CHAPTER 12 Cash Flow Estimation and Risk Analysis
Relevant cash flows
Types of risk
Total depreciable cost Equipment: $200,000
Changes in working capital Inventories will rise by $25,000
Accounts payable will rise by $5,000
Effect on operations New sales: 100,000 units/year @ $2/unit
Variable cost: 60% of sales
Life of the project
Economic life: 4 years
Depreciable life: MACRS 3-year class
Salvage value: $25,000
Tax rate: 40%
Determining project value Estimate relevant cash flows
Calculating annual operating cash flows. Identifying changes in working capital. Calculating terminal cash flows.
0 1 2 3 4
Initial OCF1 OCF2 OCF3 OCF4 Costs + Terminal
NCF0 NCF1 NCF2 NCF3 NCF4
Initial year net cash flow
Find Δ NOWC. ⇧ in inventories of $25,000
Funded partly by an ⇧ in A/P of $5,000 Δ NOWC = $25,000 - $5,000 = $20,000
Combine Δ NOWC with initial costs. Equipment -$200,000 Installation -40,000 Δ NOWC -20,000 Net CF0 -$260,000
Determining annual depreciation expense
Year Rate x Basis Depr 1 0.33 x $240 $ 79 2 0.45 x 240 108 3 0.15 x 240 36 4 0.07 x 240 17 1.00 $240 Due to the MACRS ½-year convention, a 3-year asset is depreciated over 4 years.
Annual operating cash flows
1 2 3 4
Revenues $200.0 $200.0 $200.0 $200.0
- Op Costs -120.0 -120.0 -120.0 -120.0
- Depr’n Expense -79.2 -108.0 -36.0 -16.8
Operating Income (BT) 0.8 -28.0 44.0 63.2
- Tax (40%) 0.3 -11.2 17.6 25.3
Operating Income (AT) 0.5 -16.8 26.4 37.9
+ Depr’n Expense 79.2 108.0 36.0 16.8
Operating CF $79.7 $91.2 $62.4 $54.7
(Thousands of dollars)
Terminal net cash flow
Recovery of NOWC $20,000 Salvage value 25,000 Tax on SV (40%) -10,000 Terminal CF $35,000 Q. How is NOWC recovered? Q. Is there always a tax on SV? Q. Is the tax on SV ever a positive cash flow?
Should financing effects be included in cash flows?
No, dividends and interest expense should not be included in the analysis.
Financing effects have already been taken into account by discounting cash flows at the WACC of 10%.
Deducting interest expense and dividends would be “double counting” financing costs.
Should a $50,000 improvement cost from the previous year be included in the analysis?
No, the building improvement cost is a sunk cost and should not be considered.
This analysis should only include incremental investment.
If the facility could be leased out for $25,000 per year, would this affect the analysis?
Yes, by accepting the project, the firm foregoes a possible annual cash flow of $25,000, which is an opportunity cost to be charged to the project.
The relevant cash flow is the annual after- tax opportunity cost.
A-T opportunity cost = $25,000 (1 – T)
If the new product line decreases the 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 (in the case of complements) or negative (substitutes).
Proposed project’s cash flow time line
0 1 2 3 4
-260 79.7 91.2 62.4 54.7
Terminal CF → 35.0
89.7 Enter CFs into calculator CFj Key and
enter I/YR = 10%. NPV = -$4.03 million IRR = 9.3% MIRR = 9.6% Payback = 3.3 years
-260 79.7 91.2 62.4 89.7
0 1 2 3 4
Evaluating the project: Payback period
Payback = 3 + 26.7 / 89.7 = 3.3 years.
Cumulative: -260 -180.3 -89.1 -26.7 63.0
If this were a replacement rather than a new project, would the analysis change?
Yes, the old equipment would be sold, and new equipment purchased.
The incremental CFs would be the changes from the old to the new situation.
The relevant depreciation expense would be the change with the new equipment.
If the old machine was sold, the firm would not receive the SV at the end of the machine’s life. This is the opportunity cost for the replacement project.
What are the 3 types of project risk?
What is stand-alone risk?
The project’s total risk, if it were operated independently.
Usually measured by standard deviation (or coefficient of variation).
However, it ignores the firm’s diversification among projects and investor’s diversification among firms.
What is corporate risk?
The project’s risk when considering 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.
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.
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.
Which risk is the easiest to measure?
Stand-alone risk is the easiest to measure. Firms often focus on stand- alone risk when making capital budgeting decisions.
Focusing on stand-alone risk is not theoretically correct, but it does not necessarily lead to poor decisions.
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.
In addition, corporate risk is likely to be highly correlated with its market risk.
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.
Resulting changes in NPV are noted.
What are the advantages and disadvantages of sensitivity analysis?
Identifies variables that may have the greatest potential impact on profitability and allows management to focus on these variables.
Does not reflect the effects of diversification.
Does not incorporate any information about the possible magnitudes of the forecast errors.
What if there is expected inflation of 5%, is NPV biased?
Yes, inflation causes the discount rate to be upwardly revised.
Therefore, inflation creates a downward bias on PV.
Inflation should be built into CF forecasts.
Annual operating cash flows if expected inflation = 5%; Adjust Revenues and Op. Costs by 5% annually
1 2 3 4 Revenues 210 220 232 243 Op. Costs (60%) -126 -132 -139 -146 - Deprn Expense -79 -108 -36 -17 - Oper. Income (BT) 5 -20 57 80 - Tax (40%) 2 -8 23 32 Oper. Income (AT) 3 -12 34 48 + Deprn Expense 79 108 36 17 Operating CF 82 96 70 65
Considering inflation: Project net CFs, NPV, and IRR
0 1 2 3 4
-260 82.1 96.1 70.0 65.1
Terminal CF → 35.0
Enter CFs into calculator CFLO register, and enter I/YR = 10%. NPV = $15.02 million.
IRR = 12.6%.
Perform a scenario analysis of the project, based on changes in the sales forecast
Suppose we are confident of all the variable estimates, except unit sales. The actual unit sales are expected to follow the following probability distribution:
Case Probability Unit Sales
Worst 0.25 75,000
Base 0.50 100,000
Best 0.25 125,000
All other factors shall remain constant and the NPV under each scenario can be determined.
Case Probability NPV
Worst 0.25 ($27.8)
Base 0.50 $15.0
Best 0.25 $57.8
Determining expected NPV, NPV, and CVNPV from the scenario analysis
E(NPV) = 0.25(-$27.8)+0.5($15.0)+0.25($57.8)
NPV = [0.25(-$27.8-$15.0) 2 + 0.5($15.0-
$15.0)2 + 0.25($57.8-$15.0)2]1/2
CVNPV = $30.3 /$15.0 = 2.0.
If the firm’s average projects have CVNPV ranging from 1.25 to 1.75, would this project be of high, average, or low risk?
With a CVNPV of 2.0, this project would be classified as a high-risk project.
Perhaps, some sort of risk correction is required for proper analysis.
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 correlation is not perfectly positive (i.e., ρ 1), we would expect it to contribute to the lowering of the firm’s total risk.
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.
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 -$2.18 (using inflation adjusted CFs).
If, however, it were a low-risk project, we would use a 7% cost of capital and the project NPV is $34.17.
What subjective risk factors should be considered before a decision is made?
Numerical analysis sometimes fails to capture all sources of risk for a project.
If the project has the potential for a lawsuit, it is more risky than previously thought.
If assets can be redeployed or sold easily, the project may be less risky.
What is real option analysis?
Real options exist when managers can influence the size and riskiness of a project’s cash flows by taking different actions during the project’s life.
Real option analysis incorporates typical NPV budgeting analysis with an analysis for opportunities resulting from managers’ decisions.
What are some examples of real options?
Investment timing options – as to when to begin a project, now or later
Abandonment/early shutdown options if project is not profitable, e.g. New Coke
Growth/expansion options, if first project is profitable, e.g. Starbucks in India
Flexibility options, to modify operations, e.g. BMW plant in S.C. for both coupes and SUVs