Question

A suburban taxi company is considering buying taxis with diesel engines instead of gasoline engines. The cars average 80,000 km a year. Use an annual cash flow analysis to determine the more economical choice if interest is 6%. Diesel GasolineVehicle cost $24,000 $19,000Useful life, in years 5 4Fuel cost per lite 88 92Mileage, in km/liter 16 11Annual repairs $900 $700Annual insurance premium 1,000 1,000End-of-useful-life resale value 4,000 6,000

Answer 1

The diesel engine offers relatively lower uniform annual cost that is $11287.93, so diesel engine taxis should be chosen.

Explanation:

R = 6%

Useful life n = 5 years

Annual distance covered = 80000 KM

For a diesel car,

Annual fuel cost = (80000/16)*.88 = $4400

Present value of total cost = vehicle cost + present value of the fuel cost + present value of annual repair cost + present value of annual premium – present value of resale value

Present value of total cost = 24000 + 4400*(1-1/1.06^5)/.06 + 900*(1-1/1.06^5)/.06 + 1000*(1-1/1.06^5)/.06 - 4000/1.06^5

Present value of total cost = $47548.86

Let, uniform annual cost = EUAC1

Then,

EUAC1 = 47548.86/((1-1/1.06^5)/.06) = $11287.93

For a gasoline car,

Useful life = 4 years

Annual fuel cost = (80000/11)*.92 = $6690.91

Present value of total cost = vehicle cost + present value of the fuel cost + present value of annual repair cost + present value of annual premium – present value of resale value

Present value of total cost = 19000 + 6690.91*(1-1/1.06^4)/.06 + 700*(1-1/1.06^4)/.06 + 1000*(1-1/1.06^4)/.06 - 6000/1.06^4

Present value of total cost = $43322.83

Let, uniform annual cost = EUAC2

Then, EUAC2 = 43322.83/((1-1/1.06^4)/.06)

EUAC2 = $12502.6

Since diesel engine offers relatively lower uniform annual cost that is $11287.93, so diesel engine taxis should be chosen.