Question

Consider the following two tractors a company can purchase. The following tables provide the costs the company will incur (in thousands of dollars) in the lifetime of each tractor.

	Initial Cost	Operating Costs per Year	Expected Life
Diesel	$19,000	$9,000	6
Gasoline	$9,000	$12,000	5

The transportation firm can only afford one of the tractors. The two tractors have identical production capabilities. The firm's cost of capital is 2%.

a) Find the present value of the costs of using the two tractors.

Diesel =   (A)

Gasoline =   (B)

b) Given that the net present value of the costs of the Diesel tractor are (A) and of the Gasoline tractor are (B), what are the equivalent annual costs for each machine?

EACDiesel=    (AA)

EACGasoline=    (BB)

c) Given that the equivalent annual cost of the Diesel tractor is (AA) and of the Gasoline tractor if (BB), which tractor should the company buy?

Diesel OR Gasoline ?

Answer 1

a.Computation of present value of costs

Present value of costs = Initial cost + Present value of Annual operating costs

Present value of costs for Diesel tractor

Initial cost = 19000

Operating cost per year = 9000

Expected life = 6 years

Cost of capital = 2%

Present value of operating costs = Operating costs per year x annuity factor

= 9000 x 5.6014 = 50413

Present value of costs for diesel tractor = 19000 + 50413 = 69412

Present value of costs for Gasoline tractor

Initial cost = 9000

Operating cost per year = 12000

Expected life = 5 years

Cost of capital = 2%

Present value of operating costs = 12000 x 4.7134 = 56561

Present value of costs for Gasoline tractor = 9000 + 56561 = 65561

b.Computation of Equvalent Annual Costs (EAC)

Equvalent Annual Cost = Present value of costs / Annuity factor

EAC for diesel tractor = 69412 / 5.6014 = 12392

EAC for gasoline tractor = 65561 / 4.7134 =13909

c. Equvalent annual cost is the annual cost associated with owning and operating an asset over its estimated useful life. It is used as a decision making criteria to compare the costs and choose between different investment alternatives.

As EAC is a cost the project with lower EAC should be accepted. Here diesel tractor has lower EAC of 12392 compared to Gasoline tractor which has an EAC of 13909. So the company should buy diesel tractor as it has lower Equvalent annual cost.

Working note

Present value of interest factor annuity = (1 - (1 + r)^-n) / r

Annuity factor for diesel = (1- (1+0.02)^-6) / 0.02

  = (1- (1.02)^-6) / 0.02

= (1- 0.8879) / 0.02

= 0.1121 / 0.02

= 5.60

Annuity factor for gasoline = (1- (1+0.02)^-5) / 0.02

= (1- 0.9057) / 0.02

= 0.0943 / 0.02

   = 4.71