Question

4.42 Frontier Airlines hedged the cost of the jet fuel by purchasing options that allowed the airline to buy fuel at a fixed price for 2 years. The savings in fuel costs were $140,000 in month 1, $141,000 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

$3,129,414.40

Step-by-step explanation:

i = 18% compounded monthly = 18% / 12 = 1.5% = 0.015

n = 2 yrs = 2 * 12 = 24 months

Growth(g) = 1% = 0.01

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

Present value of geometric series = $140000 * [1 - (1+0.01)^24 / (1+0.015)^24] / (0.015 - 0.01)

Present value of geometric series = $140000 * 1 - 0.8882352 / 0.005

Present value of geometric series = $140000 * 0.1117648 / 0.005

Present value of geometric series = $140000 * 22.35296

Present value of geometric series = $3,129,414.40

Thus, the present worth of the savings at an interest rate of 18% per year, compounded monthly is $3,129,414.40