11 - 1

Lecture FourteenCash Flow Estimation and Other

Topics in Capital Budgeting

Relevant cash flows

Working capital in capital budgeting

Unequal project lives

Inflation

11 - 2

Proposed Project

Cost: $200,000 + $10,000 shipping + $30,000 installation. Depreciable cost: $240,000.

Inventories will rise by $25,000 and payables by $5,000.

Economic life = 4 years.Salvage value = $25,000.MACRS 3-year class.

11 - 3

Sales: 100,000 units/yr @ $2.

Variable cost = 60% of sales.

Tax rate = 40%.

WACC = 10%.

11 - 4

Set up, without numbers, a time line for the project’s cash flows.

0 1 2 3 4

OCF1 OCF2 OCF3 OCF4InitialCosts(CF0)

+Terminal CF

NCF0 NCF1 NCF2 NCF3 NCF4

11 - 5

Equipment -$200

Installation & Shipping -40

Increase in inventories -25

Increase in A/P 5

Net CF0 -$260

NWC = $25 - $5 = $20.

Investment at t = 0:

11 - 6

Modified Accelerated Cost Recovery System (MACRS)

Major Classes and Asset Lives for MACRS

Class Type of Property

3-year Certain special manufacturing tools

5-year Automobiles, light-duty trucks, computers, andcertain special manufacturing equipment

7-year Most industrial equipment, office furniture, andfixtures

10-year Certain longer-lived types of equipment

27.5-year Residential rental real property such as apartmentbuildings

39-year All non-residential real property, includingcommercial and industrial buildings

11 - 7

Recovery Allowance Percentage for Personal Property (MACRS)

Ownership Class of InvestmentYear 3-Year 5-Year 7-Year 10-Year

1 33% 20% 14% 10%2 45 32 25 183 15 19 17 144 7 12 13 125 11 9 96 6 9 77 9 78 4 79 710 611 3

100% 100% 100% 100%

11 - 8

What’s the annual depreciation?

Due to 1/2-year convention, a 3-year asset is depreciated over 4 years.

Year Rate x Basis Depreciation

1 0.33 $240 $ 792 0.45 240 1083 0.15 240 364 0.07 240 17

1.00 $240

11 - 9Computing the Cash Inflow from Operations

REV - TAX +TAX ADV. of DEPR.

27,000 - 27,000 (0.40) + 16,500 (0.4)

27,000 - 10,800 + 6,600

+ 6,600 = $22,80016,200

REV - DEPR. - TAX + DEPR.

27,000 - 16,500 - TAX + 16,500

- 10,500 (0.40) + 16,500

- 4,200 + 16,500 = $22,800

10,500

10,500

REV 27,000 REV 27,000 DEP 16,500 Tax 10,800 NIBT 10,500 10,800

Tax 4,200 4,200 16,200 NIAT 6,300 6,600

+ DEP 16,500 DEPR Ad. 6,600 (1)CASH FLOW

22,800$ CASH FLOW

22,800$

(1) 16,500 (0.40) = 6,600

REV after Tax, but bef.

11 - 101. Net investment at t=0:Cost of new machine $82,500Net investment outlay (CF0) $82,500

2. After-taxYear Earnings TDep Annual CFt

1 $16,200 $6,600 $22,8002 16,200 10,560 26,760 3 16,200 6,270 22,470 4 16,200 3,960 20,160 5 16,200 3,630 19,830 6 16,200 1,980 18,180 7 16,200 0 16,200 8 16,200 0 16,200

Notes:a. The after-tax earnings is $27,000 (1 - T) = $27,000 (0.6) = $16,200b. Find Dep over Years 1 - 8:

The old machine was fully depreciated; therefore,Dep = depreciation on the new machine.

TDep or Tax(1) (2) (3) (4) advantage of Depr.

Year Dep Rate Dep Basis Depreciation Tax Rate = (4) x Tax Rate

1 0.20 $82,500 $16,500 0.40 $6,6002 0.32 82,500 26,400 0.40 10,560 3 0.19 82,500 15,675 0.40 - 4 0.12 82,500 9,900 - - 5 0.11 82,500 9,075 - - 6 0.06 82,500 4,950 - -

7-8 0.00 82,500 0 - -

11 - 113. Now find the NPV of the replacement machine:

Year CFt PVIF (12%) Product

1 $22,800 0.8929 $20,3582 26,760 0.7972 21,333 3 22,470 0.7118 15,994 4 20,160 0.6355 12,812 5 19,830 0.5674 11,252 6 18,180 0.5066 9,210 7 16,200 0.4523 7,327 8 16,200 0.4039 6,543

Sum = PV inflows = $104,829Less: Cost = CF0 82,500

NPV = $22,329

Alternatively, place the cash flows on a time line:

With a financial calculator, input the appropriate cash flows into thecash flow register, input I = 12, and then solve for NPV = $22,329.

The NPV of the investment is positive; therefore, the new machineshould be bought.

0 1 2 3 4 5 6 7 812%

-82,500 22,800 26,760 22,470 20,160 19,830 18,180 16,200 16,200

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Operating cash flows:

1 2 3 4Revenues $200 $200 $200 $200Op. Cost, 60% -120 -120 -120 -120Depreciation -79 -108 -36 -17Oper. inc. (BT) 1 -28 44 63Tax, 40% -- -11 18 25

1 -17 26 38 Add. Depr’n 79 108 36 17 Op. CF 80 91 62 55

Oper. inc. (AT)

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Net Terminal CF at t = 4:

Salvage Value 25Tax on SV (40%) -10

Recovery of NWC $20

Net termination CF $35

Q. Always a tax on SV? Ever a positive tax number?

Q. How is NWC recovered?

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11 - 1411 - 9

Should CFs include interest expense? Dividends?

No. The cost of capital is accounted for by discounting at the 10% WACC, so deducting interest and dividends would be “double counting” financing costs.

11 - 1511 - 10

Suppose $50,000 had been spent last year to improve the building. Should this cost be included in the analysis?

No. This is a sunk cost.Analyze incremental investment.

11 - 1611 - 11

Suppose the plant could be leased out for $25,000 a year. Would this affect

the analysis?

Yes. Accepting the project means foregoing the $25,000. This is an opportunity cost, and it should be charged to the project.

A.T. opportunity cost = $25,000(1 - T) = $25,000(0.6) = $15,000 annual cost.

11 - 1711 - 12

If the new product line would decrease sales of the firm’s other lines, would

this affect the analysis?

Yes. The effect on other projects’ CFs is an “externality.”

Net CF loss per year on other lines would be a cost to this project.

Externalities can be positive or negative, i.e., complements or substitutes.

11 - 18

Here are all the project’s net CFs (in thousands) on a time line:

Enter CFs in CF register, and I = 10%.

NPV = -$4.03IRR = 9.3%

k = 10%0

79.7

1

91.2

2

62.4

3

54.7

4

-260Terminal CF 35.0

89.7

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11 - 19

MIRR = ?10%

What’s the project’s MIRR?

Can we solve using a calculator?

0

79.7

1

91.2

2

62.4

3

89.7

4

-260

374.8-260

68.6110.4

10%10%

106.1

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11 - 20

4 10 -255.97 0

TV = FV = 374.8N I/YR PV PMT FV

Yes. CF0 = 0CF1 = 79.7CF2 = 91.2CF3 = 62.4CF4 = 89.7 I = 10NPV = 255.97

INPUTS

OUTPUT

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11 - 21

Use the FV = TV of inputs to find MIRR

4 -260 0 374.8

9.6N I/YR PV PMT FV

MIRR = 9.6%. Since MIRR < k = 10%, reject the project.

INPUTS

OUTPUT

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11 - 22

What’s the payback period?

0

79.7

1

91.2

2

62.4

3

89.7

4

-260

Cumulative:-26.7-260 -89.1-180.3 63.0

Payback = 3 + 26.7/89.7 = 3.3 years.

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11 - 23

If this were a replacement rather than a new project, would the analysis

change?

Yes. The old equipment would be sold, and the incremental CFs would be the changes from the old to the new situation.

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The relevant depreciation would be the change with the new equipment.

Also, if the firm sold the old machine now, it would not receive the SV at the end of the machine’s life. This is an opportunity cost for the replacement project.

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11 - 25

NPV

CF

k

v Cost

kt

nt

tt t

t

0 1 1

Re.

Q. If E(INFL) = 5%, is NPV biased?

A. YES.

k = k* + IP + DRP + LP + MRP.

Inflation is in denominator but not innumerator, so downward bias to NPV.

Should build inflation into CF forecasts.

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11 - 26

Consider project with 5% inflation. Investment remains same, $260. Terminal CF remains same, $35.

Operating cash flows:1 2 3 4

Revenues $210 $220 $232 $243Op. cost 60% -126 -132 -139 -146Depr’n -79 -108 -36 -17Oper. inc. (BT) 5 -20 57 80Tax, 40% 2 -8 23 32Oper. inc. (AT) 3 -12 34 48Add Depr’n 79 108 36 17Op. CF 82 96 70 65

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11 - 27

Here are all the project’s net CFs (in thousands) when inflation is

considered.

Enter CFs in CF register, and I = 10%.

NPV = $15.0IRR = 12.6%

k = 10%0

82.1

1

96.1

2

70.0

3

65.0

4

-260Terminal CF 35.0

100.0

Project should be accepted.

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11 - 28

S and L are mutually exclusive and will be repeated. k = 10%. Which is better?

Expected Net CFs

Year Project S Project L

0 ($100,000) ($100,000)

1 60,000 33,500

2 60,000 33,500

3 -- 33,500

4 -- 33,500

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S L

CF0 -100,000 -100,000

CF1 60,000 33,500

Nj 2 4

I 10 10

NPV 4,132 6,190

Q. NPVL > NPVS. Is L better?

A. Can’t say. Need replacement chain analysis.

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Note that Project S could be repeated after 2 years to generate additional profits.

Use replacement chain to calculate extended NPVS to a common life.

Since S has a 2-year life and L has a 4-year life, the common life is 4 years.

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11 - 31

L:

S:

0 1 2 310%

33,500

4

0 1 2 310%

60,000

4

33,50033,50033,500-100,000

60,00060,00060,000-100,000

NPVL = $6,190 (already to Year 4)

NPVS = $7,547 (on extended basis)

-100,000-40,000

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11 - 32

Equivalent Annual Annuity (EAA)

That annuity PMT whose PV equals the project’s NPV.

S:0 110%

EAAS

210%

EAAS

PV1

PV2

4,132 = Previously determined NPVS.

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11 - 33

Project S (EAA):

2 10 -4132 0

EAAS = 2380.82

N I/YR PV PMT FV

4 10 -6190 0

EAAL = 1952.76

N I/YR PV PMT FV

The higher annuity is better.

Project L (EAA):

INPUTS

OUTPUT

INPUTS

OUTPUT

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11 - 34

The project, in effect, provides an annuity of EAA.

EAAS > EAAL , so pick S.

Replacement chains and EAA always lead to the same decision.

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11 - 35

If the cost to repeat S in two years rises to $105,000, which would be

best?

0

60,000

1 2 3 4

-100,000 60,000 60,000

NPVS = 3,415 < NPVL = 6,190.

Now choose L.

10%

60,000-105,000 -45,000

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11 - 36 11-11The Erley Equipment Company purchased a machine 5 years ago at a cost of $100,000. The machine had an expected life of 10 years at the time of purchase, and an expected salvage value of $10,000 at the end of 10 years. It is being depreciated by the straight line method toward a salvage value of $10,000, or by $9,000 per year.

A new machine can be purchased for $150,000, including installation costs. During its 5-year life, it will reduce cash operating expenses by $50,000 per year. Sales are not expected to change. At the end of its useful life, the machine is estimated to be worthless. MACRS depreciation will be used, and the machine will be depreciated over its 3-year class life rather than its 5-year economic life. (See Table 11A-2 for MACRS recovery allowance percentages.)

The old machine can be sold today for $65,000. The firm’s tax rate is 35 percent. The appropriate discount rate is 16 percent.

a) If the machine is purchased, what is the amount of the initial cash flow at Year 0?

b) What incremental operating cash flows will occur at the end of Years 1 through 5 as a result of replacing the old machine?

c) What incremental terminal cash flow will occur at the end of Year 5 if the new machine is purchased?

d) What is the NPV of this project? Should Erley replace the old machine?

11 - 37a. Old depreciation = $9,000 per year

Book value = $100,000 - 5 ($9,000) = $55,000Gain = $65,000 - $55,000 = $10,000Tax on book gain = $10,000 (0.35) = $3,500

Price ($150,000)SV (old machine) $65,000Tax effect ($3,500)Initial outlay ($88,500)

b. Recovery Depreciation Depreciation Depreciation Change inYear Percentage Basis Allowance, New Allowance, Old Depreciation

1 33% $150,000 $49,500 $9,000 $40,5002 45% 150,000 67,500 9,000 58,500 3 15% 150,000 22,500 9,000 13,500 4 7% 150,000 10,500 9,000 1,500 5 9,000 (9,000)

Annual cash flows = CFt = (Operating expenses) (1 - T) + (Depreciation) (T)

CF1 = ($50,000) (0.65) + ($40,500) (0.35) = $32,500 + $14,175 = $46,675

CF2 = ($50,000) (0.65) + ($58,500) (0.35) = $32,500 + $20,475 = $52,975

CF3 = ($50,000) (0.65) + ($13,500) (0.35) = $32,500 + $ 4,725 = $37,225

CF4 = ($50,000) (0.65) + ($ 1,500) (0.35) = $32,500 + $ 525 = $33,025

CF5 = ($50,000) (0.65) + (-$9,000) (0.35) = $32,500 - $ 3,150 = $29,350

11 - 38

c. Salvage value on new machine 0$ Salvage value on old machine (opportunity cost) (10,000)Terminal CF (10,000)$

d.

NPV = $42,407

Therefore, the firm should replace the old machine.

0 1 2 3 4 5

16%

(88,500) 46,675 52,975 37,225 33,025 29,350(10,000)19,350