Question

​Lease-versus-purchase decision Personal Finance Problem Joanna Browne is considering either leasing or purchasing a new Chrysler Sebring convertible that has a​ manufacturer's suggested retail price​ (MSRP) of $33,000. The dealership offers a 3​-year lease that requires a capital payment of $3,500 ​($3,100 down payment​ + $400 security​ deposit) and monthly payments of $493. Purchasing requires a $2,600 down​ payment, sales tax of 6.4% ($2,112​), and 36 monthly payments of $903. Joanna estimates the value of the car will be $17,000 at the end of 3 years. She can earn 4.8% annual interest on her savings and is subject to a 6.4% sales tax on purchases. Make a reasonable recommendation to Joanna using a​ lease-versus-purchase analysis​ that, for​ simplicity, ignores the time value of money.

a.  Calculate the total cost of leasing.

b.  Calculate the total cost of purchasing.

c.  Which should Joanna​ do?

*Please show work if possible

Answer 1

Ans.

MSRP of the car = $33,000

a) If Joanna plans to Lease

Down Payment = $ 3,500

The Capital payment is = 493*12*3 = $ 17,748

Opportunity Cost of Initial Investment = $ 3,500 * 4.8% * 3 = $ 504

The total cost of leasing involves = $ 3,500 + $ 17,748 + 504 = $21,752

b) If Joanna plans to Purchase,

The cost of purchasing involves

Down Payment $ 2,600

Sales Tax = $ 2,112

Total Loan Payments = 36 * $ 903 = $ 32,508

Opportunity Cost of Initial Investment = $ 2,600 * 4.8% * 3 = $ 374.4

Therefore the cost of purchasing includes = $ 2,600 + $ 2,112 + $ 32,508 + $ 374.40 = $ 37,594.40

Estimated trade-in value of car = $ 17,000 ( given)

The cost of purchasing = $ 37,594.40 - $ 17,000 = $ 20,594.40

c)

The total cost of purchasing is $20,594.40 ( less) as compared to the cost of leasing i.e $21,752, so Joanna should purchase the car instead of leasing.