Blank L., Tarquin A. Engineering Economy (McGraw-Hill Series in Industrial Engineering and Management)

SEC

TION

17.4

Deprecia

ti

on Recapture and

Ca

pital Gains (Losses)

Analy

ze

r I :

DR

= 130,

000

- 43,2

00

= $86,8

00

Year 3

Tl

= J 00,

000

-

30

,0

00

- 28,8

00

+ 86,800 = $128,

000

Year 3 taxes = 128,

000

(0.35) = $

44

,800

Total taxes = 14,

000

+

7700

+

44,800

= $66,

50

0

Analyzer

2:

DR

=

22

5,

000

- 64,8

00

= $ 160,2

00

Year 3

Tl

= 1

00

,

000

- 10,

000

-

43

,

200

+ 160,200 = $207,000

Year 3 t

axe

s =

207,000

(0.35) = $72,

450

Total taxes = 15,

750

+

6300

+ 72,450 =

$94

,

500

Now

, analyzer J has a cons

id

erab

le

advantage in total taxes ($94,500 versus

$66,

500

).

Solution

by

Computer

(a) The Ex

ce

l so

lu

tion is concentrated

in

rows 5 through 9 (analyzer I) and rows

15

th

rough 19 (analyzer 2)

of

Figure 17--4. The

ce

ll

tags

re

fl

ect

th

at

the same e

qu

a-

tions discussed above are a

pp

lied. The total taxes are in cells

H9

and H 19 for ana-

lyzers I and 2, resp

ec

ti

vel

y.

As

expecte

d, anal

yze

r J has a s

li

ght edge

in

total taxe

s.

~

E-Solve

~

Microsoft Excel - Example 17.6

II

A25

A

1

2

Gross Operating

Investment Book

Ta

xa

ble

3

income

ex

penses

and sale depreciation value

income

4 Year

GI

E P and S D

BY

TI

Taxes

5

0 $(150,000) $150,000

6 100,000

$(3

0,000) 30,000 $120,000

40

,000 $14,000

7 100,000

$(30,000)

48

,000 $ 72,000

22,

000 $ 7,700

8

100

,0

00

$(30,000)

28,800 $ 43,200

41

,2

00 $14,420

9

Totals $36,120

10

Revised 3 100,000

$(30,000)

.$

130,000 28,800 43,200 $128,000

$ 44,800

~

= SUM(H

6:

H

7)

+ H I 0 I

11 Totals

$66,5(10

12

= BIO+ CIO- EIO

+(

D I 0- F l

O)

13

A

na

lyZ

er

2

14

Year

GI

E P and S D

BY

TI

15 0

$ (225,000)

$225,000

16

100,000

.$

(10,000)

45,000 $180,000

45,

000 $15,750

17

100,000

$

(1

0,000)

72,000

$1

08,000 18,000 $ 6,300

18

100,000

$ (10,000)

43,200

$ 64,800 46,800 ' $16,

38

0

1 9 Totals $38

,4

30

':

1"tf

Revi

sed 3 1

00

,000 $ (1 0,000)

$ 225,000 43,200

.$

64

,8

00 $ 207,000

$72,450

21

Totals

~

94

,

5[1

0

22

23

=

SU

M(H I6:H17)+H20

R

ea

dy

Figure

17-4

Analysis of impact of depreciation recapture on total taxe

s,

Example 17.

6.

585

586

Setting MARR

CHAPTER

17

After-Tax Economic Analysis

(b) When the purchased analyzer is sold in year 3 (at $130,000 in

DlO

for analyzer 1

and at

$225,000 in

D20

for analyzer 2), the depreciation recapture, TI, and taxes are

recalculated. Rows 10 and

11,

and rows 20 and 21, present the increased TI, and

taxes. Now, analyzer

I has a substantial $28,000 advantage in total taxes.

Comment

Note that no time value

of

money is considered in these analyses, as we have used

in

previous alternative evaluations. In the next Section we will rely upon

PW

,

AW,

and

ROR analyses at an established

MARR

to make an after-tax decision based upon

CFAT values.

17.5 AFTER-TAX

PW,

AW,

AND

ROR

EVALUATION

The required after-tax MARR is established using the market interest rate, the

corporation's effective tax rate, and its average cost

of

capital. The

CFAT

estimates are used to compute the PW or

AW

at the after-tax MARR. When

positive and negative

CFAT

values are present, the result

of

PW or

AW

< 0

indicates the MARR is not met. For a single project or mutually exclusive

alternative selection, apply the same logic

as

in Chapters 5 and 6. The guidelines

are as follows:

One project.

PW

or

AW 2': 0,

the

project

is financially viable because

the

after-tax

MARR

is

met

or

exceeded.

Two or more alternatives. Select

the

alternative

with

the

best (numerically

largest)

PW

or

AW value.

If

only cost

CFAT

amounts are estimated, calculate the after-tax savings gener-

ated

by

the operating expenses and depreciation. Assign a plus sign to each sav-

ing a

nd

apply the selection guideline above.

Remember, the equal-service assumption requires that the

PW analysis be

performed over the least common multiple (LCM)

of

alternative lives. This re-

quirement must be met for every

analysis-before

or after taxes.

Since the

CFAT

estimates usually vary from year

to

year in

an

after-tax evalu-

ation,

th

e spreadsheet offers a much speedier analysis than solution by hand. For

A W analysis,

use PMT with

an

embedded NPV function

over

one life cycle

of

the

m alternative. The gener

al

format is

as

follows, with the NPV function in italics.

E-Solve

PMT(MARR,n

,NPV(MARR,ye

ar

_LCFAT.· year _n_CFAT) + y

ear

_O_CFAT)

For

PW

analysi

s,

obtain the PMT function results first, followed

by

the PV func-

tion taken over the alternatives' LCM. (There is an LCM function in Excel.) The

cell containing the

PMT function result is entered

as

the A value. The general

format is

PV(MARR, LCM_years,

PMTJesulc

cell)

SECTION 17.5 After-Tax PW,

AW,

and ROR Evaluation

Paul is designing the interior walls

of

an industrial building. In some places, it is important

to r

ed

uce noise trans

mi

ss

ion acro

ss

the wall. Two construction options

-s

tncco

on

metal

lath (S) a

nd

bricks (B)

--eac

h have about the same transmission loss, approximately

33

decibels. This will reduce

noi

se attenuation costs in adjacent office areas. Paul has esti-

mated the first costs and after-tax savings each year for both designs.

Use the

CFAT

values

and an after-tax MARR

of

7%

pe

r year to determine which is economically better. Solve

both

by

hand a

nd

by

compnt

er.

Plan S Plan B

Year CFAT Year CFAT

0

$- 28,800

0

$-50,000

1- 6

5,400 14,200

7-

tO

2,040 2 13,300

to

2,792 3

12,400

4 11,500

5

10,600

Solution by Hand

In

this examp.le, both

AW

and PW analyses are shown. Develop the A W relations using the

CFAT

values over each plan's lif

e.

Select the larger value.

AWs

= [- 28,800 + 5400(P

/A

,7

%,6) + 2040(P/A,7

%,

4)(P/F

,7%,6)

+ 2792(P / F,7%, 10)](A/ P,7%,

10)

= $422

AW

B

= [- 50,000 + 14,200(P

/F,

7%,l)

+

...

+

10,600(P/F)

%,

5)](A/P,7

%,

5)

= $327

Both plans are

fi

nancially viab

le

; select plan S because

AWs

is

larger.

For the

PW

ana

ly

si

s,

the LCM is

10

years. Use the AW values and the

PIA

factor for

the LCM of

10

years

to

select stucco

on

metal lath, plan

S.

PW

s

=

AW

s

(P/A,7%,1O) = 422(7.0236) = $2964

PW

B

=

AW

B

(P/A,7%,1O) = 327(7.0236) = $2297

Solution by

Computer

The

AW

and PW values are

di

splayed

in

rows

17

and

18

of

Figure

17

-

5.

The functions

have been set up differently here than

in

previous examples because of the unequal lives.

Follow along

in

the cell tags, which are shown in the order of development for each alter-

native. For plan

S,

fir

st the NPV function

in

B

18

is developed for PW, followed by the PMT

function in B

17

for the

AW

value. Note the minus sign in PMT to ensure that the function

resul

ts

in

the correct sign on

th

e PW value. This is not necessary for the NPV function, be-

cause

it

takes

th

e cash flow sign from the ce

ll

entry itself.

The opposite order

of

f

un

ction development is used for plan B. The PMT

in

C17 uses

an

embedded NPV functi

on

over the 5-year life. Again, note the minus sign. Finally, the PV

function

in

C

18

displays the PW

va

lu

e over

10

years.

587

::

I

~

E·Solve

588

CHAPTER 17 After-Tax Economic Analysis

X Microsoft

hcel

- Example 17.7 I!lIiiII3

A

ft

er-tax

Iv1ARR

= 7%

Plan S

Year

CFAT

0

$(28,800)

$

5,400

2

$

5,400

3

$

5,400

4

$

5,400

5

$

5,400

6

$

5,400

7

$

2,040

8

$

2,

040

9

$

2,0

40

10

$

4,832

$422

$ 2,963

Plan B

CFAT

$(

50,000)

$ 14,200

$ 13,300

$ 12,400

$ 11,500

$ 10,600 ,

~--.:.----.;..---.

$327

::::.--i

= PMT($C$2,S

,-(

NPV($C$2

,C7C

II

)+

C6)) I

$2297

,

---"

=

PV

($C$2,IO,- C I7) I

I

~ ~ ~

I She

et

I Sheet2 Sheet3

Ready

I .r

-,'--

Figure

17-5

After-t

ax

PW and AW evaluation, Example 17.7.

Comment

It

is important to remember the minus signs

in

PMT

and PV functions when utiliz

in

g

th

em

to obtain the corresponding

PW

and AW values, respective

ly.

If

the minus is omitted,

th

e

AW and

PW values are the opposite

of

th

e con-ect cash flow direction.

Then

it may appear

that the plans are not financially viable

in

that they do not retum at least

th

e after-tax

MARR. This is what would happen

in

this example. However, we

know

they are finan-

cially viable, based on

th

e previous solution by hand. (Refer to Excel online help for more

det

a

il

s on sign convention

in

PMT,

PV

, and NPV functions.)

To utilize the ROR method apply exactly the same procedures as

in

Chapter 7

(single proj

ec

t) and Chapt

er

8 (two

or

more alternatives) to the CFAT serie

s_

A

PW

or

AW relation is developed to estimate the rate

of

return i* for a project,

or

D.i

* for the

in

cremental CFAT betw

ee

n two alternatives_ Multiple roots may exist

in the CFAT

se

ries, as they

ca

n for any cash flow series.

For

a single project, set

SECTION 17.5 After-Tax PW,

AW,

a

nd

ROR Evaluation

the PW or

AW

equal to zero and solve for i*.

l = n

Present worth:

0 = L CFAT, (P/F,i*,t)

[17.15]

,= 1

{= n

Annual worth:

0 = L

CFAT,(P/F,i*,t)(A/P,i*,n)

[17.16]

,= 1

Spreadsheet solution for

i*

may be helpful for relatively complex CFAT series.

It

is

performed

lI

s

in

g the

IRR

function with the general format

IRR(yeacO

_CFAT:yea

cn

_C

FAT)

If

the

af

ter-tax

ROR

is important to the analysis, but the details

of

an after-tax

study are not

of

interest, the before-tax

ROR

(or

MARR)

can be adjusted with the

effect

iv

e tax rate Te using the approximating relation

B

et

ROR

after-tax

ROR

elore- ax =

1 - Te

[17.17]

For example, assume a company has an effective tax rate

of

40

% and normally

uses an

af

ter-tax

MARR

of

12% per year for economic analyses that consider

taxes

exp

li

citly. To approximate the effect

of

taxes without performing the de-

tails

of

an after-tax study, the before-tax

MARR

can be estimated as

0.12

Before-tax

MARR

=

---

-

20

% per year

-

0.40 -

If

the decision concerns the economic viability

of

a project, and the resulting

PW

or

AW

va

lu

e

is

close to zero, the deta

il

s

of

an after-tax analysis should be

developed.

EXAMPLE

17.8

.~,

A fiber o

pti

cs manufacturing company operating

in

Hong Kong h

as

spent $50,000 for a

5-year-life machine that

ha

s a projected $20,000 annual CFBT and annual depreciation

of

$

10

,000. The company has a Te

of

40%. (a) Determine the after-tax rate

of

return.

(b) Approximate

th

e before tax return.

Solution

(a) The CFAT

in

year 0 is $- 50,000. For years 1 through 5, combine Equations

[1

7.8] a

nd

[17

.9

] to estimate the

CFAT.

CFAT = CFBT - taxes = CFBT - (GI - E -

D)(T

e)

= 20,000 - (20,000 - 10,000)(0.40)

= $[6,000

589

~

E·Solve

590

CHAPTER 17 Afte

r-

Tax

Eco

no

mi

c Analysis

Since

th

e CFAT for years I through 5 has

th

e same value, use

th

e P

IA

factor

in

Equa

ti

on

[17

.15].

0 = - 50,000 + 16,000(P/A,i*,5)

(P/ A,i

*,

5) = 3.125

So

lu

tion gives i

'"

= 1

8.

03% as

th

e

af

ter-tax rate of return.

(b) U

se

Equa

ti

on

[1

7.17] for the before-tax return estimate.

. 0.1803

Before-tax ROR = 1 _ 0.40 = 30.05%

The ac

tu

al before-tax i* using

CFBT

= $20,000 for 5 y

ear

s is 2

8.

65

% from the

rela

ti

on

0 = - 50,000 + 20,000(P/A,i*,5)

The t

ax

effect will be s

li

ght

ly

overestimated if a MARR

of

30.05% is

Ll

sed

in

a

before-tax analysis.

A rate of return evaluation performed by hand on two

or

more alte

rn

a

ti

ves

mu

st utilize a

PW

or AW rela

ti

on to determine the incremental return

t1

i*

of

the

in

cremental CFAT series between two alternatives. Solution by comput

er

is

accomp

li

shed us

in

g

th

e incremental

CF

AT values and the

IRR

functio

n.

The

equations and proce

dur

es applied are the same as in Chapter 8 for selection from

mutua

ll

y exclusive alte

rn

a

ti

ves us

in

g the

ROR

method. You should review and

understand the fo

ll

owing sections before proceeding further with this sectio

n.

Section 8.4

Section 8.5

Section 8.6

ROR

eva

luation us

in

g P

W:

incremental and breakeven

ROR

evalua

ti

on us

in

g AW

In

cremental

ROR

analysis

of

multiple, mutua

ll

y exclusive

alte

rn

atives

From this review, several important facts should be recalled:

Selection

guideline:

The fundamental rule of incremental

ROR

eva

lu

ation at

a stated MA

RR

is as follow

s:

Select

the

one

alternativ

e

that

requires

the

largest

initial

investment

,

provided

the

extra

investment

is

justified

relative

to

another

justified

alternative.

Incremental

ROR:

Incremental analysis must be performed.

Ove

ra

ll

i* va

l-

ues ca

nn

ot be depended upon to select the correct alte

rn

a

ti

ve, unlike the

PW

or A W method at the

MARR

, w

hi

ch will a

lwa

ys indicate the correct

alte

rn

a

ti

ve.

Equal-

s

ervic

e

assumption:

Incremental ROR analysis requires that the

a

lt

e

rn

atives be evaluated over equal time periods. The LCM

of

th

e two

alte

rn

a

ti

ve

li

ves must be used to

fin

d the

PW

or AW

of

incremental cash

SECTION

17.5

After-Tax PW,

AW,

and ROR Evaluation

flows. (The only exception, mentioned in Section 8.5, occurs when the AW

anal ysis

is

performed on actual cash flows, not the increments; then one-

life-cycle analysis is acceptable over the respective alternative lives.)

Revenue

and

service

alternatives:

Revenue alternatives (positive and nega-

tive cash ftows) may be treated differently from service alternatives (cost-

only

cashftow

estimates).

For

revenue alternatives, the overall

i*

may be

used to perform an initial screening. Alternatives that have

i*

<

MARR

can be removed from further evaluation. An

i*

for cost-only (service)

alternatives cannot be determined, so incremental analysis is required with

all alternatives included.

These principles and the same procedures developed in Chapter

8 are applied

to the CFAT series. The summary table

in

the rear

of

the

book

(which is also

Table

10

- 2) details the requirements

of

all evaluation techniques. For the

ROR

method,

in

the column labeled "Series to Evaluate" change the words cash flows

to CFAT values. Additionally, use the after-tax

MARR

as the decision guideline

(far right column). Now, all entries for the

ROR

method are correct for an after-

tax analysis.

Once the CFAT series are developed, the breakeven ROR can be obtained

using a plot

of

PW vs. i*. Solution

of

the

PW

relation for each alternative over

the

LCM

at several interest rates can be accomplished by hand

or

by using the

591

NPY spreadsheet function.

For

any after-tax

MARR

greater than the breakeven

(-/-----

--0

ROR, the extra investment is not justified. [ PW

vs.

i*

.

Example

17

.9 illustrates an after-tax

ROR

evaluation

of

two alternatives

'----

------'"

solved by hand.

The

next section includes additional examples solved by com-

puter using incremental

ROR

analysis and the breakeven plot

of

PW

vs. i*.

EXAMPLE

17.9

.

Johnson Controls must decide between two alternatives in its northeast plant: sys-

tem

I-a

single robot assembly system for lCs will require a $100,000 investment now;

and system

2-a

combination of two robots requires a total

of

$130,000. Management

intends

to

implement one

of

the plans. This manufacturer expects a 20% after-tax return

on

technology investments. Select one

of

the systems, if the following series

of

cost

CFAT

values have been estimated for the next 4 years.

System 1

CFAT,

$

System 2

CFAT,

$

Solution

o

- 100,000

- 130,000

1

-35,000

- 20,000

Year

2 3 4

-30,000 -20,000 -15,000

- 20,000

-10,0

00

-5,000

System 2

is

the alternative with the extra investment that must be justified. Since lives

are equal, select

PW

analysis

to

estimate

t:.i*

for the incremental

CFAT

series shown

here.

All

cash

flows

have been divided

by

$1000.

592

~

E-Solve

CHAPTER 17 After-Tax Economic Analysis

Year

o 2

3

4

Incremental

CFAT, $1000

-3

0

+15

+ 10

+

10

+

10

A

PW

relation is s

et

up

to estimate the after-tax incremental return.

-

30

+

15(P

/ F,tli*,I) +

10(P

/A,

t1i

*,3)(P/ F,t1i*,

J)

= 0

Solution indicates an incremental after-tax return

of

20.10%, which

just

exceeds

th

e

20% MARR.

The

extra investment in system 2 is marginally justified.

17

.6 SPREADSHEET APPLICATIONS-AFTER-TAX

INCREMENTAL

ROR

ANALYSIS

Two spreadsheet examples

of

after-tax

ROR

analysis are presented

in

this sec-

tion. Both examples build upon earlier solutions

in

this chapter. The first exam-

ple determines the incremental rate

of

return i1i':' and highlights the use

of

a

PW

vs

. i plot. The second example illustrates incremental ROR analysis when

the CFAT estimates must be calculated

Llsing

MACRS depreciation.

The

procedure outlined in Section 8.6 for performing an incremental

ROR

analysis

of

two

or

more alternatives

is

used in each example below. This proce-

dure should be reviewed and understood before proceeding.

In

Example 17.7, Paul estimated the CFAT for interior

wa

ll

materials to reduce sound tran -

mission; plan S is

to

construct with stucco on metal lath, and plan B is to const

ru

ct

us

in

g

brick. Figure

17- 5 presented both a

PW

analysis over 10 years and an

AW

analysis over the

respective

li

ves. Alternative S was selected. After reviewing this earlier solution, perform

an

ROR evaluation

at

the after-tax

MARR

of

7% per year.

So

lut

i

on

by

Computer

The

LCM

is

10

years for the incremental ROR analysis, and plan B requires the extra

investment that must be justified. Apply the procedure in Section 8.6 for incremental

ROR

anal

ys

is. Figure

17

-6

shows the estimated CFAT for each alternative a

nd

the incremental

CFAT series. Since these are revenue alternatives, the

i* is calculated first to en

su

re that

th

ey both make at least the

MARR

of

7%. Cells C14 and D14 indicate they do. The

lRR

fl.lllction in ce

ll

E14

is

applied to the incremental CFAT, indicating that tli* = 6.35

%.

Since

this

is

lower than the MARR, the extra investment in brick walls is not justified. Plan S

is

selected,

th

e same as with

th

e

PW

and A W methods.

In rows 17 through 21, Figure 17-6, the NPV function is used to find the PW

of

the al-

terna

ti

ves' CFAT series at various i values.

The

graph indicates that the breakeven i* occurs

at 6.35

%-

th

e same result as with the

IRR

function above. Whenever the after-tax MARR

is above 6.35

%,

as is the case here with MARR = 7%, the extra investment in plan B is

not justified.

SECTION 17.6 Spreadsheet Application

s-A

Fter-Ta

x Incremental ROR Analysis

X Microsoll EKcel Br.Jf3

E.Ue

~dit

y'iew

Insert

FQ.rmat

Iools

!;lata

~i

ndow

A27

A

8 C 0 F

G H

K

L

Pl

anS

Plan 8

8-

S

Year CF

ln

CFAT Incr. CFAT

I--+-Plan S

-.-

Plan

8 I

0 -$28,800 ·$50,000 -$21,200

$5,400

$14,200

$8,800

$8,000

5

$5,400 $13,300 $7,900

$5,400

$12,400

$7,000

$5,400 $11,500 $6,100

$6,000

$5,400 -$39,400

-$44,800

$5,400 $14,200 $8,800

$5,000

10

$2,040 $13,300 $11,260

.-

:

$4,000

«

'

11

$2,040 $12,400 $10,360

"-

$3,000

'12

$2,040 $11,500 $9,460

u

0

13

10

$48

32

$10600

$5768

~

$2,000

.1.1

ROR

9

.4

9%

8,05%

6

,3

5%

$1,000

15

j§.

Rate Pl

an

S

$0

17

FW@

5%

$5,721

·

$1

,000

4

'

~

18

FW@

6% $4,296

-$2

,0

00

19 F

W@

7% $2,963

~FW@

8% $1,715

21

FW@

9% $544

22

23

= lRR(E3

:EI

3)

24

= NPV(

B21

,

D4:DI

3)+ D3

Ready

--n~

INCJ

M

I

F

ig

ure

17-6

After-tax evaluation

of

two alte

rn

atives with a plot of PW

vs

. i, Example 17.10.

Comment

Note that

th

e

in

cremental CFAT se

ri

es has three sign changes.

The

cumulative se

ri

es also

has three sign changes (Norstrom's critelion). Accordingly, there may

be

multiple

t1i

*

va

lue

s.

The application

of

th

e lRR hlJ1ction us

in

g the

"g

uess" option finds no o

th

er

r

ea

l

number roots

in

the normal rate

of

retum range.

EXAMPLE 17,11 •

;:;:

.

IJ1

Example

17

.6 an after-tax analysis

of

two bone cell analyzers was initiated due to a new

3-year NBA contract. The criterion used

to select analyzer I was the total taxes for the

3 years. The complete spreadsheet solution is

in

Figure 17-4.

Continue the s

pr

eadsheet analysis by performing an after-tax ROR evaluation, assum-

in

g the analyzers

aJ'e

so

ld

after 3 years at

th

e

aJ110unts

estimated

in

Example 17.6: $1

30

,000

For

analyzer

land

$225,000 for analyzer 2. The after-tax MARR is 10%

per

year.

M

I~

>I

G

~r:-

593

594

CHAPTER 17 After-T

ax

Econo

mi

c Analysis

Solution by Computer

Figure

17

-7

is

an updated copy

of

the spreadsheet in Figure

17

- 4 to include the sale

of

the

analyzer

in

year 3. The CFAT series (column I) is determined

by

th

e relation

CFAT

=

CFBT - taxes, with the taxable income determined using Equation [17.14]. For example,

in year 3

wh

en analyzer 2 is sold for S = $225,000, the

CFAT

calculation is

CFAT

3

= CFBT - (

TI

)(Te) = GI - E - P + S - (

Gl-E

- D +

DR

)(T

e

)

The depreciation recapture

DR

is the amount above the year 3 book value received at sale

time.

By

Equation [17.12], using the book value

in

cell F18,

DR

= selling price - BV

3

= 225,000 - 64,800 =

$J60

,200

Now, the

CFAT

in

year 3 for analyzer 2 can be determine

d.

CFAT

3

= 100,000 - 10,000 + 0 + 2

25

,000

- (100,

000-10

,000- 43,200 + 160,200)(0.35)

= 315,000 - 207,000(0.35) = $242,550

The ce

ll

Blank L., Tarquin A. Engineering Economy (McGraw-Hill Series in Industrial Engineering and Management)

Подождите немного. Документ загружается.