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CHAPTER 21 -
12. The decision to lease results in a debt capacity that is lowered by the present value of the aftertax
lease payments. The aftertax lease payment is:
13. a. Since both companies have the same tax rate, there is only one lease payment that will result in
a zero NAL for each company. We will calculate cash flows from the depreciation tax shield
first. The depreciation tax shield is:
b. To generalize the result from part a:
Let T1 denote the lessor’s tax rate.
Let T2 denote the lessee’s tax rate.
The value to the lessor is:
ValueLessor =
−P+∑
t=1
NL(1 − T1)+ D(T1)
[1 + R (1 − T1)]t
And the value to the lessee is:
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ValueLessee =
P−∑
t=1
NL(1 − T2)+ D(T2)
[1 + R (1 − T2)]t
Since all the values in both equations above are the same except
T1
and
T2
, we can see
that the values of the lease to its two parties will be opposite in sign only if T1 = T2.
c. Since the lessor’s tax bracket is unchanged, the zero NAL lease payment is the same as we
found in part a. The lessee will not realize the depreciation tax shield, and the aftertax cost of
debt will be the same as the pretax cost of debt. So, the lessee’s maximum lease payment will
be:
14. The decision to buy or lease is made by looking at the incremental cash flows. The loan offered by
the bank merely helps you to establish the appropriate discount rate. Since the deal they are offering
is the same as the market-wide rate, you can ignore the offer and use 9 percent as the pretax discount
rate. In any capital budgeting project, you do not consider the financing which was to be applied to a
specific project. The only exception would be if a specific and special financing deal were tied to a
specific project (like a lower-than-market interest rate loan if you buy a particular car).
a. The incremental cash flows from leasing the machine are the lease payments, the tax savings on
the lease, the lost depreciation tax shield, and the saved purchase price of the machine. The
lease payments are due at the beginning of each year, so the incremental cash flows are:
Year 0 Year 1 Year 2 Year 3 Year 4
Lease:
Lease payment –$830,000 –$830,000 –$830,000 –$830,000
The aftertax discount rate is:
So, the NAL of leasing is:
Since the NAL is negative, the company should buy the equipment.
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b. The company is indifferent at the lease payment which makes the NAL of the lease equal to
zero. The NAL equation of the lease is:
15. a. The different borrowing rates are irrelevant. A basic tenant of capital budgeting is that the
return of a project depends on the risk of the project. Since the lease payments are affected by
b. Since both companies have the same tax rate, there is only one lease payment that will result in
a zero NAL for each company. We will calculate cash flows from the depreciation tax shield
The aftertax cost of debt is the lessee’s cost of debt, which is:
Using all of this information, we can calculate the lease payment as:
c. Since the lessor’s tax bracket is unchanged, the zero NAL lease payment is the same as we
found in part b. The lessee will not realize the depreciation tax shield, and the aftertax cost of
debt will be the same as the pretax cost of debt. So, the lessee’s maximum lease payment will
be:
16. The APR of the loan is the lease factor times 2,400, so:
To calculate the lease payment we first need the net capitalization cost, which is the base capitalized
cost plus any other costs, minus any down payment or rebates. So, the net capitalized cost is:
The depreciation charge is the net capitalized cost minus the residual value, divided by the term of
the lease, which is:
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And the taxes on each monthly payment will be:
The monthly lease payment is the sum of the depreciation charge, the finance charge, and taxes,
which will be:
Challenge
17. With a four-year loan, the annual loan payment will be
The aftertax loan payment is found by:
Aftertax payment = Pretax payment – Interest tax shield
So, we need to find the interest tax shield. To find this, we need a loan amortization table since the
interest payment each year is the beginning balance times the loan interest rate of 8 percent. The
interest tax shield is the interest payment times the tax rate. The amortization table for this loan is:
Year
Beginning
balance Total payment
Interest
payment
Principal
payment
Ending
balance
So, the total cash flows each year are:
Aftertax loan payment OCF Total
cash flow
Year 1: $1,751,141 – ($464,000)(.35) = $1,588,740.67 – 1,606,000 = –$17,259.33
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So, the NAL with the loan payments is:
18. a. The decision to buy or lease is made by looking at the incremental cash flows, so we need to
find the cash flows for each alternative. The cash flows if the company leases are:
Cash flows from leasing:
The tax benefit of the lease is the lease payment times the tax rate, so the tax benefit of the
lease is:
We need to remember the lease payments are due at the beginning of the year. So, if the
company leases, the cash flows each year will be:
Year 0 Year 1 Year 2 Year 3 Year 4 Year 5
Aftertax savings $19,140 $19,140 $19,140 $19,140 $19,140
The amount the company borrows and the repayment schedule are irrelevant since the company
maintains a target debt–equity ratio. So, the cash flows from buying the machine will be:
Cash flows from purchasing:
And the deprecation tax shield will be:
Year 0 Year 1 Year 2 Year 3 Year 4 Year 5
Aftertax savings $21,120 $21,120 $21,120 $21,120 $21,120
Purchase –$365,000
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Now we can calculate the incremental cash flows from leasing versus buying by subtracting the
net cash flows from buying from the net cash flows from leasing. The incremental cash flows
from leasing are:
Year 0 Year 1 Year 2 Year 3 Year 4 Year 5
The aftertax discount rate is:
b. As long as the company maintains its target debt–equity ratio, the answer does not depend upon
c. The amount of displaced debt is the PV of the incremental cash flows from Year 1 through Year
5.
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