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 upfront costs the consultancy will require the oil producer to absorb.What is the maximum that these upfront 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

To calculate the maximum upfront cost, we need to find the present value of the five-year cost of providing crude oil assaying services to the oil producer, which is $120,000 per year. Using the formula for present value of an annuity, we get:

PV = 120,000 * [(1 - (1 + 0.1)^-5) / 0.1] = $480,664.28

Now we need to find the upfront cost that will make the equivalent annual annuity to the oil company under $150,000. Let's call this upfront cost X. Then, we can use the formula for equivalent annual annuity to solve for X:

150,000 = (PV - X) * 0.1 * (1 + 0.1) / [1 - (1 + 0.1)^-5]

Solving for X, we get:

X = PV - [150,000 * (1 - (1 + 0.1)^-5) / 0.1 * (1 + 0.1)]

X = $113,723.61

Therefore, the maximum upfront cost that the oil producer can absorb while keeping the equivalent annual annuity under $150,000 is $113,723.61, which is answer (B).

A Consultancy Calculates That It Can Supply Crude Oil Assaying