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CHAPTER 11 Cash Flow Estimation And Chapter 12 Risk. Need to be in class for this ch. Relevant Cash Flows New Investment Replacement Investment Measuring Risk Market Risk (Beta) Project Risk Considerations. Capital Budgeting Processes.

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chapter 11 cash flow estimation and chapter 12 risk
CHAPTER 11 Cash Flow EstimationAnd Chapter 12 Risk
  • Need to be in class for this ch.
  • Relevant Cash Flows
  • New Investment
  • Replacement Investment
  • Measuring Risk
  • Market Risk (Beta)
  • Project Risk Considerations
capital budgeting processes
Capital Budgeting Processes
  • Capital budgeting process consists of the following steps:
    • Determine (estimate) the expected cash flows of available projects
    • Apply decision criteria such as NPV and IRR
  • In this class you are given all the information to forecast cash flows but they are subject to error
    • Estimating project cash flows is the most difficult and error-prone part of capital budgeting
example proposed project
Example 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.


  • Sales: 100,000 units/yr @ $2.
  • Var. cost = 60% of sales.
  • Tax rate = 40%.
  • WACC = 10%.
three categories of cash flow
Three “categories” of Cash Flow
  • Initial Cost, including installation and change in net Working Capital
  • Operating Cash Flows
    • Need: Returns/Savings

Tax Depreciation

    • Set up a modified income statement for each year
  • Terminal Cash Flow
    • Need to consider taxes and return of working capital
set up without numbers a time line for the project s cash flows





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
















what s the annual depreciation
What’s the annual depreciation?

Due to 1/2-yr conv., a 3-yr asset

is depreciated over 4 years.

operating cash flows
Operating cash flows:

This is an income statement with no interest.

net terminal cf at t 4
Net Terminal CF at t = 4:

Q. Always a tax on SV?

Q. Ever a positive tax number?

Q. How is NWC recovered?

tax on sv do a side calculation
Tax on SVDo a “side” calculation!

Selling Price

- adjusted basis

= Taxable gain (loss if negative)

x tax rate

= Tax (tax credit if negative)

  • The tax basis when you sell an asset is the initial basis less accumulated depreciation (adjusted basis).
  • The sign (negative or positive) can be confusing. You just have to think.
calculator workout
Calculator Workout
  • Draw the time line for this project and put the cash flows on the time line (on board).
  • Compute the NPV and IRR
  • Note we are skipping Profitability Index
what s the payback period







What’s the Payback Period?











Payback = 3 + 26.7 / 89.7 = 3.3 years.

Numbers slightly rounded to fit onto slide better.

should cfs include int expense dividends
Should CFs include int. 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.
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.

suppose the plant could be leased out for 25 000 a year would this affect the analysis
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. opp. cost = $25,000 (1 - T) = $25,000(0.6) = $15,000 annual cost.
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 neg., i.e., complements or substitutes.
another example
Another Example
  • Given the following information, calculate the NPV and IRR of a proposed project: Cost = $40,000; estimated life = 3 years; increase in accounts receivable = $10,000; estimated salvage value = $10,000; net income before taxes and depreciation = $20,000 per year; method of depreciation = 3-year MACRS; tax rate = 40 percent; required rate of return = 12 percent.
  • (see spreadsheet key LectExample.xls)
if this were a replacement rather than a new project would the analysis change
If this were a replacement rather than a new project, would the analysis change?

Yes. The cash flows would be the incremental

cash flow or changes in cash flow.

1. The old equipment would be sold now

2. You would calculate the change in revenue

and expenses.

3. The relevant depreciation would be the change with the new equipment.

4. Also, if the firm sold the old machine now, it would not receive the SV at the end of the machine’s life.


Replacement Problem

9-3 Atlantic Control Company purchased a machine two years ago at a cost of $70,000. At that time, the machine’s expected economic life was six years and its salvage value at the end of its life was estimated to be $10,000. It is being depreciated using the straight line method so that its book value at the end of six years is $10,000. In four years, however, the old machine will have a market value of $0.

  A new machine can be purchased for $80,000, including shipping and installation costs. The new machine has an economic life estimated to be four years. Three-year MACRS depreciation will be used. During its four-year life, the new machine will reduce cash operating expenses by $20,000 per year. Sales are not expected to change. But the new machine will require net working capital to be increased by $4,000. At the end of its useful life, the machine is estimated to have a market value of $2,500.

  The old machine can be sold today for $20,000. The firm’s marginal tax rate is 40 percent. The appropriate required rate of return is ten percent.

  a. If the new machine is purchased, what is the amount of the initial investment outlay at Year 0?

  b. What incremental operating cash flows will occur at the end of Years 1 through 4 as a result of replacing the old machine?

  c. What is the terminal cash flow at the end of Year 4 if the new machine is purchased?

  d. What is the NPV of this project? Should Atlantic replace the old machine?

operating cash flow






Cost Savings





-Depreciation change










-Taxes (40%)










Depreciation add back





Operating Cash Flow





Operating Cash flow

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


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.

what does risk mean in capital budgeting
What does “risk” mean in capital budgeting?
  • Risk relates to uncertainty about a project’s future profitability.
  • Is NPV, IRR, large? Will taking on project increase firm’s and stockholders’ risk?
chapter 12
Chapter 12
  • Read chapter 12 for background on the remaining slides in this set.
  • There will not be a usual chapter homework for chapter 12
  • There will be questions on the chapter handed out in lab.
is risk analysis based on historical data or subjective inputs
Is risk analysis based on historical data or subjective inputs?
  • Can sometimes use historical data, but generally can’t.
  • So, risk analysis is usually based primarily on subjective judgment.
what three types of risk are relevant in capital budgeting
What three types of risk are relevant in capital budgeting?

1. Stand-alone risk

2. Within-firm risk

3. Market risk

how is each type of risk measured and how do they relate to one another
How is each type of risk measured, and how do they relate to one another?

1. Stand-Alone Risk:

Risk of the project if it were

investor’s only asset. Ignores

diversification. Measured by

the std. dev. or CV of NPV.

2 within firm corporate risk
2. Within-Firm (Corporate) Risk:
  • Reflects the project’s effect on corporate earnings stability. Considers firm’s other assets (diversification within the firm).
  • Depends on (1) project’s std. dev. and (2) its correlation with returns on other projects.
  • Measured by the project’s beta versus total corp. earnings.
3 market risk
3. Market Risk:
  • Project’s risk to a well-diversified investor. Takes account of firms’ and stockholders’ other assets. Total diversification.
  • Depends on project’s correlation with the stock market. Stock market beta.
how is each type of risk used
How is each type of risk used?
  • Market risk is theoretically best.
  • However, creditors, customers, suppliers, and employees are affected by within-firm risk.
  • Therefore, within-firm risk is also relevant.
Stand-alone risk is easiest to measure, intuitive.
  • Core projects correlated with other assets, so stand-alone risk reflects within-firm risk; Maybe??
  • If project is correlated with the economy, stand-alone risk also may reflect market risk; Not likely??
what is sensitivity analysis
What is sensitivity analysis?
  • Shows how changes in a variable such as sales affect NPV or IRR.
  • Each variable is fixed except for one.
  • Change this one variable to see effect on NPV or IRR.

*Salvage Value

sensitivity graph
Sensitivity Graph

NPV (000s)

Unit sales



% change

from base


Steeper sensitivity lines show greater risk. Small changes result in large declines in NPV.
  • Unit sales line is steeper than salvage value or k, so NPV is moresensitive to changes in unit sales than in salvage value or k.
weaknesses of sensitivity analysis
Weaknesses of sensitivity analysis:

1. Does not reflect diversification.

2. Does not incorporate info. about

the likelihood of changing variables, i.e.,

steep sales line not a problem if sales

won’t fall.

Why useful?

1. Gives idea of project risk.

2. Identifies dangerous variables.

what is scenario analysis
What is scenario analysis?
  • Examines several possible situations, usually worst case, most likely case, and best case.
  • Indicates range of possible outcomes.

Assume we know all variables except

unit sales, which could range from

75,000 to 125,000 (or 75 to 125). Here

are the scenario NPVs:

E(NPV) = $15.0

(NPV) = $30.3

Problem 6 in lab


Standard Deviation:

NPV = $30.3

Coefficient of Variation:

define monte carlo simulation
Define Monte Carlo simulation.
  • A type of scenario analysis which brings in probabilities of input variables.
  • Computer selects values for variables based on probability distributions.
NPV and IRR are calculated.
  • Process is repeated 1,000’s of times.
  • End result: Prob. distr. of NPV and IRR.

Prob. Density










advantages of simulation analysis
Advantages of simulation analysis?
  • Reflects probability of each input.
  • Shows range of NPVs, expected NPV, NPV, and CVNPV.
  • Simulation fairly easy to do with a spreadsheet (@risk)
disadvantages of simulation
Disadvantages of simulation:
  • Difficult to specify probability distributions and correlations. (If you have historical data there is software to help)
  • If inputs are bad, output will be bad: GIGO = Garbage In, Garbage Out!
Sensitivity, scenario, and simulation analysis all ignore diversification.
  • Thus, they measure only stand-alone risk.
find the project s market risk and cost of capital based on the capm given these inputs
Find the project’s market risk and cost of capital based on the CAPM, given these inputs:

Target debt ratio = 50%.

kd = 12% Tax rate = 40%

kRF = 10% BetaProject = 1.2

Market risk premium = 6%.

Beta = 1.2, so project has more market risk than average.
  • Project’s required return on equity:
project s market risk vs the firm s overall risk
Project’s market risk vs. the firm’s overall risk:
  • Project’s WACC = 12.2% vs. company WACC = 10%.
  • Risk adjusted discount rate
  • So project’s market risk must be greater than average.

Problem 15, Hudson Furniture in lab

estimating project beta
Estimating project beta:

1. Pure-play. Find several publicly

traded companies exclusively in

project’s business.

Use average of their betas as

proxy for project’s beta.

Hard to find such companies.


2. Accounting beta.

    • Run regression between “project’s” rate of return and S&P index rate of return.
    • Accounting betas are correlated with market betas. But hard to get data on projects’ rate of return before the cap. bud. decision has been made.
    • Usually accounting data for a division of the company is used for the “project”