Question

Gasworks, Inc., has been approached to sell up to 3.4 million gallons of gasoline in three months at a price of $2.80 per gallon. Gasoline is currently selling on the wholesale market at $2.70 per gallon and has a standard deviation of 59 percent.

  

If the risk-free rate is 5 percent per year, what is the value of this option? Use the two-state model to value the real option. (Enter your answer in dollars, not millions of dollars, e.g., 1,234,567. Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

  

Value of contract

$

Answer 1

Risk-Free Rate = 5 %, Tenure of Real Option = 3 months or (3/12) = 0.25 years, Underlying Asset = Gasoline, Current Asset Price = S0 = $ 2.7 per gallon and Strike Price of Real Option = $ 2.8 per gallon (this is a put option as the underlying asset of the real option is to be sold in the future), Standard Deviation = 59 %

Upward Move Factor = u = e^[Standard Deviation x (Tenure)^(1/2)] = e^[0.59 x (0.25)^(1/2)] = 1.34313

and Downward Move Factor = d = 1/u = 1/1.34313 = 0.74453

Risk-Neutral Probability of Price moving Up = p = [EXP(0.05 x 0.25) - d] / [u - d] = [EXP(0.05 x 0.25) - 0.74453] / [1.34313 - 0.74453] = 0.44779

If Price Moves up:

Price of Gasoline = S0 x u = 2.7 x 1.34313 = $ 3.626451 and Payoff = $ 0 (as asset price is more than strike price)

If Price Moves down:

Price of Gasoline = S0 x d = 2.7 x 0.74453 = $ 2.010231 and Payoff = (2.8 - 2.010231) = $ 0.789769

Expected Value of Payoffs = E(Pf) = 0.44779 x 0 + (1-0.44779) x 0.789769 = $ 0.436118339

Put Price = Present Value of Expected Payoff = 0.436118339 / EXP (0.05 x 0.25) = $ 0.43070079 ~ $ 0.43 per gallon

Contract Size = 3.4 million gallons (as this is the maximum value that Gasworks can sell)

Price per Contract = 3.4 x 0.43 = $ 1.462 million