Question

you are considering purchase of a new furnace. its initial cost, including installation, is $3 000, and it will cost $200 a year in fuel over its 10-year life. you expect that it can then be sold for $300. if your marr is 10%, what is the equivalent annual cost of owning the furnace?

Answer 1

The equivalent annual cost (EAC) of owning the furnace is $668.04. It is calculated by considering the initial cost, the annual fuel cost, and the resale value of the furnace over its 10-year life, while taking into account the minimum attractive rate of return (MARR) of 10%.

Step-by-step explanation:

To find the equivalent annual cost of owning the furnace, we need to consider the initial cost, the fuel cost, the resale value, and the time value of money. The equivalent annual cost (EAC) formula is given by EAC = (Initial Cost - Resale Value) / Annuity Factor + Annual Fuel Cost, where the Annuity Factor is calculated using the present worth factor formula. In this case, the EAC can be calculated as follows:

1. Calculating the Annuity Factor: Annuity Factor = (1 - (1 + marr)^(-n)) / marr, where marr is the minimum attractive rate of return (10% in this case) and n is the life of the furnace (10 years). Annuity Factor = (1 - (1 + 0.1)^(-10)) / 0.1 = 6.14457
2. Calculating the EAC: EAC = (Initial Cost - Resale Value) / Annuity Factor + Annual Fuel Cost = (3000 - 300) / 6.14457 + 200 = 468.04 + 200 = $668.04

Therefore, the equivalent annual cost of owning the furnace is $668.04.