Estimating After-Tax Incremental Cash Flows

(1)

(2)

Estimating After-Tax

Incremental Cash Flows

Estimating After-Tax

Incremental Cash Flows



_{Cash (not accounting income) flowss}



_{Operating (not fnancing) flowss}



_{After-tax flowss}



_{Incremental flowss}



_Cash

_{(not accounting income)}

_flowss



_Operating

_{(not fnancing)}

_flowss



_{After-tax flowss}



_{Incremental flowss}

(3)

Estimating After-Tax

Incremental Cash Flows

Estimating After-Tax

Incremental Cash Flows



_Ignore

_{sunk costs}



_Include

_{opportunity costs}



_Include

_{project-driven changes in}

wsorking capital net of

spontaneous changes in current

liabilities



_Include

_{efects of inflation}



_Ignore

_{sunk costs}



_Include

_{opportunity costs}



_Include

_{project-driven}

_{changes in}

wsorking capital

net of

spontaneous changes in current

liabilities



_Include

_{efects of inflation}

Principles that must be

(4)

Tax Considerations

and Depreciation



_{Generally, proftable frms prefer to}

use an accelerated method for tax

reporting purposes (MACRS).



Depreciation

represents the systematic

allocation of the cost of a capital asset

(5)

Depreciation and the

MACRS Method



_{Everything else equal, the greater the}

depreciation charges, the lowser the

taxes paid by the frm.



_{Depreciation is a noncash expense.}



_{Assets are depreciated (MACRS) on}

one of eight diferent property

classes.



_{Generally, the half-year convention is}

(6)

MACRS Sample Schedule

Recovery Property Class

Year 3-Year 5-Year 7-Year 1 33.33% 20.00% 14.29% 2 44.45 32.00 24.49 3 14.81 19.20 17.49 4 7.41 11.52 12.49 5 11.52 8.93 6 5.76 8.92

7 8.93

(7)

Depreciable Basis

In tax accounting, the fully installed cost of an asset. This is the amount that, by laws, may be wsritten of over time for tax

purposes.

Depreciable Basis =

(8)

Capitalized Expenditures

Capitalized Expenditures are

expenditures that may provide

benefts into the future and

therefore are treated as capital

outlays and not as expenses of the

period in wshich they wsere incurred.

(9)

Sale or Disposal of

a Depreciable Asset



_{Often historically, capital gains}

income has received more favorable

U.S. tax treatment than operating

income.



Generally, the sale of a “capital asset” (as

defined by the IRS) generates a capital

gain (asset sells for more than book

(10)

Capital Budgeting: The process of planning for purchases of long-term assets.

For example: Our firm must decide whether to purchase a new plastic molding machine for $127,000.

How do we decide?

 _{Will the machine be}_profitable_?  _{Will our firm earn a}_{high rate of}

return on the investment?

 _{The relevant project information}

(11)

 _{The cost of the new machine is}

$127,000.

 _{Installation will cost}_$20,000_.

 _$4,000_{in net working capital will be}

needed at the time of installation.

 _{The project will increase revenues by}

$85,000 per year, but operating costs will increase by 35% of the revenue increase.

 _{Simplified straight line depreciation is}

used.

 _{Class life is}₅_{years, and the firm is}

planning to keep the project for 5

years.

 _{Salvage value at the end of year 5 will}

be $50,000.

 _14%_{cost of capital;}_34%_{marginal tax}

(12)

Capital Budgeting Steps

1) Evaluate Cash Flows

Look at all incremental cash

flows occurring as a result

of the project.



_{Initial outlay}



_{Diferential Cash Flows}

_over

the life of the project (also

referred to as annual cash

flows).

(13)

1) Evaluate Cash

Flows

(14)

1) Evaluate Cash

Flows

0

1

2

3

4

5

6 . . .

n

(15)

1) Evaluate Cash

Flows

0

1

2

3

4

5

6 . . .

n

Annual Cash Flows

Initial

(16)

1) Evaluate Cash

Flows

0

1

2

3

4

5

6 . . .

n

Terminal

Cash flow

Annual Cash Flows

Initial

(17)

2)

Evaluate the Risk of the

Project

 _{We’ll get to this in the next}

chapter.

 _{For now, we’ll assume that the}

risk of the project is the same as the risk of the overall firm.

 _{If we do this, we can use the}

firm’s cost of capital as the discount rate for capital

investment projects.

(18)

3) Accept or Reject the

Project

(19)

Step 1: Evaluate Cash Flows

a) Initial Outlay: What is the cash flow at “ttime 0?�

(Purchase price of the asset)

+ (shipping and installation costs) (Depreciable asset)

+ (Investment in working capital) + After-tax proceeds from sale of

old asset

(20)

(127,000)

+ (shipping and installation costs) (Depreciable asset)

old asset

(21)

(127,000) + ( 20,000)

(Depreciable asset)

old asset

(22)

(127,000) + ( 20,000) (147,000)

old asset

(23)

(127,000) + (20,000) (147,000) + (4,000)

+ After-tax proceeds from sale of old asset

(24)

(127,000) + (20,000) (147,000) + (4,000) + 0

(25)

 _a)_{Initial Outlay:}_{What is the cash}

flow at “ttime 0?�

(127,000) Purchase price of asset

+ (20,000) Shipping and installation

(147,000) Depreciable asset

+ (4,000) Net working capital

+ 0 Proceeds from sale of old asset

(26)

Step 1: Evaluate Cash

Flows

(127,000) Purchase price of asset

+ (20,000) Shipping and installation

(147,000) Depreciable asset + (4,000) Net working capital

+ 0 Proceeds from sale of old asset

(27)

Step 1: Evaluate Cash

Flows

(28)

For Each Year, Calculate:

Incremental revenue

- Incremental costs

- Depreciation on project

Incremental earnings

before taxes

- Tax on incremental EBT

Incremental earnings after

taxes

(29)

For Years 1 - 5:

Incremental revenue

- Incremental costs

- Depreciation on project

Incremental earnings

before taxes

- Tax on incremental EBT

Incremental earnings after

taxes

(30)

For Years 1 - 5:

85,000

- Incremental costs

- Depreciation on project

Incremental earnings

before taxes

- Tax on incremental EBT

Incremental earnings after

taxes

(31)

For Years 1 - 5:

85,000

(29,750)

- Depreciation on project

Incremental earnings

before taxes

- Tax on incremental EBT

Incremental earnings

after taxes

(32)

For Years 1 - 5:

85,000

(29,750)

(29,400)

Incremental earnings

before taxes

- Tax on incremental EBT

Incremental earnings after

taxes

(33)

For Years 1 - 5:

85,000

(29,750)

(29,400)

25,850

- Tax on incremental EBT

Incremental earnings

after taxes

(34)

For Years 1 - 5:

85,000

(29,750)

(29,400)

25,850

(8,789)

Incremental earnings

after taxes

(35)

For Years 1 - 5:

85,000

(29,750)

(29,400)

25,850

(8,789)

17,061

+ Depreciation

reversal

(36)

For Years 1 - 5:

85,000

(29,750)

(29,400)

25,850

(8,789)

17,061

29,400

(37)

For Years 1 - 5:

85,000

Revenue

(29,750)

Costs

(29,400)

Depreciation

25,850

EBT

(8,789)

Taxes

17,061

EAT

29,400

Depreciation

reversal

(38)

Step 1: Evaluate Cash

Flows

c) Terminal Cash Flow: What is the cash flow at the end of the

project’s life?

Salvage value

+/- Tax efects of capital gain/loss + Recapture of net working

capital

(39)

Step 1: Evaluate Cash

Flows

50,000 Salvage value

+/- Tax efects of capital gain/loss + Recapture of net working

capital

(40)

Tax Effects of Sale of

Asset:

 _{Salvage value =}_$50,000.  _{Book value = depreciable}

(41)

Step 1: Evaluate Cash

Flows

(17,000) Tax on capital gain Recapture of NWC

(42)

Step 1: Evaluate Cash

Flows

(17,000) Tax on capital gain

(43)

Step 1: Evaluate Cash

Flows

(17,000) Tax on capital gain

(44)

Project NPV:



_{CF(0) =}

_-151,000.



_{CF(1 - 4) =}

_46,461.



_{CF(5) = 46,461 + 37,000}

=

83,461.



_{Discount rate =}

_14%.



_{NPV =}

_$27,721.



_{We would}

_accept

_the

(45)

Capital

Rationing



_{Suppose that you have}

evaluated five capital

investment projects for

your company.



_{Suppose that the VP of}

Finance has given you a

limited capital budget.



_{How do you decide which}

(46)

Capital Rationing



_{You could rank the projects}

(47)

Capital Rationing



_{You could rank the projects}

by IRR:

IRR

5%

10%

15%

20%

25%

$

(48)

Capital Rationing



_{You could rank the projects}

by IRR:

IRR

5%

10%

15%

20%

25%

$

(49)

Capital Rationing



_{You could rank the projects}

by IRR:

IRR

5%

10%

15%

20%

25%

$

(50)

Capital Rationing



_{You could rank the projects}

by IRR:

IRR

5%

10%

15%

20%

25%

$

(51)

Capital Rationing



_{You could rank the projects}

by IRR:

IRR

5%

10%

15%

20%

25%

$

(52)

Capital Rationing



_{You could rank the projects}

by IRR:

Our budget is limited

so we accept only

(53)

Capital Rationing



_{You could rank the projects}

by IRR:

Our budget is limited

so we accept only

(54)

Capital Rationing



_{Ranking projects by IRR is}

not always the best way to

deal with a limited capital

budget.



_{It’s better to pick the}

largest NPVs.



_{Let’s try ranking projects by}

(55)

Capital Rationing

occurs wshen a

constraint (or budget ceiling) is

placed on the total size of capital

expenditures during a particular

period.

Example: Julie Miller must determine wshat investment opportunities to

undertake for Basket Wonders (BW). She is limited to a maximum

(56)

Available Projects for BW

Project ICO IRR NPV

PI

A $ 500 18% $ 50 1.10

B 5,000 25 6,500 2.30 C 5,000 37 5,500 2.10 D 7,500 20

5,000 1.67

E 12,500 26 500 1.04

F 15,000 28 21,000 2.40 G 17,500 19 7,500 1.43

(57)

Choosing by IRRs for BW

Project ICO IRR

NPV PI

C $ 5,000 37% $ 5,500 2.10

F 15,000 28 21,000 2.40

E 12,500 26 500 1.04 B 5,000 25 6,500 2.30

Projects C, F, and E have the three

largest IRRs.

(58)

Project ICO IRR NPV

PI

F $15,000 28% $21,000 2.40

G 17,500 19 7,500 1.43 B 5,000 25 6,500 2.30

Projects F and G have the twso

largest NPVs

.

The resulting increase in shareholder wsealth is $28,500 wsith a $32,500 outlay.

(59)

Choosing by PIs for BW

Project ICO IRR

NPV PI

F $15,000 28% $21,000 2.40 B 5,000 25 6,500 2.30 C 5,000

37 5,500 2.10 D

7,500 20 5,000 1.67 G 17,500 19 7,500 1.43

Projects F, B, C, and D have the four largest PIs.

The resulting increase in shareholder wsealth is

(60)

Method Projects Accepted Value

Added

PI F, B, C, and D

$38,000

NPV

F and G $28,500

IRR

C, F, and E $27,000

PI

generates the

greatest

increase

in

shareholder wealth

wshen a limited capital

budget exists for a

single period

.

(61)

Problems with Project

Ranking

1) Mutually exclusive projects of unequal size (the size disparity

problem)

 _{The NPV decision may not agree}

with IRR or PI.

 _Solution:_{select the project with}

(62)

Size Disparity Example

Project A year cash flow

0 (135,000) 1 60,000 2 60,000 3 60,000

required return = 12% IRR = 15.89%

(63)

Size Disparity Example

Project B year cash flow

0 (30,000) 1 15,000 2 15,000 3 15,000

NPV = $6,027 PI = 1.20

Project A year cash flow

0 (135,000) 1 60,000 2 60,000 3 60,000

(64)

Size Disparity Example

Project B year cash flow

0 (30,000) 1 15,000 2 15,000 3 15,000

required return = 12%

IRR = 23.38%

NPV = $6,027

PI = 1.20 Project A

year cash flow

0 (135,000) 1 60,000 2 60,000 3 60,000

NPV = $9,110

(65)

Cash Flow Disparity

Let us compare a decreasing cash-flows (D) project and an increasing cash-flows (I)

project.

NET CASH FLOWS

Project D Project I END OF YEAR

(66)

D 23%

Which project is preferred?

Project IRR NPV PI

(67)

Examine NPV Profiles

(68)

Fisher’s Rate of Intersection

Discount Rate ($)

At k<10%, I is best! _{Fisher’s Rate of}

Intersection

(69)

Mutually Exclusive

Investments with

Unequal

Lives

 _{Suppose our firm is planning to}

expand and we have to select one of two machines.

 _{They difer in terms of}_economic life and capacity.

 _{How do we decide which machine to}

(70)

The after-tax cash flows

(71)

Step 1: Calculate NPV



_NPV

₁

₌

_$1,433



_NPV

₂

₌

_$1,664



_{So, does this mean #2 is}

better?



_{No! The two NPVs can’t}

(72)

Step 2: Equivalent

Annual Annuity (EAA)

method

 _{If we assume that each project}

will be replaced an infinite

number of times in the future, we can convert each NPV to an

annuity.

 _{The projects’ EAAs can be}

compared to determine which is the best project!

 _EAA:_{Simply annuitize the NPV}

(73)

EAA with your

calculator:



_{Simply “tspread the NPV}

over the life of the project�



_{Machine 1}

_:

_{PV = 1433, N =}

3, I = 14,

solve:

PMT = -617.24

.



_{Machine 2}

_:

_{PV = 1664, N =}

6, I = 14,

(74)



_EAA

₁

_{= $617}



_EAA

₂

_{= $428}



_{This tells us that:}



_NPV

₁

_{= annuity of}

_$617

_per

year.



_NPV

₂

_{= annuity of}

_$428

_per

year.



_{So, we’ve reduced a problem}

with diferent time horizons

to a couple of annuities.



_{Decision Rule:}

_{Select the}

(75)

Step 3: Convert back to

(76)

Step 3: Convert back to

NPV

 _{Assuming infinite replacement,}

the EAAs are actually

perpetuities. Get the PV by dividing the EAA by the

required rate of return.

(77)

Step 3: Convert back to

NPV

 _NPV

1 = 617/.14 = $4,407

¥

(78)

Step 3: Convert back to

NPV

 _NPV

1 = 617/.14 = $4,407

 NPV ₂ = 428/.14 = $3,057

¥

(79)

Step 3: Convert back to

NPV

 _NPV

1 = 617/.14 = $4,407

 NPV ₂ = 428/.14 = $3,057

 _{This doesn’t change the answer,}

of course; it just converts EAA to an NPV that can be

compared.

¥

(80)

Practice Problems:

Cash Flows & Other

Topics

(81)

Problem 1a

Project Information:

 _{Cost of equipment =}_$400,000_.

 _{Shipping & installation will be}_$20,000_.  _$25,000_{in net working capital required}

at setup.

 _{3-year project life, 5-year class life.}  _{Simplified straight line depreciation.}  _{Revenues will increase by}_$220,000

per year.

 _{Defects costs will fall by}_$10,000_per

year.

 _{Operating costs will rise by}_$30,000

per year.

 _{Salvage value after year 3 is}_$200,000_.  _{Cost of capital =}_12%,_{marginal tax}

(82)

Problem 1a

Initial Outlay:

(400,000) Cost of asset

+ ( 20,000)Shipping &

installation

(420,000) Depreciable

asset

+ ( 25,000)Investment in

NWC

(83)

For Years 1

- 3:

_220,000 _{Increased revenue} 10,000 Decreased defects

(30,000) Increased operating costs

(84,000) Increased depreciation

116,000 EBT

(39,440) Taxes (34%) 76,560 EAT

84,000 Depreciation reversal

160,560 = Annual Cash Flow

(84)

Terminal Cash Flow:

Salvage value

+/- Tax efects of capital

gain/loss

+ Recapture of net

working capital

Terminal Cash Flow

(85)

Terminal Cash Flow:



_{Salvage value =}

_$200,000

_.



_{Book value = depreciable}

asset - total amount

depreciated.



_{Book value = $168,000.}



_{Capital gain = SV - BV =}

$32,000

.



_{Tax payment = 32,000 x .34 =}

($10,880)

.

(86)

Terminal Cash Flow:

200,000 Salvage value

(10,880) Tax on capital

gain

25,000 Recapture of

NWC

214,120 Terminal Cash

Flow

(87)

Problem 1a Solution

NPV and IRR:



_{CF(0) = -445,000}



_{CF(1 ), (2), = 160,560}



_{CF(3 ) = 160,560 + 214,120}

= 374,680



_{Discount rate = 12%}



_{IRR = 22.1%}



_{NPV = $93,044. Accept the}

(88)

Problem 1b

Project Information:



_{For the same project,}

suppose we can only get

$100,000 for the old

equipment after year 3,

due to rapidly changing

technology.



_{Calculate the IRR and NPV}

for the project.

(89)

Terminal Cash Flow:

Salvage value

+/- Tax efects of capital

gain/loss

+ Recapture of net working

capital

Terminal Cash Flow

(90)

Terminal Cash Flow:



_{Salvage value =}

_$100,000

_.



_{Book value = depreciable}

asset - total amount

depreciated.



_{Book value = $168,000.}



_{Capital loss = SV - BV =}

($68,000)

.



_{Tax refund = 68,000 x .34 =}

$23,120

.

(91)

Terminal Cash Flow:

100,000 Salvage value

23,120 Tax on capital

gain

25,000 Recapture of

NWC

148,120 Terminal Cash

Flow

(92)

Problem 1b

Solution

NPV and IRR:



_{CF(0) = -445,000.}



_{CF(1), (2) = 160,560.}



_{CF(3) = 160,560 + 148,120}

= 308,680.



_{Discount rate = 12%.}



_{IRR = 17.3%}

_.



_{NPV = $46,067. Accept the}

(93)

Problem 2

Automation Project:

 _{Cost of equipment =}_$550,000_.

 _{Shipping & installation will be}_$25,000_.  _$15,000_{in net working capital required}

at setup.

 _{8-year project life, 5-year class life.}  _{Simplified straight line depreciation.}  _{Current operating expenses are}

$640,000 per yr.

 _{New operating expenses will be}

$400,000 per yr.

 _{Already paid consultant}_$25,000_for

analysis.

 _{Salvage value after year 8 is}_$40,000_.  _{Cost of capital =}_14%,_{marginal tax}

(94)

Problem

2 Initial Outlay:

(550,000) Cost of new

machine

+ (25,000) Shipping &

installation

(575,000) Depreciable

asset

+ (15,000) NWC

investment

(95)

For Years 1 -

5:

240,000 Cost decrease

(115,000) Depreciation

increase

125,000 EBIT

(42,500) Taxes (34%)

82,500 EAT

115,000 Depreciation

reversal

197,500 = Annual

Cash Flow

(96)

For Years 6 -

8:

240,000 Cost decrease

( 0) Depreciation

increase

240,000 EBIT

(81,600) Taxes (34%)

158,400 EAT

0 Depreciation

reversal

158,400 = Annual

Cash Flow

(97)

Terminal Cash Flow:

40,000 Salvage

value

(13,600) Tax on

capital gain

15,000 Recapture

of NWC

41,400 Terminal

Cash Flow

(98)

Problem 2 Solution

NPV and IRR:



_{CF(0) = -590,000.}



_{CF(1 - 5) = 197,500.}



_{CF(6 - 7) = 158,400.}



_{CF(10) = 158,400 + 41,400}

= 199,800.



_{Discount rate = 14%.}



_{IRR = 28.13% NPV =}

$293,543

.



_{We would}

_accept

_the

(99)

Problem 3

Replacement Project:

Old Asset (5 years old):

 _{Cost of equipment =}

$1,125,000.

 _{10-year project life, 10-year}

class life.

 _{Simplified straight line}

depreciation.

 _{Current salvage value is}

$400,000.

 _{Cost of capital =}_14%,

(100)

Problem 3

Replacement Project:

New Asset:

 _{Cost of equipment =}_$1,750,000.

 _{Shipping & installation will be}_$56,000.  _$68,000_{investment in net working}

capital.

 _{5-year project life, 5-year class life.}  _{Simplified straight line depreciation.}  _{Will increase sales by}_$285,000_per

year.

 _{Operating expenses will fall by}

$100,000 per year.

 _{Already paid}_$15,000_{for training}

program.

 _{Salvage value after year 5 is}_$500,000.  _{Cost of capital =}_14%,_{marginal tax}

(101)

Problem 3: Sell the Old

Asset



_{Salvage value =}

_$400,000

_.



_{Book value = depreciable}

(102)

Problem 3

(1,806,000) Depreciable

asset

+ ( 68,000) NWC investment

+ 456,875 After-tax

proceeds (sold

old

machine)

(103)

For Years 1 -

5:

385,000 Increased sales &

cost savings

(248,700) Extra depreciation

136,300 EBT

(47,705) Taxes (35%)

88,595 EAT

248,700 Depreciation reversal

337,295 = Diferential Cash

Flow

(104)

Terminal Cash Flow:

500,000 Salvage

value

(175,000) Tax on

capital gain

68,000 Recapture

of NWC

393,000 Terminal

Cash Flow

(105)

Problem 3 Solution

NPV and IRR:

 _{CF(0) = -1,417,125.}  _{CF(1 - 4) = 337,295.}

 _{CF(5) = 337,295 + 393,000 =}

730,295.

 _{Discount rate = 14%.}  _{NPV = (55,052.07)}.

 _{IRR = 12.55%}_.