Fin650:Project Appraisal Lecture 5

1. Fin650:Project Appraisal Lecture 5 Project Appraisal Under Uncertainty and Appraising Projects with Real Options

2. Activity Schedule: FIN650 Originally scheduled classes Makeup classes (Announced by University) Makeup classes proposed (To be finalized in consultation with students)

3. Incorporating risk into project analysis through adjustments to the discount rate, and by the certainty equivalent factor. Project Analysis Under Risk

4. Introduction: What is Risk? • Risk is the variation of future expectations around an expected value. • Risk is measured as the range of variation around an expected value. • Risk and uncertainty are interchangeable words.

5. Where Does Risk Occur? • In project analysis, risk is the variation in predicted future cash flows.

6. Handling Risk There are several approaches to handling risk: • Risk may be accounted for by (1) applying a discount rate commensurate with the riskiness of the cash flows, and (2), by using a certainty equivalent factor • Risk may be accounted for by evaluating the project using sensitivity and breakeven analysis. • Risk may be accounted for by evaluating the project under simulated cash flow and discount rate scenarios.

7. Using a Risk Adjusted Discount Rate • The structure of the cash flow discounting mechanism for risk is:- • The $ amount used for a ‘risky cash flow’ is theexpected dollar value for that time period. • A ‘risk adjusted rate’ is a discount rate calculated to include a risk premium. This rate is known as the RADR, the Risk Adjusted Discount Rate.

8. Defining a Risk Adjusted Discount Rate • Conceptually, a risk adjusted discount rate, k, has three components:- • A risk-free rate (r), to account for the time value of money • An average risk premium (u), to account for the firm’s business risk • An additional risk factor (a) , with a positive, zero, or negative value, to account for the risk differential between the project’s risk and the firms’ business risk.

9. Calculating a Risk Adjusted Discount Rate A risky discount rate is conceptually defined as: k = r + u + a Unfortunately, k, is not easy to estimate. Two approaches to this problem are: 1. Use the firm’s overall Weighted Average Cost of Capital, after tax, as k . The WACC is the overall rate of return required to satisfy all suppliers of capital. 2.A rate estimating (r + u) is obtained from the Capital Asset Pricing Model, and then a is added.

10. Calculating the WACC Assume a firm has a capital structure of: 50% common stock, 10% preferred stock, 40% long term debt. Rates of return required by the holders of each are : common, 10%; preferred, 8%; pre-tax debt, 7%. The firm’s income tax rate is 30%. WACC = (0.5 x 0.10) + (0.10 x 0.08) + (0.40 x (0.07x (1-0.30))) = 7.76% pa, after tax.

11. The Capital Asset Pricing Model • This model establishes the covariance between market returns and returns on a single security. • The covariance measure can be used to establish the risky rate of return, r, for a particular security, given expected market returns and the expected risk free rate.

12. Calculating r from the CAPM • The equation to calculate r, for a security with a calculated Beta is: • Where : is the required rate of return being calculated, is the risk free rate: is the Beta of the security, and is the expected return on the market.

13. Beta is the Slope of an Ordinary Least Squares Regression Line

14. The Regression Process The value of Beta can be estimated as the regression coefficient of a simple regression model. The regression coefficient ‘a’ represents the intercept on the y-axis, and ‘b’ represents Beta, the slope of the regression line. Where, = rate of return on individual firm i’s shares at time t = rate of return on market portfolio at time t = random error term (as defined in regression analysis) uit

15. The Certainty Equivalent Method: Adjusting the cash flows to their ‘certain’ equivalents The Certainty Equivalent method adjusts the cash flows for risk, and then discounts these ‘certain’ cash flows at the risk free rate. Where: b is the ‘certainty coefficient’ (established by management, and is between 0 and 1); and r is the risk free rate.

16. Risk is the variation in future cash flows around a central expected value. Risk can be accounted for by adjusting the NPV calculation discount rate: there are two methods – either the WACC, or the CAPM Risk can also be accommodated via the Certainty Equivalent Method. All methods require management judgment and experience. Analysis Under Risk :Summary

17. Appraising Projects with Real Options • Critics of the DCF criteria argue that cash flow analysis fails to account for flexibility in business decisions. • Real option models are more focused on describing uncertainty and in particular the managerial flexibility inherent in many investments • Real options give the firm the opportunity but not the obligation to take certain action

18. What is Options? • In finance, an option is a derivative financial instrument that specifies a contract between two parties for a future transaction on an asset at a reference price. The buyer of the option gains the right, but not the obligation, to engage in that transaction, while the seller incurs the corresponding obligation to fulfill the transaction. The price of an option derives from the difference between the reference price and the value of the underlying asset (commonly a stock, a bond, a currency or a futures contract) plus a premium based on the time remaining until the expiration of the option. Other types of options exist, and options can in principle be created for any type of valuable asset. • An option which conveys the right to buy something is called a call; an option which conveys the right to sell is called a put. The reference price at which the underlying may be traded is called the strike price or exercise price. The process of activating an option and thereby trading the underlying at the agreed-upon price is referred to as exercising it it. Most options have an expiration date. If the option is not exercised by the expiration date, it becomes void and worthless.

19. What is Real Options? Application of financial options theory to investment in a non-financial (real) asset Hence the name real options 19

20. Real Options: Link between Investments and Black-Scholes Inputs

21. Real Options in Capital Projects • Ten real options to: • Invest in a future capital project • Delay investing in a project • Choose the project’s initial capacity • Expand capacity of the project subsequent to the original investment • Change the project’s technology • Change the use of project during its life • Shutdown the project with the intention of restarting it later • Abandon or sell the project • Extend the life of the project • Invest in further projects contingent on investment in the initial project

22. What is a real option? • Real options exist when managers can influence the size and risk of a project’s cash flows by taking different actions during the project’s life in response to changing market conditions. • Alert managers always look for real options in projects. • Smarter managers try to create real options.

23. What is the single most important characteristic of an option? • It does not obligate its owner to take any action. It merely gives the owner the right to buy or sell an asset.

24. How are real options different from financial options? • Financial options have an underlying asset that is traded--usually a security like a stock. • A real option has an underlying asset that is not a security--for example a project or a growth opportunity, and it isn’t traded. (More...)

25. How are real options different from financial options? • The payoffs for financial options are specified in the contract. • Real options are “found” or created inside of projects. Their payoffs can be varied.

26. What are some types of real options? • Investment timing options • Growth options • Expansion of existing product line • New products • New geographic markets

27. Types of real options (Continued) • Abandonment options • Contraction • Temporary suspension • Flexibility options

28. Five Procedures for ValuingReal Options 1. DCF analysis of expected cash flows, ignoring the option. 2. Qualitative assessment of the real option’s value. 3. Decision tree analysis. 4. Standard model for a corresponding financial option. 5. Financial engineering techniques.

29. Analysis of a Real Option: Basic Project • Initial cost = $70 million, Cost of Capital = 10%, risk-free rate = 6%, cash flows occur for 3 years. Annual DemandProbabilityCash Flow High 30% $45 Average 40% $30 Low 30% $15

30. Approach 1: DCF Analysis • E(CF) =.3($45)+.4($30)+.3($15) = $30. • PV of expected CFs = ($30/1.1) + ($30/1.12) + ($30/1.13) = $74.61 million. • Expected NPV = $74.61 - $70 = $4.61 million

31. Investment Timing Option • If we immediately proceed with the project, its expected NPV is $4.61 million. • However, the project is very risky: • If demand is high, NPV = $41.91 million. • If demand is low, NPV = -$32.70 million.

32. Investment Timing (Continued) • If we wait one year, we will gain additional information regarding demand. • If demand is low, we won’t implement project. • If we wait, the up-front cost and cash flows will stay the same, except they will be shifted ahead by a year.

33. Procedure 2: Qualitative Assessment • The value of any real option increases if: • the underlying project is very risky • there is a long time before you must exercise the option • This project is risky and has one year before we must decide, so the option to wait is probably valuable.

34. Cost Future Cash Flows a Scenario 0 Prob. 1 2 3 4 -$70 $45 $45 $45 30% $0 40% -$70 $30 $30 $30 30% $0 $0 $0 $0 Decision Tree Analysis(Implement only if demand is not low.) NPV this $35.70 $1.79 $0.00 Discount the cost of the project at the risk-free rate, since the cost is known. Discount the operating cash flows at the cost of capital. Example: $35.70 = -$70/1.06 + $45/1.12 + $45/1.13 + $45/1.13.

35. Use these scenarios, with their given probabilities, to find the project’s expected NPV if we wait. E(NPV) = [0.3($35.70)]+[0.4($1.79)] + [0.3 ($0)] E(NPV) = $11.42.

36. Decision Tree with Option to Wait vs. Original DCF Analysis • Decision tree NPV is higher ($11.42 million vs. $4.61). • In other words, the option to wait is worth $11.42 million. If we implement project today, we gain $4.61 million but lose the option worth $11.42 million. • Therefore, we should wait and decide next year whether to implement project, based on demand.

37. The Option to Wait Changes Risk • The cash flows are less risky under the option to wait, since we can avoid the low cash flows. Also, the cost to implement may not be risk-free. • Given the change in risk, perhaps we should use different rates to discount the cash flows. • But finance theory doesn’t tell us how to estimate the right discount rates, so we normally do sensitivity analysis using a range of different rates.

38. Procedure 4: Use the existing model of a financial option. • The option to wait resembles a financial call option-- we get to “buy” the project for $70 million in one year if value of project in one year is greater than $70 million. • This is like a call option with an exercise price of $70 million and an expiration date of one year.

39. Inputs to Black-Scholes Model for Option to Wait • X = exercise price = cost to implement project = $70 million. • rRF = risk-free rate = 6%. • t = time to maturity = 1 year. • P = current stock price = Estimated on following slides. • 2= variance of stock return = Estimated on following slides.

40. Estimate of P • For a financial option: • P = current price of stock = PV of all of stock’s expected future cash flows. • Current price is unaffected by the exercise cost of the option. • For a real option: • P = PV of all of project’s future expected cash flows. • P does not include the project’s cost.

41. Step 1: Find the PV of future CFs at option’s exercise year. PV at Future Cash Flows 0 Prob. 1 2 3 4 Year 1 $45 $45 $45 $111.91 30% 40% $30 $30 $30 $74.61 30% $15 $15 $15 $37.30 Example: $111.91 = $45/1.1 + $45/1.12 + $45/1.13.

42. Step 2: Find the expected PV at the current date, Year 0. PV PV Year 0 Year 1 $111.91 High $67.82 $74.61 Average Low $37.30 PV2004=PV of Exp. PV2005 = [(0.3* $111.91) +(0.4*$74.61) +(0.3*$37.3)]/1.1 = $67.82.

43. The Input for P in the Black-Scholes Model • The input for price is the present value of the project’s expected future cash flows. • Based on the previous slides, P = $67.82.

44. Estimating s2 for the Black-Scholes Model • For a financial option, s2 is the variance of the stock’s rate of return. • For a real option, s2 is the variance of the project’s rate of return.

45. Three Ways to Estimate s2 • Judgment. • The direct approach, using the results from the scenarios. • The indirect approach, using the expected distribution of the project’s value.

46. Estimating s2 with Judgment • The typical stock has s2 of about 12%. • A project should be riskier than the firm as a whole, since the firm is a portfolio of projects. • The company in this example has s2 = 10%, so we might expect the project to have s2 between 12% and 19%.

47. Estimating s2 with the Direct Approach • Use the previous scenario analysis to estimate the return from the present until the option must be exercised. Do this for each scenario • Find the variance of these returns, given the probability of each scenario.

48. Find Returns from the Present until the Option Expires Return PV PV Year 0 Year 1 $111.91 65.0% High $67.82 $74.61 10.0% Average Low $37.30 -45.0% Example: 65.0% = ($111.91- $67.82) / $67.82.

49. Use these scenarios, with their given probabilities, to find the expected return and variance of return. E(Ret.)=0.3(0.65)+0.4(0.10)+0.3(-0.45) E(Ret.)= 0.10 = 10%. 2= 0.3(0.65-0.10)2 + 0.4(0.10-0.10)2 + 0.3(-0.45-0.10)2 2= 0.182 = 18.2%.

50. Estimating s2 with the Indirect Approach • From the scenario analysis, we know the project’s expected value and the variance of the project’s expected value at the time the option expires. • The questions is: “Given the current value of the project, how risky must its expected return be to generate the observed variance of the project’s value at the time the option expires?”