Question

Quartz Corporation is a relatively new firm. Quartz has experienced enough losses during its early years to provide it with at least eight years of tax loss carryforwards, so Quartz’s effective tax rate is zero. Quartz plans to lease equipment from New Leasing Company. The term of the lease is five years. The purchase cost of the equipment is $745,000. New Leasing Company is in the 25 percent tax bracket. There are no transaction costs to the lease. Each firm can borrow at 7 percent. a. What is Quartz’s reservation price? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.) b. What is New Leasing Company’s reservation price? (Do not round intermediate calculations and round your answer 2 deceimals places

Answer 1

Solution:

a.

Since the lessee has an effective tax rate of zero, there is no depreciation tax shield foregone. Also, the after-tax lease payment is the same as the pre-tax payment, and the after-tax cost of debt is the same as the pre-tax cost. To find the most the lessee would pay, we set the NAL equal to zero and solve for the payment, doing so, we find the most the lessee will pay is:

• NAL = 0 = $745,000 – PMT (PVIFA7%,5)
• PMT (PVIFA7%,5) = $745,000
• PMT = $745,000/(PVIFA7%,5)
• PMT = $745,000/4.1002
• PMT = $181,698.45

b.

The depreciation tax shield is:

• Depreciation Tax Shield = ($745,000/5)(.25) = $37,250

The after-tax cost of debt is:

• After-tax debt cost = 0.07(1 – 0.25) =0.0525

Using all of this information, we can calculate the minimum lease payment for the lessor as:

• NPV = 0 = -$745,000 +PMT(1 – .25)(PVIFA5.25%,5) + $37,250(PVIFA5.25%,5)
• PMT(1 – .25)(PVIFA5.25%,5) + $37,250(PVIFA5.25%,5) = $745,000
• PMT(1 – .25)(PVIFA5.25%,5) = $745,000 - $37,250 (4.2997)
• PMT(1 – .25)(PVIFA5.25%,5) = $745,000 - $160,163.825
• PMT(1 – .25)(PVIFA5.25%,5) = $584,836.175
• PMT (0.75) (4.2997) = $584,836.175
• PMT = $584,836.175/[(0.75)(4.2997)]
• PMT = $181,357.203 = $181,357

A lease payment less than $181,357 will give the lessor a negative NPV. A payment higher than $181,698.45 will give the lessee a negative NAL. In either case, no deal will be struck. Therefore, these represent the lower and upper bounds of possible lease prices during negotiations.