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# Leasing a car vs. buying a car

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You want to buy a new car, but you're not sure whether you should lease it or buy it. You can buy it for \$50,000, and you expect that it will be worth \$20,000 after you use it for 3 years. Alternatively, you could lease it for payments of \$650 per month for the 3-year term, with the first payment due immediately. The lease company did not tell you what interest rate they're using to calculate the monthly payments, but you know you could borrow money from your banker at an annual percentage rate (APR) of 8%.

a) Calculate the present value of the lease payments, assuming monthly compounding at the given APR of 8%.
b) Calculate the present value of the \$20,000 salvage value, again using monthly compounding and the given APR of 8%. Which option do you prefer, lease or buy?
c) Calculate the amount of the salvage value which would make you indifferent between leasing and buying.
d) If you were able to use this car 100% for business, rendering the lease payments tax-deductible, or alternatively, allowing you to deduct depreciation using straight-line depreciation (depreciated to expected salvage value) and assuming your tax rate is 40%, would you prefer to buy or lease the car?

#### Solution Preview

Leasing a car vs. buying a car

You want to buy a new car, but you're not sure whether you should lease it or buy it. You can buy it for \$50,000, and you expect that it will be worth \$20,000 after you use it for 3 years. Alternatively, you could lease it for payments of \$650 per month for the 3-year term, with the first payment due immediately. The lease company did not tell you what interest rate they're using to calculate the monthly payments, but you know you could borrow money from your banker at an annual percentage rate (APR) of 8%.

a) Calculate the present value of the lease payments, assuming monthly compounding at the given APR of 8%.

We calculate Present Value factor for Annuity due - PVIFA (Annuity due) or read it from financial tables
PVIFA- Annuity due( n, r%)= =(1+r%) x[1-1/(1+r%)^n]/r%

We are calculating annuity due because the first lease payment is due immediately

PVIFA
Annuity: Due

Frequency= M Monthly
No of years= 3
No of Periods= 36 =3x ...

#### Solution Summary

The solution compares the cost of leasing a car vs buying a car.

\$2.49