The owner of a taxi company is considering the replacement of his vehicles. He is planning to retire in six years’ time and is therefore only concerned with that period of time, but cannot decide whether it is better to replace the vehicles every two years or every three years.

The following data have been estimated (all values at today’s price levels):

Vehicles servicing and repair costs 

Vehicle servicing and repair costs depend on the age of the vehicle.
In the following table, year 1 represents the cost in the first year of the vehicle’s ownership; year 2 represents the cost in the second year of ownership, and so on:

Inflation New vehicle costs and trade in-values are expected to increase by 5 per cent per year.
Vehicle running costs and fares are expected to increase by 7 per cent per year. Vehicle servicing and repair costs are expected to increase by 10 per cent per year.
Required:
Advise the company on the optimum replacement cycle for its vehicles and state the net present value of the opportunity cost of making the wrong decision. Use a discount rate of 12 per cent per year. All workings and assumptions should be shown. Ignore taxation.

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Purchase cost and trade in values Taxi cost Trade-in value of taxi: after 2 years 15000 7000 4000 after 3 years Annual costs and revenues Vehicle running cost Fares charged to customers 20000 per year 40000 per year