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
