# Present Value Lease Problem-Calculating Annual Payments

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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.)

I know that there are 3 major steps that need to be accomplished in order to calculate the annual lease payment (see below); however, I am still a little uncertain as to how to complete this particular example:

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.

Thank you very much for your assistance.

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The solution explains how to calculate the annual lease payments.

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Let us do the steps

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.

First let us calculate the amount to be amortized. There are three parts in this -

Cost of Machine $200,000

PV of after tax Salvage Value

Salvage Value $35,000

Tax Rate 40%

After Tax Value =35000*(1-0.4)=$21,000

PV factor (14%, 5 years) 0.519 ( this you get from the PVIF table to find the present value of any amount you get in future)

PV of After tax Salvage Value ...

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