Chapter 11 Cash Flow Estimation & Risk Analysis

2 Topics Estimating cash flows: Relevant cash flows Working capital treatment Risk analysis: Sensitivity analysis Scenario analysis Simulation analysis

Project’s Cash Flows (CF t ) Market interest rates Project’s business risk Market risk aversion Project’s debt/equity capacity Project’s risk-adjusted cost of capital (r) The Big Picture: Project Risk Analysis NPV = + + ··· + − Initial cost CF 1 CF 2 CF N (1 + r ) 1 (1 + r) N (1 + r) 2

4 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.

5 Free Cash Flow

6 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

7 Treatment of Financing Costs Should you subtract interest expense or dividends when calculating CF? NO. We discount project cash flows with a cost of capital that is the rate of return required by all investors (not just debtholders or stockholders), and so we should discount the total amount of cash flow available to all investors. They are part of the costs of capital. If we subtracted them from cash flows, we would be double counting capital costs.

8 Sunk Costs Suppose $100,000 had been spent last year to improve the production line site. Should this cost be included in the analysis? NO. This is a sunk cost. Focus on incremental investment and operating cash flows.

9 Externalities If the new product line would decrease sales of the firm’s other products by $50,000 per year, would this affect the analysis? Yes. The effects on the other projects’ CFs are “externalities.” Net CF loss per year on other lines would be a cost to this project. Externalities will be positive if new projects are complements to existing assets, negative if substitutes.

Depreciation Methods Straight Line Decline (SLD) Asset depreciated in equal installments over its useful life. Sum of the Year’s Digits (SYD) Based upon an inverted scale which is the ratio of the number of digits in given year divided by total of all years digits. Declining Balance (DB) Asset Depreciation is straight-line depreciation calculated for the remaining balance of the asset for each year. Double Declining Balance (DDB) Doubling straight-line depreciation for the remaining balance of the asset for each year.

Straight Line Decline Method Example Investment : US$ 100 Useful Life : 4 years Depreciation Rate: ¼ = 25% Annual Depreciation: US$ 25

Sum of the Year’s Digits Method Example Investment : US$ 100 Useful Life : 4 years 4 Years Digits : ( ) = 10 1 st Year Depreciation : 4/10 x US$ 100 = US$ 40 2 nd Year Depreciation : 3/10 x US$ 100 = US$ 30 3 rd Year Depreciation : 2/10 x US$ 100 = US$ 20 4 nd Year Depreciation : 1/10 x US$ 100 = US$ 10

Declining Balance Method Example Investment : US$ 100 Useful Life : 4 years

Double Declining Balance Method Example Investment : US$ 100 Useful Life : 4 years

Depreciation Methods Compared

16 “Risk” in Capital Budgeting Uncertainty about a project’s future profitability Will taking on the project increase the firm’s and stockholders’ risk?

17 0E(NPV) Flatter distribution, larger , larger risk. NPV Probability Density

18 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

19 Results of Sensitivity Analysis Steeper sensitivity lines = greater risk Small changes → large declines in NPV Sales price & variable cost are the most sensitive

Sensitivity Ratio %  NPV = (New NPV - Base NPV)/Base NPV %  VAR = (New VAR - Base VAR)/Base VAR 14-20

21 Sensitivity Analysis: Weaknesses Does not reflect diversification Says nothing about the likelihood of change in a variable Ignores relationships among variables

22 Sensitivity Analysis: Strengths Provides indication of risk Identifies dangerous variables

23 Scenario Analysis Examines several possible situations, usually: Worst case Base case or most likely case, and Best case Provides a range of possible outcomes

24 Problems with Scenario Analysis Only considers a few possible out-comes Assumes that inputs are perfectly correlated Focuses on stand-alone risk

25 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

26 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

27 Histogram of Results

28 Advantages of Simulation Analysis Reflects the probability distributions of each input Shows range of NPVs, the expected NPV, σ NPV, and CV NPV Gives an intuitive graph of the risk situation

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

30 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

 Working Area: Option to Explore  Developed Reserves: Options of Expanding, Temporary Stopping, and Abandonment.  Delineated but Undeveloped Reserves: Option to Develop ( to Produce )  Undelineated Field: Option to Appraise Development Investment Appraisal Investment WildcatInvestment Success Probability & Expected Volume of Reserve Revised Volume = B’ Example of Decision Tree Analysis: Upstream Oil & Gas

Apply/bid license Accept Work Progr 3 D Seismic Drill a Wild-cat Appraisal Develop DROP Investment Decision Process Example of Decision Tree Analysis: Upstream Oil & Gas

33 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?

34 United Robotics Decision Tree