1. . © 2003 The McGraw-Hill Companies, Inc. All rights reserved. Project Analysis and Evaluation Chapter Ten

2. . 1 Chapter Outline Evaluating NPV Estimates Scenario and Other What-If Analyses Break-Even Analysis Operating Leverage

3. . 2 Evaluating NPV Estimates NPV estimates are just that – estimates A positive NPV is a good start – now we need to take a closer look at: –Forecasting risk – how sensitive is our NPV to changes in the cash flow estimates; the discount rate, etc. What about the sales forecast? Can be manufactured at lower costs? What about the discount rate? –Sources of value – why does this project create value?

4. . 10-2 sensitivity analysis Types of Analysis Sensitivity Analyzes effects of changes in sales, costs, etc., on project Scenario Project analysis given particular combination of assumptions Simulation Estimates probabilities of different outcomes Break Even Level of sales (or other variable) at which project breaks even

5. . 4 Sensitivity Analysis What happens to NPV when we vary one variable at a time? The greater the volatility in NPV in relation to a specific variable, the larger the forecasting risk associated with that variable Sensitivity analysis begins with a base-case situation. Then answer “what if” questions, e.g. “What if sales decline by 10%?”

6. . Net Cash Flows Example Year 0Year 1Year 2Year 3Year 4 Init. Cost-$240,0000000 Op. CF0$106,680$120,450$93,967$88,680 NWC CF-$30,000-$900-$927-$956$32,783 Salvage CF0000$15,000 Net CF-$270,000$105,780$119,523$93,011$136,463 At 10%NPV=88k

7. . Sensitivity Analysis, -30%$113$17 $85 -15%$100 $52 $86 0%$88 $88 $88 15%$76 $124 $90 30%$65 $159 $91 Resulting NPV (000s) Change from r Unit Sales Salvage Base Level 10% 1250 $25000

8. . -30 -20 -10 Base 10 20 30 Value (%) 88 NPV (000s) Unit Sales Salvage r

9. . Results of Sensitivity Analysis Steeper sensitivity lines show greater risk. That means small % changes in an input variable result in large changes in NPV. Unit sales line is steeper than salvage value or ‘r’ lines, For this project, we should worry most about the accuracy of sales forecast.

10. . Advantages - Disadvantages Advantages: –Gives some idea of stand-alone risk. –Identifies ‘dangerous’ variables. –Gives some breakeven information. Disadvantage: –Ignores relationships among variables.

11. . 10 Scenario Analysis What happens to the NPV under different cash flow scenarios? At the very least look at: –Best case – high revenues, low costs –Worst case – low revenues, high costs –Measure of the range of possible outcomes Best case and worst case are not necessarily probable, but they can still be possible Provides a range of possible outcomes.

12. . Scenario Analysis - Example Scenario Probability NPV(000) Best 0.25$ 279 Base0.5088 Worst 0.25-49 E(NPV) = $101.5  (NPV) = 75.7 CV(NPV) =  (NPV)/E(NPV) =0.75 Best scenario: 1,600 units @ $240 Worst scenario: 900 units @ $160

13. . Advantages - Disadvantages Advantages: More realistic than sensitivity analysis. Disadvantages: Only considers a few possible outcomes. Assumes that inputs are perfectly correlated-- all “bad” values occur together and all “good” values occur together.

14. . 13 Simulation Analysis Simulation is really just an expanded sensitivity and scenario analysis Simulation can estimate thousands of possible outcomes quickly: –Variables are defined with probability distributions, for example a normal distribution for sales. –Computer selects values for each variable based on given probability distributions for each “run” and the NPV is calculated. –Process is repeated many times (in 1,000’s).

15. . Simulation Example Assume: – 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

16. . 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 (unit sales and price) and the output (NPV). Display the NPV values in graphical format, verify the probabiliy of ending up with negative NPVs.

17. . Histogram of Results

18. . 17 Break-Even Analysis The crucial variable for a project is sales volume. Break-even analysis is a common tool for analyzing the relationship between sales volume and profitability There are various break-even measures –Financial break-even –> sales volume at which NPV= 0 –Accounting break-even –> sales volume at which net income = 0 Goal: How bad do sales have to get before we actually begin to lose money?

19. . 18 Example Consider the following Project: –A new product requires an initial investment of $5 million and will be depreciated to an expected book value 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 $1 million. Tax rate = 0.3 –If we assume that we can sell 300 units each year, what would be the NPV? (discount rate 20%) EBIT= [(P-v)Q – FC – D]= (10,000)300 –1,000,000 –1,000,000 = 1,000,000 OCF = EBIT (1-T)+ D = 1,000,000 (0.7)+1,000,000 = 1,700,000 NPV = -5,000,000 + 1,700,000 (PVAF 5-yr, @20%) = NPV = -5,000,000 + 1,700,000 (3) = 100,000$

20. . 19 Ex: Financial Break-Even Analysis Question: At which sales level ‘NPV = 0’? CF stream: 5,000,000OCFOCFOCFOCFOCF NPV = 0= -5,000,000 + OCF [PVAF 5y; 20%]= 5,000,000 = OCF (3) OCF = 1,672,240 OCF = 1,672,240= NI+D ; NI= 672,240 $ NI= 672,240= [(P-v)Q-FC-D]= 10,000Q–1,000,000–1,000,000 10,000Q = 672,240+2,000,000 Q=267.2units

21. . 20 Accounting Break-Even The quantity that leads to a zero net income. Project Net Income set equal to 0: NI => (Sales – VC – FC – D)(1 – T) = 0 Divide both sides by (1-T), when NI is zero, so is the pre-tax income: [Sales - VC - FC – D] = 0 Sales - VC = FC + D (QP – vQ) = FC + D Q = (FC + D) / (P – v)

22. . Ex: Accounting break-even each year? Depreciation = 5,000,000 / 5 = 1,000,000 Q = (FC + D) / (P – v) Q = (1,000,000 + 1,000,000)/(25,000 – 15,000) = 200 units Verify EBIT and OCF at Q=200 EBIT= [(P-v)Q – FC – D]= (10,000)200 – 1,000,000 – 1,000,000 = 0 OCF= EBIT + D = 0 +1,000,000 = 1,000,000 NPV = -5,000,000 + 1,000,000 (3) = -2,000,000 Observations: If a firm just breaks even on an accounting basis, NPV < 0 If a firm just breaks even on an accounting basis, OCF = Depr

23. . 22 Using Accounting Break-Even Easy to calculate Accounting break-even is often used as an early stage screening number If a project cannot break even on an accounting basis, then it is not going to be a worthwhile project Accounting break-even gives managers an indication of how a project will impact accounting profit

24. . Summary table(in 000s except Q) Q= 200Q= 267,2 Sales 5,0006,680 FC 1,000 VC 3,0004,008 Depr 1,000 EBIT 0672 TAXES00 NI0672 OCF=NI+Depr1,0001,672 NPV -2,0000 Account B_EFinancial B_E

25. . 24 Operating Leverage Operating leverage is the degree to which a project/firm is committed to fixed production costs. Heavy investment in plant equipment means high degree of operating leverage Such projects are said to be capital intensive.

26. . 25 Operating Leverage One way of measuring operating leverage: How much % change in OCF occurs for a % change in sales. % change in OCF= DOL x % change in Q ‘Degree of operating leverage’ (DOL): DOL = 1 + (FC / OCF) –The higher the fixed costs, the higher the DOL –The higher the DOL, the greater the variability in operating cash flow

27. . 26 Example: DOL Consider the previous example Suppose sales are 300 units –This meets all three break-even measures –What is the DOL at this sales level? –OCF = 1,700,000 –DOL = 1 + 1,000,000 / 1,700,000 = 1.59 What will happen to OCF if unit sales increases by 1%? –% change in OCF= DOL* % change in Q –% change= 1.59*(1%) = 1.59% –New OCF = 2,000,000(1.0159) =2,031,800

28. . 27 Financial Break-Even Analysis with taxes Let us solve the financial break-even problem with taxes. What OCF (or payment) makes NPV = 0? Actually OCF does not change, let us see: PV = 5,000,000= OCF [PVAF 5-7;20%]= OCF (2.99) OCF = 1,672,240 However, the break-even quantity will change: OCF = [(P-v)Q – FC – D](1-T) + D= OCF=(P-v)Q(1-T) – (FC + D)(1-T) + D Q= OCF+[(FC+D)(1-T)-D] / (P-v)(1-T) Q=(1672240+(2000.000)0.7 - 1000.000)) + 10000)0.7 Q= (1672240+400.000) / 7000 = 296 The question now becomes: Can we sell at least 296 units per year?