes of risk

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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.

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Sales: 100,000 units/year @ $2.

Variable cost = 60% of sales.

Tax rate = 40%.

WACC = 10%.

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Set up, without numbers, a time line for the project’s cash flows.

0 1 2 3 4

OCF1 OCF2 OCF3 OCF4InitialCosts(CF0)

+Terminal CF

NCF0 NCF1 NCF2 NCF3 NCF4

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Equipment -$200

Installation & Shipping -40

Increase in inventories -25

Increase in A/P 5

Net CF0 -$260

NOWC = $25 – $5 = $20.

Investment at t = 0:

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What’s the annual depreciation?

Due to 1/2-year convention, a 3-year asset is depreciated over 4 years.

Year Rate x Basis Depreciation

1 0.33 $240 $ 792 0.45 240 1083 0.15 240 364 0.07 240 17

1.00 $240

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Operating cash flows:

1 2 3 4Revenues $200 $200 $200 $200Op. Cost, 60% -120 -120 -120 -120Depreciation -79 -108 -36 -17Oper. inc. (BT) 1 -28 44 63Tax, 40% -- -11 18 25

1 -17 26 38 Add. Depr’n 79 108 36 17 Op. CF 80 91 62 55

Oper. inc. (AT)

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Net Terminal CF at t = 4:

Salvage Value 25Tax 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?

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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.

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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.

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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.

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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.

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

Enter CFs in CF register, and I = 10%.

NPV = -$4.03IRR = 9.3%

k = 10%0

79.7

1

91.2

2

62.4

3

54.7

4

-260Terminal CF 35.0

89.7

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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

68.6110.4

10%10%

106.1

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4 10 -255.97 0

TV = FV = 374.8

Yes. CF0 = 0CF1 = 79.7CF2 = 91.2CF3 = 62.4CF4 = 89.7 I = 10NPV = 255.97

INPUTS

OUTPUTN I/YR PV PMT FV

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Use the FV = TV of inputs to find MIRR

4 -260 0 374.8

9.6

MIRR = 9.6%. Since MIRR < k = 10%, reject the project.

INPUTS

OUTPUTN I/YR PV PMT FV

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What’s the payback period?

0

79.7

1

91.2

2

62.4

3

89.7

4

-260

Cumulative:-26.7-260 -89.1-180.3 63.0

Payback = 3 + 26.7/89.7 = 3.3 years.

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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.

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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.

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.k1

CostvRe

k1

CFNPV t

ttt

tn

0t

Q. If E(INFL) = 5%, is NPV biased?

A. YES.

k = k* + IP + DRP + LP + MRP.

Inflation is in denominator but not innumerator, so downward bias to NPV.

Should build inflation into CF forecasts.

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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 $243Op. cost 60% -126 -132 -139 -146Depr’n -79 -108 -36 -17Oper. inc. (BT) 5 -20 57 80Tax, 40% 2 -8 23 32Oper. inc. (AT) 3 -12 34 48Add Depr’n 79 108 36 17Op. CF 82 96 70 65

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Here are all the project’s net CFs (in thousands) when inflation is considered.

Enter CFs in CF register, and I = 10%.

NPV = $15.0IRR = 12.6%

k = 10%0

82.1

1

96.1

2

70.0

3

65.0

4

-260Terminal CF 35.0

100.0

Project should be accepted.

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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.

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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.

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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.

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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.

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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:

Case Probability Unit sales

Base 0.50 100,000Worst 0.25 75,000

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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

Case Probability NPV

Base 0.50 $15.0Worst 0.25 ($27.8)

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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 CVNPV.

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.

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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.

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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.

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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?

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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?

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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?