Question

Frontier Airlines hedged the cost of 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, $141,400 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

Answer:

PV of the growing annuity: 3,129,415.72

Explanation:

We need to solve for the present value of a growing annuity:

$FV = \frac{1-(1+g)^{n}\times (1+r)^{-n} }{r - g}$

g 0.01

r 0.015 (18% / 12 months)

C 140,000

n 24

$\frac{1-(1+0.01)^{24}\times (1+0.0015)^{-24} }{0.18 - 0.01}$

FV =  4,473,508.58

Now, to get the present value we solve for the present value of the future value:

$\frac{4,473,508.58 }{1.015^{24} }$

3,129,415.72