Binomial Trees

In: Business and Management

Submitted By liudika
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Problem 1: Binomial Trees and Real Options

Suppose that the spot price, 6-month forward price, 12-months forward price and 18-months forward price for wheat are 250, 260, 270.4 and 281.216 cents per bushel, respectively.[1] A farmer has a project that involves an immediate expenditure of $20,000 and a further expenditure of $90,000 in six months. The farmer collects two wheat harvests per year, and if this project is implemented, it will increase wheat that is harvested and sold by 20,000 bushels in one year and in 18 months (as compared to his typical harvest). Assume that there is no uncertainty about the harvests (all uncertainty comes from future wheat prices). The continuously compounded risk-free rate is 5% p.a.

a) If the project has no flexibility (a “yes or no” decision), what is the value of the project? Notice that you do not have to use the binomial tree to answer this question. b) Suppose that the wheat price follows a binomial tree process with parameters u=1.1 and d=0.95 (determine y from forward prices and remember to take this variable into account when computing risk-neutral probabilities). Suppose that the farmer can abandon the project in six months and avoid paying the $90,000 cost at that time (in this case, the increase in harvest will be 5,000 bushels per year instead of 20,000). What is the value of this abandonment option? Is this abandonment option a put or a call? What is its strike? Explain. c) Now, assume that there is no option to abandon. Instead, suppose that the project can be delayed for 6 months: the investments can be made in six months and in one year, and the increases in harvests will be observed in 18 months and 2 years. What is the value of this option to delay? d) If the option to abandon and the option to delay are both available, what is the value of the project? Is the value of the portfolio of these…...

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