Gasworks, Inc., has been approached to sell up to 4 million gallons of gasoline

Question

Gasworks, Inc., has been approached to sell up to 4 million gallons of gasoline in three months at a price of $3.25 per gallon. Gasoline is currently selling on the wholesale market at $3.00 per gallon and has a standard deviation of 56 percent. If the risk-free rate is 7 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 References eBook & Resources Worksheet Difficulty: 1 Basic Section: 23.3 More about the Binomial Model

Explanation / Answer

Current stock price S = 4,000,000 * 3.00 = 12,000,000

Strike price K = 4,000,000 * 3.00 = 13,000,000

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

d1= [ln($13,000,000/$12,000,000) + (.07 + .3136/2) ×(.25)] / ( .3136*.25)1/2 = -0.083366813

d2= -0.083366813 – (.56 ×.25) = -0.363366813

ormal probabilities:

N(d1) = 0.466779938

N(d2) = 0.358165445

C = SN(d1) – Ke-–RtN(d2)

C = $12,000,000( 0.466779938) – ($13,000,000* e–.056(.25))(0.358165445)

value of contract = 1,025,982.282

Related Questions

Navigate

• Browse (All)
• Browse G
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.