Question

Your firm is considering leasing a $ 51000 copier. The copier has an estimated economic life of eight years. Suppose the appropriate discount rate is 9.1 % APR with monthly compounding. Classify each lease below as a capital lease or operating lease, and explain why:

a. A four-year fair market value lease with payments of $ 1145 per month.

b. A six-year fair market value lease with payments of $ 800 per month.

c. A five-year fair market value lease with payments of $ 920 per month.

d. A five-year fair market value lease with payments of $ 1010 per month and an option to cancel after three years with a$ 9400 cancellation penalty.

Answer 1

A capital lease should satisfy any one of the following criteria:

1) Present value of lease payments is greater than 90% of the purchase price.

2) Lease term is either equal or exceeds the useful life of the asset by 75%.

3) The ownership of the asset is transferred to the lessee at the end of the lease period.

4) The lease provides a bargain purchase option for a value which is less than the market value of the asset.

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Part a)

We will calculate the present value of lease payments to determine the nature of lease because it doesn't meet any other criteria of capital lease as there is no bargain purchase option, lease term is less than 75% of the useful life of the asset (4/8=50%) and the ownership is not transferred to the lessee at the end of lease period.

The present value of lease payments can be calculated with the use of PV (Present Value) function/formula of EXCEL/Financial Calculator. The function/formula for PV is PV(Rate,Nper,PMT,FV,1) where Rate = Interest Rate, Nper = Period, PMT = Payment and FV = Future Value and 1 indicates Annuity Due.

Here, Rate = 9.1%/12, Nper = 4*12 = 48, PMT = $1,145 and FV = 0 [we use 12 since the compounding is monthly]

Using these values in the above function/formula for PV, we get,

Present Value of Lease Payments = PV(9.1%/12,48,1145,0,1) = $46,272.15

Present Value as a Percentage of Purchase Price = 46,272.15/51,000 = 90.73% or 91%

As the present value of lease payments is greater than 90% of the purchase price, this lease will be treated as capital lease.

Answer for Part a) is Capital Lease.

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Part b)

In the given case we will calculate the lease life as a percentage of useful life of the asset to determine the nature of lease because it doesn't meet any other criteria of capital lease as there is no bargain purchase option, the ownership is not transferred to the lessee at the end of lease period and the present value of lease payments is $44,595.15 [PV(9.1%/12,72,800,0,1)] which is only 87% [44,595.15/51,000] of the purchase price of asset.

Lease Life as a Percentage of Useful Life of Asset = Lease Life/Useful Life of Asset = 6/8 = 75%

As the lease term is 75% of the useful life of the asset, this lease will be classified as capital lease.

Answer for Part b) is Capital Lease.

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Part c)

We will calculate the present value of lease payments to determine the nature of lease because it doesn't meet any other criteria of capital lease as there is no bargain purchase option, lease term is less than 75% of the useful life of the asset (5/8=62.50%) and the ownership is not transferred to the lessee at the end of lease period.

The present value of lease payments can be calculated with the use of PV (Present Value) function/formula of EXCEL/Financial Calculator. The function/formula for PV is PV(Rate,Nper,PMT,FV,1) where Rate = Interest Rate, Nper = Period, PMT = Payment and FV = Future Value and 1 indicates Annuity Due.

Here, Rate = 9.1%/12, Nper = 5*12 = 60, PMT = $920 and FV = 0 [we use 12 since the compounding is monthly]

Using these values in the above function/formula for PV, we get,

Present Value of Lease Payments = PV(9.1%/12,60,920,0,1) = $44,551.36

Present Value as a Percentage of Purchase Price = 44,551.36/51,000 = 87.36% or 87%

As the present value of lease payments is less than 90% of the purchase price, this lease will be treated as operating lease.

Answer for Part c) is Operating Lease.

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Part d)

We will calculate the present value of lease payments and the cancellation penalty to determine the nature of lease because It doesn't meet any other criteria of capital lease as there is no bargain purchase option, lease term with cancellation option is less than 75% of the useful life of the asset (3/8=37.50%) and the ownership is not transferred to the lessee at the end of lease period.

The present value of lease payments can be calculated with the use of PV (Present Value) function/formula of EXCEL/Financial Calculator. The function/formula for PV is PV(Rate,Nper,PMT,FV,1) where Rate = Interest Rate, Nper = Period, PMT = Payment and FV = Future Value and 1 indicates Annuity Due.

Here, Rate = 9.1%/12, Nper = 3*12 = 36, PMT = $920 and FV = $9,400 [we use 12 since the compounding is monthly]

Present Value of Lease Payments and Cancellation Penalty = PV(9.1%/12,36,920,9400,1) = $36,269.48

Present Value as a Percentage of Purchase Price = 36,269.48/51,000 = 71.12% or 71%

As the present value of lease payments is less than 90% of the purchase price, this lease will be treated as operating lease.

Answer for Part d) is Operating Lease.