Question

A family is planning to buy a vacation cabin for $30,000. The family intends to keep the cabin for 6 years and expects the annual unkeep and taxes to amount to $900 per year. Without any major repairs, the cabin should have a resale price of $26,000. What is the equivalent annual cost of owning the cabin if the family’s acceptable interest rate is 6%?

Answer 1

The Equivalent Annual Cost of Machine A is computed as shown below:

= (Initial investment + present value of future cost) / Present value annuity factor of 6% for 6 years

Initial investment + present value of future cost is computed as follows:

= $ 30,000 + $ 900 / 1.06¹ + $ 900 / 1.06² + $ 900 / 1.06³ + $ 900 / 1.06⁴ + $ 900 / 1.06⁵ + $ 900 / 1.06⁶ - $ 26,000 / 1.06⁶  

= $ 16,096.61784

Present value annuity factor of 6% for 6 years is computed as follows:

= [ (1 – 1 / (1 + r)ⁿ) / r ]

= [ (1 - 1 / (1 + 0.06)⁶ ) / 0.06 ]

= 4.917324326

So, the equivalent annual cost is computed as follows:

= $ 16,096.61784 / 4.917324326

= $ 3,273.45 Approximately