Suppose Amazon is considering the purchase of computer servers and network infra

Question

Suppose Amazon is considering the purchase of computer servers and network infrastructure to expand its very successful business offering? cloud-based computing. In? total, it will purchase

$47.7

million in new equipment. This equipment will qualify for accelerated? depreciation:

20%

can be expensed? immediately, followed by

32%?,

19.2%?,

11.52%?,

11.52%?,

and

5.76%

over the next five years.? However, because of the? firm's substantial loss carryforwards and other? credits, Amazon estimates its marginal tax rate to be

10%

over the next five? years, so it will get very little tax benefit from the depreciation expenses.? Thus, Amazon considers leasing the equipment instead. Suppose Amazon and the lessor face the same

8.2%

borrowing? rate, but the lessor has a

35%

tax rate. For the purpose of this? question, assume the equipment is worthless after five? years, the lease term is five? years, and the lease qualifies as a true tax lease.

a. What is the lease rate for which the lessor will break? even?

b. What is the gain to Amazon with this lease? rate?

c. What is the source of the gain in this? transaction?

a. What is the lease rate for which the lessor will break? even?

Calculate the FCF below? ($ million):???(Round to three decimal? places.)

Year

0

Buy:

Capital Expenditures

$

Depreciation Tax Shield

$

Free Cash Flow (Buy)

$

Year

0

Buy:

Capital Expenditures

$

Depreciation Tax Shield

$

Free Cash Flow (Buy)

$

Explanation / Answer

Solution to part a:

To compute this amount, first we compute FCF from buying the machine.

Tax rate = 35%

Purchase cost = $47.70million

The depreciation tax shield is 0.35 * $47.7 million * 20% = $3.339 million in year 0, 0.35 * $4.47 million * 32% = $5.342 million in year 1, etc, The FCF are shown below ($ million)

Accelerated Deprecation (year)

Rate

Tax Shield

0

20%

$3.339 million

1

32%

$5.342 million

2

19.20%

$3.205 million

3

11.52%

$1.923 million

4

11.52%

$1.923 million

5

5.76%

$0.962 million

Free Cash Flow Table

Year

0

1

2

3

4

5

Buy:

Capital Expenditures

$

(47.700)

0

0

0

0

0

Depreciation Tax Shield

3.339

5.342

3.205

1.923

1.923

0.962

Free Cash Flow (Buy)

$

(44.361)

5.342

3.205

1.923

1.923

0.962

r = 5.07%              1 + r = 1.051

FCF(0) = -$44.361 million

                                                                                FCF / (1 + r)^t

(1 + r)^1 = 1.051                FCF(1) = 5.342                    5.083

(1 + r)^2 = 1.104                FCF(2) = 3.205                    2.903

(1 + r)^3 = 1.160                FCF(3) = 1.923                    1.658

(1 + r)^4 = 1.219                FCF(4) = 1.923                    1.578

(1 + r)^5 = 1.281                FCF(5) = 0.962                    0.751

                                                                                     11.973

NPV = -$44.361 million - $11.973 million

        = -$32.388 million

Tax = 35%

1 – Tax = 65%

r = 5.07%

1 / r = 19.724

1 + r = 1.051

(1 + r)^4 = 1.219

1 / (1 + r)^4 = 0.821

LP = $2.951 million

Break-even = 32.388 / 2.951

= $10.975 million

Solution to part b:

Lease payments = $10.975 million

Tax rate = 10%

Purchase Cost = $47.70 million

Accelerated Deprecation (year)

Rate

Tax Shield

0

20%

$0.954 million

1

32%

$1.526 million

2

19.20%

$0.916 million

3

11.52%

$0.550 million

4

11.52%

$0.550 million

5

5.76%

$0.275 million

Lease Years

Rate

Income Tax Savings

0

10%

$1.098 million

1

10%

$1.098 million

2

10%

$1.098 million

3

10%

$1.098 million

4

10%

$1.098 million

5

0%            

$0.000 million

Year

0

1

2

3

4

5

Buy:

Capital Expenditures

$

(47.700)

0

0

0

0

0

Depreciation Tax Shield

0.954

1.526

0.916

0.550

0.550

0.275

Free Cash Flow (Buy)

$

(46.746)

1.526

0.916

0.550

0.550

0.275

Lease:            

Lease Payments

$

(10.975)

(10.975)

(10.975)

(10.975)

(10.975)

0

Income Tax Savings

1.908

1.908

1.908

1.908

1.908

0

Free Cash Flow (Lease)

$

(9.067)

(9.067)

(9.067)

(9.067)

(9.067)

0

Lease vs Buy

Lease – Buy

$

$37.679

($10.593)

($9.983)

($9.617)

($9.617)

($0.275)

r = 7.02%

1 + r = 107.02%

L – B(0) = $37.679 million

                                                                                L - B / (1 + r)^t

(1 + r)^1 = 1.0702             L – B(1) = ($10.593)          ($9.90)

(1 + r)^2 = 1.1453             L – B(2) = ($9.983)            ($8.72)

(1 + r)^3 = 1.2257             L – B(3) = ($9.617)            ($7.85)

(1 + r)^4 = 1.3118             L – B(4) = ($9.617)            ($7.33)

(1 + r)^5 = 1.4039             L – B(5) = ($0.275)            ($0.20)

                                                                                       ($34)

NPV = $37.679 million - $34 million

        = $3.679 million

Accelerated Deprecation (year)

Rate

Tax Shield

0

20%

$3.339 million

1

32%

$5.342 million

2

19.20%

$3.205 million

3

11.52%

$1.923 million

4

11.52%

$1.923 million

5

5.76%

$0.962 million

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