Question

Machinery costs $1 million today and $100,000 per year to operate. It lasts for 5 years. What is the equivalent annual annuity if the discount rate is 7%?

A) $281,773.55
B) $200,000
C) $150,000
D) $50,000

Answer 1

To calculate the equivalent annual annuity, we need to calculate the present value of the machinery and operating costs. The equivalent annual annuity is approximately a. $281,773.55.

Step-by-step explanation:

To calculate the equivalent annual annuity, we need to first calculate the present value of the machinery and operating costs. The present value of the machinery can be calculated using the formula: PV = C/(1+r)^n, where C is the cost, r is the discount rate, and n is the number of years.

The present value of the operating costs can be calculated by multiplying the annual cost by the present value annuity factor (PVAF) for 5 years and a discount rate of 7%. The equivalent annual annuity is the sum of the present values of the machinery and operating costs.

Using this approach, the present value of the machinery is $1 million, and the present value of the operating costs is approximately $281,773.55. Therefore, the equivalent annual annuity is approximately a. $281,773.55.