Question

QUESTION 10

1. You are evaluating the purchase of a vehicle for your business. You've decided that the best choice is a car that will cost you $35,000, but you're uncertain how long you should plan on holding the car before you replace it. The table below lists the running costs and salvage value of the vehicle for each year.
   

   	1	2	3	4	5
   Running Costs	-3000	-3500	-4000	-4500	-5000
   Salvage Value	25000	20000	15000	10000	5000

   
   What is the annual equivalent cost of replacing the vehicle every 5 years? Assume your cost of capital is 7%. Enter your answer to the nearest cent. Ignore taxes.
   
   (Your answer will be a cost, and therefore a negative number. Don't forget the minus sign.)

Answer 1

All financials below are in $.

As a first step we need to find the NPV of running the car for 5 years and then replacing it.

Let C_i be the running cost in year i. Let C₀ be the initial investment and S be the salvage value at the end of year 5.

Cost of capital, R = 7%

N = Life = 5 years

=  - 47,558.99

Let's assume the annual equivalent cost of replacing the vehicle every 5 years is EAC then

PV of annuity EAC = NPV

Or, EAC / R x [1 - (1 + R)^-N] = NPV

Or, EAC / 7% x [1 - (1 + 7%)^-5] = - 47,558.99

Hence,  4.1002 EAC = - 47,558.99

Hence, the annual equivalent cost of replacing the vehicle every 5 years = EAC = - $ 11,599.20