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# Calculating Annual Lease Payments

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I am hoping someone can review/provide the exact formulas required to arrive at the final answer for this problem. I'd like to understand how to approach this type of problem.

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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 \$250,000, and it will be leased by RBH for a period of 5 years. LRU will utilize straight line depreciation of \$50,000 per year with a zero book salvage value. However, salvage value is estimated to actually be \$50,000 at the end of 5 years. LRU is required to earn 3%, quarterly after tax rate of return on the lease. LRU uses a marginal tax rate of 35%. Calculate the annual lease payments. Remember, the payments are to be considered at the beginning of each year - annuity due.
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https://brainmass.com/economics/contracts/calculating-annual-lease-payments-65068

#### Solution Preview

The first step is to calculate the total amount of the lease that has to be amortized
First let us calculate the amount to be amortized. There are three parts in this –

Cost of Machine \$250,000
PV of after tax Salvage Value
Salvage Value \$50,000
Tax Rate 35%
After Tax Value =50000*(1-0.35)=\$32,500

PV factor (3%, 20 periods) 0.554 ( this you get from the PVIF table to find the present value of any amount you get in future – since it is a quarterly rate, we take the total period as 5X4, the number of quarters in a year) Since this amount is available at the end of the lease period, we need to calculate the Present Value

PV of After tax ...

#### Solution Summary

The solution explain how to calculate lease payments given the tax rate and the required rate of return.

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## Calculate 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 \$250,000, and it will be leased by RBH for a period of 5 years. LRU will utilize straight line depreciation of \$50,000 per year with a zero book salvage value. However, salvage value is estimated to actually be \$50,000 at the end of 5 years. LRU is required to earn a 3%, quarterly after-tax rate of return on the lease. LRU uses a marginal tax rate of 35%. Calculate the annual lease payments. (Remember, these payments are to be considered at the beginning of each year-annuity due.)

Hints for students:

There are 3 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 quarterly 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.

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