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Investment Flexibility and Decision Trees

Learn about investment flexibility, decision trees, and real options to make informed investment decisions. Explore topics such as asymmetric information, capital structure, dividends, mergers and acquisitions, venture capital, and behavioral corporate finance.

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Investment Flexibility and Decision Trees

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  1. MN50324: Corporate Finance 2009/10: • Investment flexibility, Decision trees, Real Options • Asymmetric Information and Agency Theory • 3. Capital Structure and Value of the Firm. • 4. Optimal Capital Structure - Agency Costs, Signalling • 5. Dividend policy/repurchases • 6. Mergers and Acquisitions/corporate control • 7. Venture Capital/Private Equity/hedge funds • 8. Behavioural Corporate Finance. • 9. Emotional Corporate Finance • 10. Revision.

  2. 1: Investment Flexibility/ Real options. • Reminder of Corporation’s Objective : Take projects that increase shareholder wealth (Value-adding projects). • Investment Appraisal Techniques: NPV, IRR, Payback, ARR • Decision trees • Real Options • Game-theory approach!

  3. Investment Flexibility, Decision Trees, and Real Options • Decision Trees and Sensitivity Analysis. • Example: From Ross, Westerfield and Jaffe: “Corporate Finance”. • New Project: Test and Development Phase: Investment $100m. • 0.75 chance of success. • If successful, Company can invest in full scale production, Investment $1500m. • Production will occur over next 5 years with the following cashflows.

  4. Production Stage: Base Case Date 1 NPV = -1500 + = 1517

  5. Decision Tree. Date 1: -1500 Date 0: -$100 NPV = 1517 Invest P=0.75 Success Do not Invest NPV = 0 Test Do not Invest Failure P=0.25 Do Not Test Invest NPV = -3611 Solve backwards: If the tests are successful, SEC should invest, since 1517 > 0. If tests are unsuccessful, SEC should not invest, since 0 > -3611.

  6. Now move back to Stage 1. Invest $100m now to get 75% chance of $1517m one year later? Expected Payoff = 0.75 *1517 +0.25 *0 = 1138. NPV of testing at date 0 = -100 + = $890 Therefore, the firm should test the project. Sensitivity Analysis (What-if analysis or Bop analysis) Examines sensitivity of NPV to changes in underlying assumptions (on revenue, costs and cashflows).

  7. Sensitivity Analysis. - NPV Calculation for all 3 possibilities of a single variable + expected forecast for all other variables. Limitation in just changing one variable at a time. Scenario Analysis- Change several variables together. Break - even analysis examines variability in forecasts. It determines the number of sales required to break even.

  8. Real Options. A digression: Financial Options (revision) A call option gives the holder the right (but not the obligation) to buy shares at some time in the future at an exercise price agreed now. A put option gives the holder the right (but not the obligation) to sell shares at some time in the future at an exercise price agreed now. European Option – Exercised only at maturity date. American Option – Can be exercised at any time up to maturity. For simplicity, we focus on European Options.

  9. Example: • Today, you buy a call option on Marks and Spencer’s shares. The call option gives you the right (but not the obligation) to buy MS shares at exercise date (say 31/12/10) at an exercise price given now (say £10). • At 31/12/10: MS share price becomes £12. Buy at £10: immediately sell at £12: profit £2. • Or: MS shares become £8 at 31/12/10: rip option up!

  10. Factors Affecting Price of European Option (=c). • -Underlying Stock Price S. • -Exercise Price X. • Variance of of the returns of the underlying asset , • Time to maturity, T. The riskier the underlying returns, the greater the probability that the stock price will exceed the exercise price. The longer to maturity, the greater the probability that the stock price will exceed the exercise price.

  11. Options: Payoff Profiles. Buying a Call Option. Selling a put option. Selling a Call Option. Buying a Put Option.

  12. Pricing Call Options – Binomial Approach. Cu = 3 uS=24.00 q q c S=20 1- q 1- q dS=13.40 Cd=0 • S = £20. q=0.5. u=1.2. d=.67. X = £21. • 1 + rf = 1.1. • Risk free hedge Portfolio: Buy One Share of Stock and write m call options. • uS - mCu = dS – mCd => 24 – 3m = 13.40. • M = 3.53. By holding one share of stock, and selling 3.53 call options, your payoffs are the same in both states of nature (13.40): Risk free.

  13. Since hedge portfolio is riskless: 1.1 ( 20 – 3.53C) = 13.40. Therefore, C = 2.21. This is the current price per call option. The total present value of investment = £12 .19, and the rate of return on investment is 13.40 / 12.19 = 1.1.

  14. Alternative option-pricing method • Black-Scholes • Continuous Distribution of share returns (not binomial) • Continuous time (rather than discrete time).

  15. Real Options • Just as financial options give the investor the right (but not obligation) to future share investment (flexibility) • Researchers recognised that investing in projects can be considered as ‘options’ (flexibility). • “Real Options”: Option to delay, option to expand, option to abandon. • Real options: dynamic approach (in contrast to static NPV).

  16. Real Options • Based on the insights, methods and valuation of financial options which give you the right to invest in shares at a later date • RO: development of NPV to recognise corporation’s flexibility in investing in PROJECTS.

  17. Real Options. • Real Options recognise flexibility in investment appraisal decision. • Standard NPV: static; “now or never”. • Real Option Approach: “Now or Later”. • -Option to delay, option to expand, option to abandon. • Analogy with financial options.

  18. Types of Real Option • Option to Delay (Timing Option). • Option to Expand (eg R and D). • Option to Abandon.

  19. Option to Delay (= call option) Value-creation Project value Investment in waiting: (sunk)

  20. Option to expand (= call option) Value creation Project value Investment in initial project: eg R and D (sunk)

  21. Option to Abandon ( = put option) Project goes badly: abandon for liquidation value. Project value

  22. Valuation of Real Options • Binomial Pricing Model • Black-Scholes formula

  23. Value of a Real Option • A Project’s Value-added = Standard NPV plus the Real Option Value. • For given cashflows, standard NPV decreases with risk (why?). • But Real Option Value increases with risk. • R and D very risky: => Real Option element may be high.

  24. Comparing NPV with Decision Trees and Real Options (revision) • Dixit and Pyndyck (1994): Simple Example: Decide today to: • Invest in a machine at end of year: I = £1,600. • End of year: project will be worth 300 (good state forever) or 100 (bad state forever) with equal probability. • WACC = 10%. • Should we invest?

  25. Dixit and Pyndyck example • Either pre-commit today to invest in a machine that will cost £1,600 at year end. • Or defer investment to wait and see. • Good state of nature (P = 0.5): product will be worth £300. • Bad state of nature (P = 0.5): product will be worth £100.

  26. NPV of project under pre-commitment =>

  27. Value with the option to defer • Suppose cost of investment goes up to £1,800 if we decide to wait (so, cost of waiting). • Year end good state: • Year-end bad state:

  28. Value with option to defer (continued) Therefore, deferring adds value of £136.30. Increasing uncertainty; eg price in good or bad state = 400 or zero (rather than 300 or 100) => Right to defer becomes more valuable.

  29. Comparing NPV, decision trees and Real Options (continued) 0.5 545.5 0.5 Invest Pre-commitment to invest

  30. Comparing NPV, decision trees and Real Options (continued) 0.5 Max{1500,0} Invest V= 681.8 0.5 Defer Max {-700,0} Don’t Invest Value with the option to defer

  31. Simplified Examples • Option to Expand (page 241 of RWJ) If Successful Expand Build First Ice Hotel Do not Expand If unsuccessful

  32. Option to Expand (Continued) • NPV of single ice hotel • NPV = - 12,000,000 + 2,000,000/0.20 =-2m • Reject? • Optimistic forecast: NPV = - 12M + 3M/0.2 • = 3M. • Pessimistic: NPV = -12M + 1M/0.2 = - 7m • Still reject?

  33. Option to expand (continued) • Given success, the E will expand to 10 hotels • => • NPV = 50% x 10 x 3m + 50% x (-7m) = 11.5 m. • Therefore, invest.

  34. Option to abandon. • NPV(opt) = - 12m + 6m/0.2 = 18m. • NPV (pess) = -12m – 2m/0.2 = -22m. • => NPV = - 2m. Reject? • But abandon if failure => • NPV = 50% x 18m + 50% x -12m/1.20 • = 2.17m • Accept.

  35. Real Option analysis and Game theory • So far, analysis has assumed that firm operates in isolation. • No product market competition • Safe to delay investment to see what happens to economy. • In real-world, competitors (vultures) • Delay can be costly!

  36. Option to delay and Competition • Smit and Ankum model (1993) • Option to defer an investment in face of competition • Combines real options and Game-theory. • Binomial real options model: lends itself naturally to sequential game approach (see exercise 1).

  37. Option to delay and competition (continued) • Smit and Ankum incorporate game theory (strategic behaviour) into the binomial pricing model of Cox, Ross and Rubinstein (1979). • Option to delay increases value (wait to observe market demand) • But delay invites product market competition: reduces value (lost monopoly advantage). • cost: Lost cash flows • Trade-off: when to exercise real option (ie when to delay and when to invest in project).

  38. Policy implications of Smit and Ankum analysis. • How can firm gain value by delaying (option to delay) in face of competition? • Protecting Economic Rent: Innovation, barriers to entry, product differentiation, patents. • Firm needs too identify extent of competitive advantage.

  39. Real Options and Games (Smit and Trigeorgis 2006) • Game theory applied to real R and D/innovation cases: • Expanded (strategic) NPV = direct (passive) NPV + Strategic (commitment) value + flexibility Value. • Innovation race between Philips and Sony => Developing CD technology.

  40. Each firm’s dominant strategy: invest early: => Prisoner’s dilemma. How to collaborate/coordinate on wait, wait?

  41. Asymmetric Innovation Race/Pre-emption • Asymmetry: P has edge in developing technology, but limited resources. • S tries to take advantage of this resource weakness • Each firm chooses effort intensity in innovation • Low effort: technology follower, but more flexibility in bad states • High effort: technology leader, higher development costs, more risk in bad state.

  42. “Grab the dollar” game

  43. Sequential Investment Game High effort -100m,-100m S High effort Low effort 100m, 10m P High effort 10m, 200m Low effort S Low effort 200m, 100m

  44. European Airport Expansion Case: Real Options Game (Smit 2003)

  45. Two-stage Investment Game (Imai and Watanabe 2004)

  46. Option to delay versus competition: Incorporating contracts/ Legal system (RF)

  47. Option to delay versus competition: Incorporating contracts/ Legal system (continued)

  48. Use of Real Options in Practice

  49. In practice, NPV not always used:Why Not?. • -Agency (incentive) problems: eg Short-term compensation schemes => Payback. • Behavioural:- • Managers prefer % figures => IRR, ARR • Managers don’t understand NPV/ Complicated Calculations. • Payback simple to calculate. • Other Behavioural Factors (see later section on Behavioural Finance!!) • Increase in Usage of correct DCF techniques (Pike): • Computers. • Management Education.

  50. Game-theoretic model of NPV. • Israel and Berkovitch RFS 2004. • NPV is seen as standard value-maximising technique. • But IB’s game-theoretic approach considers the impact of agency and assymetric information problems

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