Chapter 21 - LEASE

8/8/2019 Chapter 21 - LEASE

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Answers to End-of-Chapter Problems B-187

Chapter 21: Leasing

21.1 a. Leasing can reduce uncertainty regarding the resale value of the asset that isleased.

b. Leasing does not provide 100% financing although it may look as though it does.Since firms must try to maintain their optimal debt ratio, the use of lease simplydisplaces debt. Thus, leasing does not provide 100% financing.

c. Although it is true that leasing displaces debt, empirical studies show that thecompanies that do a large amount of leasing also have a high debt-to-equity ratios.

d. If the tax advantages of leasing were eliminated, leasing would probably disappear.The main reason for the existence of long-term leasing is the differential in the taxrates paid by the lessee and the lessor.

21.2 a. NPV (lease) = $250,000 - L5

08.0

= $250,000 - 3.9927 L= $0

L = $62,614.11The lease payment is Quartza reservation price.

b. Depreciation = $250,000 / 5= $50,000 per annum

Depreciation tax shield

= $50,000 0.35= $17,500

After-tax discount rate

= 0.08 (1 - 0.35)= 0.052

NPV (lease) = -$250,000 + L (1 - 0.35)5

052.0 + $17,5005

052.0

= $0L = $62,405.09This lease payment is New Leasing Cos reservation price.

c. If the lease price is greater than Quartzs reservation price, the lease is a negativeNPV proposal for Quartz. Quartz would rather purchase the equipment than leaseat a payment above its reservation price. Thus, the lessees reservation price is themaximum of the negotiation range.


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Answers to End-of-Chapter ProblemsB-188

21.3 Incremental cash flows from leasing instead of purchasing:

Lease minus Buy Year 0 Year 1 - 5Lease

Lease payment -$94,200Tax benefit of lease payment $32,970

Buy (minus)Cost of machine -(-$350,000)Lost depreciation tax benefit -$350,000/5 0.35

= -$24,500

Total $350,000 -$85,730

NPV = $350,000 - $85,730( )

5

65.011.0

= -$102.66 < $0The firm should buy the machine.

24.4 Maxwells reservation price:

NPV (lease) = $200,000 - L5

10.0

= $200,000 - 3.7908 L= $0

L = $52,759.50Mercers reservation price:

Depreciation = $200,000 / 5= $40,000 per annum

Depreciation tax shield= $40,000 0.35= $14,000

After-tax discount rate= 0.10 (1 - 0.35)= 0.065

NPV (lease) = -$200,000 + L (1 - 0.35)5

065.0 + $14,0005

065.0

= $0L = $52,502.94

Therefore, the negotiation range is from $52,502.94 to $52,759.50.

21.5 Reservation payment of Raymond:Value of lease = $100,000 - 0.75 L ( )

575.008.0 = $0

L = $31,652.85Reservation payment of Liberty:

Value of lease = -$100,000+L = $24,962.04

Therefore, the negotiation range is from $24,962.04 to $31,652.85. For lease paymentshigher than $31,652.85, Raymond will not enter into the arrangement. For lease paymentslower than $24,962.04, Liberty will not enter into the arrangement.

( )5

65.008.035.05

000,100


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21.6 a. The lease payment, which makes both parties equally well off, is the payment,which equates the NPVs for the firms. Since the tax rates of the two firms areequal, the perspective of the lessor is the opposite of the perspective of the lessee.

This condition ensures that the NPV is zero.After-tax cash flows to the lessor

= L (1 - 0.34) + Depreciation (0.34)Depreciation = $86.87 / 2 = $43.435The NPV is zero when the NPV of the lessors after-tax cash flows equals the costof the asset. The appropriate discount rate is the after-tax rate. That rate is 6.6% [=

10% 0.66].

$86.87 = [0.66 L + $43.435 (0.34)]2

066.0

$86.87 = [0.66 L + $43.435 (0.34)] (1.8181)L = $50.02

b. Generalize the result from part a.

Let T1 denote the lessors tax rate.Let T2 denote the lessees tax rate.Let P denote the purchase price of the asset.Let Dep equal the annual depreciation expense.Let N denote the length of the lease in years.

Value to the lessor = +

++

=

N

1tt

1

11

)]T1(r1[

)T(Dep)T1(LP

Value to the lessee = +

+

=

N

1tt

2

22

)]T1(r1[

)T(Dep)T1(LP

The values of the lease to its two parties will be opposite in sign only if T1 = T2.c. Since the lessors tax bracket is unchanged, the lease has a zero NPV to the lessor

when the lease payment is $50.02.If the lessee pays no taxes, the pre-tax and after-tax lease payment are the same.Also, one of the lessees cash flows is the depreciation that is foregone when leasingis chosen over purchasing. If the lessees tax rate is zero, it will not benefit fromdepreciation. Thus, if the lessee chooses leasing, the lost depreciation is no longer acash flow. The lease has a zero NPV to the lessee when L = $50.05.

L2

10.0 = $86.87

L = $86.87 / 1.7355= $50.05

If L > $50.05 the NPV to the lessee is < $0.

If L < $50.05 the NPV to the lessee is > $0.If L > $50.05 the NPV to the lessor is > $0.If L < $50.05 the NPV to the lessor is < $0.

Both parties have positive NPV for $50.02 < L < $50.05.

21.7 a. Assume that 10% is the market-wide interest rate. The decision to buy or lease ismade by looking at the incremental cash flows.


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Cash flows from leasing:Year 0 1 2 3 4 5

A/T savings* $3,960 $3,960 $3,960 $3,960 $3,960Lease payment -2,100 -2,100 -2,100 -2,100 -2,100Tax benefit** 714 714 714 714 714

Net cash flows 2,574 2,574 2,574 2,574 2,574* After tax savings on operations

= $6,000 0.66= $3,960

** Tax benefit

= $2,100 0.34= $714

Cash flows from purchasing:Year 0 1 2 3 4 5

A/T savings* $5,940 $5,940 $5,940 $5,940 $5,940Purchase -15,000Dep tax shield** 1,020 1,020 1,020 1,020 1,020

Net cash flows -15,000 6,960 6,960 6,960 6,960 6,960* After tax savings on operations

= $9,000 0.66= $5,940

** Depreciation = $15,000 / 5 = $3,000 per annumDepreciation tax shield

= $3,000 0.34= $1,020

Incremental cash flows from leasing vs. purchasing:Year 0 1 2 3 4 5

Lease $2,574 $2,574 $2,574 $2,574 $2,574Purchase -15,000 6,960 6,960 6,960 6,960 6,960

L P 15,000 -4,386 -4,386 -4,386 -4,386 -4,386

NPV of the incremental cash flows:

The cash flows must be discounted at the after tax rate which is 6.6% [= 10% 0.66].

NPV = $15,000 - $4,3865

066.0

= $15,000 - $4,386 (4.1445)= -$3,177.78

Since the NPV of the lease-vs.-buy incremental cash flows is negative, Farmershould buy, not lease the equipment.

b. As long as the company maintains its target debt-equity ratio, the answer does notdepend upon the form of financing used for the direct purchase. A financial leasewill displace debt regardless of the form of financing.

c. The amount of displaced debt is the PV of the incremental cash flows from year onethrough five.

PV = $4,386 (4.1445) = $18,177.78


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21.8 Redwood:

Year 0 Year 1 - 6 Year 7

Cost of machine $420,000 $0 $0Lease payment -L -L $0

$420,000 - L = A60.06 LL = $70,978.03

American:Year 0 Year 1 - 6 Year 7

Cost of machine -$420,000 $0 $0Dep tax shield $21,000 $21,000A/T lease payment 0.65 L 0.65 L $0

Value of lease

= -$420,000 + $21,000 ( )7

65.006.0 + 0.65 L + 0.65 L ( )6

65.006.0

= -$420,000 + $21,000 (6.0243) + 4.0685 L = $0L = $72,137The negotiating range is from $72,137 to $70,978.03.

21.9 The decision to buy or lease is made by looking at the incremental cash flows.a. Cash flow from leasing:

Year 0 1 2 3

Lease payment -$1,200,000 -$1,200,000 -$1,200,000Tax benefit* 420,000 420,000 420,000

Net cash flow -$780,000 -$780,000 -$780,000*Tax benefit = $1,200,000 x .35 = $420,000

Cash flow from purchasing:Year 0 1 2 3

Purchase cost -$3,000,000Dep tax shield* $350,000 $350,000 $350,000

Net cash flow -3,000,000 350,000 350,000 350,000*Depreciation tax shield = [$3,000,000 / 3] x 35% = $350,000

Incremental cash flows from leasing vs. purchasing:Year 0 1 2 3

Lease -$780,000 -$780,000 -$780,000Purchase (minus) $3,000,000 -350,000 -350,000 -350,000

Net cash flow $3,000,000 -1,130,000 -1,130,000 -1,130,000

After-tax discount rate

= 0.12 0.65= 0.078

NPV of incremental cash flows

= $3,000,000 - $1,130,0003

078.0

= $3,000,000 - $1,130,000 (2.5864)= $77,339.09


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Therefore, Wolfson should lease the machine.b. Wolfson is indifferent at the lease payment which makes the NPV of the incremental

cash flows zero.

NPV = $0= $3,000,000 - (0.65 L + $350,000)

3

078.0

= $3,000,000 - (0.65 L + $350,000) (2.5864)L = $1,246,002.96

Chapter 21 - LEASE

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