A company is deciding whether to lease or buy a car. The lease would be for four
ID: 2383549 • Letter: A
Question
A company is deciding whether to lease or buy a car.
The lease would be for four years and requires a $7,500 payment. The company also has an initial cost of $2,500 for transporting the car. At the end of the lease, the van will return to the leasing company.
If they buy the car, it costs $31,000. This option will involve $2,250 annual payments for the car. They could sell the van for $10,000 at the end of the sixth year.
The cost of capital is 8%. Should the company lease or buy the car (use time value of money)?
Explanation / Answer
Option 1: Lease
Lease Rental = $ 7500 (Assumed its annual Rental)
Initial Cost = $ 2500
Present Value of Lease rental
Total PV of Lease Rental (Sum Total of 4 Years) = $24840.95
Total PV of cash Outflow = PV of Lease Rental + Initial Cost
= 24840.95 + 2500 = $27340.95
Option 2: Buy the Car
Initial Cost = $ 31,000
Annual Payment = $ 2250
Present Value of Annual Payment. (Since the Van can only be sold at the end of 6th Year it is assumed that annual payment for the car need to be made for 6 years. However for sake of your convenience i am also showing the detail working if the annual payment is made only for 4 years)
If Annual Payment is made for 6 Years
Total PV of Annual Payment from above data : $10,401.48
Sale Value at the end of 6 year : $31,000
PV of Sale Value : 10000 * 0.63017 = $6301.70
PV of Net Cash Outflow = Initial Cost + PV of Annual Payment - PV of Sale Value
= 31,000 + 10,401.48 - 6301.70 = $35099.78
If Annual Payment is made for 4 Years
Total PV of Annual Payment : $7452.28
PV of Total Cash outflow = Initial Cost + PV of Annual payment - PV of Sale value
= 31,000 + 7452.28 - 6301.70 = $32150.59
PV of cash Outflow in Lease = $ 27340.95 (from Option 1)
PV of Cash outflow if Buy the Car = $35099.78 (If Annual payment for 6 years)
PV of Cash outflow if Buy the Car = $32150.59 (If Annual payment for 4 years)
Since cash outflow is lower in case of Lease , Company should opt for Lease
Particulars Year 1 Year 2 Year 3 Year 4 Cost of Capital @ 8 % 0.925926 0.857339 0.793832 0.73503 Annual Rent 7500 7500 7500 7500 PV of Lease rental 6944.444 6430.041 5953.742 5512.724Related Questions
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