Question

Lease versus purchase JLB Corporation is attempting to determine whether to lease or purchase research equipment. The firm is in the 40% tax bracket, and its after-tax cost of debt is currently 8%. The terms of the lease and of the purchase are as follows:

Lease Annual end-of-year lease payments of $25,200 are required over the 3-year life of the lease. All maintenance costs will be paid by the lessor; insurance and other costs will be borne by the lessee. The lessee will exercise its option to purchase the asset for $5,000 at termination of the lease.

Purchase The research equipment, costing $60,000, can be financed entirely with a 14% loan requiring annual end-of-year payments of $25,844 for 3 years. The firm in this case will depreciate the equipment under MACRS using a 3-year recovery period. (See Table 4.2 on page 120 for the applicable depreciation percentages.) The firm will pay $1,800 per year for a service contract that covers all maintenance costs; insurance and other costs will be borne by the firm. The firm plans to keep the equipment and use it beyond its 3-year recovery period.

a. Calculate the after-tax cash outflows associated with each alternative.

b. Calculate the present value of each cash outflow stream, using the after-tax cost of debt.

c. Which alternative—lease or purchase—would you recommend? Why?

Answer 1

Calculate the after-tax cash flows:

Calculate the depreciation expense for each year using MACRS 3-years depreciation rate. Then calculate after-tax cash flows using the given information under each alternative.

Extracting the information:

Lease:

Purchase:

MACRS 3-year depreciation is used

Working Notes:

Amount of depreciation is calculated using MACRS 3-year depreciation rate.

Calculate annual depreciation for each year using MACRS 3 year’s rate:

To calculate the depreciation expense, multiply the beginning book value with the depreciation rate to obtain the depreciation expense and then deduct the depreciation from the beginning book value to obtain ending book value. The following table shows the calculation for each year.

a) Step 1: Calculate each year’s lease payment:

Every-year the payment of lease is the same; therefore, we will compute the cash outflow for one year, which is equal to the first two years. As per the given information, lessee will exercise the option to purchase the asset for $5,000 at the termination of the lease, which is 3^rd year.

Therefore, the cash flows for each year would be $15,120. In this problem, the total number of years is three. Hence, the cash flows for year-1, year-2 is $15,120, and for the third year, adds the termination value.

Step 2: Calculation of after-tax cash outflow under purchase option

This calculates by deducting the tax shield from the total of amount of annual payment. Tax shield can be obtained on the amount of interest, amount spent on maintenance and depreciation of the equipment.

Calculate interest for each year:

To calculate the interest for each year, multiply the interest rate with the equipment cost to obtain the interest payment. This interest payment deducts from the annual payment to result in amortized principal. Hence, the amortized principal balance deducts from the original principal amount to have the year-end balance.

Calculation of tax shield:

To calculate the tax shield, add the maintenance cost, depreciation expense and interest and multiply it with the tax rate. The calculations illustrates in the following table.

Calculation of after-tax cash outflows:

To calculate the after-tax cash flows, add the annual payment to the maintenance cost and deduct the tax shield. The calculations illustrates in the following table.

b) Step 1: Calculation of present value of cash outflow of lease

Year 1 to Year 3 cash outflow is as per Part a) Step 1and other variables are as per given information

First, we have to determine the present value factor using the formula and then multiply with the respective year’s cash outflow. Summation of these present values of cash outflow will give the total present value of cash outflows.

We can determine the present value using the following formula for PVIF @8% for 1, 2 and 3 years

Calculation of total present value of cash outflows of lease:

To calculate the total present value of cash outflows, multiply the present value interest factor with the cash flows of each year. Then add all the present value of cash outflows from year-1 to year-3 to obtain the total present value of cash outflows.

Step 2: Calculation of present value of cash outflow of purchase

Year 1 to Year 3 cash outflow is as per Part a) Step 2and other variables are as per given information

First, we have to determine the present value factor using the formula and then multiply with the respective year’s cash outflow. Summation of these present values of cash outflow will give the total present value of cash outflows.

We can determine the present value using the following formula for PVIF @8% for 1, 2 and 3 years

Calculation of total present value of cash outflows of purchase:

To calculate the total present value of cash outflows, multiply the present value interest factor with the cash outflows of each year. Then add all the present value of cash outflows from year-1 to year-3 to obtain the total present value of cash outflows.

c) If we compare the total present value of lease and purchases, it is clear that the total present value of cash outflow of purchase is higher than lease. Thus, the firm should opt for leasing the equipment.