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## REAL OPTIONS

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**REAL OPTIONS**The Options on Real Assets**PROJECT APPRAISAL - DCF**• Evaluation method of capital budgeting exercise by discounting the cash flows to find NPV is flawed because values so arrived ignore the value of managerial actions that are available later. • The implied assumption is that nothing would alter after the decision is made. • Conventional project appraisal by DCF method treats the project passive and static i.e. the set of assumptions made now remain valid for times to come. Financial Management II Rajiv Srivastava**CAPITAL BUDGETINGLimitations**• Capital budgeting decisions are seldom routine. They are strategic in nature. • Management has the flexibility to make decisions subsequent to implementation of project. • Managerial interventions have cash flow implications. • Capital budgeting done on the basis of static cash flows ignores the strategic value of the subsequent interventions. Financial Management II Rajiv Srivastava**STANDARD CAPITAL BUDGETING**• Standard techniques to evaluate capital budgeting decisions consider only the present information. • It assumes that all managerial actions are absent once the cash flow estimates are prepared. • Capital budgeting decisions are not passive and static. Instead they are subject to managerial actions with several options as time progresses. • options to reduce capacity utilisation, • undertake intensive advertising campaign if volumes are not picking up. • options such as increase production, raise prices, develop more product variants etc. • In fact each capital budgeting decision is a complex set of options. Financial Management II Rajiv Srivastava**HOW TO VALUE**• Do the managerial actions have some value? • In NPV we never attached a value to the options that are available. • The worth of the project must be evaluated as Real value of capital budgeting decision = Conventional NPV + Value of the options Financial Management II Rajiv Srivastava**OPTIONS ON REAL ASSETS**• The ability of the management to influence the cash flows of the project subsequently is referred as option on real asset. • Options on real assets are many but we confine normally to three types • option to delay, • option to expand and • option to abandon. Financial Management II Rajiv Srivastava**OPTION TO DELAY**• Option to delay refers to the decision of timing of implementation of project. • Deferment of the project may yield higher NPV than if implemented now. • Higher NPV may result from • more clarity on the information as time progresses, • greater reliability of input estimates used, or • use of lower discount rate as uncertainties of cash flows reduce as time progresses. Financial Management II Rajiv Srivastava**OPTION TO EXPAND**• Option to expand refers to the managerial flexibility to • increase production, • increase price, or • add product variants etc. • These actions based on experience gathered in the interim enhance the cash flows • It is like a call option with exercise price equal to the cost of additional investment required at a later date. Financial Management II Rajiv Srivastava**OPTION TO ABANDON**• Option to abandon refers to the flexibility of the management to exit the project realising the salvage value. • It is exercised when the cash flows of the project fail to meet the bare minimum expectations. • It is equivalent to a put option with exercise price equal to the salvage value. Financial Management II Rajiv Srivastava**VALUING REAL OPTIONS**• Standard capital budgeting analysis on the discounted cash flow basis treats the situation as now or never. • If the NPV of the project is negative we reject it. Value of embedded options may make a negative NPV project into a positive NPV proposition. • How to value • Comparing NPVs of different alternatives • Using binomial approach • Using Black – Scholes model Financial Management II Rajiv Srivastava**VALUING REAL OPTIONSDCF Method**• One way to value real option is to use DCF approach. • DCF approach compares the NPVs of the same project if implemented at different points of time. • Since option to implement now or later are mutually exclusive we choose the timing of implementation that provides the largest NPV. Financial Management II Rajiv Srivastava**VALUING REAL OPTIONSBinomial Method**• Many real options situations are apt for valuation by binomial method. • Major advantage of binomial method over DCF method is that binomial does not require the values of the probabilities of the various scenarios. • The current price of the asset is assumed to contain the volatility of the asset. Financial Management II Rajiv Srivastava**VALUING REAL OPTIONSBased on Financial Options**• Valuation of real options can be done by model developed for financial assets i.e. Black Scholes Model (BSM) • Valuation of real options with BSM would have following limitations: • non-tradability of real options • exercise not being instantaneous • problems of estimating the volatility of the cash flows and • inability to clearly define the option. Financial Management II Rajiv Srivastava**BASIC OPTIONS - CALL & PUT**• An OPTION is a right but not an obligation to buy/sell an asset at a predetermined price on or before a given date. • The underlying asset: stock, index, currency, futures, commodity etc. • CALL OPTION Right to buy an asset • PUT OPTION Right to sell an asset Financial Management II Rajiv Srivastava**FEATURES OF OPTIONS**• HOLDER WRITER Who holds the option Who gives the option WRITER/SELLER of the option is under obligation to perform; HOLDER/BUYER has no such obligation. Option Writer has to be paid a premium upfront. • EXERCISE/STRIKE PRICE MATURITY DATE Price at which the right Time up to which the can be exercised. right is available. • AMERICAN EUROPEAN Exercised on or before Exercised only on maturity maturity Financial Management II Rajiv Srivastava**PAY OFF – CALL OPTION**Pay Off BUYERWRITER When S < X - c + c When S > X S-X-c - (S-X-c) Spot Price c X Financial Management II Rajiv Srivastava**PAY OFF – PUT OPTION**• BUYER WRITER • When S < X X-S-p- (X-S-p) • When S > X - p + p Pay Off X Spot Price p Financial Management II Rajiv Srivastava**BINOMIAL METHOD**AssetCall 125 25 80% 100 20% 75 0 • Probabilities of up and down movement are not required, for no arbitrage argument. • Consider a portfolio of • 1 Long Share and • 2 Short Calls with X = 100 and maturity of 1 year • Value of portfolio at expiry Up move 125 – 2 x 25 = 75 Down move 75 – 2 x 0 = 75 • Outcome of portfolio is certain, and hence it must yield no more than the risk free rate of return. Financial Management II Rajiv Srivastava**VALUING CALL WITH BINOMIAL**Cost of setting the portfolio of 1 long stock and 2 short calls, is 100 – 2c where c is the value of call. Rs 75 is the value after one year and is certain, therefore cost of portfolio must equal the present value of Rs 75 discounted at risk free rate, r = 10% (assumed) With current stock price known this would give the value of the 1 year call with X = 100 100 – 2c = e-rT x 75 = 75 x 0.9048 c = 32.14/2 = Rs 16.07 Financial Management II Rajiv Srivastava**VALUING CALL ……..**T = 0 At Maturity, T AssetCall ΔuS cu S, c ΔdS cd Riskless portfolio Δ long stock and 1 short call; Value of portfolio at expiry is same i.e. ΔuS – cu = ΔdS - cd Value of portfolio at T = 0 ΔS – c = (ΔuS – cu) e-rT c = [p cu + (1- p)cd] e-rT Where For the example, we have Δ = ½ and p =(1.1052 - 0.75)/0.5 = 0.7103 Call value, c = (0.7103 x 25 – 0.2897 x 0) x 0.9048 = Rs 16.07 Financial Management II Rajiv Srivastava**RISK NEUTRAL VALUATION**If the binary state of prices is correct the market as a whole must agree to the same expected price, E(S1) of the stock. To have universally acceptable E(S1) the expected returns offered by the stock [E(S1) - S0]/S0 can be no greater than the risk free rate of return, r. Under risk neutral valuation all investors are neutral to risk, i.e. the underlying asset earns the risk free rate of return, i.e. E(S1) = (1+ r) x S0, or with continuous compounding E(S1) = erT x S0 = Futures price, F While computing futures price therefore we use risk free rate assuming risk neutral world. Financial Management II Rajiv Srivastava**RISK NEUTRAL VALUATION**If p is probability of up move, then expected value of the asset at maturity = [p x 125 + (1 – p) x 75] Under risk neutrality it must give 10% return therefore, [p x 125 + (1 – p) x 75 ]= 100 x e0.10 x 1 Therefore p = 0.7103 and 1 – p = 0.2897 Same risk neutral probabilities would apply to the call. Call value at T = [0.7103 x 25 + 0.2897 x 0] = Rs 17.7575 The call value today, c = call value at maturity discounted at risk free rate (10%) = [0.7103 x 25 + 0.2897 x 0] e-0.10 x 1 = Rs 16.07 Financial Management II Rajiv Srivastava**REAL WORLD AND RISK NEUTRAL WORLD**If in the real world the expected return from the stock is 20% and not 10% (the risk free rate), then with binary states the probability of up move, p* must be [p* x 125 + (1 – p*) x 75 ]= 100 x e0.20 x 1 or p* = 0.9428 Then the value of the call at maturity in real world would be = p* x 25 + (1 – p*) x 0 = = 0.9428 x 25 = Rs 23.57 Actual value of call in risk neutral world is Rs 16.07. The appropriate discount rate would then be 38.31% in the real world (riskier than what applies to asset, 20%). Financial Management II Rajiv Srivastava**VALUE A VACANT LAND**• A piece of land can be used for making 8 apartments now or after 1 year. The market value of each apartment today is Rs 60 lakh. The cost of building apartments is Rs 360 lakh. • The net profit if built today 60 x 8 – 360 = Rs 120 lakh • The firm has an option to delay the project by one year • Uncertainty about the value of the apartment a year later. With only two scenarios Buoyant Sluggish Market Value Rs75 lakh Rs 54 lakh Financial Management II Rajiv Srivastava**VALUE A VACANT LAND**• Should the builder defer the construction? • Conventional capital budgeting process - Construct now with positive NPV of Rs 120 lakh . • Additional information available • Cost of construction remains same after 1 year at Rs 360 lakh • Interest rate = 12% p.a. • Opportunity cost = loss of rental for one year Rs 5 lakh p.a. Financial Management II Rajiv Srivastava**BINOMIAL MODEL**Situation Value Payoff 70 70 x 8 – 360 = 200 Buoyant 60 Sluggish 49 49 x 8 – 360 = 32 Financial Management II Rajiv Srivastava**BINOMIAL MODEL**• Probability of rising and falling prices are built in the current value of the flat. If probability of buoyant condition is p then p x 70 + (1 - p) x 49 = 60 x 1.12 Gives p = 0.7913 Situation 70 70 x 8 – 360 = 200 Buoyant Call Value = (0.7913 x 200 + 0.2087 x 32)/1.12 60 = 164.94/1.12 = Rs 147.26 lakh Sluggish 49 49 x 8 – 360 = 32 Financial Management II Rajiv Srivastava**VALUE A VACANT LAND**• Let us value the option to build 12 flats on the land. The value of each apartment today is Rs 60 lakh. The cost of building apartments is Rs 590 lakh. • The net profit if built today 60 x 12 – 590 = Rs 130 lakh • The firm has an option to delay by one year • Uncertainty about the value of the apartment a year later. With only two scenarios Buoyant Sluggish Market Value Rs75 lakh Rs 54 lakh Financial Management II Rajiv Srivastava**BINOMIAL MODEL**Situation Value Payoff 70 70 x 12 – 590 = 250 Buoyant 60 Sluggish 49 49 x 12 – 590 = -2 Financial Management II Rajiv Srivastava**BINOMIAL MODEL**• Probability of rising and falling prices are built in the current value of the flat. If probability of buoyant condition is p then p x 70 + (1 - p) x 49 = 60 x 1.12 Gives p = 0.7913 Situation 70 70 x 12 – 590 = 250 Buoyant Call Value = (0.7913 x 250 – 0.2087 x 0)/1.12 60 = 197.82/1.12 = Rs 176.63 lakh Sluggish 49 49 x 12 – 590 = -2 (0) Financial Management II Rajiv Srivastava**OPTION TO DELAY**Now or Never ???? Vs. Now or Later**TIMING DECISION - DCF**• Assume a software firm SOFTBANK has developed a new banking product but is uncertain about its demand potential. • Only 2 possible outcomes • HIGH DEMAND: Cash flows of Rs 50 lacs for 4 years • LOW DEMAND: Cash flows of Rs 30 lacs for 4 years • CAPITAL OUTLAY : Rs. 100 lacs • LIFE : 4 years • SOFTBANK knows that there is no competitor emerging in the product developed and it can afford to delay implementation of the project. • The managers at SOFTBANK estimate equal likelihood of the ‘good’ and ‘not so good’ demand scenario. Financial Management II Rajiv Srivastava**TIMING DECISION - DCF**• The expected annual cash flow would be Rs. 40 lacs (0.50 x 50 + 0.50 x 30). • 12% discount rate is considered appropriate for the risk of the cash flows. • The expected NPV of the project if launched now is Rs. 21.49 lacs • With positive NPV the project must be implemented now. Financial Management II Rajiv Srivastava**OPTION TO DELAY**• The decision to implement a year later will depend upon the demand scenario prevailing then. • If the demand remains good SOFTBANK must go ahead with the launch else it must drop altogether. • The above situation can be considered as 2 mutually exclusive options and the decision will be based on the rule of higher NPV. Option I : Launch now Option II : Launch a year later. Cost of implementing a year later remains same at Rs 100 lacs • Option I and II are mutually exclusive as selection of one precludes the other. Financial Management II Rajiv Srivastava**OPTION TO DELAY - NPVs**Financial Management II Rajiv Srivastava**OPTION TO DELAY - NPVs**• NPVs need to be compared must coincide in time. • Since the expected NPV of Option II is greater the product must be launched a year later. • The value of the option to wait for one year, therefore is the difference of the two NPVs i.e. Rs. 1.67 lacs. • Assumptions: • The firm implements the project if the demand scenario is ‘good’ in Year 1. • Firm abandons the project if the demand scenario is ‘not so good’ in Year 1. • The initial outlay and the cash flows from for next four years remain same. (Should it be discounted at the same rate as that of cash flows??) • The discount rate too remains same at 12%??? Financial Management II Rajiv Srivastava**NPV – Some Issues**Initial investment • must be discounted at much lower rate than WACC – the applicable rate for discounting the project cash inflows. Some recommend the use of risk free rate. • This will increase the value of initial investment and decrease the NPV of the delay option. Discount Rate • Use of same WACC under both the options is fallacious because of increased certainty of the cash flow in option to delay. Under Option II we do not make investment if low demand is experienced in Year 1. Therefore, discount rate under Option II should be lower than the one used in Option I, not because the rates have fallen or changed but because there is less uncertainty under Option II than under Option I. • This will increase the NPV of the delay option. Financial Management II Rajiv Srivastava**OPTION TO DELAY - BINOMIAL**Financial Management II Rajiv Srivastava**Option to Wait; Binary Option Pricing**Present Value % Return 151.87 +51.87% 100 91.92 -8.88% Binomial Presentation Financial Management II Rajiv Srivastava**Option to Delay - Binomial**• The firm has option to delay by one year implying thereby that it implements the project with • Exercise price, X = Rs. 100 lacs. • Payoff is like call option • Good demand = Rs. 51.87 lacs. • Low demand = Nil Financial Management II Rajiv Srivastava**Option to Delay – A Call Option**• Using risk neural method to value the call option, the probability of high demand as p, then the payoff of the two branches must yield return equal to risk free rate taken as 9%. Then p x 51.87% + (1 – p) x (-8.88%) = 9% p = 29.43% • With probability, p of 29.43% the value of the call is computed at Rs. 15.26 lacs. Value of the call = 0.2943 x 51.87 + 0.7551 x 0 = Rs. 15.26 lacs Financial Management II Rajiv Srivastava**OPTION TO DELAYBLACK SCHOLES MODEL**Financial Management II Rajiv Srivastava**Inputs for BSM**• Option to wait resembles a call option on a stock (option to buy at predetermined price within specified time), and we can use BSM to value the option to wait. To value this call option we require following five inputs: • The Exercise Price ‘E’ • The Expiration Time ‘t’ • The Risk free rate ‘rf’ • The Spot Price of the underlying asset ‘S’ • The Variance of return ‘σ2’ Financial Management II Rajiv Srivastava**Inputs of BSM**• Here first three inputs are straight forward . • The exercise price ‘E’ = Rs. 100 lacs, the value of initial investment. • The time to expiry of this option, t = one year. • Risk free rate can be obtained from yield on the government securities. Let us assume this at 6%. • The underlying asset on the option is the cash flow of the delayed project. The expected present value of the cash inflows only of the project (not the expected NPV which is the intrinsic value of the option) will be equivalent to the spot price, S. Financial Management II Rajiv Srivastava**The Underlying Asset**Financial Management II Rajiv Srivastava**The Variance**Financial Management II Rajiv Srivastava**BSM – Option to Delay**• The values of the input are Spot Price, S= Rs. 108.48 lacs, Exercise Price, X = Rs. 100 lacs Time to expiry, t = 1 year Interest Rate, rf = 6% Standard Deviation, σ = 28% • Inserting the values, Value of call option = Rs. 19.83 lacs. Financial Management II Rajiv Srivastava**OPTION TO EXPAND**Financial Management II Rajiv Srivastava**OPTION TO EXPAND - DCF**• Option to expand relates to the flexibility of management to start small and depending upon the outcome set up another big related venture. • This flexibility cannot be exercised unless the initial investment is made. • Most firms start a venture on experimental basis keeping investment small to limit the risk. • Most such projects are likely to be negative NPV projects • With conventional approach of positive NPV or IRR in excess of cost they stand rejected. • Examples of such projects are numerous. Financial Management II Rajiv Srivastava**OPTION TO EXPAND – Grow Motors**• An Electric Car may be launched at a cost of Rs 200 crore with expected inflow of Rs 75 crore p.a. for next three years. At 10%, it has NPV of - Rs 13.49 crore. • The launch of Phase I of Electric Car presents an opportunity to improve upon the performance that is likely to • expand the market, • decrease the price and • increase the volumes and hence improve NPV later. • Follow-on investment can be made after 3 years with Year 3 outlay of Rs 600 crore and present value (Year 3) of inflows is Rs 1,000 crore. Financial Management II Rajiv Srivastava