Chapter 21 – Leasing 2, 3
21.2 7
th
ed., 21.8 8
th
ed.
The reservation payment is found by setting the NPV of the lease to
$0, and then solving for the lease payment.
a.
For Quartz Corp, the lessee:
Since Quartz's effective tax rate is 0, the after tax discount rate is 8%.
(The aftertax cost of
debt = the pretax cost of debt.)
Also, with no taxes, there is no depreciation tax shield foregone.
To find the most that the lessee would pay, we Set the NPV = 0, and solve for the payment
(L):
NPV (lease)
= Cost

after tax PV(lease payments)
(
5
08
.
0
Α
) is found using financial calculator with PMT = 1, N = 5, I = 8, FV = 0, => PV =
3.99271
0
= $250,000  L (
5
08
.
0
Α
)
= $250,000  L (3.99271)
L
= $62,614.11
The lease payment is Quartz’s reservation price.
i.e. for L > 62,614.11, Quartz will have NPV<0.
b.
For New Leasing, the lessor:
NPV
= Cost
+
after tax PV(Lease payments)
+
PV(Depreciation tax shield)
Depreciation
= $250,000 / 5
= $50,000 per annum
Depreciation tax shield
= $50,000
×
0.35
= $17,500
Aftertax discount rate
= 0.08 (1  0.35)
= 0.052
As in part a., set NPV = 0, and solve for L:
NPV (lease)
=
0
= $250,000 + L (1  0.35)
5
052
.
0
Α
+ $17,500
5
052
.
0
Α
PMT = .65, N = 5, I = 5.2, FV = 0
=> PV = 2.798669
PMT = 17,500, N = 5, I = 5.2, FV = 0
=> PV = 75,348.785957
NPV = 0 = $250,000 + 2.7987L + $75,348.79
=> 2.7987L = 174,651.214
L
= $62,405.09 (if hold all decimal places) or $62,420.01 (if rounded)