Question

Your roommate is looking for a new car and evaluating two different options. One is a BMW 5 series, which costs $60,000 and has an average maintenance cost of $1,000 in the first year and $1,500 in each of the following years (She would choose a 5 year lease). The other option is a Acura which costs $50,000 and has an average maintenance cost of $500 in the first year and $1,000 in years 2-3, and $2,000 in years 4-7 (She would chose a 7 year lease). Which option should your roommate choose based on the EAC? Use a cost of capital of 8.5%

Answer 1

NPV of costs = Present value of all costs

BMW = -60,000 – 1000*PVF(8.5%, 1 year) – 1500*PVAF(8.5%, 2- 5 years)

= -60,000 – 1000*0.922 -1500*3.019

= -$65,450.5

EAC = NPV/PVAF(8.5%, 5 years)

= -65,450.5/3.941

= -$16,607.59

NPV of Acura = -50,000 – 500*PVF(8.5%, 1 year)- 1000*PVAF(8.5%, 2-3 years) – 2000*PVAF(8.5%, 4-7 years)

= -50,000 – 500*0.922 – 1000*1.632 -2000*2.564

= -$57,221

EAC = 57221/PVAF(8.5%, 7 years)

= -$57221/5.1185

= -$11,179.25

Hence, Acura should be chosen since lower EAC