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. Thus, Quartz’s effective tax rate is zero. Quartz plans to lease equipment from New Leasing Company. The term of the lease is four years. The purchase cost of the equipment is $970,000. New Leasing Company is in the 30 percent tax bracket. There are no transaction costs to the lease. Each firm can borrow at 10 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.)
Reservation price $
b. What is New Leasing Company’s reservation price? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)
Reservation price $

Answer 1

Answer:

a. Quartz’s reservation price = $306,006.68

b. New Leasing Company’s reservation price = $234,034.25

Explanation:

Given:

Cost = Cost of the equipment = $970,000

n = number of years of lease term = 4

r = cost of borrowing rate = 10%, or 0.10

t = tax rate = 30%, or 0.30

DF = Discounting factor or PV of $1 = ((1-(1/(1 + r))^n)/r) = ((1-(1/(1 + 0.10))^5)/0.10) = 3.16986544634929

a. What is Quartz’s reservation price? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

The implication of the zero effective tax rate is that depreciation tax shield foregone does not exist. In addition, there is no difference between the after-tax lease payment and the pre-tax payment, and there is also no difference between the pre-tax cost of debt and the after-tax cost.

Quartz’s reservation price can therefore be calculated by setting net advantage to leasing (NAL) equal to zero and solve as follows:

NAL = 0 = Cost – (PMT * DF) ………… (1)

Substituting the relevant values into equation (1), we have:

0 = $970,000 – (PMT * 3.16986544634929)

$970,000 = PMT * 3.16986544634929

PMT = $970,000 / 3.16986544634929

PMT = $306,006.68

Quartz’s reservation price = PMT = $306,006.68

b. What is New Leasing Company’s reservation price? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Depreciation tax shield = (Cost / n) * t = ($970,000 / 4) * 30% = $72,750

New r = After-tax debt cost = r * (1 - t) = 0.10 * (1 - 0.30) = 0.07

New DF = ((1-(1/(1 + New r))^n)/New r) = ((1-(1/(1 + 0.07))^5)/0.07) = 4.10019743594759

The New Leasing Company’s reservation price can therefore be calculated by setting NPV to zero as follows:

NPV = 0 = -Cost + (PMT * (1 – t) * New DF) + (Depreciation tax shield * New DF)

0 = -$970,000 + (PMT * (1-0.30) * 04.10019743594759) + ($72,750 * 4.10019743594759)

$970,000 - ($72,750 * 4.10019743594759) = PMT * (1-0.30) * 04.10019743594759

$671,710.636534813 = PMT * 2.87013820516331

PMT = $671,710.636534813 / 2.87013820516331

PMT = $234,034.25

New Leasing Company’s reservation price = PMT = $234,034.25