# Calculate Lessee's Reservation Payment for Leasing a New Machine

## How to calculate the lessee's reservation payment for leasing a new machine?

What factors need to be considered in determining the lessee's reservation payment?

## Lessee's Reservation Payment Calculation:

The lessee's reservation payment, which is the lease payment at which the net present value (NPV) of the lease relative to purchase is $0, is $97,576.10.

When considering leasing a new machine, the lessee must calculate the reservation payment to determine the point at which the NPV of leasing is equal to the NPV of purchasing the machine. This calculation involves taking into account various financial factors such as lease payments, purchase cost, salvage value, depreciation, tax rate, and discount rate.

For the lease, the annual lease payments of $100,000 for 6 years with the first payment occurring immediately are considered. The NPV of these lease payments is calculated using the present value of an annuity formula and a discount rate of 5% to determine the present value of the lease.

On the other hand, for purchasing the machine, the initial cost of $510,000, salvage value of $5,000, annual depreciation expense using straight-line method, pre-tax cash flows, tax rate of 25%, and discount rate of 5% are taken into consideration to calculate the NPV of the purchase.

By adjusting the lease payment amount, the lessee can find the payment at which the NPV of the lease relative to the purchase is $0. In this case, the lessee's reservation payment is determined to be $97,576.10.

It is essential for the lessee to understand the financial implications of leasing versus purchasing a new machine and make an informed decision based on the calculated reservation payment.