1. Project Interactions

2. Applying the models So far we have discussed simple projects that are mutually exclusive and made some assumptions Competing projects have the same lives We know the future cash flows with certainty Management does not have the ability to make decisions that change the cash flows after the project is started. This chapter expands on the basic decision variables (NPV, IRR etc) in cases where projects with different lives are compared, cash flows are uncertain, and we discuss the value & impact of management.

3. Capital Rationing Choosing among projects when limited by the amount of resources available. Previously we assumed that the firm could undertake any positive NPV project, however it may be limited by available resources.

4. Spending Limits Assume that the company has a limit on the amount of funds that it believes it can raise. Example: 3 projects Spending limit of 12M ProjectInvestment NPV A12,000,00018,000,000 B7,000,00014,000,000 C5,000,00010,000,000 Which project(s) should it undertake?

5. Using Profitability Index Given the spending limits, the firm should also look at the return per dollar invested. ProjectInvestment NPVPI A12,000,00018,000,0001.5 B7,000,00014,000,0002.0 C5,000,00010,000,0002.0 While B & C have a lower NPV individually they both have a higher profitability index.

6. Problems Profitability index can be misleading if looked at alone. ProjectInvestment NPVPI A10,000,00014,000,0001.4 B5,000,000 6,000,0001.2 C5,000,00010,000,0002.0 The firm should still look at the total amount of NPV!

7. Problems with Profitability Index If more than one constraint is to be rationed then PI can be misleading. For example, if one project depends upon another. Also PI ignores the amount of wealth created.

8. Comparing Projects with Unequal Lives Replacement Chain Approach Repeat projects until they have the same life span. Compare a two year project with a four year project by repeating the two year project

9. Comparing Projects with Unequal Lives Equivalent Annual Annuity (finding an annualized NPV) To Find EA find the NPV of the Project Use the NPV as the PV of an annuity and solve for payment Choose the project with the highest EAA

10. Abandonment Decisions Often one question is when to stop a project. By quitting at different points in time the NPV and EAA will vary due to the changes in salvage value. Use EAA and treat each abandonment time as a separate project.

11. Uncertain Cash Flows So far we have assumed that we can estimate the cash flows from the project with certainty. However, it is difficult to correctly forecast future cash flows – how can the risks associated with changes in the economic environment and the difficulties with forecasting cash flows be accounted for?

12. Three Types of Risk Stand Alone Risk Views project in isolation With-in firm (Corporate Risk) Looks at the firms portfolio of projects and how they interact Market Risk Risk from the view of a well diversified investor.

13. Definitions Risk Exposure to a chance of injury or loss Probability The likelihood an event occurs Risk vs. Uncertainty Risk – the probability of the outcome is known Uncertainty – includes judgment concerning the probability

14. Definitions and Terms Continued Objective Prob –can measure prob. precisely Subjective Prob. – Includes judgment or opinion Variation Risk – We want to look at a range of possible outcomes

15. Issues in Risk Measurement 1.Stand Alone Risk is the easiest to measure 2.Market Risk is the most important to the shareholder 3.To evaluate risk you need three things i.Standard deviation of the projects forecasted returns ii.Correlation of the projects forecasted returns with the firms other assets iii.Correlation of the projects forecasted returns with the market

16. Issues in Risk Management con’t 4.Using the numbers in 3) you can find the corporate beta and market beta coefficient (equal to ((   ost projects have a + correlation with other projects and a coefficient < 1 6.Most projects are positively correlated with the market with coefficient < 1 7.Corporate risk should also be examined 1.More important to small business 2.Investors may look at things other than market risk 3.Firm Stability is important to creditors, suppliers etc

17. Stand Alone Risk (Review) The easiest approach to measuring stand alone risk is to use the standard deviation of the projects returns. Just like security analysis you need to be careful looking at only standard deviation – don’t forget coefficient of variation

18. Measuring Stand Alone Risk Quick Review Sensitivity Analysis Scenario Analysis Monte Carlo Simulation

19. Applying Sensitivity and Scenario Analysis In our examples we simplified the problem by changing the aggregate cash flows. When evaluating the project, any assumptions about inputs can change – impacting the incremental cash flows. A few of many possible examples: Changes in variable input costs Changes in sales Changes in tax laws

20. Probability Review Mutually exclusive events If A occurs then B cannot. Example considering building a new sports arena. There are two sites North and South. Prob North =.5 Prob South =.25 This implies the prob that the stadium is built is.5 +.25 =.75

21. Probability Review 2 Independent Events Example Exxon is considering two drilling sites, gulf coast and Alaska P(A) = New oil from gulf coast =.7 P(B) = Prob of oil in Alaska =.4 Event BNo Event B (.4) (.6) Event A (.7).28.42 No event A (.3).12.18

22. Probability Review 3 Dependent Events Prob of one event depends upon the other North Side is voting on bonds for the new arena, 80% chance of the bond passing If passed there is a 60% chance the stadium gets built in North. If the bonds fail there is a 30% chance that the stadium gets built in North

23. Prob Review 3 con’t North North Selected Rejected Bond(.8)(.6) (.8)(.4) Passes (.8)=.48=.32 Bond (.2)(.3)(.2)(.7) Fails (.2)=.06=.14

24. Decision Trees So far our decision making has ignored the role of management. We know that things change as a project progresses and decision trees attempt to account for this.

25. Project Example Peripherals Inc. is considering making a new copier/printer. Stage 1: Conduct a market study to investigate potential sales, cost = $500,000 Stage 2: If sizable market exists at time t=1 spend 1,000,000 to build prototype (80% prob) Stage 3: If it passes all test spend $10,000,000 at time t=2 60% prob Stage 4: Year t = 3 to t = 6 High demand (20% prob) $12M in CF each yr Avg Demand (60% prob) $5M in CF each yr Low Demand (20% prob) –$2M in CF each yr

26. Building the decision tree t = 0 t = 1 -1,000,000 80% -500,000 20% 0 Stage 1 and Stage 2 represented on the tree

27. Building the decision tree t = 1 t = 2 -10,000,000 60% -1,000,000 40% 0 Stage 2 and Stage 3 represented on the tree

28. Stage 1 to 3 t=0 t=1 t=2 -10,000,000 60% -1,000,000 80% -500,000 40% 0 20% 0

29. Decision Tree Continue to Build the tree (on the board in class) When finished find the NPV of each branch and multiply it times the probability for each branch to find the expected NPV.

30. Real Options Opportunities arise that present the management with the ability to make a choice. The decision points in the above decision tree represent this. For example: At time t=2, if we realize that the project is going to produce only -$2,000,000 each year we would not proceed with the project. There is an option to abandon the project.

31. Real Options Three main components 1. Determining the value of a real option. 2. Identifying the optimal response to changing conditions. 3. Structuring projects to create real options.

32. Valuing a Real Option Using the Decision Tree In the earlier decision tree. Assume we can abandon the project if we find out that it is going to result in – 2,000,000 CF each year. We would need to recalculate the NPV of that branch without the –2,000,000 CF’s NPV = -9,364,795.92 instead of –14,207,508.52 The total NPV is then 1,235,339.21 instead of 770,438.80 an increase of 464,900.41

33. Other Benefits If the reduction in uncertainty decreases the risk the firm can lower the WACC increasing the NPV even further. The key is building the decision points into the capital budgeting process from the beginning

34. Real Options and Financial Management Flexibility Option -- Switch inputs during the production process. Capacity options – Ability to manage capacity in response to changing economic conditions. New Product Options – May accept initial negative NPV if it allows rights to future goods. Timing Options – Allow you to postpone or increase production.

35. Value of Real Options In each case the option can add value to the project. You would want to compare the added value of the option to the cost of implementing the option. Example – it costs an extra 10Million to build a plant that could allow inputs to be switched. Given the volatility in the price of the inputs – you estimate the real option to switch inputs is worth $20 Million

36. Characteristics of Real Options Real options often increase the value of a project The value of most real options increases: As the longer the amount of time that exists before the option needs to be exercised increases The source of risk becomes more volatile If interest rates increase.

37. Options Call Option – the right to buy an asset at some point in the future for a designated price. Put Option – the right to sell an asset at some point in the future at a given price

38. Call Option Profit Call option – as the price of the asset increases the option is more profitable. Once the price is above the exercise price (strike price) the option will be exercised If the price of the underlying asset is below the exercise price it won’t be exercised – you only loose the cost of the option. The Profit earned is equal to the gain or loss on the option minus the initial cost.

39. Profit Diagram Call Option Profit Spot CostPrice S S-X-C X

40. Call Option Intrinsic Value The intrinsic value of a call option is equal to the current value of the underlying asset minus the exercise price if exercised or 0 if not exercised. In other words, it is the payoff to the investor at that point in time (ignoring the initial cost) the intrinsic value is equal to max(0, S-X)

41. Payoff Diagram Call Option Payoff Spot Price S S-X X X

42. Put Option Profits Put option – as the price of the asset decreases the option is more profitable. Once the price is below the exercise price (strike price) the option will be exercised If the price of the underlying asset is above the exercise price it won’t be exercised – you only loose the cost of the option.

43. Profit Diagram Put Option Profit Spot Price Cost X S X-S-C

44. Put Option Intrinsic Value The intrinsic value of a put option is equal to exercise price minus the current value of the underlying asset if exercised or 0 if not exercised. In other words, it is the payoff to the investor at that point in time (ignoring the initial cost) the intrinsic value is equal to max(X-S, 0)

45. Payoff Diagram Put Option Profit Spot Price Cost X S X-S

46. Pricing an Option Black Scholes Option Pricing Model Based on a European Option with no dividends Assumes that the prices in the equation are lognormal.

47. Inputs you will need S = Current value of underlying asset X = Exercise price t = life until expiration of option r = riskless rate  2 = variance

48. PV and FV in continuous time e = 2.71828 y = lnx x = e y FV = PV (1+k) n for yearly compounding FV = PV(1+k/m) nm for m compounding periods per year As m increases this becomes FV = PVe rn =PVe rt let t =n rearranging for PV PV = FVe -rt

49. Black Scholes Value of Call Option = SN(d 1 )-Xe -rt N(d 2 ) S = Current value of underlying asset X = Exercise price t = life until expiration of option r = riskless rate  2 = variance N(d ) = the cumulative normal distribution (the probability that a variable with a standard normal distribution will be less than d)

50. Black Scholes (Intuition) Value of Call Option SN(d 1 ) - Xe -rt N(d 2 ) The expected PV of cost Risk Neutral Value of S of investment Probability of if S > X S > X

51. Black Scholes Value of Call Option = SN(d 1 )-Xe -rt N(d 2 ) Where:

52. Application to Real Options Investment OptionReal Option Stock PricePV of projects Cash Flows Exercise PriceExpenditure required to acquire projects assets Time to ExpireLength of time the decision can be deferred Variance Riskiness of projects assets

53. Example Disney – Can spend 100M to create a Spanish version of the Disney channel PV of future CF’s = $80M Initial investment = $100M The resulting NPV of the project is 80M – 100M = -$20 Million

54. A Real Option Assume the expansion will provide political connections resulting in an advantage if they expand into South America. Assume the expansion would cost $150M and could be taken at any time over the next ten years The firm believes that the NPV of expanding is 100M. S = 100M X = 150M r =.065 Variance =.40

55. Plugging into the Black Scholes Model Value of Call Option = SN(d 1 )-Xe -rt N(d 2 ) = 100(.8648) – 150e (-.065)(10) (.435) = 52.3 Million Original NPV = 80M – 100M = - 20M Add the value of the option = Total Value of Project -20M+52.3 = 32.3M

56. Put Option The black scholes value is similar for a put option Value of put option = Xe -rt N(-d 2 )-SN(-d 1 )

57. Option to Abandon An example of a real option that corresponds to a put option would be an option to abandon a project in the future.

58. Developing Prob Estimates History – What happened last year… Experiments – Test programs, market surveys etc… Judgment – Subjective adjustment

59. Structuring Project Cash Flows to Help Manage Risk Variable and Fixed Costs Pricing Strategy Sequential Investment Financial Leverage

60. Measuring Corporate and Market Risk Corporate and Market beta’s