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Buy or Lease

In: Business and Management

Submitted By salbazaz
Words 747
Pages 3
Amy is trying to decide if she should buy a car or lease the same car. The car salesman has told her that she can buy the car for $27,000. She will need a down payment of $2,700. The remainder will be financed with a loan. It will cost her 4.5% compounded semi-annually. She will make 60 monthly payments at the end of each month. If she leases the car, Amy will not put any money down. However, she will be required to pay $12,500 at the end of the lease. Amy will make 60 monthly lease payments of $250. The lease payments will be made at the beginning of each month. Assume the appropriate interest rate is 7.3% compounded semi-annually.

a) Draw two detailed timelines and label all components displaying the details of leasing and buying the car. b) What are the (1) effective annual rates (EAR) and the (2) effective periodic rates (EPR) of the (i) bank loan rate and (ii) the lease rate? c) What is the present value of the car if Amy buys the car as opposed to leasing? What is the present value if Amy leases the car as opposed to buying? d) If Amy had the option to make 48 monthly payments to buy or lease the car, what would be the new monthly loan payments and the monthly lease payments? e) Using the information from part c) and d), summarize if Amy should buy or lease the car under the 48 month plan or the 60 month plan.

S O L U T I O N
a)
Purchasing the car
Given: PV FV PMT n (yr) r 27000 0 ? 5 4.50% Solve for PMT PMT= $453.03 Timeline: yr 0 yr 1 yr 2 yr 3 yr 4 yr 5
PMT= 2700 12*$453 12*$453 12*$453 12*$453 12*$453

Leasing the car
Given: PV FV PMT n (yr) r ? 12500 250 5 7.30% Solve for PV PV= $12,536 Timeline:
0 yr 1 yr 2 yr 3 yr 4 yr 5
PMT= 12*$250 12*$250 12*$250 12*$250 12*$250+$12500

b) i) EAR= (1+APR/m)^m-1
= (1+0.045/2)^2-1
= 0.04550625 The effective annual rate is 4.551%. EPR= (1+EAR)^(1/f)-1
= (1+0.4551)^(1/12)-1
= 0.00371532 The effecive periodic rate is 0.372%. ii) EAR= (1+APR/m)^m-1
= (1+0.073/2)^2-1
= 0.07433225 The effective annual rate is 7.433%. EPR= (1+EAR)^(1/f)-1
= (1+0.07433)^(1/12)-1
= 0.005992828 The effective periodic rate is 0.599%. c)
Under the bank loan method, the present value of the car is $27000 if interest is charged at 4.5% APR, with a $2700 down payment. Under the lease option, the present value is the present worth of the payments plus the value today of $12500 five years from now. PV= $12535.7+PV(7.3%/2,10,0,-12500) $21,270
The present value of the car under the leasing plan is $21,269.77. d)
Purchasing the car
Given: PV FV PMT n (yr) r 27000 0 ? 4 4.50% Solve for PMT PMT= $554.12 Timeline: yr 0 yr 1 yr 2 yr 3 yr 4
PMT= 2700 12*$554 12*$554 12*$554 12*$554

With a 48 month period, the new monthly loan payments would be $554.12. Leasing the car
Given: PV FV PMT n (yr) r $12,536 12500 ? 5 7.30% Solve for PMT PMT= $301.93 Timeline:
0 yr 1 yr 2 yr 3 yr 4
PMT= 12*$302 12*$302 12*$302 12*$302 With a 48 month lease, assuming the present value of the payments is $12,536, the monthly payments would be $301.93. e)
Under the 48 month or 60 month plan, the present value of the car is always $27,000. Under the 60 month leasing plan, the present value of the car is $21,269.77.
Under the 48 month leasing plan the present value is $12,536 plus the value today of $12,500 four years from now. PV= $12536+PV(7.3%/2,8,0,-12500)
= $21,919
The present value of the car under the 48 month leasing plan is $21,919.00 The cheapest plan for Amy would be to use the 60 month leasing option.

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