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 $15,500 to purchase and which will have OCF of –$1,500 annually throughout the vehicle’s expected life of three years as a delivery vehicle; and the Toyota Prius, which will cost $22,000 to purchase and which will have OCF of –$800 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.)

Answer 1

Answer:

The Scion xA EAC: -7,953.41

The Toyota Prius EAC: -8,043.16

Explanation:

The equivalent cost is the PMT of the present worth of the asset, so the first step to solve for EAC is to calculate the present worth:

The Scion xA:

Purchase 15,500

Present value of the cash flow needs:

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

C 1,500

time 3

rate 0.12

$1500 \times \frac{1-(1+0.12)^{-3} }{0.12} = PV$

PV $3,602.7469

Present worth: 15,500 + 3,602.75 = 19,102.75

Now, we calcualte the PMT:

$PV \div \frac{1-(1+r)^{-time} }{rate} = C$

PV 19,103

time 3

rate 0.12

$19102.75 \div \frac{1-(1+0.12)^{-3} }{0.12} = C$

C  $ 7,953.410

Toyota Prius:

Purchase: 22,000

present value of annual OCF

$C \times \frac{1-(1+r)^{-time} }{rate} = PV$

C 800

time 4

rate 0.12

$800 \times \frac{1-(1+0.12)^{-4} }{0.12} = PV$

PV $2,429.8795

present worth: 24,429.88

Equivalent annual cost:

$PV \div \frac{1-(1+r)^{-time} }{rate} = C$

PV 24,430

time 4

rate 0.12

$24,429.88 \div \frac{1-(1+0.12)^{-4} }{0.12} = C$

C: $ 8,043.158