Question

Determine Car Lease Payments:

The term of the lease is 5 years, for 60 monthly payments. The current value of the car is $100,000, and the residual value at the end of year 5 is $42,000.

1.) The annual interest rate (APR) on the lease is 3.0%. Assuming you do not put down any money upfront, what is the monthly lease payment? Please list the formula.

2.) If there is an upfront sales tax of $4,640 you have to pay, but you choose to embed the cost in the monthly payments instead, what is the monthly lease payment?

3.) Including the sales tax above, if you paid a down payment of $5,000, what is the new monthly lease payment?

Problem can be solved by hand or through Excel. Please show work!

Answer 1

Requirement 1 Current Value of Car 1,00,000 Residual Value Monthly interest rate (3%/12) Term (in months) PVIF (0.25%, 60) Present Value of Residual value (42000*0.8609) 42,000 0.25% 60 0.8609 36,158 $ Present Value of Minimum Lease Payments $ 63,842 (Current Value of car-PV of Residual Value) (100000-36158) PVAF (0.25%, 60) 55.6524 $ 1,147 Monthly Lease Payments (PV of MLP/PVAF) = (63842/55.6524) The Monthly lease payment in this case is $ 1,147.

Requirement 2 Present Value of Minimum Lease Payments $ 63,842 (Current Value of car-PV of Residual Value) (100000-36158) (+) Upfront Sales Tax embedded $ 4,640 Sub-Total 68,482 PVAF (0.25%, 60) 55.6524 $ 1,231 Monthly Lease Payments (PV of MLP/PVAF) = (68482/55.6524) The Monthly lease payment in this case is $ 1,231. Requirement 3 Present Value of Minimum Lease Payments $ 63,842 (Current Value of car-PV of Residual Value) (100000-36158) (+) Upfront Sales Tax embedded 4,640 (-) Down Payment -5,000 Sub-Total 63,482 PVAF (0.25%, 60) 55.6524 $ 1,141 Monthly Lease Payments (PV of MLP/PVAF) = (63482/55.6524) The Monthly lease payment in this case is $ 1,141.