Present Value of a Lease with Advanced Payments

With a lease, often there is an amount to be paid up-front and an option to buy at the back-end. A company is leasing a machine for 4 years. Monthly payments are $2,400; an additional $2,400 payment at the beginning of the leasing period replaces the final payment. The leasing agreement includes an option to buy the machine for $15,000 at the end of the leasing period. What is the capitalized value of the lease, assuming that the interest rate paid to borrow the funds is 18% compounded monthly?

Part 1: Find the present value of the payments

Variable	Enter
Clear
Pmt Timing	Beg
Future Val	0
Payment	-2,400
Intrst/Yr%	18.0
Periods	47
Periods/Yr	12
Cmpnds/Yr	12

Periods is 4 years at 12 periods per year less 1 advance payment. Compute Present Val by scrolling to its variable and choosing Calculate from the menu.

Calculating shows present value equal to $81,735.58. Choose Show Calculator from the template's menu, choose Template:Recall from the Calculator menu and save it to memory.

Part 2: Present value of the buy option

Variable	Enter
Future Val	-15,000
Payment	0
Periods	48

Compute Present Val by scrolling to its variable and choosing Calculate from the menu.

Calculating shows present value equal to $7,340.43.

Part 3: Calculate

Choose Show Calculator from the template's menu. Choose Template:Recall from the Calculator menu, add it to the present value of the payments stored in the calculator memory (from Part 1) and $2,400 for the advanced payment.

The present value of the lease is $91,476.00.