Question

An oil company believes that a newly discovered deposit will generate revenues of $1,380,000 each year for the foreseeable future. The extraction cost, however, will be $81,420 over the next year and increase at a rate of 4% each year as they deposit is depleted. If the company’s opportunity cost of capital is 10%, for how many years can you extract the oil before the cost of extraction overtakes the revenues it generates?

No Excel or Financial Calculator Please.

Answer 1

revenue per year = 1,380,000

Cost of extraction = $81,420 for next year.

Cost of extraction increases 4% per year.

How many years can you extract the oil before the cost of extraction overtakes the revenues.

that is

revenue = Cost of extraction

revenue = Cost of extraction * ( 1 + g)ⁿ

Here g = increase in growth of cost of extraction

n = number of year it will take to equal to revenue

1,380,000 = $ 81,420 * ( 1 + 0.04)ⁿ

(1.04)ⁿ = 1,380,000 / 81420

(1.04)ⁿ = 16.949152542372881356

Here we apply log values or trace the present value of anniuty table at 4% where we find 16.9496 in number of years.

Here i apply log values

log(1.04)ⁿ = log(16.949152542372881356)

n log 1.04 = log(16.949152542372881356)

n = log(16.949152542372881356) / log 1.04

n = 72.1613 years

At 72.1613 year,

Cost of extraction = Revenue.

years can you extract the oil before the cost of extraction overtakes the revenues it generates = 72 years