Aalto. Derivatives LECTURE 5. Professor: Matti SUOMINEN. 17 Pages

Transcription

1 Aalto Derivatives LECTURE 5 Professor: Matti SUOMINEN 17 Pages

2 REAL OPTIONS / OPTIONS IN CAPITAL BUDGETING Traditional NPV calculations do not take into account the value of flexibility in investments. Some examples: 1. Option to delay investment 2. Option to expand / contract 3. Option to abandon 4. Option to switch outputs or inputs Can we use the same option valuation approach for non-financial assets as we developed for financial assets? What is the underlying security? 2

3 SOME EXAMPLES WHERE REAL OPTIONS ARE IMPORTANT: High technology companies: Option to use developed technology elsewhere. Movie producers: Option to produce sequels to films. Paper companies: Option to switch paper type. Option to temporarily shut down the production. Brand products: Option to introduce other products under the same brand. Option to expand marketing to overseas. Natural resource industries: Option to expand / contract. Option to defer. 3

4 In principle we can use the same techniques to price real options as financial options. The use of option pricing techniques is most straightforward: If the underlying is traded. If we can replicate the underlying indirectly. If the underlying has zero beta. In real options the underlying security is typically the value of the project if the project is taken. 4

5 Example: 1 year lease on a gold mine Extract up to 100,000 oz. Cost of extraction is $270 per oz. Current market price of gold is $300 per oz. Volatility of gold price is 22.3% p.a. Interest rate is 10% p.a. Here the options approach is straightforward as the underlying is traded. In addition gold futures and shares of gold producers can be used to replicate the movements in gold prices. 5

6 Options Approach: The lease can be seen as a call option on 100,000 oz of gold with EX = 27M. First calculate: u d σ Δt = e = 1 = = u p = ( 1+ r ) d f u d = 6

7 We can now build the Gold price tree : 300 And value the lease: 7

8 MULTIPLE OPTIONS 2-year lease on a gold mine. Lease for year 1 Lease for year 2 Gold price:

9 Lease value: ( )*100K = 19.9 M 2 nd year prod. = 1 st year prod. = ( )*100K = 10.5 M ( )*100K = 3.0 M 2 nd year prod. = 1 st year prod. = 0.0 M 0.0 M 9

10 OPTION TO EXPAND Suppose at time t=1, we can expand production for t=2. Up-front capital investment (at t=1) = $1.5 M. With the new investment, can mine up to 125,000 oz per year, at a per unit cost of $280 per oz. How much would you pay at t=0 for this option? Start by considering value of expansion at nodes A and B: Gold price: A B

11 At A (value of second year production at t=1): Currently: 19.9 M 13.0 M 3 M If Expand: ( )*125K = 23.6 M ( )*125K = 2.5 M Increase in value at A if expand = Value of option to expand at A = 11

12 At B (value of second year production at t=1): Currently: 3 M 1.8 M 0 M If Expand: ( )*125K = 2.5M = 0 M Worse off with expansion Value of option to expand at B = 12

13 Value of option to expand at t=0: Total value of the lease: old lease value + value of option to expand 13

14 Review questions for lecture 5: Q1. Suppose you, as an entrepreneur, have an opportunity to invest $84 million in an oil extraction project whose gross value is $100m at t=0, and each year will either move up by 80% or down by 40%, depending on oil price fluctuations. Thus, over two years, the value of the project (i.e. the value, in millions of dollars, of its subsequent expected cash flows appropriately discounted back to that year) is given by the following tree: The risk-free rate is 8%. (a) What is the NPV or value of the project? (b) What is the risk-neutral probability? (c) Suppose that the investment of $84m necessary to implement the oil project can be staged as a series of instalments : $24m at t=0 and $60m with earned interest (i.e. $60m x 1.08 = $64.8m) at t=1. You have to pay the up-front cost if you are going to take on the project. However, you need not pay the t=1 instalment, if you feel you are better off abandoning the project. What is the NPV of the project? What is the value of the option to abandon? 14

15 Q2: Describe the real option in the following two cases: a) Noreal corporation is developing a commercial center to Evry, near Paris. Due to a decline in the demand for office space in the Paris region they have decided to complete only half of the planned buildings before year 2015 as originally scheduled. b) Samuel Rappaport, a real estate speculator in Philadelphia made a fortune by buying strategically located, distressed properties at bargain prices at times when the real estate markets were depressed (and developing those properties at that time would only have led to large losses). Q3: Getting married can be seen as an irreversible investment and can best be understood in terms of the real option theory. Assume that every month you meet a new potential partner and must decide whether to take the big leap and get married. If you decline the opportunity then this potential partner walks away and you must wait a whole month before the next one arrives. Assume that the potential partners are of two types: with probability 0.2 they are very nice, with probability 0.8 they are, well, not so nice. You derive a utility of 10 for being married to a very nice person, a utility 6 for being married to a not so nice person. Your utility from being single is 5. Once married you live happily ever after (infinitely long). You discount future with a monthly discount rate 0.9. There is a one time cost to getting married equal to 5 utility units. When should you get married? 15

16 Answers: Q1. a) = $16m. b) p = 1 + rf d = = Alternatively, from the project value tree note that u d (180p + 60 (1-p))/1.08= 100. This implies p = 0.4. c) We solve for the new value of the project by starting at t=2 and working backwards. At t=2 we get the same values as are given in the question (there are no decisions at t=2). At t=1, we have to decide whether to invest $64.8m and continue. The salvage value if we abandon is zero. Thus, the value of the project in the up state at t=1 is max(value if continue, value if abandon) = max( ,0) = 115.2, so the firm should continue. Similarly, the value of equity in the down state at t=1 is max( ,0) = 0, so the firm should abandon. The value of the project at t=0, is (p (1- p) 0)/1.08 less the initial investment of $24 which gives an NPV of $ The option to abandon is the increase in value over and above the case without staged investment, i.e (16) = max( ,0) = ( p ( 1 p) 0) 108. = max( ,0) = 0 Q2: a) They have exercised an option to delay the investment or an option to contract (depending whether they plan to complete the second half of their project anymore or not). This kind of staged investment is also known as Time to Build Option. b) Rappaport was buying options to defer, American call options to develop those properties should the real estate markets pick up. Time after time during real estate booms he exercised his right to develop the properties that he owned, sold them, only to buy new property when the real estate markets were again in depression. 16

17 Q3: Of course, if you meet a very nice person you should not hesitate to get married. The question is what to do when you meet a not so nice person. If you meet a not so nice person getting married is still a positive NPV transaction: * = 6/0.1-5 = 55 > 5/0.1 = 50 = utility from being single forever. However it may pay to defer the investment (to see whether the next potential partner is very nice). It pays to defer, if utility from getting married next period is higher than from getting married today to a not so nice person. That is, if * 0.2 * 10/ * 0.8 * 6/ * 5 > 6/0.1-5 ð 61.7 > 55 It thus pays to defer and wait for the right one. 17