I will thumbs up correct anwser. Gasworks, Inc., has been approached to sell up

Question

I will thumbs up correct anwser.

Gasworks, Inc., has been approached to sell up to 6 million gallons of gasoline in three months at a price of $4.35 per gallon. Gasoline is currently selling on the wholesale market at $4.00 per gallon and hasa standard deviation of 56 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

Explanation / Answer

Current stock price S = 6,000,000 * 4 = 24,000,000

Strike price K = 6,000,000 * 4.35 = 26,100,000

d1= [ln(S/K) + (R + ?2/2)(t) ] / (?2t)1/2

d1= [ln($24,000,000/$26,100,000) + (.05 + .3136/2) ×(.25)] / ( .3136*.25)1/2 =

d2= -0.11493387 – (.56 ×.25) =

-0.39493

Normal probabilities:

N(d1) =

0.454248769

N(d2) =

0.346445846

  

C = SN(d1) – Ke-–RtN(d2)

C = $24,000,000(0.454248769) – ($26,100,000* e–.05(.25))(0.346445846)

value of contract = 1,972,058

-0.11493387

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