CHAPTER

1. CHAPTER 8 Risk Analysis, Real Options, and Capital Budgeting

2. Chapter Outline 8.1 Decision Trees 8.2 Sensitivity Analysis, 8.3 Break-Even Analysis 8.4 Scenario Analysis, Options 8.5 Monte Carlo Simulation 8.6 Summary and Conclusions

3. 8.1 Decision Trees • Allow us to graphically represent the alternatives available to us in each period and the likely consequences of our actions. • This graphical representation helps to identify the best course of action.

4. “A” “B” “C” “D” “F” Example of Decision Tree Squares represent decisions to be made. Circles represent receipt of information e.g. a test score. Study finance The lines leading away from the squares represent the alternatives. Do not study

5. Capital Investment Decision: (SEC) • Solar Electronics Corporation (SEC) has recently developed the technology for solar powered jet engines and presently is considering test marketing of the engine. A corporate planning group, including representatives from production, marketing, and engineering, has recommended that the firm go ahead with the test and development phase. • This preliminary phase will last one year and cost $100 million. Furthermore, the group believes that there is a 75% chance that tests will prove successful. • Cost of capital is 15%. • If the initial tests are successful, Solar Electronics Corporation can go ahead with full-scale production. This investment phase will cost $1500 million. Production will occur over the next 5 years. Annual sales would be 30% of the market of 10,000. Sales price is $2 million per unit. • If the initial tests are not successful, and Solar Electronics Corporation still goes ahead with full-scale production; the investment will cost $1500 million, and annual sales would then be 682 units over the next 5 years.

6. SEC: NPV of Full-Scale ProductionFollowing Successful Test

7. SEC: NPV of Full-Scale ProductionFollowing Failure of Test

8. Invest = NPV $ 0 Decision Tree for SEC The firm has two decisions to make: Invest To test or not to test. To invest or not to invest. NPV = $1,517 Success 75% prob. Test Do not invest NPV = $0 Failure NPV = –$3,612 (Sales units=682) 25% prob. Do not test

9. NPV of the project Expected payoff at date 1= (Prob. of success x Payoff if successful) +(Prob. Of failure x Payoff if failure) =(.75x$1,517)+(.25x0) =$1,138 million The NPV of the testing computed at date 0 (in million) is Since NPV is positive, so we should test.

10. Calculation of accounting BEP BEPQ =Net Fixed charges/Net Contribution =(Fixed cost + Depreciation) *(1-Tc)/(Sales Price-Variable cost)*(1-Tc) =[(1791+300)*(1-.34)]/[(2-1)*(1-.34)] =1380/.66=2,091 engines is the break-even point for an accounting profit

11. Sensitivity Analysis: SEC • We can see that NPV is very sensitive to changes in revenues. For example, when sales drop from 4,000 units to 3,000, a 25% drop in revenue leads to a 59% drop in NPV. For every 1% drop in revenue, we can expect roughly a 2.4% drop in NPV: Similarly, when sales drop from 3,000 to 2,500 units then 1% drop in revenue makes 4.4% drop in NPV.

12. Figure: Accounting BEP $ in million Total Revenue Total Cost $4,182 Fixed cost (including depreciation)=$2,091 2,091 Output (sales units)

13. Present Value BEPQ • The Equivalent Annual Cost (EAC) of the investment of $1,500 (in million) is: After tax fixed charges: =EAC + (Fixed costs x(1-Tc))-(Depreciation*Tc) =$447.5 +($1,791*.66 - $300*.34)=$1,528 So, present value BEPQ =After tax fixed charges/After tax contribution

14. + TVC +D +FC $147.5 0.66 Break-Even Revenue SEC Work backwards from OCFBE to Break-Even Revenue Total Revenue $4,630 Total Variable cost $2,315 Fixed cost $1,791 Depreciation $300 EBIT $223.5 Tax (34%) $76.0 Net Income $147.5 OCF = $147.5+ $300 $447.5

15. SEC: NPV of Full-Scale ProductionFollowing Successful Test

16. Financial Break-even • Expected pay-off at date 1=(.75*0)+(.25*0)=0 • We fail to finance the test of $100. • For that we need a pay-off of $115 at date 1 • Thus the NPV needed at date 1 is 115/.75=$153million • The cost of investment becomes=$1,500+$153=$1,653m • EAC=1653/3.352155=$493 • Net profit required is ($493-$300(dep))=$193 • Before tax profit is (net profit/(1-T))=$193/.66=$292.75 • Total contribution needed=$292.75+$300+$1,791=$2,383.75 • So, (P-VC)Q=2,383.75 • (2-1)2,383=2,383.75

17. SEC: Financial BEP of Full-Scale ProductionFollowing Successful Test

18. Sensitivity Analysis

19. Example 2: Stewart Pharmaceuticals • Stewart Pharmaceuticals Corporation is considering investing in the development of a drug that cures the common cold. • A corporate planning group, including representatives from production, marketing, and engineering, has recommended that the firm go ahead with the test and development phase. • This preliminary phase will last one year and cost $1 billion. Furthermore, the group believes that there is a 60% chance that tests will prove successful. • If the initial tests are successful, Stewart Pharmaceuticals can go ahead with full-scale production. This investment phase will cost $1.6 billion. Production will occur over the following 4 years.

20. NPV Following Successful Test Note that the NPV is calculated as of date 1, the date at which the investment of $1,600 million is made. Later we bring this number back to date 0. Assume a cost of capital of 10%. PVIFA=3.1699

21. NPV Following Unsuccessful Test Note that the NPV is calculated as of date 1, the date at which the investment of $1,600 million is made. Later we bring this number back to date 0. Assume a cost of capital of 10%.

22. Invest = NPV $ 0 Decision Tree for Stewart Pharmaceutical The firm has two decisions to make: Invest To test or not to test. To invest or not to invest. NPV = $3.4 b Success Test Do not invest NPV = $0 Failure NPV = –$91.46 m Do not test

23. Decision to Test • Let’s move back to the first stage, where the decision boils down to the simple question: should we invest? • The expected payoff evaluated at date 1 is: The NPV evaluated at date 0 is: So, we should test.

24. Sensitivity Analysis: Stewart • We can see that NPV is very sensitive to changes in revenues. In the Stewart Pharmaceuticals example, a 14% drop in revenue leads to a 61% drop in NPV. For every 1% drop in revenue, we can expect roughly a 4.26% drop in NPV:

25. Scenario Analysis: Stewart • A variation on sensitivity analysis is scenario analysis. • For example, the following three scenarios could apply to Stewart Pharmaceuticals: • The next years each have heavy cold seasons, and sales exceed expectations, but labor costs skyrocket. • The next years are normal, and sales meet expectations. • The next years each have lighter than normal cold seasons, so sales fail to meet expectations. • For each scenario, calculate the NPV.

26. Break-Even Analysis • Common tool for analyzing the relationship between sales volume and profitability • There are two common break-even measures • Accounting break-even: sales volume at which net income = 0 • Financial break-even: sales volume at which net present value = 0

27. Break-Even Analysis: Stewart • Another way to examine variability in our forecasts is break-even analysis. • In the Stewart Pharmaceuticals example, we could be concerned with break-even revenue, break-even sales volume, or break-even price. • To find zero NPV, we start with the break-even operating cash flow. • EAC=1600/3.1699=504

28. Accounting BEPQ • BEP=(1,800+200)*(.66)/($10-($3,000/700))*(.66)=385 TR TC $3,850 385 Quantity of sales

29. + VC +D +FC $104.75 0.66 Break-Even Revenue: Stewart • Work backwards from OCFBE to Break-Even Revenue Revenue $5,358.71 Variable cost $3,000 Fixed cost $1,800 Depreciation $400 EBIT $158.71 Tax (34%) $53.96 Net Income $104.75 OCF = $104.75+ $400 $504.75

30. $5,358.71 PBE = = $7.66 / dose 700 Break-Even Analysis: PBE • Now that we have break-even revenue of $5,358.71 million, we can calculate break-even price. • The original plan was to generate revenues of $7 billion by selling the cold cure at $10 per dose and selling 700 million doses per year, • We can reach break-even revenue with a price of only: $5,358.71 million = 700 million × PBE

31. Dorm Beds Example • Consider a project to supply the University of Missouri with 10,000 dormitory beds annually for each of the next 3 years. • Your firm has half of the woodworking equipment to get the project started; it was bought years ago for $200,000: is fully depreciated and has a market value of $60,000. The remaining $100,000 worth of equipment will have to be purchased. • The engineering department estimates that you will need an initial net working capital investment of $10,000. • The project will last for 3 years. Annual fixed costs will be $25,000 and variable costs should be $90 per bed. • The initial fixed investment will be depreciated straight line to zero over 3 years. It also estimates a (pre-tax) salvage value of $10,000 (for all of the equipment). • The marketing department estimates that the selling price will be $200 per bed. • You require an 8% return and face a marginal tax rate of 34%.

32. Dorm Beds OCF0 What is the OCF in year zero for this project? Cost of New Equipment $100,000 Net Working Capital Investment $10,000 Opportunity Cost of Old Equipment* $39,600 $149,600 *Calculation of Opportunity Cost of Old Equipment: Market value $60,000 Book value 0 Profit (Loss) $60,000 Tax (34%) ($20,400) Net salvage value $39,600

33. Dorm Beds OCF1,2 What is the OCF in years 1 and 2 for this project? Revenue 10,000× $200 = $2,000,000 Variable cost 10,000 × $90 = $900,000 Fixed cost $25,000 Depreciation 100,000 ÷ 3 = $33,333 EBIT $1,041,666.67 Tax (34%) $354,166.67 Net Income $687,500 OCF = $687,500 + $33,333 $720,833.33

34. Dorm Beds OCF3 Revenue 10,000× $200 = $2,000,000 10,000 × $90 = Variable cost $900,000 $25,000 Fixed cost 100,000÷ 3 = Depreciation $33,333 $1,041,666.67 EBIT $354,166.67 Tax (34%) $687,500 Net Income $720,833.33 OCF =$687,500 + $33,333 = We get our NWC back and sell the equipment. Since the book value and market value of net working capital is same, so there is no tax effect. Thus, and net cash flow becomes $10,000. The salvage value of equipment $10,000 and the book value is zero. So the capital gain of $10,000 is taxable. Thus, the after-tax salvage value is $6,600 = $10,000 × (1 – .34) Thus, OCF3 = $720,833.33 + $10,000 + $6,600 = $737,433.33

35. NPV of Dorm Beds

36. Dorm Beds Break-Even Analysis • In this example, we should be concerned with break-even price. • Let’s start by finding the revenue that gives us a zero NPV. • To find the break-even revenue, let’s start by finding the break-even operating cash flow (OCFBE) and work backwards through the income statement.

37. Dorm Beds Break-Even Analysis The PV of the cost of this project is the sum of $149,600 today less $6,600 of net salvage value and $10,000 as return of NWC in year 3. Let us find out the Equivalent Annual Cost (EAC) of the investment:

38. $19,603.13 0.66 Break-Even Revenue Work backwards from OCFBE to Break-Even Revenue Revenue 10,000× $PBE = $988,035.04 Variable cost 10,000 × $90 = $900,000 Fixed cost $25,000 Depreciation 100,000 ÷ 3 = $33,333 EBIT $29,701.71 Tax (34%) $10,098.58 Net Income $19,603.13 OCF = $19,603.13 + $33,333 $52,936.46

39. Break-Even Analysis • Now that we have break-even revenue we can calculate break-even price • If we sell 10,000 beds, we can reach break-even revenue with a price of only: PBE× 10,000 = $988,035.34 PBE= $98.80

40. $ 988 , 035 . 04 = = Break - even sales volume 4 , 941 beds $ 200 Common Mistake in Break-Even • What’s wrong with this line of reasoning? • With a price of $200 per bed, we can reach break-even revenue with a sales volume of only: As a check, you can plug 4,941 beds into the problem and see if the result is a zero NPV.

41. $19,603.13 0.66 Don’t Forget that Variable Cost Varies Revenue QBE× $200 = $88,035.04 + QBE×$110 Variable cost QBE× $90 = $? Fixed cost $25,000 Depreciation 100,000 ÷ 3 = $33,333 EBIT $29,701.71 Tax (34%) $10,098.58 Net Income $19,603.13 OCF = $19,603.13 + $33,333 $52,936.46

42. $88,035.04 QBE = = 801 beds $110 Break-Even Analysis • With a contribution margin of $110 per bed, we can reach break-even revenue with a sales volume of only: • If we sell 10,000 beds, we can reach break-even gross profit with a contribution margin of only $8.80: CMBE ×10,000 = $88,035.04 CMBE = $8.80 • If variable cost = $90, then break-even price (PBE) = $98.80

43. 8.4 Options • One of the fundamental insights of modern finance theory is that options have value. The phrase “We are out of options” is surely a sign of trouble. Because corporations make decisions in a dynamic environment, they have options that should be considered in project valuation. • The Option to Expand • Has value if demand turns out to be higher than expected. • The Option to Abandon • Has value if demand turns out to be lower than expected. • The Option to Delay • Has value if the underlying variables are changing with a favorable trend.

44. The Option to Expand • Imagine a start-up firm, Campusteria, Inc. which plans to open private (for-profit) dining clubs on college campuses. • The test market will be your campus, and if the concept proves successful, expansion will follow. • The start-up cost of the test dining club is only $30,000 (this covers leaseholder improvements and other expenses for a vacant restaurant near campus).

45. 4 $ 2 , 550 å = - + = - NPV $ 30 , 000 $ 21 , 916 . 84 t ( 1 . 10 ) = t 1 Campusteria pro forma Income Statement We plan to sell 25 meal plans at $200 per month with a 12-month contract. Variable costs are projected to be $3,500 per month. Fixed costs (the lease payment) are projected to be $1,500 per month. We can depreciate our capitalized leaseholder improvements.

46. The Option to Expand: • Note that while the Campusteria test site has a negative NPV, we now evaluate the possibility of expansion of sales. If sales grows at the rate 40% annually over the next 4 years, and the investment has the excess capacity to produce the higher level of sales, Then cost benefit takes following form. Find out the value of the expansion option.

47. The Option to Expand: NPV is $4,730 which is positive Value of the managerial option=21,916+4,730=$26,646

48. Discounted Cash Flows and Options • We can calculate the market value of a project as the sum of the NPV of the project without options and the value of the managerial options implicit in the project. M = NPV + Opt • A good example would be comparing the desirability of a specialized machine versus a more versatile machine. If they both cost about the same and last the same amount of time the more versatile machine is more valuable because it comes with options.

49. The Option to Abandon: Example • Suppose that we are drilling an oil well. The drilling rig costs $300 today and in one year the well is either a success or a failure. • The outcomes are equally likely. The discount rate is 10%. • The PV of the successful payoff at time one is $575. • The PV of the unsuccessful payoff at time one is $0.

50. Expected Payoff Prob. Success Successful Payoff Prob. Failure Failure Payoff = × + × $287.50 = –$38.64 NPV = Expected Payoff –$300 + = (0.50×$575) + (0.50×$0) = $287.50 1.10 The Option to Abandon: Example Traditional NPV analysis would indicate rejection of the project.