Question

2. If the owner earns 6% interest on her investment determine the equivalent annual cost of owning an SUV with the following costs: (EOY = end of year)

Initial down payment = $2200

Annual payments = $5500, EOY1 – EOY4

Prepaid insurance = $1500, growing 6% annually

Gas and oil, and minor maintenance = $2000 growing 8% annually.

Replacement tires = $750 at EOY4 and $800 at EOY8

Major maintenance = $2400 at EOY5

Salvage value = $3750 at EOY9

Answer 1

i = 6%

Present value of geometric series = C*[(1+g)^n /(1+i)^n - 1] / (g-i)

When i = g, P =C*n / (1+i)

Here Prepaid insurance and gas and oil are geometric series

Insurance is prepaid so, it occurs at EOY 0 to EOY 8 and in case of insurance i = g, therefore

Presesnt value of insurence = 1500 + 1500*1.06*8 / (1+0.06) = 1500 + 12000 = 13500

Present value of oil & gas = 2000*[(1+0.08)^9 /(1+0.06)^9 - 1] / (0.08-0.06)

= 2000*[(1.08)^9 /(1.06)^9 - 1] / (0.02)

= 2000 * 9.160388

= 18320.776

Present value of all costs = 2200 + 5500*(P/A,6%,4) + 13500 + 18320.776 + 750*(P/F,6%,4) + 800*(P/F,6%,8) + 2400*(P/F,6%,5) - 3750*(P/F,6%,9)

= 2200 + 5500*3.465105 + 13500 + 18320.776 + 750*0.79209 + 800*0.62741 + 2400*0.74725 - 3750*0.59189

= 53748.624

EUAC = 53748.624*(A/P,6%,9)

= 53748.624*0.147022

= 7902.23