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Ch 12

Cash Flow Estimation and Risk Analysis

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Estimating cash flows

NPV, IRR and PI computations are straightforward.

The difficult part is estimating cash flows accurately occurring in the future.

Estimating accurate cash flows for a large capital spending is critical.

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0 1 2 3 4

InitialOutlay

OCF1 OCF2 OCF3 OCF4

+ Terminal CF

NCF0 NCF1 NCF2 NCF3 NCF4

Timing of project CFs

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Identifying the relevant cash flows

Only cash flows are relevant, not accounting income.

Costs of Fixed Assets Depreciation Changes in Net Working Capital Interest Expense

Focus on incremental cash flows Incremental cost: cash flows that occur if and only if we

accept the project (i.e., CF with project – CF without project).

Example: Sunk cost, Opportunity cost, and erosion or externalities

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Only cash flows are relevant.

Only cash flows are relevant, not accounting income (or cost). The accounting income (or cost) ignores time value of money.

Example: Consider the firm buying a building for $100,000 today. How much of $100,000 will be recorded as an accounting expense in the current year? Assume a straight-line depreciation over 20 years. What is the true capital expense in the current year? The entire $100,000 is an immediate cash outflow.

Capital budgeting analysis focuses on cash inflows and outflows when they occur.

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Noncash charge In calculating net income,

accountants usually subtract depreciation from revenue.

However, depreciation is noncash charge. You never write a check made out to “depreciation”.

Depreciation must be added back when estimating a project’s cash flow.

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Working Capital Expenditures

Many capital investments require additions to working capital

Net working capital (NWC) = current assets minus current liabilities

Increase in NWC is a cash outflow; decrease a cash inflow

• An example… We have to buy inventory to support sales although

we haven’t collected cash yet Thus, usually, in the earlier years of the project life,

increase in NWC is treated as cash outflow. However, recall that when the project winds down, we

enjoy a return of net working capital.

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NO. The costs of capital are already incorporated in the analysis since we use them in discounting.

If we included them as cash flows, we would be double counting capital costs.

Should CFs include interest expense? Dividends?

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Forget sunk costs but include opportunity costs

Forget sunk costs. Example: The Coca-Cola is launching a new brand in the beverage market. Previously, the company paid a consulting firm $300,000 to perform a test-marketing analysis. Is this expenditure relevant to the decision of introducing a new brand? NO!

Include opportunity costs. Example: Lexmark Co. has an empty land that can be used to build a new factory. Alternatively, Lexmark could sell the land out. Currently, a real estate appraisal concludes that the current market price of the land is $1 million. If Lexmark decides to build new factory on that land, should Lexmark include $1 millions as a part of initial cash outlay? YES!

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Include all incidental or side effects.

Consider Erosion or externalities (e.g., product cannibalization).

Example 1: Suppose the Innovative Motors Corporation (IMC) is determining the NPV of a new convertible sports car. Some of the customers who would purchase the new convertibles are owners of IMC’s compact sedan. Suppose the NPV of the sports car and the NPV of lost sales due to the transfer from sedan to convertible sports car is $100 million and -$150 million, respectively. What is the net NPV of a new convertible sports car project? Net NPV = $100 million - $150 million = -$50 million. REJECT!

Example 2: Pepsi One case.

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Consider after-tax cash flow. Pay tax (cash outflow) or receive tax credit

(cash inflows) Taxes = (Market Value – Book Value ) * Tax

Rate

Example: Suppose you bought your Mustang for $15,000 five years ago. Today you decide to sell Mustang for $9,000 and buy new BMW for $30,000. Assume you depreciate your Mustang on a straight-line basis over 10 years of life with a zero salvage value. What is the net cash flow? Assume the tax rate is 30%.

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Consider after-tax cash flow.

Annual Depreciation $15,000 / 10 = $1,500Book value $7,500 ($15,000 – ($1,500* 5

years))Market value $9,000Gain from sale $1,500Tax (30%) $450 ($1,500*30%)

Net cash flow = - $30,000 + $9000 – $450 = -$21,450

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Depreciation

Modified Accelerated Cost Recovery System (MACRS)

Depreciable Basis Purchase Price + Shipping and

Installation Costs Sale of a Depreciable Asset

Taxes = (Market Value – Book Value ) * Tax Rate

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Modified Accelerated Cost Recovery System (MACRS)

Year 3-year 5-year 7-year 10-year

1 33% 20% 14% 10%

2 45 32 25 18

3 15 19 17 14

4 7 12 13 12

5 11 9 9

6 6 9 7

7 9 7

8 4 7

9 7

10 6

11 3

100% 100% 100% 100%

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Example: Campbell Co. The Campbell Company is evaluating the

proposed acquisition of a new milling machine. The machine’s base price is $108,000, and it would cost another $12,500 to modify it for special use by your firm. The machine falls into the MACRS 3-year class, and it would be sold after 3 years for $65,000. The machine would require an increase in net working capital (inventory) of $5,500. The milling machine would have no effect on revenues, but it is expected to save the firm $44,000 per year in before-tax operating costs, mainly labor. Campbell’s marginal tax rate is 35 percent. The project’s cost of capital is 12 percent.

Microsoft Excel Worksheet

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0 1 2 3 4

InitialOutlay

OCF1 OCF2 OCF3 OCF4

+ Terminal CF

NCF0 NCF1 NCF2 NCF3 NCF4

Timing of project CFs

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Initial Cash Outlay at t=0

Purchase Price$108,000

Modification $ 12,500 Increase in NWC $ 5,500 Initial Cash Outlay $126,000

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Operating Cash Flows Depreciation

Depreciable Basis = Cost + Additional Cost= $108,000+ 12,500 = $120,500

Depreciation Schedule (MACRS 3-year class)

Year % Basis Depreciation

1 33% $120,500 $39,765

2 45% $120,500 $54,225

3 15% $120,500 $18,075

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Let’s set up Income Statement to find Operating Cash Flows

Year 1 Year 2 Year 3

Net Revenue (or Gross Margin)

$44,000 $44,000 $44,000

- Depreciation ($39,765)

($54,225)

($18,075)

= EBT $4,235 -$10,225 $25,925

- Taxes (40%) ($1,482) ($3,579) ($9,074)

= Net Income $2,753 -$6,646 $16,851

+ Depreciation $39,765 $54,225 $18,075

= Net Operating Cash Flow

$42,518 $47,579 $34,926

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Terminal Cash FlowAccumulated Depreciation (t=3)= Depreciation (t=1) + Depreciation (t=2) + Depreciation (t=3)= $39,765 + $54,225 + $18,075= $ 112,065

Book Value = Depreciable basis - Accumulated Depreciation (t=3)

= $120,500 – $112,065 = $8,435

Book value $ 8,435 Market value $65,000Gain from sale $56,565Tax (35%) $19,798 ($56,565*35%)

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Terminal Cash Flows

Proceeds form sale 65,000Tax on gain -19,798Recovery of NWC 5,500

Terminal Cash Flow $50,702

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Timing of project CFs: Campbell Co.

0 1 2 3

InitialOutlay

42,518 47,579 34,926

+ 50,702

-126,000 42,518 47,579 85,628

NPV = $10,841 Accept!

IRR = 16.37% > 12% (cost of capital) Accept!

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Sensitivity and Scenario Analyses

Why sensitivity and scenario analysis? In some cases, we may face forecasting risk or

estimation risk. Forecasting risk – how sensitive is our NPV to

changes in the cash flow estimates, the more sensitive, the greater the forecasting risk

For example, we may miscalculate future cash flows. We also overestimate or underestimate the required return or cost of capital (Discussed in Ch 9)

So we need to conduct “what-if” analysis to see how sensitive the NPV, IRR and others to varying input values.

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Project Risk Analysis

What does “risk” mean in capital budgeting?

Uncertainty about a project’s future profitability.

Measured by NPV, IRR, beta.

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What three types of risk are relevant in capital budgeting?

Stand-alone risk

Corporate risk

Market (or beta) risk

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

1. Stand-Alone Risk: The project’s risk if it were the firm’s

only asset and there were no shareholders.

Ignores both firm and shareholder diversification.

Measured by the of NPV, IRR, or MIRR.

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0 E(NPV)

Probability Density

Flatter distribution, larger , larger stand-alone risk.

NPV

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2. Corporate Risk: Reflects the project’s marginal effect

on corporate earnings stability. Considers firm’s other assets

(diversification within firm). Depends on:

project’s , andits correlation with returns on firm’s other assets.

Measured by the project’s corporate beta.

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Profitability

0 Years

Project X

Total Firm

Rest of Firm

1. Project X is negatively correlated to firm’s other assets.

2. If correlation < 1.0, some diversification benefits.3. If correlation = 1.0, no diversification effects.

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3. Market Risk: Reflects the project’s effect on a well-

diversified stock portfolio. Takes account of stockholders’ other

assets.

Depends on project’s and correlation with the stock market.

Measured by the project’s market beta.

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How is each type of risk used?

Stand-alone risk is easiest to measure, more intuitive.

Core projects are highly correlated with other assets, so stand-alone risk generally reflects corporate risk.

If the project is highly correlated with the economy, stand-alone risk also reflects market risk.

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Measuring Stand-Alone Risk

Three techniques Sensitivity Analysis Scenario Analysis Monte Carlo Simulation

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What is sensitivity analysis?

Shows how changes in a variable such as unit sales affect NPV or IRR.

Each variable is fixed except one. Change this one variable to see the effect on NPV or IRR.

Answers “what if” questions, e.g. “What if sales decline by 30%?”

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IllustrationChange

fromBase Level

Resulting NPV (000s)

Unit Sales

Salvage WACC

-30% $ 10 $78 $105

-20 35 80 97

-10 58 81 89

0 82 82 82

+10 105 83 74

+20 129 84 67

+30 153 85 61

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-30 -20 -10 Base 10 20 30 Value

82

NPV(000s)

Unit Sales

Salvage

k

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Steeper sensitivity lines show greater risk. Small changes result in large declines in NPV.

Unit sales line is steeper than salvage value or WACC, so for this project, should worry most about accuracy of sales forecast.

Results of Sensitivity Analysis

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Pros and Cons of Sensitivity Analysis

Pros Gives some idea of stand-alone risk. Identifies dangerous variables. Gives some breakeven information.

Cons Does not reflect diversification. Says nothing about the likelihood of

change in a variable, i.e. a steep sales line is not a problem if sales won’t fall.

Ignores relationships among variables.

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What is scenario analysis?

Examines several possible situations, usually worst case, most likely case, and best case.

Provides a probability, likelihood of each case occurrence

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Assume we know with certainty all variables except unit sales, which could range from 900 to 1,600.

E(NPV) = $ 82(NPV) = 47

Scenario Probability

NPV(000)

Worst 0.25 $ 15Base 0.50 82Best 0.25 148

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Are there any problems with scenario analysis?

Only considers a few possible out-comes. Assumes that inputs are perfectly correlated--all

“bad” values occur together and all “good” values occur together.

Focuses on stand-alone risk, although subjective adjustments can be made.

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What is a simulation analysis? A computerized version of scenario analysis

which uses continuous probability distributions.

Computer selects values for each variable based on given probability distributions. NPV and IRR are calculated. Process is repeated many times (1,000 or

more). End result: Probability distribution of NPV and

IRR based on sample of simulated values.

Computer-intensive

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0 E(NPV) NPV

Probability Density

x x x x x x x x x x x x x x x x x x x x x x x x x x x x

xx xx x x x

x x x x x xx x x x x

x x x x x x x x x x x x x x x x x x x x x x x x x

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Pros and Cons of Simulation Analysis

Reflects the probability distributions of each input.

Shows range of NPVs, the expected NPV and NPV.

Difficult to specify probability distributions and correlations.

If inputs are bad, output will be bad:“Garbage in, garbage out.”

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Sensitivity, scenario, and simulation analyses do not provide a decision rule. They do not indicate whether a project’s expected return is sufficient to compensate for its risk.

Sensitivity, scenario, and simulation analyses all ignore diversification. Thus they measure only stand-alone risk, which may not be the most relevant risk in capital budgeting.