A consultancy calculates that it can supply crude oil assaying services to a small oil producer for $120 000 per year for five years. There are some up-front costs the consultancy will require the oil producer to absorb. What is the maximum that these up-front costs could be, if the equivalent annual annuity to the oil company is to be under $150 000, given that the cost of capital is 10%?

Question

Quizplus · Accepted Answer

The equivalent annual annuity (EAA) can be calculated using the formula for the present value of an annuity. Given that the EAA is $150,000, the cost of capital is 10%, and the term is 5 years, we can calculate the present value (PV) of these payments. The formula for the PV of an annuity is EAA x [(1 - (1 + r)^-n) / r], where r is the interest rate (0.10) and n is the number of periods (5). Plugging in the numbers, we get $150,000 x [(1 - (1 + 0.10)^-5) / 0.10] = $568,810. This is the total amount the oil producer can afford to pay over the five years, including the up-front costs and the annual service fee of $120,000 for five years. The present value of the annual service fees alone is $120,000 x [(1 - (1 + 0.10)^-5) / 0.10] = $455,086. Subtracting this from the total amount gives the maximum up-front costs: $568,810 - $455,086 = $113,724.

A Consultancy Calculates That It Can Supply Crude Oil Assaying