Question

A manufacturing company purchased electrical services for the next 5 years to be paid for with $70,000 now. The service after 5 years will be $15,000 per year beginning with the sixth year. After 2 years service the company, having surplus profits, requested to pay for another 5 years service in advance. If the electrical company elected to accept payment in advance, what would each company set as a fair settlement to be paid if (a) the electrical company considered 15% compounded annually as a fair return, and (b) the manufacturing company considered 12% a fair return?

Answer 1

To calculate the fair settlement to be paid by the manufacturing company for the advance payment of electrical services, we need to determine the present value of the future cash flows using the provided interest rates.

Given:

Initial payment: $70,000

Annual service cost after 5 years: $15,000

Interest rate for the electrical company: 15% compounded annually

Interest rate for the manufacturing company: 12%

(a) Fair settlement based on the electrical company's 15% interest rate:

First, we calculate the present value of the annual service cost after 5 years using the formula for the present value of a future cash flow:

PV = FV / (1 + r)^n

PV = $15,000 / (1 + 0.15)^5

PV = $15,000 / 1.925

PV ≈ $7,792.21

The fair settlement for the manufacturing company to pay would be the sum of the initial payment and the present value of the future cash flows:

Fair settlement = $70,000 + $7,792.21

Fair settlement ≈ $77,792.21

(b) Fair settlement based on the manufacturing company's 12% interest rate:

Similarly, we calculate the present value using the manufacturing company's interest rate:

PV = $15,000 / (1 + 0.12)^5

PV = $15,000 / 1.7623

PV ≈ $8,507.78

The fair settlement for the manufacturing company to pay would be:

Fair settlement = $70,000 + $8,507.78

Fair settlement ≈ $78,507.78

Therefore, the fair settlement amounts would be approximate:

(a) $77,792.21 if the electrical company's interest rate is considered fair.

(b) $78,507.78 if the manufacturing company's interest rate is considered fair.