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**Capital Budgeting: Estimating Cash Flows and Analyzing Risk**

CHAPTER 13 Capital Budgeting: Estimating Cash Flows and Analyzing Risk

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**Chapter Topics Estimating cash flows: Risk Analysis: Decision Trees**

Issues in Project Analysis Depreciation & Tax Effects on Salvage Value Inflation Risk Analysis: Sensitivity Analysis Scenario Analysis Simulation Analysis Decision Trees Real Options

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**Relevant Cash Flows: Incremental Cash Flow for a Project**

Project’s incremental cash flow is: Corporate cash flow with the project Minus Corporate cash flow without the project.

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**Free Cash Flow Capital Expenditures = FA + Deprec**

ΔNOWC = Current Operating Assets – Current Operating Liabilities Current Operating Assets excludes Marketable Securities Current Operating Liabilities excludes Notes Payable

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**Free Cash Flow “Investment outlay CF = CF0**

“Operating CF” = Net Income + Non-cash items (deprec) each year “NOWC CF” = Net working capital requirements each year “Salvage CF” = After-tax salvage value of assets and NOWC recovery

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**Issues in Project Analysis**

Purchase of Fixed Assets …………… Y Non-cash charges …………………….. Y Changes in Net Working Capital……Y Interest/Dividends …………..……….. N “Sunk” Costs …………………………….. N Opportunity Costs …………………….. Y Externalities/Cannibalism …………… Y Tax Effects ………………………..…….. Y

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**Depreciation Basics MACRS 0 Recovery Period = Class Life**

Straight Line Salvage Value MACRS 0 Recovery Period = Class Life 1/2 Year Convention

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**MACRS Depreciation Classes**

TABLE 13.1

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MACRS Depreciation TABLE 13.2

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**Annual Depreciation Expense (000s)**

SCC (Minicase): Equipment cost $200 Shipping Installation Book Depr Value % 0.33 0.45 0.15 0.07 x Basis = Year 1 2 3 4 Depr $ 79.2 108.0 36.0 16.8 $240

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**Tax Effect on Salvage Net Cash flow from sale = Sale proceeds**

- taxes paid Tax basis = difference between sales price and book value, where: Book value = Original basis - Accumulated depreciation

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**Tax Effect on Salvage Net Salvage Cash Flow = SP - (SP-BV)(T) Where:**

SP = Selling Price BV = Book Value T = Corporate tax rate

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**Example: If Asset Sold After 3 Years**

BV (EOY 3) = $17 IF: Selling price = $20 TCF = $20 - (20-17)(.4) = $18.8 IF: Selling price = $10 TCF = $10 - (10-17)(.4) = $12.8

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**Adjusting for Inflation**

Nominal r > real r The cost of capital, r, includes a premium for inflation Nominal CF > real CF Nominal cash flows incorporate inflation If you discount real CF with the higher nominal r, then your NPV estimate is biased downward.

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**Real vs. Nominal Cash flows**

INFLATION Real vs. Nominal Cash flows Real Nominal

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**Real vs. Nominal Cash flows**

INFLATION Real vs. Nominal Cash flows 2 Ways to adjust Adjust WACC Cash Flows = Real Adjust WACC to remove inflation Adjust Cash Flows for Inflation Use Nominal WACC

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**Regency Integrated Chips**

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**RIC – Depreciation & Salvage Value**

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**RIC – Sales, Costs and NWC**

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**RIC – Cash Flow Estimation**

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**RIC: Cash Flow Analysis**

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Excel Functions

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**RIC Background Data Salvage Value Key Basic Calculations**

Cash Flow Estimation Cash Flow Analysis

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**“Risk” in Capital Budgeting**

Uncertainty about a project’s future profitability Measured by σNPV, σIRR, beta Will taking on the project increase the firm’s and stockholders’ risk?

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**Three types of relevant risk**

Stand-alone risk Corporate risk Market (or beta) risk

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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 σ or CV of NPV, IRR, or MIRR.

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**Probability Density 0 E(NPV) NPV Flatter distribution,**

larger , larger stand-alone risk. NPV

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Corporate Risk Reflects the project’s effect on corporate earnings stability. Considers firm’s other assets (diversification within firm). Depends on project’s σ, and its correlation, ρ, with returns on firm’s other assets. Measured by the project’s corporate beta.

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**Project X is negatively correlated to firm’s other assets → big diversification benefits**

If r = 1.0, no diversification benefits. If r < 1.0, some diversification benefits Profitability Project X Total Firm Rest of Firm Years

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Market Risk Reflects the project’s effect on a well-diversified stock portfolio. Takes account of stockholders’ other assets. Depends on project’s σ and correlation with the stock market. Measured by the project’s market beta.

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Conclusions on Risk 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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Sensitivity Analysis Shows how changes in an input variable affect NPV or IRR Each variable is fixed except one Change one variable to measure the effect on NPV or IRR Answers “what if” questions

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**RIC: Sensitivity Analysis**

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**RIC: Sensitivity Graph**

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**Results of Sensitivity Analysis**

Steeper sensitivity lines = greater risk Small changes → large declines in NPV Unit sales line is steeper than salvage value or r, so for this project, should worry most about accuracy of sales forecast

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**RIC: Sensitivity Analysis**

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**Sensitivity Ratio If SR>0 Direct relationship**

14-37 Sensitivity Ratio %NPV = (New NPV - Base NPV)/Base NPV %VAR = (New VAR - Base VAR)/Base VAR If SR>0 Direct relationship If SR<0 Inverse relationship

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**RIC: Sensitivity Ratios**

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**RIC: Sensitivity Ratios & Graph**

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**Sensitivity Analysis: Weaknesses**

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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**Sensitivity Analysis: Strengths**

Provides indication of stand-alone risk Identifies dangerous variables Gives some breakeven information

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**Scenario Analysis Examines several possible situations, usually:**

Worst case Base case or most likely case, and Best case Provides a range of possible outcomes

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**RIC: Scenario Analysis**

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**RIC: Scenario Analysis**

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**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

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**Monte Carlo Simulation Analysis**

A computerized version of scenario analysis which uses continuous probability distributions Computer selects values for each variable based on given probability distributions

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**Monte Carlo Simulation Analysis**

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 Generally shown graphically

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Histogram of Results

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**Advantages of Simulation Analysis**

Reflects the probability distributions of each input Shows range of NPVs, the expected NPV, σNPV, and CVNPV Gives an intuitive graph of the risk situation

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**Disadvantages of Simulation Analysis**

Difficult to specify probability distributions and correlations If inputs are bad, output will be bad: “Garbage in, garbage out”

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**Disadvantages of Sensitivity, Scenario and Simulation Analysis**

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 They measure only stand-alone risk, which may not be the most relevant risk in capital budgeting

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**Subjective risk factors**

Numerical analysis may not capture all of the risk factors inherent in the project For example, if the project has the potential for bringing on harmful lawsuits, then it might be riskier than a standard analysis would indicate

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**Decision Trees A technique for reducing risk**

Analyze multi-stage projects “Decision Nodes” Points where managers can take action based on new information Assign probabilities to each leg

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United Robotics Stage 1: (t=0) Invest $500,000 in market potential study Stage 2: (t=1) If study results positive, invest $1 million in prototype Stage 3: (t=2) Build plant at cost of $10 million Stage 4: (t=3) Product acceptance?

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**United Robotics Decision Tree**

Figure 13-5

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**United Robotics Decision Tree**

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Real Options Real options exist when managers can influence the size and risk of a project’s cash flows by taking different actions during the project’s life in response to changing market conditions Alert managers always look for real options in projects Smarter managers try to create real options

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**Types of Real Options Investment timing options Growth options**

Expansion of existing product line New products New geographic markets Abandonment options Contraction Temporary suspension Flexibility options

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