Present Value Lease Calculating Annual Lease Payments

Leases R Us, Inc. (LRU) has been contracted by Robotics of Beverly Hills (RBH) to provide lease financing for a machine that would assist in automating a large part of their current assembly line. Annual lease payments will start at the beginning of each year. The purchase price of this machine is $200,000, and it will be leased by RBH for a period of 5 years. LRU will utilize straight line depreciation of $40,000 per year with a zero book salvage value. However, salvage value is estimated to actually be $35,000 at the end of 5 years. LRU is required to earn a 14%, after-tax rate of return on the lease. LRU uses a marginal tax rate of 40%. Calculate the annual lease payments. (Remember, these payments are to be considered at the beginning of each year-annuity due.)

(in short form:
Period is 5 years
Payments are at the beginning of the year
Purchase price is $200,000
Depreciation 5 years
Straight-Line $40,000 per year
Book value at end of lease is 0
Salvage value is estimated to ve
$35,000 (100% gain & 100% taxable)
LRU has to earn 14% after tax
Tax Rate is 40%)

There are three major steps that need to be accomplished in order to calculate the annual lease payment.

Step A: You need to calculate the amount to be amortized. This would be the cost of the machine less the PV of the after tax salvage value of the machine and less the PV of the depreciation tax shield.

Step B: You need to calculate the annual after-tax required lease income. (Remember, in this step, you need to calculate it as an annuity due-a beginning of the year payment.) Take your answer from Step A as a present value, and using the number of years and the required rate of return, calculate the payment.

Step C: Calculate the lease payment. You need to adjust for the appropriate tax rate. Therefore, take your answer in Step B and divide it by (1 - the tax rate). This will give you the required lease payment.