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Binnenlandse Francqui Leerstoel VUB 2004-2005 Real Options

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##### Binnenlandse Francqui Leerstoel VUB 2004-2005 Real Options

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**Binnenlandse Francqui Leerstoel VUB 2004-2005Real Options**André Farber Solvay Business School University of Brussels**Valuation: the traditional approach**• Standard approach: V = PV(Expected Free Cash Flows) • Free Cash Flow = CF from operation + CF from investment • Valuation technique: discounting using a risk-adjusted discount rate • Setting the discount rate: Capital Asset Pricing Model VUB 03 Real options**Making Investment Decisions: NPV rule**• NPV : a measure of value creation • NPV = V-I with V=PV(Additional free cash flows) NPV rule: invest whenever NPV>0 • Underlying assumptions: • one time choice that cannot be delayed • single roll of the dices on cash flows • But: • delaying the investment might be an option • what about flexibility ? VUB 03 Real options**Capital Budgeting: What techniques are used?**VUB 03 Real options**A simple example: the widget factory**• Cost of factory I: $4,000 • Produces one widget per year forever with zero operating cost • Price of widget uncertain: t = 1 t = 2 t = 0 P2 = $300 P1 = $300 Proba = 0.50 P0 = $200 Proba = 0.50 P1 = $100 P2 = $100 Risk-free interest rate = 5% β = 0 VUB 03 Real options**Traditional NPV calculation**• Expected price = 0.5 × $300 + 0.5 × $100 = $200 • Expected cash flows What would you decide? VUB 03 Real options**What if we wait one year?**P1 = $300 → NPV = -4,000 + 300 + 300/0.05 = $2,300 DECISION: INVEST Invest →NPV = $200 Wait → DECISION: WAIT P1 = $100 → NPV = -4,000 + 100 + 100/0.05 = -$1,900 DECISION:DO NOT INVEST VUB 03 Real options**Real options take a number of forms**• If an initial investment works out well, then management can exercise the option to expand its commitment to the strategy. • For example, a company that enters a new geographic market may build a distribution center that it can expand easily if market demand materializes. • An initial investment can serve as a platform to extend a company's scope into related market opportunities. • For example, Amazon.com's substantial investment to develop its customer base, brand name and information infrastructure for its core book business created a portfolio of real options to extend its operations into a variety of new businesses. • Management may begin with a relatively small trial investment and create an option to abandon the project if results are unsatisfactory. • Research and development spending is a good example. A company's future investment in product development often depends on specific performance targets achieved in the lab. The option to abandon research projects is valuable because the company can make investments in stages rather than all up-front. VUB 03 Real options**Portlandia Ale: an example**• (based on Amram & Kulatilaka Chap 10 Valuing a Start-up) • New microbrewery • Business plan: • €4 million needed for product development (€0.5/quarter for 2 years) • €12 million to launch the product 2 years later • Expected sales € 6 million per year • Value of established firm: €22 million • (based on market value-to-sales ratio of 3.66) VUB 03 Real options**DCF value calculation**VUB 03 Real options**But there no obligation to launch the product..**• The decision to launch the product is like a call option • By spending on product development, Portlandia Ale acquires • a right (not an obligation) • to launch the product in 2 years • They will launch if, in 2 years, the value of the company is greater than the amount to spend to launch the product (€12 m) • They have some flexibility. • How much is it worth? VUB 03 Real options**Valuing the option to launch**• Let use the Black-Scholes formula (for European options) • At this stage, view it as a black box (sorry..) • 5 inputs needed: Call option on a stockOption to launch Stock price Current value of established firm Exercise price Cost of launch Exercise date Launch date Risk-free interest rate Risk-free interest rate Standard deviation of Volatility of value return on the stock VUB 03 Real options**Volatility**• Volatility of value means that the value of the established firm in 2 years might be very different from the expected value VUB 03 Real options**Using Black Scholes**• Current value of established firm = 14.46 • Cost of launch = 12.00 • Launch date = 2 years • Risk-free interest rate = 5% • Volatility of value = 40% • and…magic, magic…..value of option = € 4.96 VUB 03 Real options**The value of Portlandia Ale**• (all numbers in € millions) • Traditional NPV calculation PV(Investment before launch) - 3.83 PV(Launch) - 10.86 PV(Terminal value) +14.46 Traditional NPV - 0.23 • Real option calculation PV(Investment before launch) - 3.83 Value of option to launch + 4.96 Real option NPV + 1.13 VUB 03 Real options**Let us add an additional option**• Each quarter, Portlandia can abandon the project • This is an American option (can be exercised at any time..) • Valuation using numerical methods (more on this later..) • Traditional NPV calculation Traditional NPV - 0.23 • Real option calculation PV(Investment before launch) - 3.83 Value of options to launch and to abandon + 5.57 Real option NPV + 1.74 VUB 03 Real options**Real option vs DCF NPV**• Where does the additional value come from? • Flexibility • changes of the investment schedule in response to market uncertainty • option to launch • option to continue development VUB 03 Real options**Back to Portlandia Ale**• Portlandia Ale had 2 different options: • the option to launch (a 2-year European call option) • value can be calculated with BS • the option to abandon (a 2-year American option) • How to value this American option? • No closed form solution • Numerical method: use recursive model based on binomial evolution of value • At each node, check whether to exercice or not. • Option value = Max(Option exercised, option alive) VUB 03 Real options**Binomial option pricing model: review**• Used to value derivative securities: PV=f(S) • Evolution of underlying asset: binomial model • u and d capture the volatility of the underlying asset • Replicating portfolio: Delta × S + M • Law of one price: f = Delta × S + M uS fu S fd dS Δt M is the cash positionM>0 for investmentM<0 for borrowing r is the risk-free interest rate with continuous compounding VUB 03 Real options**Risk neutral pricing**• The value of a derivative security is equal to risk-neutral expected value discounted at the risk-free interest rate • p is the risk-neutral probability of an up movement VUB 03 Real options**Valuing a compound option (step 1)**• Each quaterly payment (€ 0.5 m) is a call option on the option to launch the product. This is a compound option. • To value this compound option:: • 1. Build the binomial tree for the value of the company 0 1 2 3 4 5 6 7 8 14.46 17.66 21.56 26.34 32.17 39.29 47.99 58.62 71.60 11.83 14.46 17.66 21.56 26.34 32.17 39.29 47.99 9.69 11.83 14.46 17.66 21.56 26.34 32.17 7.93 9.69 11.83 14.46 17.66 21.56 6.50 7.93 9.69 11.83 14.46 5.32 6.50 7.93 9.69 4.35 5.32 6.50 3.56 4.35 2.92 u=1.22, d=0.25 up down VUB 03 Real options**Valuing a compound option (step 2)**• 2. Value the option to launch at maturity • 3. Move back in the tree. Option value at a node is: Max{0,[pVu +(1-p)Vd]/(1+rt)-0.5} 0 1 2 3 4 5 6 7 8 1.744.24 7.88 12.71 18.79 26.25 35.29 46.27 59.60 0.42 1.95 4.57 8.35 13.30 19.47 26.94 35.99 0.00 0.53 2.16 4.93 8.87 13.99 20.17 0.00 0.00 0.62 2.36 5.30 9.56 0.00 0.00 0.00 0.67 2.46 0.00 0.00 0.00 0.00 0.00 0.000.00 0.00 0.00 0.00 p = 0.481/(1+rt)=0.9876 =(0.482.46+0.520.00) 0.9876-0.5 VUB 03 Real options**When to invest?**• Traditional NPV rule: invest if NPV>0. Is it always valid? • Suppose that you have the following project: • Cost I = 100 • Present value of future cash flows V = 120 • Volatility of V = 69.31% • Possibility to mothball the project • Should you start the project? • If you choose to invest, the value of the project is: • Traditional NPV = 120 - 100 = 20 >0 • What if you wait? VUB 03 Real options**To mothball or not to mothball**• Let analyze this using a binomial tree with 1 step per year. • As volatility = .6931, u=2, d=0.5. Also, suppose r = .10 => p=0.40 • Consider waiting one year.. V=240 =>invest NPV=140 V=120 V= 60 =>do not invest NPV=0 • Value of project if started in 1 year = 0.40 x 140 / 1.10 = 51 • This is greater than the value of the project if done now (20) • Wait.. • NB: you now have an American option VUB 03 Real options**Waiting how long to invest?**• What if opportunity to mothball the project for 2 years? V = 480 C = 380 V=240 C = 180 V=120 C = 85 V = 120 C = 20 V= 60 C = 9 V = 30 C = 0 • This leads us to a general result: it is never optimal to exercise an American call option on a non dividend paying stock before maturity. • Why? 2 reasons • better paying later than now • keep the insurance value implicit in the put alive (avoid regrets) 85>51 => wait 2 years VUB 03 Real options**Why invest then?**• Up to know, we have ignored the fact that by delaying the investment, we do not receive the cash flows that the project might generate. • In option’s parlance, we have a call option on a dividend paying stock. • Suppose cash flow is a constant percentage per annum of the value of the underlying asset. • We can still use the binomial tree recursive valuation with: p = [(1+rt)/(1+t)-d]/(u-d) • A (very) brief explanation: In a risk neutral world, the expected return r (say 6%) is sum of capital gains + cash payments • So:1+r t = pu(1+ t) +(1-p)d(1+ t) VUB 03 Real options**American option: an example**• Cost of investment I= 100 • Present value of future cash flows V = 120 • Cash flow yield = 6% per year • Interest rate r = 4% per year • Volatility of V = 30% • Option’s maturity = 10 years • Binomial model with 1 step per year • Immediate investment : NPV = 20 • Value of option to invest: 35 WAIT VUB 03 Real options**Value of future cash flows**(partial binomial tree) 0 1 2 3 4 5 120.0 162.0 218.7295.2 398.4 537.8 88.9 120.0 162.0 218.7 295.2 65.9 88.9 120.0 162.0 48.8 65.9 88.9 36.1 48.8 26.8 Investment will be delayed. It takes place in year 2 if no down in year 4 if 1 down Early investment is due to the loss of cash flows if investment delayed. Notice the large NPV required in order to invest Optimal investment policy VUB 03 Real options**A more general model**• In previous example, investment opportunity limited to 10 years. • What happened if their no time frame for the investment? • McDonald and Siegel 1986 (see Dixit Pindyck 1994 Chap 5) • Value of project follows a geometric Brownian motion in risk neutral world: • dV = (r- ) V dt + V dz • dz : Wiener process : random variable i.i.d. N(0,dt) • Investment opportunity :PERPETUAL AMERICAN CALL OPTION VUB 03 Real options**Rule: Invest when present value reaches a critical value V***If V<V* : wait Value of project f(V) = aVif V<V* V-I if V V* Optimal investment rule VUB 03 Real options**Optimal investment rule: numerical example**• Cost of investment I = 100 • Cash flow yield = 6% • Risk-free interest rate r = 4% • Volatility = 30% • Critical value V*= 210 • For V = 120, value of investment opportunity f(V) = 27 Sensitivity analysis V* 2% 341 4% 200 6% 158 VUB 03 Real options**Value of investment opportunity for different volatilities**VUB 03 Real options**Some Applications of Real Options**• Valuing a Start-Up • Exploring for Oil • Developing a Drug • Investing in Infrastructure • Valuing Vacant Land • Buying Flexibility VUB 03 Real options