Question

You are trying to pick the least-expensive car for your new delivery service. You have two choices: the Scion xA, which will cost $21,500 to purchase and which will have OCF of –$2,700 annually throughout the vehicle’s expected life of three years as a delivery vehicle; and the Toyota Prius, which will cost $30,000 to purchase and which will have OCF of –$1,400 annually throughout that vehicle’s expected 4-year life. Both cars will be worthless at the end of their life. You intend to replace whichever type of car you choose with the same thing when its life runs out, again and again out into the foreseeable future.

    

If the business has a cost of capital of 12 percent, calculate the EAC. (Negative amounts should be indicated by a minus sign. Round your answers to 2 decimal places.)

     

Scion's EAC	$
Toyota's EAC	$

  

Which one should you choose?

Toyota Scion

Answer 1

Equivalent Annual Cost (EAC) for Scion xA

Period	Annual Cash Flow ($)	Present Value factor at 12%	Present Value of Cash Flow ($)
1	-2,700	0.892857	-2,410.71
2	-2,700	0.797194	-2,152.42
3	-2,700	0.711780	-1,921.81
TOTAL		2.401831	-6,484.94

Net Present Value (NPV) = Present Value of annual cash inflows – Initial Investment

= -$6,484.94 - $21,500

= -$27,984.94

Equivalent Annual Cost (EAC) for Scion xA

Equivalent Annual Cost (EAC) = Net Present Value / [PVIFA 12%, 3 Years]

= -$27,984.94 / 2.401831

= -$11,651.50 (Negative)

Equivalent Annual Cost (EAC) for Toyota Prius

Period	Annual Cash Flow ($)	Present Value factor at 12%	Present Value of Cash Flow ($)
1	-1,400	0.892857	-1,250.00
2	-1,400	0.797194	-1,116.07
3	-1,400	0.711780	-996.49
4	-1,400	0.635518	-889.73
TOTAL		3.037349	-4,252.29

Net Present Value (NPV) = Present Value of annual cash inflows – Initial Investment

= -$4,252.29 - $30,000

= -$34,252.29

Equivalent Annual Cost (EAC) for Toyota Prius

Equivalent Annual Cost (EAC) = Net Present Value / [PVIFA 12%, 4 Years]

= -$34,252.29 / 3.037349

= -$11,277.03 (Negative)

DECISION

We should choose “Toyota Prius”, Since it has the lowest EAC of -$11,277.03.

NOTE    

The Formula for calculating the Present Value Factor is [1/(1 + r)ⁿ], Where “r” is the Discount/Interest Rate and “n” is the number of years.