After deciding to buy a new car, you can either lease the car or purchase it on

ID: 2614903 • Letter: A

Question

After deciding to buy a new car, you can either lease the car or purchase it on a two-year loan. The car you wish to buy costs $32,000. The dealer has a special leasing arrangement where you pay $93 today and $493 per month for the next two years. If you purchase the car, you will pay it off in monthly payments over the next two years at an APR of 7 percent. You believe you will be able to sell the car for $20,000 in two years.

What break-even resale price in two years would make you indifferent between buying and leasing?

Explanation / Answer

Purchase Option:

Cash Outflow = $ 32000 and Cash Inflow = PV of Breakeven Resale Price after two years (let the same be denoted by $ K)

Therefore, Net Cash Outflow = 32000 - K

Leasing Option:

Cash Outflow at present = $ 93 and $ 493 of monthly payments for two years at an APR of 7 % per annum /0.0or 0.5833 % per month

Therefore, total value of cash outflow = 93 + 493 x (1/0.005833) x [1-{1/(1.005833)^(24)}] = $ 11104.25

If the total cash outflows under the two options are equal only then will the person be indifferent between the leasing and purchase option.

32000 - K = 11104.25

K = $ 20895.75

This value is the PV of the breakeven resale price.

Resale Price after two years = 20895.75 x (1.005833)^(24) = $ 24025.87 approximately.

NOTE: If compounding is considered to be annual then the breakeven resale price would be 20895.75 x (1.07)^(2) = $ 23923.54

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After deciding to buy a new car, you can either lease the car or purchase it on

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After deciding to buy a new car, you can either lease the car or purchase it on

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