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The machine should be bought since the IRR is greater than 14% and the NPV is positive.

Annual Lease Payments. Fairchild Leasing Company is setting up a capital lease with Gemi

8.34

Trucking, Inc. The lease will cover a $36,000 delivery truck. The terms of the lease call for a 12

percent return to the truck lessor. The lease is to run for 5 years.

Based on these data, determine (a) the annual lease payment and ( b ) the annual lease

payment if the lessor desires 10 percent on its lease.

SOLUTION

amount --=

- $369000 $9,987 (rounded)

Annual lease payment = A =

PVIFA12%,,5 3.6048

- $36'000 - $9,497 (rounded)

$36'000 ---

A=

PVIFAloyo,s 3.7908

Annual Lease Payments. Star Wars Leasing, Inc., is setting up a financial lease covering a $36,000

8.35

truck. The lease arrangement requires beginning-of-year payments and the life of the lease is 5

years. The company wants equal annual lease payments that will allow it to earn 12 percent on

its investment.

251

CAPITAL BUDGETING (INCLUDING LEASING)

CHAP. 81

Based on these data, determine (a) the annual lease payment and (6) the annual lease

payment if the desired rate of return is only 10 percent.

SOLUTION

Since the lease payment is made in advance, the straightforward application of the formula (i.e.,

(a)

A = amountIPVIFA) does not work. The equation can be set up as follows:

+ A PVIFA12%,4

$36,000 = A

$36,000 = A(1 + PVIFA12%,4)

$36,000 - $36,000 - $367000- $8,917 (rounded)

---

A=

1 + PVIFA129/u,4 1+ 3.0373 4.0373

- $367000

$36,000 =-=367000

$

$8,633 (rounded)

A=

1+ PVIFA10yo,4 1+ 3,1699 4.1699

Lease versus Purchase Decision. Carter Company wishes to expand its productive capacity. In

8.36

order to do so it must acquire a new tractor costing $40,000.The machine can be purchased or

leased. The firm is in the 40 percent tax bracket and its after-tax cost of debt is currently 6

percent.

If the firm purchased the machine, the purchase would be totally financed with a 10 percent

loan requiring equal annual end-of-year payments over 5 years. The machine would be

depreciated straight-line over its 5-year life. A salvage value of zero is anticipated. The life of a

lease would be 5 years. The lessor intends to charge equal annual lease payments that will enable

it to earn 15 percent on its investment. In doing the following calculations, round your answers

to the nearest dollar.

(a) Calculate the annual lease payment required in order to give the lessor its desired return.

(6) Calculate the annual loan payment paying 10 percent interest. (c) Determine the after-tax

cash outflows associated with each alternative. ( d ) Find the present value of the after-tax cash

outflows using the after-tax cost of debt. (e) Which alternative (i.e., lease or purchase) would you

recommend? Why?

SOLUTION

$40,000 - $40,00 $1 ,932

--=

Annual lease payment A=

=

PVIFAIS%.S 3.3522

$40,000 --=

- $40,000 $10,552

Annual loan payment A =

=

PVIFAlo%,s 3.7908

Data pertaining to a lease agreement are as follows:

( c ) and (d)

PV of

Year Payment AftepTax Cost PV Factor at 6% outflow

$1

1-5 1,932 $7,159 4.2124 $30,157

Data pertaining to a purchase agreement are as follows:

Payment ($)

Year Principal ($) Balance ($)

Interest ($) Depreciation ($)

1 4,000 6,552 33,448

10,552 8,000

2 10,552 3,345 7,207 26,24 1 8,000

3 10,552 2,624 7,928 18,313 8,000

4 10,552 1,83 1 8,721 9,592 8,000

5 10,552 959 9,593 8,OOo

CAPITAL BUDGETING (INCLUDING LEASING) [CHAP. 8

252

PV of

Total ($1 PV Factor

Tax AftePTax

Year (Interest+ Dep.) Cash Outflow ($) at 6% oufflow

Savings ($)

5,752 0.9434 $ 5,426

1 12,000 4,800

0.8900 5,352

6,014

2 4,538

11,345

6,302 0.8396 5,291

3 10,624 4,250

6,620 0.7921 5,244

4 9,831 3,932

6,968 0.7473 5,207

3,584

5 8,959

$26,520

The purchase alternative is preferable because the PV of the purchase cash outflow is less than the

(e)

PV of the lease cash outflow.

83

.7 Lease versus Purchase Decision. Sanchez Co. is considering a capital lease providing additional

warehouse space for its department stores. The price of the facility is $330,000. The leasing

arrangement requires beginning-of-year payments which, for tax purposes, cannot be deducted

until the end of the year. The life of the lease is 5 years and the facility has zero expected salvage

value. The lessor wants a 5 percent return on its lease. Assume that the firm is in the 40 percent

tax bracket and its after-tax cost of debt is currently 7 percent. Find the present value of the

after-tax cash outflows using the after-tax cost of debt as the discount rate. Round your answer

to the nearest dollar.

SOLUTION

$330,000

Annual lease payment (for the beginning-of-year payment situation) =

1+ PVIFA1s%.4

- $330,000 - $330,000

--= $85,603

1 + 2.8550 3.8550

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