Question

A contractor is planning to buy an office trailer for $28000. They intend to keep the trailer for 5 years and expect that maintenance will remain at $950 per year over this period. The trailer is also subject to an annual tax which will be $55 at the end of the first year but is expected to increase by %20 each year after that.
What is the equivalent annual cost of owning this trailer when the interest rate is 9%?

Answer 1

Ans. Cashflow in,

Year 0 = -$28000

Year 1 = - (950 + 55) = -$1005

Year 2 = - (950 + 1.20*55) = -$1016

Year 3 = - (950 + 1.20^2 * 55) = -$1029.2

Year 4 = - (950 + 1.20^3 * 55) = -$1045.04

Year 5 = - (950 + 1.20^4 * 55) = -$1064.05

The present value of the given cashflow at 9% interest rate,

PV = -28000 - 1005/(1+0.09) - 1016/(1+0.09)^2 - 1029.2/(1+0.09)^3 - 1045.04/(1+0.09)^4 - 1064.05/(1+0.09)^5

=> PV = -$32003.79

Thus, for annual equivalent cost, A,

PV = A*(P/A, 9%, 5)

=> -32003.79 = A*[(1-1/(1+0.09)^5)/0.09]

=> A = -$8227.933

Thus, the annual equivalent cost is $8227.933