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:
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
C 1,500
time 3
rate 0.12
[tex]1500 \times \frac{1-(1+0.12)^{-3} }{0.12} = PV\\[/tex]
PV $3,602.7469
Present worth: 15,500 + 3,602.75 = 19,102.75
Now, we calcualte the PMT:
[tex]PV \div \frac{1-(1+r)^{-time} }{rate} = C\\[/tex]
PV 19,103
time 3
rate 0.12
[tex]19102.75 \div \frac{1-(1+0.12)^{-3} }{0.12} = C\\[/tex]
C $ 7,953.410
Toyota Prius:
Purchase: 22,000
present value of annual OCF
[tex]C \times \frac{1-(1+r)^{-time} }{rate} = PV\\[/tex]
C 800
time 4
rate 0.12
[tex]800 \times \frac{1-(1+0.12)^{-4} }{0.12} = PV\\[/tex]
PV $2,429.8795
present worth: 24,429.88
Equivalent annual cost:
[tex]PV \div \frac{1-(1+r)^{-time} }{rate} = C\\[/tex]
PV 24,430
time 4
rate 0.12
[tex]24,429.88 \div \frac{1-(1+0.12)^{-4} }{0.12} = C\\[/tex]
C: $ 8,043.158