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

PV of the growing annuity: 3,129,415.72

Step-by-step explanation:

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

`FV = (1-(1+g)^(n)* (1+r)^(-n) )/(r - g)`

g 0.01

r 0.015 (18% / 12 months)

C 140,000

n 24

`(1-(1+0.01)^(24)* (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:

`(4,473,508.58 )/(1.015^(24) )`

3,129,415.72