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: 100 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? 180 60 324 108 36
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 2013 as originally scheduled. b) Nokia spent 6 billion US dollars to purchase small digital map supplier, Navteq, in year 2007. They did so, to be better positioned to develop the next generation of mobile phones with location services.
16 Answers: Q1. a) 100 - 84 = $16m. b) p = 1 108 0 6 18 0 6 0 4 + − − = − − = r d u d f . . . . . . Alternatively, from the project value tree note that (180 p + 60 (1- p ))/1.08= 100. This implies p = 0.4.