Question

3.56 Frontier Airlines hedged the cost of jet fuelby purchasing options that allowed the airline to purchase fuel at a fixed price for 2 years. If the savings in fuel costs were $140.000 in month 1. $141,400 in month 2, and amounts increasing by 1% per month through the 2-year option period, what was the present worth of the savings at an interest rate of 18% per year compounded monthly?

Answer 1

I = 18% compounded monthly = 18% / 12 = 1.5% per month

t = 2 yrs = 2 * 12 = 24 months

Present value of geometric series = A * [1 - (1+g)^n / (1+i)^n] / (I - g)

= 140000 * [1 - (1+0.01)^24 / (1+0.015)^24] / (0.015 - 0.01)

= 140000 * [1 - (1.01)^24 / (1.015)^24] / (0.005)

= 140000 * 22.35296945

= 3129415.72