Berk Chapter 22: Real Options

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<ul><li> 1. Chapter 22 Real Options</li></ul> <p> 2. Chapter Outline </p> <ul><li>22.1 Real Versus Financial Options </li></ul> <ul><li>22.2 Decision Tree Analysis </li></ul> <ul><li>22.3 The Option to Delay an Investment Opportunity </li></ul> <ul><li>22.4 Growth and Abandonment Options </li></ul> <ul><li>22.5 Applications to Multiple Projects </li></ul> <ul><li>22.6 Rules of Thumb </li></ul> <ul><li>22.7Key Insights from Real Options </li></ul> <p> 3. Learning Objectives </p> <ul><li>Define the term real option.</li></ul> <ul><li>Draw decision trees to represent alternative decisions and potential outcomes in an uncertain economy. </li></ul> <ul><li>Describe three types of real optionstiming, growth, and abandonmentand explain why it is important to consider those options when evaluating projects. </li></ul> <ul><li>Illustrate how, given the option to wait, an investment that currently has a negative NPV can have a positive value. </li></ul> <p> 4. Learning Objectives </p> <ul><li>Describe situations in which the option to wait is most valuable. </li></ul> <ul><li>Choose between investments of different lives by evaluating the option to replace or extend the shorter-lived project at the end of its original life. </li></ul> <ul><li>Discuss the situation in which equivalent annual benefit method results in optimal decision making. </li></ul> <ul><li>Describe the types of investments that should be done firstin a multi-stage investment decision, and calculate project rankings according to Eq. 22.3. </li></ul> <ul><li>Define and use the profitability index and the hurdle rate rules of thumb. </li></ul> <p> 5. 22.1 Real Versus Financial Options </p> <ul><li>Real Option </li></ul> <ul><li><ul><li>The right to make a particular business decision, such as a capital investment </li></ul></li></ul> <ul><li><ul><li>A key distinction between real options and financial options is that real options, and the underlying assets on which they are based, are often not traded in competitive markets.</li></ul></li></ul> <p> 6. 22.2 Decision Tree Analysis </p> <ul><li>Decision Tree </li></ul> <ul><li><ul><li>A graphical representation of future decisions and uncertainty resolution </li></ul></li></ul> <p> 7. 22.2 Decision Tree Analysis (cont'd) </p> <ul><li>AssumeMegan is financing part of her MBA education by running a small business. She purchases goods on eBay and resells them at swap meets.</li></ul> <ul><li><ul><li>Swap meets typically charge her $500 in advance to set up her small booth. Ignoring the cost of the booth, if she goes to every meet, her average profit on the goods that she sells is $1100 per meet. </li></ul></li></ul> <p> 8. 22.2 Decision Tree Analysis (cont'd) </p> <ul><li>The decision tree showing Megans options looks like the one on the following slide. </li></ul> <ul><li><ul><li>Because the NPV of setting up a booth is $600, the optimal decision (shown in blue) would be to set up the booth. </li></ul></li></ul> <ul><li><ul><li><ul><li>$1100 $500 = $600 </li></ul></li></ul></li></ul> <p> 9. Figure 22.1Megans Choices 10. Mapping Uncertainties on a Decision Tree </p> <ul><li>Megan is aware that attendance at swap meets is weather dependent.</li></ul> <ul><li><ul><li>In good weather her profits are $1500. </li></ul></li></ul> <ul><li><ul><li>In bad weather, she will incur a loss of $100. </li></ul></li></ul> <ul><li><ul><li><ul><li>There is a 25% chance of bad weather. </li></ul></li></ul></li></ul> <ul><li>This adds another element of uncertainty for Megan to consider. </li></ul> <p> 11. Figure 22.2Effect of the Weather on Megans Options 12. Mapping Uncertaintieson a Decision Tree (cont'd) </p> <ul><li>Decision Nodes </li></ul> <ul><li><ul><li>A node on a decision tree at which a decision is made </li></ul></li></ul> <ul><li><ul><li>Corresponds to a real option </li></ul></li></ul> <ul><li>Information Nodes </li></ul> <ul><li><ul><li>A type of node on a decision tree indicating uncertainty that is out of the control of the decision maker </li></ul></li></ul> <p> 13. Mapping Uncertaintieson a Decision Tree (cont'd) </p> <ul><li>In Megans case </li></ul> <ul><li><ul><li>The square node represents the decision to pay the fee and go to the swap meet or do nothing. </li></ul></li></ul> <ul><li><ul><li>The round node represents the uncertain state of nature, sunshine versus rain. </li></ul></li></ul> <ul><li><ul><li><ul><li>In this case, Megan must commit to going to the meet before she knows what the weather will be. </li></ul></li></ul></li></ul> <p> 14. Mapping Uncertaintieson a Decision Tree (cont'd) </p> <ul><li>In reality, Megan does not have to commit to going to the swap meet before she knows the weather conditions. </li></ul> <ul><li><ul><li>Megan understands that the $500 loss for the booth is unavoidable, but in bad weather she can simply stay home and not incur the additional $100 loss at the meet.</li></ul></li></ul> <p> 15. Figure 22.3Megans Decision Tree When She Can Observe the Weather Before She Makes the Decision to Go to the Meet 16. Real Options </p> <ul><li>Megans option to wait until she finds out what the weather is like before she decides whether she should go to the meet is a real option.</li></ul> <ul><li><ul><li>This flexibility has value to Megan. </li></ul></li></ul> <p> 17. Real Options (cont'd) </p> <ul><li>Assume Megan is risk neutral about the risk from the weather. </li></ul> <ul><li><ul><li>The value of the real option can be computed by comparing her expected profit without the real option to wait until the weather is revealed to the value with the option to wait. </li></ul></li></ul> <p> 18. Real Options (cont'd) </p> <ul><li>If Megan commits to go regardless of the weather, her expected profit is $1100. </li></ul> <ul><li><ul><li>0.75$1500 + 0.25($100) = $1100 </li></ul></li></ul> <ul><li>However, if she goes only when the weather is good, her expected profit is $1125. </li></ul> <ul><li><ul><li>0.75$1500 + 0.25$0 = $1125</li></ul></li></ul> <ul><li><ul><li><ul><li>The value of the real option is the difference, $25. </li></ul></li></ul></li></ul> <p> 19. Real Options (cont'd) </p> <ul><li>If Megan has to pay for the booth only the day before the meet, the NPV of paying for the booth (ignoring discounting for one day) is $625. </li></ul> <ul><li><ul><li>$1125 $500 = $625 </li></ul></li></ul> <ul><li><ul><li><ul><li>Since the NPV is positive, Megan should always pay for the booth. </li></ul></li></ul></li></ul> <p> 20. Real Options (cont'd) </p> <ul><li>Corporations face similar options. </li></ul> <ul><li><ul><li>The option to delay an investment opportunity </li></ul></li></ul> <ul><li><ul><li>The option to grow </li></ul></li></ul> <ul><li><ul><li>The option to abandon an investment opportunity </li></ul></li></ul> <p> 21. 22.3 The Option to Delayan Investment Opportunity </p> <ul><li>In Megans case, once the booth is paid for, there is no cost to waiting to find out about the weather.</li></ul> <ul><li>In the real world, there is often a cost to delaying an investment decision.</li></ul> <p> 22. 22.3 The Option to Delayan Investment Opportunity (cont'd) </p> <ul><li>By choosing to wait for more information the firm gives up any profits the project might generate in the interim. In addition, a competitor could use the delay to develop a competing product. </li></ul> <ul><li><ul><li>The decision to wait therefore involves atradeoff between these costs and the benefitof remaining flexible. </li></ul></li></ul> <p> 23. Investment as a Call Option </p> <ul><li>Assume you have negotiated a deal with a major restaurant chain to open one of its restaurants in your hometown.</li></ul> <ul><li><ul><li>The terms of the contract specify that you must open the restaurant either immediately or in exactly one year. </li></ul></li></ul> <ul><li><ul><li><ul><li>If you do neither, you lose the right to open the restaurant at all. </li></ul></li></ul></li></ul> <p> 24. Figure 22.4Restaurant Investment Opportunity 25. Investment as a Call Option (cont'd) </p> <ul><li>How much you should pay for this opportunity? </li></ul> <ul><li><ul><li>It will cost $5 million to open the restaurant, whether you open it now or in one year.</li></ul></li></ul> <ul><li><ul><li>If you open the restaurant immediately, you expect it to generate $600,000 in free cash flow the first year. </li></ul></li></ul> <ul><li><ul><li><ul><li>Future cash flows are expected to grow at a rate of2% per year.</li></ul></li></ul></li></ul> <ul><li><ul><li>The cost of capital for this investment is 12%. </li></ul></li></ul> <p> 26. Investment as a Call Option (cont'd) </p> <ul><li>If the restaurant were to open today, its value would be: </li></ul> <ul><li><ul><li>This would give an NPV of $1 million. </li></ul></li></ul> <ul><li><ul><li><ul><li>$6 million $5 million = $1 million </li></ul></li></ul></li></ul> <ul><li>Given the flexibility you have to delay opening for one year, what should you be willing to pay?</li></ul> <ul><li>When should you open the restaurant? </li></ul> <p> 27. Investment as a Call Option (cont'd) </p> <ul><li>The payoff if you delay is equivalent to the payoff of a one-year European call option on the restaurant with a strike price of $5 million. </li></ul> <ul><li><ul><li>Assume </li></ul></li></ul> <ul><li><ul><li><ul><li>The risk-free interest rate is 5%.</li></ul></li></ul></li></ul> <ul><li><ul><li><ul><li>The volatility is 40%.</li></ul></li></ul></li></ul> <ul><li><ul><li><ul><li>If you wait to open the restaurant you have an opportunity cost of $600,000 (the free cash flow in the first year).</li></ul></li></ul></li></ul> <ul><li><ul><li><ul><li><ul><li>In terms of a financial option, the free cash flow is equivalent to a dividend paid by a stock. The holder of a call option does not receive the dividend until the option is exercised. </li></ul></li></ul></li></ul></li></ul> <p> 28. Table 22.1Black-Scholes Option Value Parameters for Evaluating a Real Option to Invest 29. Investment as a Call Option (cont'd) </p> <ul><li>The current value of the asset without the dividends that will be missed is: </li></ul> <ul><li>The present value of the cost to open the restaurant in one year is: </li></ul> <p> 30. Investment as a Call Option (cont'd) </p> <ul><li>The current value of the call option to open the restaurant is: </li></ul> <p> 31. Investment as a Call Option (cont'd) </p> <ul><li>The value today from waiting to invest in the restaurant next year (and only opening it if it is profitable to do so) is $1.20 million. </li></ul> <ul><li><ul><li>This exceeds the NPV of $1 million from opening the restaurant today. Thus, you are better off waiting to invest, and the value of the contract is $1.20 million. </li></ul></li></ul> <p> 32. Investment as a Call Option (cont'd) </p> <ul><li>What is the advantage of waiting in this case?</li></ul> <ul><li><ul><li>If you wait, you will learn more about the likely success of the business. </li></ul></li></ul> <ul><li><ul><li>Because the investment in the restaurant is not yet committed, you can cancel your plans if the popularity of the restaurant should decline. By opening the restaurant today, you give up this option to walk away. </li></ul></li></ul> <p> 33. Investment as a Call Option (cont'd) </p> <ul><li>Whether it is optimal to invest today or in one year will depend on the magnitude of any lost profits from the first year, compared to the benefit of preserving your right to change your decision. </li></ul> <p> 34. Figure 22.5The Decision to Invest in the Restaurant 35. Factors Affecting the Timing of Investment </p> <ul><li>When you have the option of deciding when to invest, it is usually optimal to invest only when the NPV is substantially greater than zero . </li></ul> <ul><li><ul><li>You should invest today only if the NPV of investing today exceeds the value of the option of waiting. </li></ul></li></ul> <ul><li><ul><li>Given the option to wait, an investment that currently has a negative NPV can have a positive one. </li></ul></li></ul> <p> 36. Factors Affectingthe Timing of Investment (cont'd) </p> <ul><li>Other factors affecting the decision to wait </li></ul> <ul><li><ul><li>Volatility </li></ul></li></ul> <ul><li><ul><li><ul><li>The option to wait is most valuable when there is a great deal of uncertainty. </li></ul></li></ul></li></ul> <ul><li><ul><li>Dividends </li></ul></li></ul> <ul><li><ul><li><ul><li>Absent dividends, it is not optimal to exercise a calloption early.</li></ul></li></ul></li></ul> <ul><li><ul><li><ul><li>In the real option context, it is always better to wait unless there is a cost to doing so. The greater the cost, the less attractive the option to delay becomes. </li></ul></li></ul></li></ul> <p> 37. Textbook Example 22.1 38. Textbook Example 22.1 (cont'd) 39. Alternative Example 22.1 </p> <ul><li>Problem </li></ul> <ul><li><ul><li>Assume: </li></ul></li></ul> <ul><li><ul><li><ul><li>Your company is considering a new project at a cost of $12 million. </li></ul></li></ul></li></ul> <ul><li><ul><li><ul><li>The project may begin today or in exactly one year. </li></ul></li></ul></li></ul> <ul><li><ul><li><ul><li>You expect the project to generate $1,500,000 in free cash flow the first year if you begin the project today. </li></ul></li></ul></li></ul> <ul><li><ul><li><ul><li>Free cash flow is expected to grow at a rate of 3% per year.</li></ul></li></ul></li></ul> <p> 40. Alternative Example 22.1 </p> <ul><li>Problem (continued) </li></ul> <ul><li><ul><li>Assume: </li></ul></li></ul> <ul><li><ul><li><ul><li>The risk-free rate is 4% </li></ul></li></ul></li></ul> <ul><li><ul><li><ul><li>The appropriate cost of capital for this investment is 11%. </li></ul></li></ul></li></ul> <ul><li><ul><li><ul><li>The standard deviation of the projects value is 30%. </li></ul></li></ul></li></ul> <ul><li><ul><li>Should you begin the project today or waitone year? </li></ul></li></ul> <p> 41. Alternative Example 22.1 </p> <ul><li>Solution </li></ul> <ul><li><ul><li>Thus, the NPV of the project today is: </li></ul></li></ul> <ul><li><ul><li><ul><li>$18,750,000 $12,000,000 = $6,750,000 </li></ul></li></ul></li></ul> <ul><li><ul><li>The current value of the project without the dividend that will be missed is: </li></ul></li></ul> <p> 42. Alternative Example 22.1 </p> <ul><li>Solution (continued) </li></ul> <ul><li><ul><li>The present value of the cost to begin the project in one year is: </li></ul></li></ul> <p> 43. Alternative Example 22.1 </p> <ul><li>Solution (continued) </li></ul> <p> 44. Alternative Example 22.1 </p> <ul><li>Solution (continued) </li></ul> <ul><li><ul><li>The value of waiting one year to start the project is $5,927,619. </li></ul></li></ul> <ul><li><ul><li>The NPV of starting the project is $6,750,000. </li></ul></li></ul> <ul><li><ul><li><ul><li>Thus, it is optimal to begin the project today rather than wait. </li></ul></li></ul></li></ul> <p> 45. 22.4 Growth and Abandonment Options </p> <ul><li>Growth Option </li></ul> <ul><li><ul><li>A real option to invest in the future </li></ul></li></ul> <ul><li>Abandonment Option </li></ul> <ul><li><ul><li>The option to disinvest </li></ul></li></ul> <ul><li>Because these options have value, they contribute to the value of any firm that has future possible investment opportunities. </li></ul> <p> 46. Valuing Growth Potential </p> <ul><li>Future growth opportunities can be thought of as a collection of real call options on potential projects. </li></ul> <ul><li><ul><li>This can explain why young firms tend to havehigher returns than older, established firms. </li></ul></li></ul> <p> 47. Valuing Growth Potential (cont'd) </p> <ul><li>Assume StartUp Incorporated is a new company whose only asset is a patent on a new drug.</li></ul> <ul><li><ul><li>If produced, the drug will generate certain profits of $1 million per year for 17 years (after then, competition will drive profits to zero).</li></ul></li></ul> <ul><li><ul><li>It will cost $10 million today to produce the drug. </li></ul></li></ul> <ul><li><ul><li>The yield on a 17-year risk-free annuity is currently 8% per year.</li></ul></li></ul> <p> 48. Valuing Growth Potential (cont'd) </p> <ul><li>What is the value of the patent? </li></ul> <ul><li><ul><li>The NPV of investing in the drug today is: </li></ul></li></ul> <ul><li><ul><li>Given todays interest rates, it does not make sense to invest in the drug today. </li></ul></li></ul> <ul><li><ul><li>What if interest rates permanently fall (rise) to 5% (10%) in one year? </li></ul></li></ul> <p> 49. Valuing Growth Potential (cont'd) </p> <ul><li><ul><li>If rates rise to 10%, the NPV is still negative and it does not make sense to invest in the drug today. </li></ul></li></ul> <ul><li><ul><li>If rates fall to 5%, the NPV of investing in the drug today is: </li></ul></li></ul> <ul><li><ul><li><ul><li>If rates fall to 5%, the NPV is positive and it makes sense to invest in the drug today. </li></ul></li></ul></li></ul> <p> 50. Figure 22.6Start Ups Decision to Invest in the Drug 51. Valuing Growth Potential (cont'd) </p> <ul><li>Recall that to find risk-neutral probabilities, the probabilities that set the value of a financial asset today equal to the present value of its future cash flows must be solved for. </li></ul> <ul><li><ul><li>In this case, a 17-year risk-free annuity that pays $1000 per year is used. </li></ul></li></ul> <p> 52. Valuing Growth Potential (cont'd) </p> <ul><li>The value of the annuity today is: </li></ul> <p> 53. Valuing Growth Potential (cont'd) </p> <ul><li>If interest rates rise to 10% in one year, the value of the annuity will be: </li></ul> <p> 54. Valuing Growth Potential (cont'd) </p> <ul><li>If interest rates fall to 5% in one year, the value of the annuity will be: </li></ul> <p> 55. Valuing Growth Potential (cont'd) </p> <ul><li>Recall that the risk-neutral probability of interest rates increasing to 10%, , is the probability such that the expected return of the annuity is equal to the risk-free rate of 6%. </li></ul> <p> 56. Valuing Growth Potential (cont'd) </p> <ul><li>The value today of the investment opportunity is the present value of the expected cash flows (using risk-neutral probabilities) discounted at the risk-free rate: </li></ul> <p> 57. Valuing Growth Potential (cont'd) </p> <ul><li>In this example, even though the cash flows of the project are known with certainty, the uncertainty regarding future interest rates creates substantial option value for the firm. </li></ul> <ul><li><ul><li>The firms ability to use the patent and grow should interest rates fall is worth $221,693. </li></ul></li></ul> <p> 58. The Option to Expand </p> <ul><li>Consider an investment opportunity withan option to grow that requires a $10 million investment today.</li></ul> <ul><li><ul><li>In one year you will find out whether the project is successful.</li></ul></li></ul> <ul><li><ul><li><ul><li>The risk neutral probability that the project will generate $1 million per year in perpetuity is 50%, otherwise, the project will generate nothing.</li></ul></li></ul></li></ul> <ul><li><ul><li><ul><li><ul><li>At any time we can double the size of the project on theoriginal terms. </li></ul></li></ul></li></ul></li></ul> <p> 59. Figure 22.7Staged Investment Opportunity 60. The Option to Expand (cont'd) </p> <ul><li>By investing today, the expected annual cash flows are $500,000 (ignoring the option to double the size of the project). </li></ul> <ul><li><ul><li>$1 million0.5 = $500,000 </li></ul></li></ul> <p> 61. The Option to Expand (cont'd) </p> <ul><li>Computing the NPV gives: </li></ul> <ul><li><ul><li>The negative NPV suggests that you should not take on the project today.</li></ul></li></ul> <ul><