© 2003 The McGraw-Hill Companies, Inc. All rights reserved. Project Analysis and Evaluation Chapter Eleven

McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc. All rights reserved Chapter Outline Evaluating NPV Estimates Scenario and Other What-If Analyses Break-Even Analysis Operating Cash Flow, Sales Volume, and Break-Even Operating Leverage Capital Rationing

McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc. All rights reserved Evaluating NPV Estimates The NPV estimates are just that – estimates A positive NPV is a good start – now we need to take a closer look –Forecasting risk (estimation risk)– how sensitive is our NPV to changes in the cash flow estimates, the more sensitive, the greater the forecasting risk What about the sales forecasts? Can be manufactured at lower costs? What about the discount rate? Positive NPV projects are rare; found one, be suspicious.

McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc. All rights reserved What is sensitivity analysis? Shows how changes in a variable such as unit sales affect NPV or IRR, other things held constant. Sensitivity analysis begins with a base-case situation – developed using the expected values for each input. Answers “what if” questions, e.g. “What if sales decline by 30%?”

McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc. All rights reserved Sensitivity Analysis -30%$113$17 $85 -15%$100 $52 $86 0%$88 $88 $88 15%$76 $124 $90 30%$65 $159 $91 Change from Resulting NPV (000s) Base Level r Unit Sales Salvage

McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc. All rights reserved Base Value (%) 88 NPV (000s) Unit Sales Salvage r

McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc. All rights reserved Steeper sensitivity lines show greater risk. Small changes result in 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. Results of Sensitivity Analysis

McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc. All rights reserved Advantages - Disadvantages Disadvantage: –Ignores relationships among variables. Advantages: –Gives some idea of stand-alone risk. –Identifies dangerous variables. –Gives some breakeven information.

McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc. All rights reserved What is scenario analysis? Examines several possible situations, usually worst case, most likely case, and best case. Provides a range of possible outcomes.

McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc. All rights reserved Scenario ProbabilityNPV(000) Best scenario: 1,600 $240 Worst scenario: 900 $160 ProbabilityNPV Best 0.25$ 279 Base Worst E(NPV) = $101.5  (NPV) = 75.7 CV(NPV) =  (NPV)/E(NPV) =0.75

McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc. All rights reserved 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.

McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc. All rights reserved 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. (More...)

McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc. All rights reserved 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.

McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc. All rights reserved Simulation Example Assume a: – Normal distribution for unit sales: Mean = 1,250 Standard deviation = 200 –Triangular distribution for unit price: Lower bound= $160 Most likely= $200 Upper bound= $250

McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc. All rights reserved Simulation Process Pick a random variable for unit sales and sale price. Substitute these values in the spreadsheet and calculate NPV. Repeat the process many times, saving the input variables (units and price) and the output (NPV).

McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc. All rights reserved Simulation Results (1000 trials) Units PriceNPV Mean1260$202 $95,914 St. Dev.201$18 $59,875 CV0.62 Max1883 $248 $353,238 Min685$163 ($45,713) Prob NPV>097%

McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc. All rights reserved Interpreting the Results Inputs are consistent with specificied distributions. –Units: Mean = 1260, St. Dev. = 201. –Price: Min = $163, Mean = $202, Max = $248. Mean NPV = $95,914. Low probability of negative NPV (100% - 97% = 3%).

McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc. All rights reserved Histogram of Results

McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc. All rights reserved What are the advantages of simulation analysis? Reflects the probability distributions of each input. Shows range of NPVs, the expected NPV,  NPV, and CV NPV. Gives an intuitive graph of the risk situation.

McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc. All rights reserved What are the disadvantages of simulation? Difficult to specify probability distributions and correlations. If inputs are bad, output will be bad: “Garbage in, garbage out.” (More...)

McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc. All rights reserved Making A Decision Beware “Paralysis of Analysis” At some point you have to make a decision If the majority of your scenarios have positive NPVs, then you can feel reasonably comfortable about accepting the project If you have a crucial variable that leads to a negative NPV with a small change in the estimates, then you may want to forego the project

McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc. All rights reserved Break-Even Analysis and Costs two types of costs that are important in breakeven analysis: variable and fixed –Total variable costs = quantity * cost per unit –Fixed costs are constant, regardless of output, over some time period –Total costs = fixed + variable = FC + Qv Example: Your firm pays $3000 per month in fixed costs. You also pay $15 per unit to produce your product. What is your total cost if you produce 1000 units? TC = *1000 = 18,000 What if you produce 5000 units? TC = *5000 = 78,000

McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc. All rights reserved Average vs. Marginal Cost Average Cost –TC / # of units –Will decrease as # of units increases Marginal Cost –The cost to produce one more unit –Example: What is the average cost and marginal cost under each situation in the previous example –Produce 1000 units: –Average = 18,000 / 1000 = $18, Marginal= 15 –Produce 5000 units: –Average = 78,000 / 5000 = $15.60, Marginal= 15

McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc. All rights reserved Break-Even Analysis There are three common break-even measures: –Accounting break-even – sales volume where net income = 0 –Cash break-even – sales volume where operating cash flow = 0 –Financial break-even – sales volume where net present value = 0

McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc. All rights reserved Accounting Break-Even The quantity that leads to a zero net income: NI = (Sales – VC – FC – D)(1 – T) = 0 Now let us ignore taxes. QP – vQ – FC – D = 0 Q(P – v) = FC + D Q = (FC + D) / (P – v) If a firm just breaks-even on an accounting basis, cash flow = NI + Depr. = Depr.

McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc. All rights reserved Example Consider the following project –A new product requires an initial investment of $5 million and will be depreciated to an expected salvage of zero over 5 years –The price of the new product is expected to be $25,000 and the variable cost per unit is $15,000 –The fixed cost is $1 million –What is the accounting break-even point each year? Depreciation = 5,000,000 / 5 = 1,000,000 Q = (FC + D) / (P – v) Q = (1,000, ,000,000)/(25,000 – 15,000) = 200 units Operating cash flow = NI + Depr. = 1,000,000

McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc. All rights reserved Cash Break-Even Still no taxes for simplicity. What is the cash break-even quantity that makes the OCF = 0? –OCF = [(P-v) Q – FC – D] + D = –OCF = (P-v) Q – FC = 0 –Q OCF = (FC) / (P – v) –Q OCF = (1,000,000) / (25,000 – 15,000) = 100 units

McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc. All rights reserved Financial Break-Even Analysis Consider the previous example –Assume a required return of 18% What is the financial break-even point (NPV = 0)? We need to make some assumptions here: Cash flows are the same every year, no salvage and no NWC. If there were salvage and NWC, you would net it out to year 0 so that all you have in future years is OCF. Similar process to finding the bid price

McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc. All rights reserved Financial Break-Even Analysis –What OCF (or payment) makes NPV = 0? –What is the OCF that makes an investment of 5mn$ equal to an annuity for 5 years at 18%? – = OCF (PVAF 5, 18%) –OCF = / = 1,598,874 –OCF = (P-v) Q – FC –Q = (OCF + FC) / (P – v) –Q = (1,598,874 +1,000,000) / (25,000 – 15,000) = 260 units

McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc. All rights reserved Break-Even Analysis Summary Three common break-even measures: Accounting break-even = 200 units –(Q = (FC + D) / (P – v); NI = 0; OCF = Depr > 0) Cash break-even = 100 units –(Q OCF = (FC) / (P – v); OCF = 0) Financial break-even = 260 units –(Q = (OCF + FC) / (P – v); NPV = 0) We are more interested in cash flow than we are in accounting numbers From the point of project evaluation the question now becomes: Can we sell at least 260 units per year?

McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc. All rights reserved Summary Q= 100Q= 200Q= 260 Sales2,500,0005,000,0006,500,000 FC1,000,000 VC1,500,0003,000,0003,900,000 Depr1,000,000 EBIT = NI-1,000, ,000 OCF=+Depr01,000,0001,600,000 NPV-5,000,000-1,872,8003,520 Cash B_EAccount B_E Financial B_E

McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc. All rights reserved Operating Leverage Operating leverage is the degree to which a project or firm is committed to (relies on) fixed production costs. –The higher the fixed costs, the higher the operating leverage, or vice versa. Fixed costs act as a lever, ie. A small change in sales can be magnified into a large change in operating cash flows and NPV. The higher the degree of opearting leverage, the greater is the potential danger from forecasting risk, eg., due to sales forecasts.

McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc. All rights reserved Operating leverage is the relationship between sales and operating cash flow % change in OCF = DOL x % change in Q DOL = % change in OCF / % change in Q OCF = Q(P-v) – FC OCF 2 = (Q+1)(P-v) - FC OCF 2 - OCF = (P-v) DOL = (P-v)/OCF / 1/Q = (P-v) Q/OCF Or since: OCF + FC = Q(P-v) DOL = (OCF + FC) / OCF DOL = 1 + (FC / OCF)

McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc. All rights reserved Example: DOL Consider the previous example Suppose sales are 260 units –This meets all three break-even measures –What is the DOL at this sales level? –OCF = (25,000 – 15,000)*260 – 1,000,000 = 1,600,000 –DOL = 1 + 1,000,000 / 1,600,000 = What will happen to OCF if unit sales increases by 10%? –Percentage change in OCF = DOL*Percentage change in Q –Percentage change in OCF = 1.625(.1) =.1625 or 16.25% –OCF would increase to 1,600,000(1.1625) = 1,860,000

McGraw-Hill/Irwin © 2003 The McGraw-Hill Companies, Inc. All rights reserved What will happen to OCF if unit sales decreases by 10%? –Percentage change in OCF = DOL*Percentage change in Q –Percentage change in OCF = 1.625(-.1) = or % –OCF would increase to 1,600,000(0,8375) = 1,340,000 –What is the NPV with OCF= 1,340,000 ? –How can we make it less problematic?