1. Chapter 12 Cash Flow Estimation and Risk Analysis
Relevant Cash Flows
Incorporating Inflation
Types of Risk
Risk Analysis
Remember IRR NPV, we needed cash flows to compute them. Here we learn about these cash flow estimation
An important step in any investment to determine its return.
Take Chanel for example. When it decided to open up another store. It would start with it’s current Salhiya store sales.
There are risks: a) sale might not be at the same level. B) Cannibalize the Salhiya store. What can it do to stop that?
What we will learn here is how to estimate the cash flows and the risk of these cash flows that are used extensively in the industry

2. Review The value of any asset is Its book value.
Equal to its next year earnings.
The present value of its future expected cash flows.
Its future expected cash flows.
The sum of all future profits.

3. Review
Project Z costs $90,000, its expected net cash inflows are $50,000 per year for 5 years, and its WACC is 10%. What is the project’s NPV? $ $ $ $ $

4. Review
Project Z costs $90,000, its expected net cash inflows are $50,000 per year for 5 years, and its WACC is 10%. What is the project’s IRR?
17.63 %
41.82 %
47.63 % %
Can’t solve for IRR

5. Important Concepts Cash Flow vs. Accounting Numbers
Timing of Cash Flows
Incremental Cash Flows
Replacement projects
Sunk Costs
Opportunity Costs
Externalities
Cannibalization
Complementarity
Non-cash expenses such as depreciation. We only care about CFs cuz those are all that matter.
Deal with cash flows when they occur. It’s hard though to deal with daily CFs so we usually go with end of the year. More predictable CFs can be broken down. Why does it matter if we break it down if we can? If we are using annual instead of daily we are not getting the true NPV, is the true NPV higher or low?
Only care about the additional CFs the project will create. (e.g. increase in sales, reduction in costs)
In replacement costs are usually involved. You replace something to reduce costs. However you also sometimes replace things to increase production
What is sunk costs? We are only concerned with the future never the past. Give examples (feasibility study, bad investment decision). Sunk Cost Fallacy
Better ways to use the asset to achieve a higher return. Do you sell the land vs. using for a project with an NPV less than the land?
An externality is an affect not directly resulting from the project and not reflected in its CFs.
Cannibalization can also happen because of competing products not just stores.
Complementarity is when one investment increases the CFs of another. Apple’s iPod, iTunes, Macbooks

6. Free Cash Flow vs. Accounting Income
For capital budgeting purposes, the project’s cash flows, not its accounting income, is the key item.
𝐹𝐶𝐹=𝐸𝐵𝐼𝑇(1−𝑇)+𝐷e𝑝𝑟𝑒𝑐𝑖𝑎𝑡𝑖𝑜𝑛 − (𝐶𝑎𝑝𝑖𝑡𝑎𝑙 𝑒𝑥𝑝𝑒𝑛𝑑𝑖𝑡𝑢𝑟𝑒+∆𝑁𝑊𝐶)
∆𝑁𝑊𝐶= (∆𝐶𝑢𝑟𝑟𝑒𝑛𝑡 𝑎𝑠𝑠𝑒𝑡𝑠 − ∆𝑐𝑢𝑟𝑟𝑒𝑛𝑡 𝑙𝑖𝑎𝑏𝑖𝑙𝑖𝑡𝑖𝑒𝑠)
For simplicity we assume investment in fixed assets and net working capital (NWC) occurs in t=0.
[EBIT(1-T)+Dep.] is also known as Operating Cash Flows.

7. Salvage value
Salvage value: the price received for the sale of a fixed asset at the end of a project.
𝑇𝑎𝑥𝑒𝑠 𝑝𝑎𝑖𝑑 𝑜𝑛 𝑠𝑎𝑙𝑣𝑎𝑔𝑒𝑑 𝑎𝑠𝑠𝑒𝑡𝑠
=𝑇𝑎𝑥 𝑟𝑎𝑡𝑒× 𝑆𝑎𝑙𝑣𝑎𝑔𝑒 𝑣𝑎𝑙𝑢𝑒−𝐵𝑜𝑜𝑘 𝑣𝑎𝑙𝑢𝑒
𝐵𝑜𝑜𝑘 𝑣𝑎𝑙𝑢𝑒=𝑎𝑠𝑠𝑒𝑡 𝑖𝑛𝑡𝑖𝑎𝑙 𝑝𝑟𝑖𝑐𝑒−𝑎𝑐𝑐𝑢𝑚𝑢𝑙𝑎𝑡𝑒𝑑 𝑑𝑒𝑝𝑟𝑒𝑐𝑖𝑎𝑡𝑖𝑜𝑛

8. Replacement Projects
Incremental cash flows: cash flows that will occur if and only if some specific event occurs.
Expansion projects: where the firm makes an investment, such as a new store.
Replacement projects: where the firm replaces existing assets, generally to reduce costs.

9. Sunk costs
Sunk cost: it is an outlay that was incurred in the past and cannot be recovered in the future regardless of whether the project under consideration is accepted.
Because sunk costs were incurred in the past and cannot be recovered regardless of whether the project is accepted or rejected, they are not relevant in the capital budgeting analysis.
We are only concerned with the future never the past. Give examples (feasibility study, bad investment decision). Sunk Cost Fallacy

10. Opportunity Costs
The best return that can be earned on assets the firm already owns if those assets are not used for the new project.
If you already own a land should you include its cost in your cash flows?
Yes, and failure to do so would artificially and incorrectly increase the new project’s NPV

11. Externalities
Externalities: the effects of a project on other parts of the firm or the environment.
Cannibalization: a new project reduces cash flows that the firm would otherwise have had.
Complimentary: cash flows in the old operation will be increased when the new one is introduced.
Environmental externalities

12. Proposed Project Total depreciable cost Changes in working capital
Equipment: $200,000
Shipping and installation: $40,000
Changes in working capital
Inventories will rise by $25,000
Accounts payable will rise by $5,000
Effect on operations
New sales: 100,000 $2/unit
Variable cost: 60% of sales

13. Proposed Project Life of the project Tax rate: 40% WACC: 10%
Economic life: 4 years
Depreciable life: MACRS 3-year class
Salvage value: $25,000
Tax rate: 40%
WACC: 10%

14. Determining Project Value
Estimate relevant cash flows
Calculating annual operating cash flows.
Identifying changes in working capital.
Calculating terminal cash flows: after-tax salvage value and return of NWC. 1 2 3 4
Initial OCF OCF OCF OCF4
Costs
Terminal CFs
NCF NCF NCF NCF NCF4

15. Initial Year Net Cash Flow
Find NWC.
 in inventories of $25,000
Funded partly by an  in A/P of $5,000
NWC = $25,000 – $5,000 = $20,000
Combine NWC with initial costs.
Equipment $200,000
Installation ,000
NWC ,000
Net CF0 -$260,000

16. Determining Annual Depreciation Expense
Year Rate x Basis Deprec x $240 $ x x x $240 Due to the MACRS ½-year convention, a 3-year asset is depreciated over 4 years.

17. Annual Operating Cash Flows
(Thousands of dollars) 1 2 3 4
Revenues
200.0
– Op. costs
120.0
– Deprec. expense
79.2
108.0
36.0
16.8
Operating income (EBIT)
0.8
-28.0
44.0
63.2
– Tax (40%)
0.3
-11.2
17.6
25.3
Operating income (after tax)
0.5
-16.8
26.4
37.9
+ Deprec. expense
Operating CF
79.7
91.2
62.4
54.7

18. Terminal Cash Flow
Q. How is NWC recovered? Q. Is there always a tax on SV? Q. Is the tax on SV ever a positive cash flow?

19. 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.

20. 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 future cash flows.

21. 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)
= $25,000(0.6)
= $15,000

22. 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).

23. Proposed Project’s Cash Flow Time Line
-260 1 2 3 4
79.7
91.2
62.4
89.7
Enter CFs into calculator CFLO register, and enter I/YR = 10%.
NPV = -$4.03 million
IRR = 9.3%
MIRR = 9.6%
Payback = 3.3 years

24. 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.

25. Problem 12-1

26. Problem 12-2

27. Problem 12-8

28. Problem 12-20

29. What are the 3 types of project risk?
Stand-alone risk
Corporate risk
Market risk

30. 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.

31. 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 firm projects.
It is measured as the impact on the uncertainty of the firm’s stock returns. It still assumes the investor has just one stock.

32. 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.
Market risk: the risk of the project when the investor and the firm are well diversified. It is measured as the effect of the firm’s beta

33. 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 corporate risk affects creditors, customers, suppliers, and employees, it should not be completely ignored.
Does taking higher stand-along or corporate risk mean the firm will become riskier? Depends on the correlation with other projects
Market risk is the most important and the most difficult to estimate

34. 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.

35. 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.

36. Assessing Stand-alone Risk
Three techniques are used to assess stand-alone risk:
Sensitivity analysis
Scenario analysis
Monte Carlo simulation

37. 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.
When we evaluate projects we are making assumptions. Actual values might be different. So we need to see how the project’s value would change if these inputs/assumptions change.
Doing this is basically trying to figure out the project’s stand-alone risk. How is that so? Because risk is about uncertainty and we are trying to figure out how changes would affect value
Sensitivity analysis is one of those techniques. Very widely used
Give an example (e.g. change unit price, change sales)

38. 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.
Disadvantages
Does not reflect the effects of diversification.
Does not incorporate any information about the possible magnitudes of the forecast errors.

39. Slope tells u how sensitive NPV is to changes to the input
Slope tells u how sensitive NPV is to changes to the input. A higher slope means a bigger range which means more sensitive.
Projects with steeper lines are more risky

40. 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 NPV.
Inflation should be built into CF forecasts.

41. Annual Operating Cash Flows, If Expected Inflation = 5%

42. Considering Inflation: Project CFs, NPV, and IRR
Terminal CF =
-260
82.1
96.1
70.0
65.1
35.0
100.1
Enter CFs into calculator CFLO register, and enter I/YR = 10%.
NPV = $15.0 million.
IRR = 12.6%.

43. Scenario Analysis
In sensitivity analysis, we change one variable at a time..
Scenario Analysis allows us to change more than one variable at a time.
We begin with the base-case scenario, which uses the most likely set of input values.
We then specify worst-case scenario (low unit sales, low sales price, high variable costs, and so forth) and a best- case scenario.
We also incorporate the probability of having each scenario.

44. 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:
In Senstivity analysis you change one variable. But sometimes several inputs change not just one. To see how the project performs when several things change we do scenario analysis.
Explain the different cases.
Notice The probability weighting is usually this way but you can change it.

45. Scenario Analysis
All other factors shall remain constant and the NPV under each scenario can be determined.

46. Determining Expected NPV, NPV, and CVNPV from the Scenario Analysis
𝜎 𝑁𝑃𝑉 = 𝑃𝑟𝑜𝑏. 𝑠𝑡𝑎𝑡𝑒 1 × 𝑁𝑃 𝑉 𝑠𝑡𝑎𝑡𝑒 1 −𝐸 𝑁𝑃𝑉 𝑃𝑟𝑜𝑏. 𝑠𝑡𝑎𝑡𝑒 2 × 𝑁𝑃 𝑉 𝑠𝑡𝑎𝑡𝑒 2 −𝐸 𝑁𝑃𝑉 2 +…
Third technique is Monte Carlo Simulation
𝐶 𝑉 𝑁𝑃𝑉 = 𝜎 𝑁𝑃𝑉 𝐸 𝑁𝑃𝑉

47. Perhaps, some sort of risk correction is required for proper analysis.
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.

48. 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 correlation is not perfectly positive (i.e., ρ  1), we would expect it to contribute to the lowering of the firm’s overall risk.
All of this focuses on stand-alone risk. What about the others?
It’s hard to estimate correlations. However judgment can be made by manager as to what they expect
Again it’s hard to estimate the other risks. But because of high correlation among the three risks it’s safe to use stand-alone only

49. 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.

50. 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.
If, however, it were a low-risk project, we would use a 7% cost of capital and the project NPV is $34.1.

51. Monte Carlo simulation
It is a sophisticated version of scenario analysis.
The computer randomly picks a value for each variable.
Those values are then used to calculate an NPV, and that NPV is stored in the computer’s memory.
A second set of input values is selected at random and a second NPV is calculated.
This process is repeated perhaps 1,000 times, generating 1,000 NPVs. The mean of the 1,000 NPVs is determined and used as a measure of the project’s expected profitability, and the standard deviation (or perhaps the coefficient of variation) ofthe NPVs is used as a measure of risk.

52. 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 than otherwise thought.

53. Problem 12-18

54. Evaluating Projects with Unequal Lives
Machines A and B are mutually exclusive, and will be repurchased. If WACC = 10%, which is better?
Expected Net CFs
Year
Machine A
Machine B
($50,000) 1
17,500
34,000 2
27,500 3 – 4
Sometimes firms have to choose among projects that are (a) mutually exclusive (b) unequal lives and (c) can be repeated. NPV is not the proper measure of project value.
Example two types of machines with different lives

55. Solving for NPV with No Repetition
Enter CFs into calculator CFLO register for both projects, and enter I/YR = 10%.
NPVA = $5,472.65
NPVB = $3,636.36
Is Machine A better?
Need replacement chain and/or equivalent annual annuity analysis.

56. Unequal Project Lives have significantly different lives
If a company is choosing between two projects and those projects:
have significantly different lives
are mutually exclusive, and
can be repeated,
The “regular” NPV method may not work!

57. How to Deal with Unequal Project Lives?
Replacement Chain (common life) approach.
A method of comparing projects with unequal lives that assumes that each project can be repeated as many times as necessary to reach a common life. The NPVs over this life are then compared, and the project with the higher common-life NPV is chosen.
Equivalent Annual Annuities (EAA) approach.
A method that calculates the annual payments that a project will provide if it is an annuity. When comparing projects with unequal lives, the one with the higher equivalent annual annuity (EAA) should be chosen.

58. Review
The regular NPV analysis might not be appropriate for which of the following projects?
Two independent projects with unequal lives that will be repeated.
Two mutually exclusive projects with unequal lives that will not be repeated.
Two mutually exclusive projects with unequal lives that will be repeated.
Two independent projects with unequal lives that will be not be repeated.
None of the above

59. Replacement Chain
Use the replacement chain to calculate an extended NPVB to a common life.
Since Machine B has a 2-year life and Machine A has a 4-year life, the common life is 4 years.

60. Replacement Chain NPVB = $6,641.62 (on extended basis)
-50,000 34,000 27,500 34,000 27,500
-50,000
-22,500 1 2 3
10% 4
NPVB = $6, (on extended basis)
NPVA = $5,472.65
Choose B

61. Equivalent Annual Annuity
Using the NPVs over each project’s stated life (not extended life), the EAA is the annual payment that the project would provide if it were an annuity.
Machine A
Enter N = 4, I/YR = 10, PV = , FV = 0; solve for PMT = EAA = $1,
Machine B
Enter N = 2, I/YR = 10, PV = , FV = 0; solve for PMT = EAA = $2,
Machine B is better!
Both methods give similar results.
EAA is easier to do
Replacement chain allows you to change CF estimates when the equipment is replaced

62. Conclusions about Unequal Lives
Replacement chain and EAA methods always result in the same decision.
EAA is a bit easier to implement
Replacement chain method is often easier to explain to senior managers.
As a general rule, the unequal life issue never arises for independent projects or mutually exclusive projects that will not be repeated.
It can be an issue when we compare mutually exclusive projects that will be repeated at the end of their initial lives.

63. Problem 12-14

64. So what did we talk about?