Question

Instead of buying, the dealer offers to lease you a car worth $29500 for $698/mo. for 36 months with $6250 down, lease payments due at the beginning of the month. Assume that if you buy the car, the estimated value in 3 years will be $885. Should you lease or buy, and how much of an advantage does it provide you? (Assume that an APR of 5.5% is correct.)

Group of answer choices

Doesn't matter, the costs differ by less than $100                                                   

BUY, < $700

BUY, > $700

LEASE, > $700

LEASE, < $700

Answer 1

Purchase value of car	29,500.00
Salvage value of car after 3 years	885.00
Down payment	6,250.00
lease payments (Annuity due)	698.00
no. of periods	36
APR	5.50%
monthly rate ---> (APR /12)	0.46%

Present value of leasing option

Present value of leasing = Down payment + PV of lease annuity due

Present value of leasing = Down payment + lease payment x ((1-((1+monthly rate)^-no. of periods))/monthly rate) x (1+ monthly rate)

Present value of leasing = 6250 + 698 x ((1-((1+0.46%)^-36))/0.46%) x (1+ 0.46%)

Present value of leasing = 6250 + 698 x 33.1072 x 1.0046

Present value of leasing = 6250 + 23215.12

Present value of leasing = $ 29,465.12

Present value of buy option

Present value of buy option = Purchase price - PV of salvage value

Present value of buy option = Purchase price - (Salvage value x (1+APR)^-no. of years)

Present value of buy option = 29500 - (885 x 0.8516)

Present value of buy option = 29500 - 753.6781

Present value of buy option = $ 28.746.32

Therefore buy option looks more advantageous as PV of lease option is higher than PV of buy option.
Present value of lease option	29,465.12
Present value of buy option	28,746.32
Quantum of advantage (in $)	$                                                                            718.79
Therefore the right answer if Option 2 ---> Buy, >$ 700

Hope this helps you answer the question. Please provide your feedback or rating on the answer.

Thanks