Question

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 has a 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. (Do not round intermediate calculations and enter your answer in dollars, not millions of dollars, rounded to 2 decimal places, e.g., 1,234,567.89.)

Answer 1

1. Computation of U and D using Binomial Model

A B c D Binomial Option Pricing Model: Visualizin 2 S (S 0) 3 r( 4 G (sigma) 4.00 current share price 5% riskfree rate p.a 56% 1.32 u EXP(a AT^O.5)| 0.76 d EXP(- AT^o.5) 5 u 6 d 7 X 8 T 9 n 10 AT 11 P 4.35 0.25 1 0.25 AT T/n 0.4526 p [ exp(rAT) - d 1/ (u -d)

A E Binomial Option Pric 2 S (S 0) 3 r (rf) (sigma) 1 4 current share price riskfree rate p.a 0.05 4 0.56 +EXP(B4*B10^0.5) |= +EXP(-B4*B10^0.5) 4.35 5 EXP(o*ATA0.5)| EXP(-o ATA0.5 U 6 d 7 X 8 T 10.25 l1 JAT T/n 10 AT 11 p -+ B8 / B9 (EXP(B10 B3)-$B$6)V(Ep = [ exp(rAT) d 12

u = 1.32 & d = 0.76

Price at Upward Trend = u * Wholesale Price = 1.32 * 4 = $5.28

Price at Downward Trend = d * Wholesale Price = 0.76 * 4 = $3.04

Value at upward trend = Price at upward trend - Strike Price = $5.28 - 4.35 = $0.93

Value at Downward Trend = 0

Quarterly return = 0.05 / 4 = 1.25%

Computation of Probability of upward and downward trend

Quarterly return = PU * (1.32 - 1) + PD * (0.76 - 1)

0.0125 = PU * (1.32 - 1) + (1-PU) * (0.76 - 1)

0.0125 = 0.32 * PU - 0.24 + 0.24 * PU

Probability of Upward Trend = 0.2525 / 0.56 = 45.09%

Probability of Downward Trend = 1 - 45.09% = 54.91%

Value of Contract = (Probability of Upward * Value at Upward) / (1 + (5%/4))

Value of Contract = (0.93 * 0.4509 / 1.0125)

Value of Contract = $0.4142

Value of Entire Contract = 6000000 * 0.4142

Value of Entire Contract = 2484920.63