Chapter 14.pdf

Contemporary Engineering Economics, Fifth Edition, by Chan S. Park. ISBN: 0-13-611848-8 © 2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.

Chapter 14 Replacement Decisions Sunk Costs, Opportunity Costs, and Cash Flows 14.1 (a) Sunk cost = $12,000- $2,000 = $10,000. (b) Opportunity cost = $2,000. (c) PW (15%) D = $2, 00 000 + $10, 00 000( P / A,15%, 3) = $24,832 PW (15%)C = $15,000 + $3,000( P / A,15%,3) − $5,000( P / F ,15%,3)

= $18,562 ∴ The

net incremental benefit in present value is $6,270 associated with replacing the old machine tools at an interest rate of 15%.

14.2 (a) Purchase cost = $15,000, market value = $6,000, sunk cost = $15,000 - $6,000 = $9,000 (b) Opportunity cost = $6,000 (c)

PW (15%) = −$6, 00 000 − $1, 50 500 − $3, 00 000( P / F,15%,1)

−($3, 50 500 − $3, 00 000)( P / F ,15%, 2) 2) = −$10,486.77 AEC (15%) = $10, 48 486.77( A / P,15%, 2) 2) = $6,450.58 (d) PW (15%) = −$7, 500 − $3, 00 000( P / F,15%,1) − $3, 500( P / F,15%, 2) 2)

−$3, 800( P / F ,15%, 3) − $4, 500( P / F,15%, 4) 4 ) −$9, 80 800( P / F ,15%, 5) 5) = −$22,698.98 AEC (15%) = $22, 69 698.98( A / P,15%, 5) 5) = $6,771.46

Page | 1


14.3 (a) Opportunity cost = $30,000 (b) Assume that the old machine’s machine’s operating cost cost is $30,000 per per year. Then the new machine’s operating operating cost is zero per year. The cash flows associated with retaining the defender for two more years are 0

n

1

2

Cash Flows: -$30,000 -$30,000 -$18,000 AEC D

,000 − $12,00 ,000)( A / P,12%,2) ,2) + $12,00 ,000(0.12) = ($30,00 +$30,000 = $42,090.57

(c) Cash flows for the challenger: Year 0: -$165,000; -$165,000; Years 1-7: 0; Year 8: 8: $5,000 AECC = ($165, 00 000 − $5, 00 000)( A / P,12%, 8) 8) + $5, 00 000(0.12)

= $32,808.45 (d) Since AEC D > AEC C , we should replace the defender now.

14.4 (a) Initial cash outlay for the new machine = $120,000 (b) Cash flows for the defender: Year 0: -$10,000 Years 1-5: 0 (c)

= $10, 00 000( A / P,15%, 5) = $2, 983 000 − $30, 00 000)( A / P,15%, 7) 7) +$30, 00 000(0.15) ] AEC (15%)C = [($120, 00 −$50,000 = −$23,868

AEC (15%) D

We should purchase the new machine because it has a higher annual equivalent cash flow. 14.5 (a) Cash flows Year: 0 Defender -$10K Challenger Challenge r -$75K

1 0 $30K

2 0 $30K

3 0 $30K

4 0 $30K

5 $5K $30K Page | 2


14.3 (a) Opportunity cost = $30,000 (b) Assume that the old machine’s machine’s operating cost cost is $30,000 per per year. Then the new machine’s operating operating cost is zero per year. The cash flows associated with retaining the defender for two more years are 0

n

1

2

Cash Flows: -$30,000 -$30,000 -$18,000 AEC D

,000 − $12,00 ,000)( A / P,12%,2) ,2) + $12,00 ,000(0.12) = ($30,00 +$30,000 = $42,090.57

(c) Cash flows for the challenger: Year 0: -$165,000; -$165,000; Years 1-7: 0; Year 8: 8: $5,000 AECC = ($165, 00 000 − $5, 00 000)( A / P,12%, 8) 8) + $5, 00 000(0.12)

= $32,808.45 (d) Since AEC D > AEC C , we should replace the defender now.

14.4 (a) Initial cash outlay for the new machine = $120,000 (b) Cash flows for the defender: Year 0: -$10,000 Years 1-5: 0 (c)

= $10, 00 000( A / P,15%, 5) = $2, 983 000 − $30, 00 000)( A / P,15%, 7) 7) +$30, 00 000(0.15) ] AEC (15%)C = [($120, 00 −$50,000 = −$23,868

AEC (15%) D

We should purchase the new machine because it has a higher annual equivalent cash flow. 14.5 (a) Cash flows Year: 0 Defender -$10K Challenger Challenge r -$75K

1 0 $30K

2 0 $30K

3 0 $30K

4 0 $30K

5 $5K $30K Page | 2


(b)

= −$10 K + + $5K ( P / F ,15%,5) ,15%,5) = −$7,514 PW (15%)C = − $75K + + $30 K ( P / A,15%,5) = $25,565 PW (15%) D

eplace the defender

14.6 (a) and (b) Cash flows: Year: 0 1 2 3 4 5 Defend Defender er -$5 -$5,50 ,5000 $21,00 $21,000 0 $21,00 $21,000 0 $22,20 $22,200 0 Challenger -$36,500 $24,000 $24,000 $24,000 $24,000 $30,300

• Revenue for defender = ($19 - $12) × 3,000 = $21,000 per year • Revenue for challenger = ($19 - $11) × 3,000 = $24,000 per year (c)

[

AE D (12%) = − ($5, 50 500 − $1, 20 200)( A / P,12%, 3) 3) + $1, 220 00(0.12)

]+$21, 00000

= $19,065.70 AEC (12%) = − [($36, 50 500 − $6, 30 300)( A/ P,12%, 5) 5) + $6, 330 00(0.12) ]+$24, 000 00 = $14,866.23 New equipment should not be acquired now because it has a lower AE value.

Economic Service Life 14.7 Annual changes in MV Interest rate Marke rket Value lue

n

0 1 2 3 4 5 6 7 8

$200,000 $130,000 $104,000 $83,200 $66,560 $53,248 $42,598 $34,079 $27,263

20% 12% O&M Costs CR(12%)

$20,000 $20,000 $20,000 $20,000 $20,000 $22,000 $25,000 $28,000

$9 $94,000 $69,283 $58,614 $51,920 $47,100 $43,396 $40,446 $38,044

OC(12%)

AE AEC(12 (12%)

$2 $20,000 $20,000 $20,000 $20,000 $20,000 $20,246 $20,718 $21,310

$114,000 $89,283 $78,614 $71,920 $67,100 $63,642 $61,163 $59,354

Page | 3


The economic life of the asset is eight years; that is, *

N

= 8 years. Thus, AEC * = $59,354

14.8 (a) Interest i = 12% Defender: Ye a r 0 1 2 3 4

OC $3, 200 $3, 700 $4, 800 $5, 850

MV $7, 700 $4, 300 $3, 300 $1,100 0

AE OC

$3, 200 $3, 436 $3, 840 $4, 261

CR (12%) Total AE(12%) $4, 324 $2, 999 $2, 880 $2, 535

$7, 524 $6, 435 $6, 720 $6, 796

The defender’s remaining useful (economic) life is 2 more years with an AEC value of $6,435, i.e., N D = 2, AEC D = $6, 435 . (b) N C = 10 years 000( A / P,12%,10) + $1, 00 000 − $2, 50 500( A / F ,12%,10) AECC = $31, 00

= $6,344 Since AEC D > AEC C , the defender should be replaced now. 14.9 (a) Economic service life = 4 years: Year OR MV AEOR 0 $8,000 1 $4,000 $4,200 $4,000 2 $3,400 $2,940 $3,717 3 $2,710 $2,058 $3,419 4 $1,917 $1,411 $3,104 5 $1,004 $1,008 $2,774

CR(12%) Total AE $4,760 $3,347 $2,721 $2,332 $2,061

-$760 $370 $698 $772 $713

When N = = 4, we have the largest AE value. The economic life of the the system is 4 years. years. (Note that we want to maximize maximize our operating revenue.)

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(b) The economic service life varies with the interest rate: Inte Intere rest st rat ratee Econ Econom omic ic ser servic vicee life life Maxi Maximu mum m annu annual al rev reven enue ue 1% 5% 10% 15% 20% 25% 30% 40%

3 years 4 years 4 years 4 years 4 years 5 years 5 years 6 years

$1,333 $1,127 $876 $613 $341 $77 -$191 -$760

• Maximize annual revenue at its economic service life varies inversely with •

the interest rate. Economic service life increases as the interest rate increases in our example. As the interest rate increases, increases, the capital cost will will also increase. However, the annual equivalent equivalent revenue will decrease. Thus, the the net effect is that the marginal increase in the capital cost is less than the decrease in the annual equivalent revenue, resulting in extending the service life.

14.10 (a) Interest i = 10% OC

MV

A E OC

C R( R(1 0 %) %)

A EC EC (1 00% %)

0 1 2 3

$2, 5 00 $ 3, 2 0 0 $ 5, 3 0 0

$ 1 5, 0 0 0 $ 1 2, 8 0 0 $ 8,1 0 0 $ 5, 2 0 0

$2, 500 $2, 8 33 $ 3, 5 7 9

$ 3, 7 0 0 $4, 786 $4, 4 61

$6, 200 $7 , 619 $ 8, 0 3 9

4 5

$6, 5 00 $7 , 80 0

$ 3, 5 0 0 0

$4, 2 08 $4, 796

$ 3, 9 7 8 $ 3, 9 5 7

$ 8, 1 8 6 $ 8, 7 5 3

OC

MV

A E OC

C R( R (1 0 % )

A E C( C(1 0 %) %)

$2,500 $ 3, 2 0 0 $ 5, 3 0 0 $6,500 $7 ,800

$ 1 5, 0 0 0 $12, 800 $ 8,1 0 0 $ 5, 2 0 0 $ 3, 5 0 0 0

$2, 500 $2, 826 $ 3, 5 3 8 $ 4 ,1 3 1 $4, 675

$4, 450 $ 5, 4 5 9 $ 5, 0 7 2 $4,553 $4, 475

$6, 950 $ 8, 2 8 5 $ 8, 6 1 0 $ 8, 6 8 4 $ 9,1 5 0

n

(b) Interest i = 15% n

0 1 2 3 4 5 ∴ In

both cases, the economic e conomic service life is 1 year. Page | 5


Replacement Decision with an Infinite Planning Horizon and No Technological Change 14.11 It is assumed that the required service period is very long.

= $6, 000( A / P,12%, 6) + $2, 000 − $1, 500( A/ F ,12%, 6) = $3,274.52 AECC = $21, 000( A / P,12%,12) + $1, 000 − $500( A/ F ,12%,12) = $4,369.46

AEC D

We should continue to use the present machine. The economic advantage is $4,369.46-$3,274.52 = $1,094.94 per year. 14.12 (a) and (b) n

0 1 2 3

Defender Challanger -$4,000 -$6,000 -$3,000 -$2,000 -$4,500 -$3,000 -$5,000 -$2,000

AECC (15%) = ($6, 000 +

$1,000 )( A / P,15%, 3) + $2, 000 1.152

= $4,959.04 AEC D (15%) = ($4, 000 +

$3, 000 $4, 500 $5, 000 )( A / P,15%, 3) + + 1.15 1.152 1.153

= $5,824.62 Now is the time to replace the defender.

14.13 (a) Opportunity cost = $0 (b) The cash flows are: Year: 0 1 2 3 4 5 Defender $0 -$3K -$3K -$3K -$3K -$3K Challenger -$10K 0 0 0 0 0 C-D -$10K $3K $3K $3K $3K $3K (c) PW (i )C − D = −$10, 000 + $3, 000( P / A, i,5)

=0 We find i* = 15.24% . Since i* > MARR, the firm should buy the challenger. Page | 6


14.14 (a)

= −$1,000( A / P,15%,5) + $10,000 − $7,000 = $2,701.68 AE C = −$12,000( A / P,15%,5) + $11,500 − $5,000 + $2,000( A / F ,15%,5) = $3,216.84

AE D

Yes, the new machine should be purchased now.

(b) Let P as the current market value of the old machine

− P( A / P,15%,5) + $10,000 − $7,000 = $3,216.84 We find P = −$726.9 . Let P as the cost of new machine

− P( A / P,15%,5) + $11,500 − $5,000 + $2,000( A / F ,15%,5) = $2,701.68 We find P = $13,727 .

14.15 Assume that the old system has a current market value of P.

= P( A / P,14%,5) + $20, 000 AECC = $200, 000( A / P,14%,10) + $5, 000 −$18, 000( A/ F ,14%,10) = $42,411.86

AEC D

Let AEC D = AEC C and solve for P. We find that P = $76,941.73. If the resale value of the defender is higher than $76,941.73, the installation of the system is justified.

Page | 7


14.16

= $60,000( A / P,12%,10) + $18,000 = $28,619 AEC (12%) C = ($200,000 − $20,000)( A / P,12%,10) + $20,000(0.12) + $4,000 = $38,257

AEC (12%) D

Since AEC D

14.17

< AEC C , do not replace the defender.

AECC = $53, 500( A / P,12%, 5) − $12, 000( A/ F ,12%, 5)

AEC D

+$4, 200 + $500( A / G,12%, 5) = $18,039.80 = $8, 500( A / P,12%, 5) + $8, 700 = $11,057.98

Since AECC

> AEC D , don’t purchase the challenger.

14.18 (a) Economic service life: n

0 1 2 3 4

OR

MV

AEOR

$35,550 $31,013 $25,794 $19,794

$20,000 $17,000 $14,450 $12,283 $10,440

$35,550 $33,390 $31,095 $28,660

CR(10%) AE(10%) $5,000 $4,643 $4,332 $4,060

$40,550 $38,033 $35,427 $32,720

The economic life of the cab is one year. These cabs should be replaced every year. (b) Rate of return calculation: PW ( i) = −$20,000 +

$35,550 + $17,000 =0 1+ i

Solving for i yields 162.75%. The internal rate of return with one-year replacement cycle is 162.75%.

Page | 8


14.19 For the challenger, we have: AECC = $50, 000( A / P,14%,12) + $3, 000 − $6, 000 − $3, 000( A / F ,14%,12)

= $5,724 For the defender, since salvage value at year 10 is $1,000 and the problem is stated that if sold at the end of first year, it will bring $1,500. We assume the market values will be declined same amount (($1,500-$1,000)/4 = $125) for the next years. Year

OC

0 1 2 3 4 5 N D

MV

AEOC

CR(14%) AEC(14%)

$2,000 $3,800 $3,800 $3,800 $3,800 $3,800

$1,500 $1,375 $1,250 $1,125 $1,000

$3,800 $3,800 $3,800 $3,800 $3,800

$780 $572 $498 $458 $431

$4,580 $4,372 $4,298 $4,258 $4,231

= 5 years, AEC D = $4,231 with i = 14%.

Since AEC C > AEC D , the new machine should not be purchased.

14.20

= $15, 000 + $48, 000( A / P,15%,10) + $12, 000 −$5, 000( A/ F ,15%,10) = $36,317.84 AECOption 2 = ($84, 000 − $6, 000)( A / P,15%,10) + $24, 000 −$9, 000( A/ F ,15%,10) = $39,098.39 AECOption 1

Since AECOption 1

< AEC Option 2 , Option 1 should be selected.

Page | 9


Replacement Problem with a Finite Planning Horizon 14.21 (a) AEC D = $12,000( A / P,12%,1) + $3,750 − $9,600( A / F ,12%,1)

= $7,590 AEC C = $18,000( A / P,12%,1) + $3,300 − $13,500( A / F ,12%,1) = $9,960 Since AEC D < AEC C , the defender should not be replaced now. (b) Defender

Annual changes in MV Annual increases in A/T O&M Interest rate Market Value

n

0 1 2 3

20% 35% 12% O&M Costs CR(12%) OC(12%) AEC(12%)

$12,000 $9,600 $7,680 $6,144

$3,750 $5,063 $6,834

$3,840 $3,478 $3,175

$3,750 $4,369 $5,100

$7,590 $7,847 $8,275

Challenger

Annual changes in MV Annual increases in A/T O&M Interest rate Market Value

n

0 1 2 3

$18,000 $13,500 $10,125 $7,594

AEC 1 2 3

25% 30% 12% O&M Costs CR(12%) OC(12%) AEC(12%)

$3,300 $4,290 $5,577

$6,660 $5,875 $5,244

$3,300 $3,767 $4,303

$9,960 $9,642 $9,547

Defender Challenger $7,590 $9,960 $7,847 $9,642 $8,275 $9,547 Page | 10


The annual equivalent cost of the defender is less than that of the challenger for every year. Therefore, if total service life is 3 years, we should keep the defender for 3 years in order to optimize the replacement strategy. 14.22 There are several plausible scenarios. Some of the most feasible scenarios are; ( j0 , 2), ( j,3), ( j, 3), ( j, 2) : PW (12%) = $17, 601 ( j0 ,1), ( j, 3), ( j,3), ( j,3) : PW (12%) = $18, 081 ( j0 ,3), ( j,3), ( j,3), ( j,1) : PW (12%) = $17,597 ( j0 ,3), ( j, 3), ( j, 4) : PW (12%) = $17, 221 ( j0 , 4), ( j,3), ( j,3) : PW (12%) = $18, 384 ∴It

appears that the ( j0 , 3), ( j,3), ( j, 4) option becomes the best strategy. Keep the defender for 3 years; replace it with challenger j and keep it for 3 years; replace it with another challenger and keep it for 4 years. 14.23 There are several plausible scenarios. Some of the most feasible scenarios are; ( j0 , 3), ( j,3), ( j, 2) : PW (12%) = $67, 526 ( j0 , 2), ( j,3), ( j,3) : PW (12%) = $67,390 ( j0 ,1), ( j, 3), ( j,3), ( j,1) : PW (12%) = $66,856 ( j0 , 4), ( j,3), ( j,1) : PW (12%) = $65,820 ( j0 , 4), ( j, 4) : PW (12%) = $65,958

∴It

appears that the ( j0 , 3), ( j,3), ( j, 2) option becomes the best strategy. Keep the defender for 3 years; replace it with challenger j and keep it for 3 years; replace it with another challenger and keep it for 2 years.

Page | 11


14.24

= $12, 000 + $4, 000( P / A,11%, 6) − $2, 000( P / F,11%, 6) = $27,852.86 PWC = [$10, 000 + $2, 000( P / A,11%, 3) − $4, 000( P / F,11%, 3)] × [1 + ( P / F ,11%,3)] = $20,709.66 Since PWC < PWD , replace now.

PW D

14.25

= $4, 000 + $12, 000( A / P,11%, 6) − $2, 000( A/ F ,11%, 6) = $6,583.77 AEC = $2, 000 + $10, 000( A / P,11%, 3) − $4, 000( A/ F ,11%, 3) = $4,895.28 AE D

Since AEC

< AE D , replace now.

Replacement Analysis with Tax considerations 14.26 (a) Comments: Sunk cost can be defined as either the difference between book value and market value or the cost that has already been expended ($). book value = $15,000 − ($3,000 + $4,800 + $1, 440) = $5,760 market value = $6,000 In this example, if the sunk cost is defined as the difference between book value and market value, there would be no sunk cost as the market value exceeds the book value. However, the difference between the purchase cost ($15,000) and the current market value ($6,000) may be viewed as another sunk cost that should not be considered in the replacement analysis.

(b) Opportunity cost of not replacing the truck: Book value = $15,000 − ($3,000 + $4,800 + $1,440) = $5,760 Market value = $6,000 Taxable gain = $6,000 − $5,760 = $240 Gains tax = $240 × 0.40 = $96 Net proceeds from sale = $6,000 − $96 = $5,904

Page | 12


The opportunity cost for not replacing the old machine now, which is $5,904, is viewed as an investment required to keep the old machine. Since the market value is less than the original purchase cost, there would be no capital gains. The taxable gain in the amount of $96 in (b) is an ordinary gain. (c) Equivalent annual cost of operating the truck for two more years: Cash Flow Elements Investment Net proceeds 0.6(O&M) cost + (0.40) Dn Net cash flow

0 -$5,904

End of Period 1

2

-$900

-$1,800 $691

$2,491 -$2,100 $346

-$6,804

-$1,109

$737

PW (12%) = −$7, 207 AEC (12%) = $4, 264

(d) Equivalent annual cost of owning and operating the truck for 5 years: Cash Flow Elements 0 Investment -$5,904 Net proceeds 0.6(O&M -$900 cost) + (0.40) Dn Net cash flow -$6,804

1

2

3

4

5

-$1,800 $691

-$2,100 $691

-$2,280 $346

-$2,700 0

0 -$5,880 0

-$1,109

-$1,409

-$1,934

-$2,700

-$5,880

PW (12%) = −$15, 346.37 AEC (12%) = $4,257.23

Page | 13


14.27 (a) Book value = 0 Ordinary gains = $30,000 - 0 = $30,000 Gains tax = $30,000 × 0.4 = $12,000 Opportunity cost = $30,000 - $12,000 = $18,000

(b) , (c) and (d): Replace the defender now with the challenger.

Page | 14


Option 1: Keep the defender n

Depreciation Book value Market value

0 $0 0 $30,000

1 $0 0

2 $0 0 $12,000

0

0 7,200

$0

$7,200

AEC(10%) =

$6,943

1 $23,579 $141,422

2 $40,409 $101,013

3 $28,859 $72,155

4 $20,609 $51,546

$30,000

$30,000

$30,000

$30,000

Cash Flow Statement

+(.4)*(Depreciation) Opportunity cost

(18,000)

Net Cash Flow

($18,000) PW (10%) = ($12,050)

Option 2: Replace the defender n

Depreciation Book value Market value Savings in O&M cost

0 $165,000

5 $14,735 $36,812 $0 $30,000

6 $14,718 $22,094 $0 $30,000

7 $14,735 $7,359 $0 $30,000

8 $7,359 $0 $0 $30,000


Option 1: Keep the defender n


0 $0 0 $30,000

1 $0 0

2 $0 0 $12,000

0

0 7,200

$0

$7,200

AEC(10%) =

$6,943

1 $23,579 $141,422

2 $40,409 $101,013

3 $28,859 $72,155

4 $20,609 $51,546

$30,000

$30,000

$30,000

9,431 18,000

16,163 18,000

$27,431

$34,163

AEC(10%) =

$3,741

Cash Flow Statement


(18,000)

Net Cash Flow

($18,000) PW (10%) = ($12,050)



0 $165,000

$30,000

5 $14,735 $36,812 $0 $30,000

6 $14,718 $22,094 $0 $30,000

7 $14,735 $7,359 $0 $30,000

8 $7,359 $0 $0 $30,000

11,543 18,000

8,243 18,000

5,894 18,000

5,887 18,000

5,894 18,000

3,000 2,944 18,000

$29,543

$26,243

$23,894

$23,887

$23,894

$23,944

Cash Flow Statement

Investment Net proceeds from sale +(.4)*(Depreciation) (1 - 0.4)*(Savings)

(165,000)

Net Cash Flow

($165,000) PW (10%) = ($19,956)

Page | 15


16

14.28 (a) Based on the opportunity cost approach: Cost basis = $120,000 Gains or losses at the time of disposal: • Old machine: Total depreciation = $50,000 Book value = 0 Market value = 0 Taxable gain = $0

• New machine: Total depreciation = $109,272 Book value = $10,728 Salvage value = $30,000


16

14.28 (a) Based on the opportunity cost approach: Cost basis = $120,000 Gains or losses at the time of disposal: • Old machine: Total depreciation = $50,000 Book value = 0 Market value = 0 Taxable gain = $0

• New machine: Total depreciation = $109,272 Book value = $10,728 Salvage value = $30,000 Taxable gain = $19,272 Gains tax = $7,709 (b) Cash flow for the old machine: Cash Flow Elements Investment Net proceeds + (0.40) Dn Net cash flow

0 -$26,000

1

2

$4,000 $4,000

3 $4,000

4

5

$4,000

0 $4,000

-$26,000 $4,000 $4,000 $4,000 $4,000 $4,000

(c) Replacement analysis: Replace the old machine now. PW (12%) old = −$26, 000 + $4, 000( P / A,12%,5)

= −$11,581 AE (12%) old = −$11,581( A / P,12%, 5) = −$3, 213 PW (12%) new = −$120, 000 + $36,859( P / F,15%,1) +  + $54, 445( P / F ,12%, 7) = $57,855 AE (12%) new = $57,855( A / P,12%, 7) = $12, 677

Page | 16


17

Financial Data

n

Depreciation Book value Salvage value Savings in O&M cost

0

1 $17,148 ($137,148)

2 $29,388 ($166,536)

3 $20,988 ($187,524)

4 $14,988 ($202,512)

5 $10,716 ($213,228)

6 $10,716 ($223,944)

$50,000

$50,000

$50,000

$50,000

$50,000

$50,000

7 $5,352 ($229,296) $30,000 $50,000

6,859 30,000

11,755 30,000

8,395 30,000

5,995 30,000

4,286 30,000

4,286 30,000

22,304 2,141 30,000

($120,000)

$36,859

$41,755

$38,395

$35,995

$34,286

$34,286

$54,445

PW (12%) =

$57,855

($120,000)

Cash Flow Statement


(120,000)

Net Cash Flow

AE (12%) =

$12,677

14.29 (a) & (b): Decision - Replace the defender now. (1) Keep the defender n


0 $9,600 14,400 $10,000

1 $5,760 8,640

2 $5,760 2,880

3 $2,880 0

4 $0 0

5 $0 0 5,000

2,016

2,016

1,008

0

0 3,250

$2,016

$2,016

$1,008

$0

$3,250

AE (12%) =

($2,012)

1 $15,000 $60,000

2 $24,000 $36,000

3 $14,400 $21,600

4 $8,640 $12,960

$30,000

$30,000

$30,000

$30,000

5 $4,320 $8,640 $0 $30,000

Cash Flow Statement


(13,220)

Net Cash Flow

($13,220) PW (12%) = ($7,251)

(2) Replace the defender n


0 $75,000

Cash Flow Statement


(75,000)

Net Cash Flow

($75,000) PW (12%) = $14,760

5,250 19,500

8,400 19,500

5,040 19,500

3,024 19,500

3,024 1,512 19,500

$24,750

$27,900

$24,540

$22,524

$24,036

AE (12%) =

$4,095

Page | 17


18

14.30 (a), (b) & (c) Decision: Do not replace the defender now.

(1) Keep the defender n

Depreciation Book value Market value Revenue

0

1

2

3

$21,000

$21,000

$1,200 $21,000

$12,600

$12,600

$12,600

$12,600

$12,600

720 $13,320

AE (10%) =

$11,491

1 $7,300 $29,200

2 $11,680 $17,520

3 $7,008 $10,512

4 $4,205 $6,307

$24,000

$24,000

$24,000

$24,000

5 $2,102 $4,205 $6,300 $24,000

$5,500

Cash Flow Statement

+(1-0.4)*(Revenue) Opportunity cost Net proceeds from sale Net Cash Flow

(3,300) ($3,300)

PW (10%) = $28,575 (2) Replace the defender n

Depreciation Book value Market value Revenue

0 $36,500

Cash Flow Statement


(36,500)

Net Cash Flow

($36,500) PW (10%) = $31,771

2,920 14,400

4,672 14,400

2,803 14,400

1,682 14,400

5,462 841 14,400

$17,320

$19,072

$17,203

$16,082

$20,703

AE (10%) =

$8,381

Page | 18


19

14.31 (a) Interest i = 10% Defender: MARR Holding Period 0 1 2 3 4

10%

1 $1,116 $2,233 $2,233 $2,233

Permitted Annual Depreciation Amounts over the Holding Period 2 3 4 5

$1,115 $2,230 $2,230

$1,117 $2,233

6

7

$3,200 $3,200 $3,200 $3,200

Holding Period 0 1 2 3 4

Expected Market Value $7,700 $4,300 $3,300 $1,100 $0

1

2

3

$1,115

4

Book Value $7,810 $6,694 $4,463 $2,231 $0

$1,116 $3,348 $5,579 $7,810

Annual O&M Costs over the Holding Period Holdi ng Period 0 1 2 3 4

Total epreciatio

8

5

6

7

8

Total PW Total PW o of A/T O&M Costs O&M Costs

`

$3,700 $3,700 $3,700

Taxable Gains ($2,394) ($1,163) ($1,131) $0

$4,800 $4,800

Gains Tax ($838) ($407) ($396) $0

$2,909 $5,967 $9,573 $13,569

$5,850 Net A/T A/T Operating Costs (in PW) Market over the Holding Period Value O&M Costs Tax Shield Total OC $8,285 $5,138 $1,891 $355 $1,536 $3,707 $3,879 $1,033 $2,846 $1,496 $6,223 $1,649 $4,574 $0 $8,820 $2,209 $6,611

OC(10%)

$1,689 $1,640 $1,839 $2,086

$1,891 $3,879 $6,223 $8,820

Total CR(10%) AEC(10%)

$3,976 $3,009 $2,880 $2,614

$5,665 $4,648 $4,719 $4,699

Page | 19


20

After-Tax Opportunity Cost of Keeping the Defender now:

Note that the cost of retaining the defender on after-tax basis is $8,285, instead of $7,700. The scheduled depreciation amount during the fourth year of ownership with a 7-year MACRS property is $3,122. Period (n) 1 2 3 4 5 6 7 8

Depreciation $3,573 $6,122 $4,373 $3,122 $2,232 $2,231 $2,231 $1,116

Book Value $21,427 $15,305 $10,932 $7,810 $5,578 $,3347 $1,116 0


20

After-Tax Opportunity Cost of Keeping the Defender now:

Note that the cost of retaining the defender on after-tax basis is $8,285, instead of $7,700. The scheduled depreciation amount during the fourth year of ownership with a 7-year MACRS property is $3,122. Period (n) 1 2 3 4 5 6 7 8

Depreciation $3,573 $6,122 $4,373 $3,122 $2,232 $2,231 $2,231 $1,116

Book Value $21,427 $15,305 $10,932 $7,810 $5,578 $,3347 $1,116 0

Since the asset will be disposed of during the recovery period, the allowed depreciation amount will be (0.5) ($3,122) = $1,561. Then, the book value becomes $9,370, instead of $7,810. With the market value of $7,700, there will be a loss of $1,670. The tax credit on this loss will be $1,670(0.35) = $584.50. Finally, the net proceeds from sale of old asset will be $8,285 (= $7,700 + $584.50). The defender’s remaining useful (economic) life is 2 more years with an AEC value of $4,648, i.e., N D = 2, AEC D = $4, 648 .

Page | 20


21

(b) N C = 10 years , AEC C = $4319.2 Input Tax Rate(%) = MARR(%) =

Output PW(i) = AEC(%) =

35% 10%

0

1

2

3

($26,540) $4,319.2

4

5

6

7

8

9

10

Income Statement

Revenues (savings) Expenses: O&M Depreciation

$1,000 $4,430

$1,000 $7,592

$1,000 $5,422

$1,000 $3,872

$1,000 $2,768

$1,000 $2,765

$1,000 $2,768

$1,000 $1,383

$1,000 $0

$1,000 $0

Taxable Income Income Taxes (%)

($5,430) (1,900)

($8,592) (3,007)

($6,422) (2,248)

($4,872) (1,705)

($3,768) (1,319)

($3,765) (1,318)

($3,768) (1,319)

($2,383) (834)

($1,000) (350)

($1,000) (350)

Net Income

($3,529)

($5,585)

($4,174)

($3,167)

($2,449)

($2,447)

($2,449)

($1,549)

($650)

($650)

Cash Flow Statement

Operating Activities: Net Income Depreciation Investment Activities: Investment Salvage Gains Tax Net Cash Flow

$

(3,529) $ $4,430

(5,585) $ $7,592

(4,174) $ $5,422

(3,167) $ $3,872

(2,449) $ $2,768

(2,447) $ $2,765

(2,449) $ $2,768

(1,549) $ $1,383

(650) $ $0

(650) $0

$ (31,000) $

2,500 ($875)

$ (31,000)

$900

$2,007

$1,248

$705

$319

$318

$319

($166)

($650) $

Page | 21


22

(c) Marginal analysis: • From n = 1 to n = 2: $4,719(1.10) − $3,679 + $3,700(0.65) = $3,916.9 < $4,319.2

• From n = 2 to n = 3: $3,679(1.10) − $1,468 + $4,800(0.65) = $5,698.9 > $4,319.2

Keep the defender for two years, which happens to be the same as the economic service life as calculated before. (In general, you should not expect this to happen all the time.)

975


22

(c) Marginal analysis: • From n = 1 to n = 2: $4,719(1.10) − $3,679 + $3,700(0.65) = $3,916.9 < $4,319.2

• From n = 2 to n = 3: $3,679(1.10) − $1,468 + $4,800(0.65) = $5,698.9 > $4,319.2

Keep the defender for two years, which happens to be the same as the economic service life as calculated before. (In general, you should not expect this to happen all the time.) 14.32 (a) Economic service life = 6 years with MARR of 15%

Page | 22


23

Tax Rat e MARR ol di ng Per i od 0 1 2 3 4 5 6

40% 15%

1 $2, 000 $2, 000 $2, 000 $2, 000 $2, 000 $2, 000 0.2

2

$1, 600 $3, 200 $3, 200 $3, 200 $3, 200 0.32

I nvest men $10, 000 Book val u $10, 000 Permi t t ed Annual Depr eci ati on Amount s over t he Hol di ng Per i od 3 4 5 6 7 8

$960 $1, 920 $1, 920 $1, 920

$576 $1, 152 $1, 152

$576 $1, 152

0.192

0.1152

0.1152

$576 0.0576

Annual O&M Cost s over t he Hol di ng Per i od ol di ng Per i od 0 1 2 3 4 5 6

ol di ng Per i od 0 1 2 3 4 5 6

1

2

3

4

5

Tot al Book epr eci at i o Val ue $10, 000 $2, 000 $8, 000 $3, 600 $6, 400 $6, 160 $3, 840 $7, 696 $2, 304 $8, 848 $1, 152 $10, 000 $0

6

7

8

Tot al PW Total PWo of A/T O&M Cost s O&M Cost s

` $1, 500 $1, 500 $1, 500 $1, 500 $1, 500 $1, 500 Expect ed Mar ket Val ue $5, 300 $3, 900 $2, 800 $1, 800 $1, 400 $600

$2, 100 $2, 100 $2, 100 $2, 100 $2, 100

Taxabl e Gai ns

$2, 700 $2, 700 $2, 700 $2, 700

Gai ns Tax

($2,700) ($1, 080) ($2,500) ($1, 000) ( $1, 040) ( $416) ( $504) ( $202) $248 $99 $600 $240

$3, 400 $3, 400 $3, 400

$4, 200 $4, 200

$1, 304 $2, 892 $4, 668 $6, 612 $8, 700 $10, 818

$4, 900

$783 $1, 735 $2, 801 $3, 967 $5, 220 $6, 491

Net A/ T A/ T Oper at i ng Cost s ( i n PW) Tot al Mar ket over t he Hol di ng Per i od OC( 15%) CR( 15%) AEC( 15%) Val ue O&M Cost s ax Shi el Tot al OC $6, 380 $4, 900 $3, 216 $2, 002 $1, 301 $360

$783 $1, 735 $2, 801 $3, 967 $5, 220 $6, 491

$696 $1, 180 $1, 916 $2, 300 $2, 547 $2, 761

$87 $556 $885 $1, 667 $2, 673 $3, 730

$100 $342 $387 $584 $797 $986

$5, 120 $5, 220 $3, 872 $4, 214 $3, 454 $3, 841 $3, 102 $3, 686 $2, 790 $3, 588 $2, 601 $3,587

Page | 23


24

(b) Economic service life = 5 years with MARR of 10%

Tax Rate

40%

Investment

$10,000

MARR

10%

Book value

$10,000

Permitted Annual Depreciation Amounts over the Holding Period

Holding Period 1

2

3

4

Total 5

6

7

8

Depreciation

Value $10,000

$2,000

$8,000

$3,600

$6,400

$6,160

$3,840

$7,696

$2,304

$8,848

$1,152

$10,000

$0

0 1

$2,000

2

$2,000

$1,600

3

$2,000

$3,200

$960

4

$2,000

$3,200

$1,920

$576

5

$2,000

$3,200

$1,920

$1,152

$576

6

$2,000

$3,200

$1,920

$1,152

$1,152

$576

Annual O&M Costs over the Holding Period

Total PW

Holding Period

Total PW of 1

2

3

4

5

Book

6

7

8

of A/T

O&M Costs O&M Costs

`

0 1

$1,500

2

$1,500

$2,100

3

$1,500

$2,100

$2,700

4

$1,500

$2,100

$2,700

$3,400

5

$1,500

$2,100

$2,700

$3,400

$4,200

6

$1,500

$2,100

$2,700

$3,400

$4,200

Expected

$4,900

Net A/T

A/T Operating Costs (in PW) over the Holding Period

Holding

Market

Taxable

Gains

Market

Period

Value

Gains

Tax

Value

O&M Costs Tax Shield

$1,364

$818

$3,099

$1,860

$5,128

$3,077

$7,450

$4,470

$10,058

$6,035

$12,824

$7,694 Total

OC(10%)

CR(10%)

AEC(10%)

Total OC

0 1

$5,300

($2,700)

($1,080)

$6,380

$818

$727

$91

$100

$4,620

$4,720

2

$3,900

($2,500)

($1,000)

$4,900

$1,860

$1,256

$603

$348

$3,429

$3,776

3 4

$2,800

($416) ($202)

$3,216 $2,002

$3,077

$2,074

$1,003

$403

$3,050

$3,453

$1,800

($1,040) ($504)

$4,470

$2,520

$1,950

$615

$2,723

$3,339

5

$1,400

$248

$99

$1,301

$6,035

$2,820

$3,215

$848

$2,425

$3,273

6

$600

$600

$240

$360

$7,694

$3,093

$4,601

$1,056

$2,249

$3,306

Page | 24


25

14.33 (a) At i = 12%, the economic service life = 8 years: Tax Rate MARR

40% 12%

Holding Period 0 1 2 3 4 5 6 7 8 9 10

1

Investment $30,000 Book value $30,000 Permitted Annual Depreciation Amounts over the Holding Period 3 4 5 6 7

2

$3,000 $3,000 $3,000 $3,000 $3,000 $3,000 $3,000 $3,000 $3,000 $3,000

$3,000 $3,000 $3,000 $3,000 $3,000 $3,000 $3,000 $3,000 $3,000

$3,000 $3,000 $3,000 $3,000 $3,000 $3,000 $3,000 $3,000

$3,000 $3,000 $3,000 $3,000 $3,000 $3,000 $3,000

$3,000 $3,000 $3,000 $3,000 $3,000 $3,000

$3,000 $3,000 $3,000 $3,000 $3,000

8

$3,000 $3,000 $3,000 $3,000

$3,000 $3,000 $3,000

9

$3,000 $3,000

10

$3,000

Annual O&M Costs over the Holding Period Holding Period 0 1 2 3 4 5 6 7 8 9 10

Holding Period 0 1 2 3 4 5 6 7 8 9 10

1

2

3

4

5

6

7

Total Depreciation $3,000 $6,000 $9,000 $12,000 $15,000 $18,000 $21,000 $24,000 $27,000 $30,000

Book Value $27,000 $24,000 $21,000 $18,000 $15,000 $12,000 $9,000 $6,000 $3,000 $0

Total PW Total PW of of A/T O&M Costs O&M Costs

8 `

$3,000 $3,000 $3,000 $3,000 $3,000 $3,000 $3,000 $3,000 $3,000 $3,000 Expected Market Value

$20,000 $18,000 $16,000 $14,000 $12,000 $10,000 $8,000 $6,000 $4,000 $2,000

$3,450 $3,450 $3,450 $3,450 $3,450 $3,450 $3,450 $3,450 $3,450

Taxable Gains ($7,000) ($6,000) ($5,000) ($4,000) ($3,000) ($2,000) ($1,000) $0 $1,000 $2,000

$3,968 $3,968 $3,968 $3,968 $3,968 $3,968 $3,968 $3,968

$4,563 $4,563 $4,563 $4,563 $4,563 $4,563 $4,563

Gains Tax

Net A/T Market Value

($2,800) ($2,400) ($2,000) ($1,600) ($1,200) ($800) ($400) $0 $400 $800

$22,800 $20,400 $18,000 $15,600 $13,200 $10,800 $8,400 $6,000 $3,600 $1,200

$5,247 $5,247 $5,247 $5,247 $5,247 $5,247

$6,034 $6,034 $6,034 $6,034 $6,034

$6,939 $6,939 $6,939 $6,939

A/T Operating Costs (in PW) over the Holding Period O&M Costs Tax Shield Total OC $1,607 $3,257 $4,952 $6,692 $8,478 $10,312 $12,196 $14,125 $16,110 $18,149

$1,071 $2,028 $2,882 $3,645 $4,326 $4,934 $5,477 $5,961 $5,961 $5,961

$536 $1,229 $2,070 $3,047 $4,153 $5,379 $6,719 $8,164 $10,149 $12,188

$7,960 $7,960 $7,960

$9,177 $9,177

$10,554

OC(12%)

$600 $727 $862 $1,003 $1,152 $1,308 $1,472 $1,643 $1,905 $2,157

$2,679 $5,429 $8,253 $11,153 $14,130 $17,187 $20,326 $23,541 $26,850 $30,249

$1,607 $3,257 $4,952 $6,692 $8,478 $10,312 $12,196 $14,125 $16,110 $18,149

CR(12%)

Total AEC(12%)

$10,800 $8,128 $7,156 $6,613 $6,244 $5,966 $5,741 $5,551 $5,387 $5,241

$11,400 $8,856 $8,018 $7,616 $7,396 $7,274 $7,213 $7,195 $7,291 $7,398

Page | 25


26

(b) At i = 20%, the economic service life = 10 years Tax Rate MARR Hol di ng Per i od 0 1 2 3 4 5 6 7 8 9 10

40% 20%

1 $3,000 $3,000 $3,000 $3,000 $3,000 $3,000 $3,000 $3,000 $3,000 $3,000

I nvest ment $30, 000 Book val ue $30, 000 Permi t t ed Annual Depreci ati on Amount s over t he Hol di ng Per i od 3 4 5 6 7 8

2

$3,000 $3,000 $3,000 $3,000 $3,000 $3,000 $3,000 $3,000 $3,000

$3,000 $3,000 $3,000 $3,000 $3,000 $3,000 $3,000 $3,000

$3,000 $3,000 $3,000 $3,000 $3,000 $3,000 $3,000

$3,000 $3,000 $3,000 $30 $3,000 $3,000

$3,000 $3,000 $3,000 $3,000 $3,000

$3,000 $3,000 $3,000 $3,000

$3,000 $3,000 $3,000

9

$3,000 $3,000

10

$3,000

Annual O&M Cost s over t he Hol di ng Per i od Hol d i ng Per i od 0 1 2 3 4 5 6 7 8 9 10

Hol di ng Per i od 0 1 2 3 4 5 6 7 8 9 10

1

2

3

4

5

6

7

Tot al epr eci at i o

Book Val ue

$3, 000 $6, 000 $9, 000 $12, 0 00 $15, 0 00 $18, 0 00 $21, 000 $21, 030 $27, 000 $30, 000

$27, 000 $24, 000 $21, 000 $18, 0 00 $15, 0 00 $12, 0 00 $9, 000 $8, 970 $3, 000 $0

Tot al PW Tot al PW o of A/ T O&M Cost s O&M Cost s

8 `

$3, 000 $3, 000 $3, 000 $3, 000 $3, 000 $3, 000 $3, 000 $3, 000 $3, 000 $3, 000 Expect ed Mar ket Val ue $20, 000 $18, 000 $16, 000 $14, 000 $12, 000 $10, 000 $8,000 $6,000 $4,000 $2,000

$3, 450 $3, 450 $3, 450 $3, 450 $3, 450 $3, 450 $3, 450 $3, 450 $3, 450

Taxabl e Gai ns ( $7, 000) ( $6, 000) ( $5, 000) ( $4, 000) ( $3, 000) ( $2, 000) ( $1, 000) ( $2, 970) $1, 000 $2, 000

$3, 968 $3, 968 $3, 968 $3, 968 $3, 968 $3, 968 $3, 968 $3, 968

$4, 563 $4, 563 $4, 563 $4, 563 $4, 563 $4, 563 $4, 563

$5, 247 $5, 247 $5, 247 $5, 247 $5, 247 $5, 247

$6, 034 $6, 034 $6, 034 $6, 034 $6, 034

$6,939 $6,939 $6,939 $6,939

$7, 980 $7, 980 $7, 980

$9, 177 $9, 177 $10, 554

$2, 500 $4, 896 $7, 192 $9, 393 $11, 501 $13, 522 $15, 459 $17, 315 $19, 093 $20, 798

$1, 500 $2, 938 $4, 315 $5, 636 $6, 901 $8, 113 $9, 275 $10, 389 $11, 456 $12, 479

Gai ns Tax

Net A/ T A/ T Oper at i ng Cost s ( i n PW) Mar ket over t he Hol di ng Per i od Val ue O&M Cost s ax Shi el d Tot al OC

OC( 20%)

CR( 20%)

Tot al AEC( 20%)

( $2, 800) ( $2, 400) ( $2, 000) ( $1, 600) ( $1, 200) ( $800) ( $400) ( $1, 188) $400 $800

$22, 800 $1, 500 $20, 400 $2, 938 $18, 000 $4, 315 $15, 600 $5, 636 $13, 200 $6, 901 $10, 800 $8, 113 $8, 400 $9, 275 $7, 188 $10, 389 $3, 600 $11, 456 $1, 200 $12, 479

$600 $723 $849 $977 $1, 107 $1, 240 $1, 373 $1, 632 $1, 642 $1, 776

$13, 200 $10, 364 $9, 297 $8, 683 $8, 258 $7, 934 $7, 672 $7, 383 $7, 269 $7, 109

$13, 800 $11, 086 $10, 145 $9, 660 $9, 365 $9, 173 $9, 046 $9, 014 $8, 911 $8, 886

$1, 000 $1, 833 $2, 528 $3, 106 $3, 589 $3, 991 $4, 326 $4, 127 $4, 837 $5, 031

$500 $1, 104 $1, 788 $2, 529 $3, 312 $4, 123 $4, 950 $6, 262 $6, 619 $7, 448

Page | 26


27

(c) At i = 0%, the economic service life = 5 years:

• Capital recovery cost: gain = Sn − Bn gain tax = tm ( S n − Bn ) net proceeds = (1 − tm ) Sn + tm Bn

= (1 − 0.40)(22, 000 − 2000 n) + 0.40(30, 000 −3, 000 n) I − (1 − tm ) Sn − tm Bn CR = n

= =

4, 800 − 2, 400 n n

4,800 n

− 2,400

• Equivalent annual O&M cost:

( )

A/T O&M = (1 − t m ) ⎡3,000 1.15

⎣⎢

⎤ ⎦⎥

( ) ∑ 1,800 (1.15) =

= 1,800 1.15

n −1

n −1

n

AE O & M

n −1

n =1

n

∑ ( ) n

= 1,800

n =1

1.15

n −1

n

1,800 (1.15 − 1) (1.15n − 1) = = 12,000 n n 1.15 − 1 n

• Depreciation tax credit:

∑ AE =

n n =1

D

(t m × Dn ) n

= 1,200 • Minimum total annual equivalent cost:

Page | 27


28

AE =

=

4,800 n

4,800 n

− 2, 400 + 12, 000 + 12, 000

= 12, 000

1.15n n

−

(1.15 n −1)

(1.15 n −1) n

7, 200 n

n

−1, 200

− 3, 600

− 3, 600

Using Excel with trial and error method, we can get the n = 5 years.

Year 1 2 3 4 5 6 7 8 9 10 11 12 13

AE (i) 3000 735 83.5 -152.98 -212.74

-173.88 -68.54 88.53 290.50 534.67 820.79 1150.25 1525.65

AE

1

2

3

4

5

6

7

8

9

10 11 12 13

Page | 28


14.34 Economic service life With i = 12% and tax rate = 40%: Economic service life = 1 year

Tax Rate MARR Holding Period 0 1 2 3 4 5

Holding Period 0 1 2 3 4 5

Holding Period 0 1 2 3 4 5

40% 12%

1 $3,000 $3,000 $3,000 $3,000 $3,000 0.2

1

Investment $15,000 Book value $15,000 Permitted Annual Depreciation Amounts over the Holding Period 3 4 5 6 7

2

$2,400 $4,800 $4,800 $4,800 0.32

8

$1,440 $2,880 $864 $2,880 $1,728 $864 0.192 0.1152 0.1152 Annual O&M Costs over the Holding Period

2

3

4

5

6

7

8

Total Depreciation

Book Value

$3,000 $5,400 $9,240 $11,544 $13,272

$12,000 $9,600 $5,760 $3,456 $1,728

Total PW of O&M Costs

Total PW of A/T O&M Costs

$2,232 $4,783 $8,556 $12,686 $17,112

$1,339 $2,870 $5,133 $7,612 $10,267

` $2,500 $2,500 $2,500 $2,500 $2,500 Expected Market Value $12,800 $8,100 $5,200 $3,500 $0

$3,200 $3,200 $3,200 $3,200

Taxable Gains $800 ($1,500) ($560) $44 ($1,728)

$5,300 $5,300 $5,300

Gains Tax $320 ($600) ($224) $18 ($691)

$6,500 $6,500 Net A/T Market Value $12,480 $8,700 $5,424 $3,482 $691

$7,800 A/T Operating Costs (in PW) over the Holding Period O&M Costs Tax Shield Total OC $1,339 $2,870 $5,133 $7,612 $10,267

$1,071 $1,837 $3,012 $3,642 $4,057

$268 $1,033 $2,121 $3,970 $6,210

OC(12%)

$300 $611 $883 $1,307 $1,723

CR(12%)

$4,320 $4,772 $4,638 $4,210 $4,052

Total AEC(12%)

$4,620 $5,383 $5,521 $5,517 $5,775

Page | 29


14.35

(a) Challenger Financial Data

n

Depreciation Book value Market value Savings

0

1 $21,435 $150,000 $128,565 $150,000 $30,000

2 $36,735 $91,830

3 $26,235 $65,595

4 $18,735 $46,860

5 $13,395 $33,465

6 $13,380 $20,085

7 $13,395 $6,690

8 $6,690 $0

9-10 $0 $0

$30,000

$30,000

$30,000

$30,000

$30,000

$30,000

$30,000

$30,000

18,000 8,574

18,000 14,694

18,000 10,494

18,000 7,494

18,000 5,358

18,000 5,352

18,000 5,358

18,000 2,676

18,000 0

($150,000) $26,574

$32,694

$28,494

$25,494

$23,358

$23,352

$23,358

$20,676

$18,000

7

8

9-10.

Cash Flow Statement

+(1-0.40)*(Savings) +(.4)*(Depreciation) Investment

(150,000)

Net Cash Flow PW (10%) = $3,889

AE (10%) = $633

(b) Defender Financial Data

n

Depreciation Book value Current market value

0 $72,000

1 $12,000 $60,000

2 $12,000 $48,000

3 $12,000 $36,000

4 $12,000 $24,000

5 $12,000 $12,000

6 $12,000 $0

4,800

4,800

4,800

4,800

4,800

4,800

$4,800

$4,800

$4,800

$4,800

$4,800

$4,800

Cash Flow Statement

+(.4)*(Depreciation) Investment Net Cash Flow PW (10%) = ($7,895)

(28,800) ($28,800)

AE (10%) = ($1,285)

Therefore, buy the callenger.

Page | 30


(c) Defender with a current market value of $ 45,000 Financial Data

n

Depreciation Book value Current market value

0

1 2 3 4 5 6 $12,000 ####### ####### ###### ###### ###### $72,000 $60,000 ####### ####### ###### ###### $0 $45,000

7

8

9-10.

Cash Flow Statement

+(.4)*(Depreciation) Investment

4,800

4,800

4,800 4,800

4,800 4,800

(55,800)

Net Cash Flow

($55,800) $4,800 $4,800 $4,800 $4,800 $4,800 $4,800

PW (10%) = ($34,895)

AE (10%) = ($5,679)

Therefore, buy the challenger.

(d) Challenger with an extended service life of 12 years Financial Data

n

Depreciation Book value Savings

0

1 2 3 4 5 6 7 8 9-12 $21,435 ####### ####### ###### ###### ###### ####### $6,690 $150,000 ######## ####### ####### ###### ###### ###### $6,690 $0 $15,000 ####### ####### ###### ###### ###### ####### ###### ######

Cash Flow Statement

+(.4)*(Depreciation) +(0.60)*(Savings) Investment

(150,000)

Net Cash Flow

######## $17,574 ####### ####### ###### ###### ###### ####### ###### $9,000

PW (10%) = ($45,390)

8,574 14,694 10,494 7,494 9,000 9,000 9,000 9,000

AEC(10%) = $6,662

5,358 5,352 9,000 9,000

5,358 2,676 0 9,000 9,000 9,000

Therefore, do not buy the challenger.

Page | 31


14.36 (a) and (b): (a) Defender (Model A) Original Investment $150,000 0

n

Dep reciatio n Book value Current market value

1 $26,235 $65,601

2 $18,735 $46,866

5 $13,395 $6,696

6 $6,690 $6

10,494

7,494

5,358

5,352

5,358

2,676

$10,494

$7,494

$5,358

$5,352

$5,358

$2,676

AE (10%) =

($1,948)

1 2 3 4 $42,870 $73,470 $52,470 $37,470 $300,000 $257,130 $183,660 $131,190 $93,720 $75,000 $75,000 $75,000 $75,000

5 $26,790 $66,930 $75,000

6 $26,760 $40,170 $75,000

7 $26,790 $13,380 $75,000

8 $13,380 $0 $75,000

$75,000

$75,000

$91,836 $0

3 4 $13,395 $13,380 $33,471 $20,091

Cash Flow Statement

+(.4)*(Depreciation) Investment

(36,734)

Net Cash Flow

($36,734)

PW (10%) =

Decision: Replace Model A with Model B (b) It is rather difficult to predict wh at techn olo gical ad van ces wo uld be made on typical equipment in the future.If the industrial engineer had expected a more efficient lathe to be available in one or two years, he could defer the replacement decision.Since Model A was already placed in s ervice, the amoun t of $ 150,000 expended is a sunk cost, and it should not be considered in future replacement decisions.

($8,483)

(b) Challenger (Model B) 0

n

Depreciation Book value Savings

9

10

Cash Flow Statement

+(.4)*(Depreciation) +(0.60)*(Savings ) Investment

17,148 45,000

29,388 45,000

20,988 45,000

14,988 45,000

10,716 45,000

10,704 45,000

10,716 45,000

5,352 45,000

0 45,000

0 45,000

$62,148

$74,388

$65,988

$59,988

$55,716

$55,704

$55,716

$50,352

$45,000

$45,000

A E (10%) =

$10,266

(300,000)

Net Cash Flow

($300,000)

PW (10%) =

$63,079

Th erefo re, b uy t he ch alle ng er.

Page | 32


14.37 Replacement Analysis (a) Keep th e defender Financial Data

n

Depreciation Book value Current market value O&M cost

-4 $20,000

-3 $2,858 $17,142

-2 $4,898 $12,244

-1 $3,498 $8,746

0 $2,498 $6,248 $6,000

1 $1,786 $4,462

2 $1,784 $2,678

3 $1,786 $892

4 $892 $0

5

6

$2,000

$2,000

$2,000

$2,000

$2,000

$0 $1,500 $2,000

(1,400) 536

(1,400) 535

(1,400) 536

(1,400) 268

(1,400) 0

(1,400) 0

$0

Cash Flow S tatement

(-0.7)*(O&M cost) +(.3)*(Depreciation) Investment Net p roceeds from sale

(6,074) 1,050

Net Cas h Flow PW (10% ) =

$0 ($10,064)

$0

$0

A EC(10% ) =

$2,311

$0

($6,074)

($864)

($865)

($864)

4 $2,623 $6,560 $1,000

5 $1,875 $4,685 $1,000

6 $1,873 $2,812 $1,000

7 $1,875 $937 $1,000

8 $937 ($0) $1,000

($1,132)

($1,400)

($350)

10-11 $0 ($0) $1,000

12

(b) Replace the d efender Financial Data

Depreciation Book value O&M cost

n

$21,000

1 $3,001 $17,999 $1,000

2 $5,143 $12,856 $1,000

3 $3,673 $9,183 $1,000

9 $0 ($0) $1,000

$0 ($0) 1000


14.37 Replacement Analysis (a) Keep th e defender Financial Data

n

Depreciation Book value Current market value O&M cost

-4 $20,000

-3 $2,858 $17,142

-2 $4,898 $12,244

-1 $3,498 $8,746

0 $2,498 $6,248 $6,000

1 $1,786 $4,462

2 $1,784 $2,678

3 $1,786 $892

4 $892 $0

5

6

$2,000

$2,000

$2,000

$2,000

$2,000

$0 $1,500 $2,000

(1,400) 536

(1,400) 535

(1,400) 536

(1,400) 268

(1,400) 0

(1,400) 0

$0


(-0.7)*(O&M cost) +(.3)*(Depreciation) Investment Net p roceeds from sale

(6,074) 1,050

Net Cas h Flow

$0

PW (10% ) =

($10,064)

$0

$0

A EC(10% ) =

$2,311

$0

($6,074)

($864)

($865)

($864)

($1,132)

($1,400)

($350)

12

(b) Replace the d efender Financial Data

n


$21,000

1 $3,001 $17,999 $1,000

2 $5,143 $12,856 $1,000

3 $3,673 $9,183 $1,000

4 $2,623 $6,560 $1,000

5 $1,875 $4,685 $1,000

6 $1,873 $2,812 $1,000

7 $1,875 $937 $1,000

8 $937 ($0) $1,000

9 $0 ($0) $1,000

10-11 $0 ($0) $1,000

900 (700)

1,543 (700)

1,102 (700)

787 (700)

563 (700)

562 (700)

563 (700)

281 (700)

0 (700)

0 (700)

$0 ($0) 1000


+(.3)*(Depreciation) (-0.7)*(O&M cost) Investment Net p roceeds from sale

0 (700)

(21,000) 350

Net Cas h Flow

($21,000)

PW (10% ) =

($21,113)

$200

$843

$402

A EC(10% ) =

$3,099

$87

($137)

($138)

($137)

($419)

($700)

($700)

($350)

Page | 33


14.38 (a) and (b): Replace defender now Option 1 : Keep the defender n

Depreciation Book value Expected Market value O&M cost Cash Flow Statement (-0.6)*(O&M cost) +(.4)*(Depreciation) Investment Net proceeds from sale

0

$4,000

1

2

3

$0 $0 $3,000 $3,000

$0 $0 $2,000 $4,500

$0 $0 $1,000 $6,000

(1,800) 0

(2,700) 0

(3,600) 0

(2,400) 600


14.38 (a) and (b): Replace defender now Option 1 : Keep the defender n

Depreciation Book value Expected Market value O&M cost

1

$4,000

Cash Flow Statement (-0.6)*(O&M cost) +(.4)*(Depreciation) Investment Net proceeds from sale

2

3

$0 $0 $3,000 $3,000

$0 $0 $2,000 $4,500

$0 $0 $1,000 $6,000

(1,800) 0

(2,700) 0

(3,600) 0

(2,400) 600

Net Cash Flow PW (12%) =

0

($2,400) ($8,295)

($1,800)

($2,700)

($3,000)

AEC(12%) =

$3,454

1 $2,000 $4,000 $2,000

2 $2,667 $1,333 $3,000

3 $444 $889 $4,000

800 (1,200)

1,067 (1,800)

178 (2,400)

Option 2 : Replace the defender n


0 $6,000

Cash Flow Statement +(.4)*(Depreciation) (0.6)*(O&M cost) Investment Net proceeds from sale

(6,000) 1,556


($6,000) ($7,416)

($400)

AEC(12%) =

($733)

($667)

$3,088

Page | 34


14.39 (a), (b), and (c): Option 1 : Keep the defender Financial Data

n


0

1

$4,000 $0

$800 $3,200 $0 $0

2 $800 $2,400 $0 $0

3 $800 $1,600 $0 $0

4 $800 $800 $0 $0

5 $800 $0 $0 $0

0 320

0 320

0 320

0 320

0 320

$320

$320

$320

$320

$320

AEC(10%) =

$102

1 $1,429 $8,571 $0 $3,000

2 $2,449 $6,122 $0 $3,000

3 $1,749 $4,373 $0 $3,000

4 $1,249 $3,124 $0 $3,000

5 $446 $2,678 $0 $3,000

572 1,800

980 1,800

700 1,800

500 1,800

178 1,800

Cash Flow Statement

(-0.6)*(O&M cost) +(.4)*(Depreciation) Investment Net proceeds from sale

(1,600)

Net Cash Flow

($1,600) PW (10%) =

($387)

Option 2 : Replace the defender Financial Data

n

Depreciation Book value Expected Market value Savings in O&M cost

0 $10,000 $0

Cash Flow Statement

+(.4)*(Depreciation) (0.6)*(Savings in O&M cost) Investment Net proceeds from sale

(10,000) 1,071

Net Cash Flow

($10,000) PW (10%) =

Incremental cash flow

($205)

$2,372

$2,780

AEC(10%) =

$54

($8,400) $2,052 IRR= 10.82% Replace the defender now.

$2,460

$2,500

$2,300

$3,049

$2,180

$1,980

$2,729

Page | 35


14.40 (a) Replacement analysis Option 1 : Keep the defender Financial Data

n


0

1

2

3

4

5

$0 $1,000

$0 $0 $0 $7,000

$0 $0 $0 $7,000

$0 $0 $0 $7,000

$0 $0 $0 $7,000

$0 $0 $0 $7,000

($4,200) $0

($4,200) $0

($4,200) $0

($4,200) $0

($4,200) $0

($4,200)

($4,200)

($4,200)

($4,200)

($4,200)

2 $2,939 $7,346 $5,000 $1,500

3 $2,099 $5,248 $5,000 $1,500

4 $1,499 $3,749 $5,000 $1,500

5 $535 $3,214 $5,000 $1,500

1,176 (3,000) 900

840 (3,000) 900

600 (3,000) 900

214 (3,000) 900

Cash Flow Statement

(-0.6)*(O&M cost) +(.4)*(Depreciation) Investment Net proceeds from sale

($600)

Net Cash Flow

($600)

PW (12%) =

($15,740)

AEC(12%) =

$4,366

Option 2 : Replace the defender Financial Data

0

n

Depreciation Book value O&M cost Increased Revenue

$12,000

1 $1,715 $10,285 $5,000 $1,500

Cash Flow Statement

+(.4)*(Depreciation) -(0.6)*(O&M cost) (0.6)*(Revenue) Investment Net proceeds from sale

686 (3,000) 900 (12,000)

2,485

Net Cash Flow

($12,000)

PW (12%) = Incremental cash flow

($15,510)

($1,414) AEC(12%) =

($924)

($1,260)

($1,500)

$2,940

$2,700

$600

$4,303

($11,400) $2,786 $3,276 IRR= 12.76% > 12% Replace the defender.

$4,800

(b) Break-even market value: Let X denote the current market value of the old machine. Then, the opportunity cost for not replacing the old machine now is given by X − 0.4 X = 0.6 X PW (12%) defender = −0.6 X − $4,200( P / A,12%,5)

= −0.6 X − $15,140 This present value must be the same as the present value of the challenger.

Page | 36


−0.6 X − $15,140 = −$15,510 X = $616.67 14.41 Replacement analysis: Let X denote the current market value of the old callswitching system: AE (10%) defender = −$20,000(0.60) − 0.60 X ( A / P,10%,5)

= −$12,000 − (0.6 X )(0.2638) = −$12,000 − 0.158 X AE (10%) challenger = −$152,409( A / P,10%,10) = −$24,804 To justify the new call-switching system now, we must have AE (14%) defender < AE (14%) challenger

−$12,000 − 0.158 X < −$24,804 X > $81,038 • Challenger: Financial Data

n

Depreciation Book value Salvage value O&M cost

0 $200,000

1 $40,000 $160,000

2 $64,000 $96,000

3 $38,400 $57,600

4 $23,040 $34,560

5 $23,040 $11,520

$5,000

$5,000

$5,000

$5,000

$5,000

(3,000) 16,000

(3,000) 25,600

(3,000) 15,360

(3,000) 9,216

(3,000) 9,216

$6,2 16

$6,2 16

Cash Flow Statement

-(0.6)*(O&M cost) +(.4)*(Depreciation) Investment Net p rocee ds fr om sal e

(200,000)

Net C ash F low

Financial Data

($20 0,00 0)

n

Depreciation Book value Salvage value O&M cost Cash Flow Statement -(0.6)*(Savings in O&M cost) +(.4)*(Depreciation) Investment Net p rocee ds fr om sa le Net C ash F low PW (10%) = A EC(1 0% ) =

$13 ,000

6 $11,520 $0

$22, 600

7

$12, 360

8

9

10

$0 $0

$0 $0

$0 $0

$0 $0

$5,000

$5,000

$5,000

$5,000

$5,000

(3,000) 4,608

(3,000) 0

(3,000) 0

(3,000) 0

(3,000) 0 10,8 00

$1,6 08

($3, 000)

($3,0 00)

($3, 000)

$7,8 00

($152,409) $ 24 ,8 04

Page | 37


14.42Defender analysis (a) and (b): Keep the defender for three years. 

Defender: Tax Rate MARR

35% 18%

Holding Period 0 1 2 3

1 $4,000 $4,000 $4,000

Investment $12,725 Book valu $15,000 Permitted Annual Depreciation Amounts over the Holding Period 3 4 5 6 7

2

$4,000 $4,000

8

Total Depreciation $4,000 $8,000 $12,000

$4,000

Annual O&M Costs over the Holding Period Holding Period 0 1 2 3

$4,500 $4,500 $4,500

Holding Period 0 1 2 3

Expected Market Value $11,500 $5,200 $3,500 $1,200

1

2

3

4

5

6

7

8

Total PW of O&M Costs

Book Value $15,000 $11,000 $7,000 $3,000 Total PW of A/T O&M Costs

` $5,300 $5,300

$3,814 $7,620 $11,333

$6,100

Net A/T A/T Operating Costs (in PW) Market over the Holding Period Value O&M Costs ax Shiel Total OC $12,725 ($5,800) ($2,030) $7,230 $2,479 $1,186 $1,292 ($3,500) ($1,225) $4,725 $4,953 $2,192 $2,761 ($1,800) ($630) $1,830 $7,366 $3,044 $4,322

Taxable Gains

Gains Tax

OC(18%)

CR(18%)

$1,525 $1,764 $1,988

$2,479 $4,953 $7,366 Total AEC(18%)

$7,786 $5,960 $5,340

$9,311 $7,724 $7,328

Page | 38




Challenger: * Challenger analysis : Financial Data

n


0 $43,500

1 $6,216 $37,284

2 $10,653 $26,631

$1,500

$1,500

3 $7,608 $19,023

4 $5,433 $13,589

5 $3,885 $9,705

$1,500

$1,500

$1,500

Cash Flow Statement

-(0.65)*(O&M cost) +(.35)*(Depreciation) Investment Net proceed s from sa le

(975) 2,176

Depreciation Book value Salvage value O&M cost Cash Flow Statement

(975) 2,663

(975) 1,902

(975) 1,360

$927

$385

(43,500)

Net Cash Flow

Financial Data

(975) 3,729

($43,500)

n

$1,201

$2,754

6 $3,880 $5,825

7 $3,885 $1,940

$1,500

$1,500

$1,688

8

9 $1,940 ($0) $1,500

10 $0 ($0)

$1,500

$0 ($0) $1,500




Challenger: * Challenger analysis : Financial Data

n

0


$43,500

1 $6,216 $37,284

2 $10,653 $26,631

$1,500

$1,500

3 $7,608 $19,023

4 $5,433 $13,589

5 $3,885 $9,705

$1,500

$1,500

$1,500

Cash Flow Statement


(975) 2,176

(975) 3,729

(975) 2,663

(975) 1,902

(975) 1,360

$927

$385

(43,500)

Net Cash Flow

($43,500)

Financial Data

n


$1,201

$2,754

6 $3,880 $5,825

7 $3,885 $1,940

$1,500

$1,500

$1,688

8

9

10

$1,940 ($0) $1,500

$0 ($0)

$0 ($0)

$1,500

$1,500

Cash Flow Statement


(975) 1,358

(975) 1,360

(975) 679

(975) 0

(975) 0 2,275

Net Cash Flow

$0 PW (18%) = A EC(18% ) =

$383

$385

($296)

($975)

$1,300

($38,619) $8,593

Page | 39


14.43Decision: Do not replace the defender now. (a) Keep the defender 0 Depreciation Book value Current market value O&M cost

$50,000 $60,000

Cash Flow Statement (-0.6)*(O &M cos t) +(.4)*(Depreciation) Opportunity cost Net p roceeds from sale Net Cash F low

2 $5,000 $40,000

3 $5,000 $35,000

4 $5,000 $30,000

5 $5,000 $25,000

6 $5,000 $20,000

7 $5,000 $15,000

8 $5,000 $10,000

9 $5,000 $5,000

10 $5,000 $0

$18,000

$18,000

$18,000

$18,000

$18,000

$18,000

$18,000

$18,000

$18,000

$18,000

($10,800) $2,000

($10,800) $2,000

($10,800) $2,000

($10,800) $2,000

($10,800) $2,000

($10,800) $2,000

($10,800) $2,000

($10,800) $2,000

($10,800) $2,000

($10,800) $2,000

($8,800)

($8,800)

($8,800)

($8,800)

($8,800)

($8,800)

($8,800)

($8,800)

($8,800)

($8,800)

4 $24,980 $62,480 $4,000

5 $17,860 $44,620 $4,000

6 $17,840 $26,780 $4,000

7 $17,860 $ 8,920 $4,000

8 $8,920 $0 $4,000

($56,000) ($56,000)

P W (10%) =

1 $5,000 $45,000

($110,072)

AEC(10%) =

$17,914

2 $48,980 $122,440 $4,000

3 $34,980 $87,460 $4,000

(b) Replace the defender 0 Depreciation Book value O&M cost

$200,000

1 $28,580 $171,420 $4,000

9 $0 $0 $4,000

10 $0 $0 $4,000


14.43Decision: Do not replace the defender now. (a) Keep the defender 0 Depreciation Book value Current market value O&M cost

$50,000 $60,000

Cash Flow Statement (-0.6)*(O &M cos t) +(.4)*(Depreciation) Opportunity cost Net p roceeds from sale Net Cash F low

2 $5,000 $40,000

3 $5,000 $35,000

4 $5,000 $30,000

5 $5,000 $25,000

6 $5,000 $20,000

7 $5,000 $15,000

8 $5,000 $10,000

9 $5,000 $5,000

10 $5,000 $0

$18,000

$18,000

$18,000

$18,000

$18,000

$18,000

$18,000

$18,000

$18,000

$18,000

($10,800) $2,000

($10,800) $2,000

($10,800) $2,000

($10,800) $2,000

($10,800) $2,000

($10,800) $2,000

($10,800) $2,000

($10,800) $2,000

($10,800) $2,000

($10,800) $2,000

($8,800)

($8,800)

($8,800)

($8,800)

($8,800)

($8,800)

($8,800)

($8,800)

($8,800)

($8,800)

($56,000) ($56,000)

P W (10%) =

1 $5,000 $45,000

($110,072)

AEC(10%) =

$17,914

2 $48,980 $122,440 $4,000

3 $34,980 $87,460 $4,000

4 $24,980 $62,480 $4,000

5 $17,860 $44,620 $4,000

6 $17,840 $26,780 $4,000

7 $17,860 $ 8,920 $4,000

8 $8,920 $0 $4,000

$0 $0 $4,000

$0 $0 $4,000

$13,992 ($2,400)

$9,992 ($2,400)

$7,144 ($2,400)

$7,136 ($2,400)

$7,144 ($2,400)

$3,568 ($2,400)

$0 ($2,400)

$0 ($2,400)

(b) Replace the defender 0 Depreciation Book value O&M cost

$200,000

Cash Flow Statement +(.4)*(Depreciation) (-0.6)*(O&M cost ) Investment Net p roceeds from sale Net Cash F low

$11,432 ($2,400)

$19,592 ($2,400)

9

10

($200,000) $12,000 ($200,000)

P W (10%) =

1 $28,580 $171,420 $4,000

($152,404)

$9,032

$17,192

$11,592

AEC(10%) =

$7,592

$4,744

$4,736

$4,744

$1,168

($2,400)

$9,600

$24,803

Page | 40


14.44 Decision: Do not replace the defender now.

Keep the defender Financial Data

Depreciation Book value Market value Operation Cost

n

0 $0 $8,500

1 $0 $0

2 $0 $0

3 $0 $0

4 $0 $0

5 $0 $0

$8,700

$8,700

$8,700

$8,700

$8,700

0

0

0

0

0

Cash Flow Statement

+(.35)*(Depreciation) O i

(5 525)


14.44 Decision: Do not replace the defender now.

Keep the defender Financial Data

n


0 $0 $8,500

1 $0 $0

2 $0 $0

3 $0 $0

4 $0 $0

5 $0 $0

$8,700

$8,700

$8,700

$8,700

$8,700

0

0

0

0

0

(5,655)

(5,655)

(5,655)

(5,655)

(5,655)

($5,655)

($5,655)

($5,655)

($5,655)

($5,655)

Cash Flow Statement

+(.35)*(Depreciation) Opportunity cost -(1-0.35)*(Operation cost)

(5,525)

Net Cash Flow

($5,525) PW (10%) = ($26,962)

AEC(10%) = $7,112

Replace the defender Financial Data

n


0 $53,500 $53,500

1 $7,645 $45,855

2 $13,102 $32,753

3 $9,357 $23,396

4 $6,682 $16,713

$4,200

$4,700

$5,200

$5,700

5 $2,386 $14,327 $12,000 $6,200

Cash Flow Statement

Investment Net proceeds from sale +(.35)*(Depreciation) -(1-0.35)*(Operation cost)

(53,500)

Net Cash Flow

($53,500) PW (10%) = ($47,323)

2,676 (2,730)

4,586 (3,055)

3,275 ( 3,380)

2,339 (3,705)

12,815 835 ( 4,030)

($54)

$1,531

($105)

($1,366)

$9,620

AEC(10%) = $12,484

Page | 41


14.45

• Defender analysis

* Keep defender: n

Depreciation Book value Market value O&M cost Cash Flow Statement -(0.6)*(O&M cost) +(.40)*(Depreciation) Opportunity cost Net proceeds from sale Net Cash Flow

0 $2,873 $7,185 $2,000

1 2 $2,054 $2,052 $5,131 $3,080 $1,500 $3,800 $3,800

3 $2,054 $1,026

4 $1,026 ($0)

5

6 $0 ($0)

$0 ($0)

$3,800

$3,800

$3,800

$3,800

($2,280) ($2,280) ($2,280) ($2,280) ($2,280) ($2,280) $822 $821 $822 $410 $0 $0 ($4,649) $600 ($4,649) ($1,458) ($1,459) ($1,458) ($1,870) ($2,280) ($1,680)

PW (10%) = ($11,917)

AEC(10%) $2,736

Page | 42


• Challenger analysis 1 $7,145 $42,855 $6,000 $3,000

2 $12,245 $30,610 $6,000 $3,000

3 $8,745 $21,865 $6,000 $3,000

4 $6,245 $15,620 $6,000 $3,000

5 $4,465 $11,155 $6,000 $3,000

6 $4,465 $6,690 $6,000 $3,000

($1,800) $3,600 $2,858

($1,800) $3,600 $4,898

($1,800) $3,600 $3,498

($1,800) $3,600 $2,498

($1,800) $3,600 $1,786

( $1,800) $3,600 $1,786

$4,658

$6,698

$5,298

$4,298

$3,586

$3,586

7 $4,460 $2,230 $6,000 $3,000

8 $2,230 $0 $6,000 $3,000

9

10

11

12

$0 $0 $6,000 $3,000

$0 $0 $6,000 $3,000

$0 $0 $6,000 $3,000

$0 $0 $6,000 $3,000

-(0.6)*(O&M cost) (0.6)*(Savings) +(.4)*(Depreciation) Investment Net proceeds from sale

($1,800) $3,600 $1,784

($1,800) $3,600 $892

($1,800) $3,600 $0

($1,800) $3,600 $0

($1,800) $3,600 $0

( $1,800) $3,600 $0

Net Cash Flow

$3,584

Financial Data

Depreciation Book value Savings O&M cost

0 $50,000

Cash Flow Statement

-(0.6)*(O&M cost) (0.6)*(Savings) +(.4)*(Depreciation) Investment Net proceeds from sale Net Cash Flow

Financial Data

Depreciation Book value Savings O&M cost

($50,000) ($50,000)

Cash Flow Statement

$1,800

PW (10%) = ($22,733) Do not buy the new machine.

$2,692

$1,800

$1,800

$1,800

$3,600

AEC(10%) = $3,336

Page | 43


14.46 Option 1:

n

1 $6,859 $41,141

2 $11,755 $29,386

3 $8,395 $20,990

4 $5,995 $14,995

5 $4,286 $10,709

$27,000

$27,000

$27,000

$27,000

$27,000

(16,200) 2,744

(16,200) 4,702

(16,200) 3,358

(16,200) 2,398

(16,200) 1,715

($13,456)

($11,498)

($12,842)

($13,802)

($14,485)

6 $4,282 $6,427

7 $4,286 $2,141

8 $2,141 $0

$27,000

$27,000

$27,000

$27,000

$0 $0 $5,000 $27,000

-(0.40)*(O&M cost) +(.40)*(Depreciation) Investment Net proceeds from sale

(16,200) 1,713

(16,200) 1,715

(16,200) 856

(16,200) 0

(16,200) 0

Net Cash Flow

($14,487)

Financial Data

Depreciation Book value Current Market value O&M cost

0 $48,000 $6,000

Cash Flow Statement

(-0.60)*(O&M cost) +(.40)*(Depreciation) Opportunity cost Investment Net proceeds from sale

(3,600) (48,000)

Net Cash Flow

($51,600)

n

Financial Data


9

10 $0 $0

Cash Flow Statement

PW (12%) = ($129,093)

3,000 ($14,485)

($15,344)

($16,200)

($13,200)

AEC(12%) = $22,847

Page | 44


Option 2: n


0 $84,000

Cash Flow Statement (-0.60)*(O&M cost) +(.40)*(Depreciation) Investment Net proceeds from sale

1 $12,004 $71,996 $24,000

2 $20,572 $51,425 $24,000

3 $14,692 $36,733 $24,000

4 $10,492 $26,242 $24,000

5 $7,501 $18,740 $24,000

(14,400) 4,801

(14,400) 8,229

(14,400) 5,877

(14,400) 4,197

(14,400) 3,000

($9,599)

($6,171)

($8,523)

($10,203)

($11,400)

6 $7,493 $11,248

7 $7,501 $3,746

8 $3,746 ($0)

$24,000

$24,000

$24,000

$24,000

$0 ($0) $9,000 $24,000

(14,400) 2,997

(14,400) 3,000

(14,400) 1,499

(14,400) 0

(14,400) 0

(84,000)

Net Cash Flow

($84,000)

n

Depreciation Book value Salvage value O&M cost Cash Flow Statement -(0.40)*(O&M cost) +(.40)*(Depreciation) Investment Net proceeds from sale Net Cash Flow PW (12%) = ($140,744) Option 1 is better.

9

10 $0 ($0)

5,400 ($11,403)

($11,400)

($12,901)

($14,400)

($9,000)

AEC(12%) = $24,910

Page | 45


14.47 The remaining useful life of the defender is 1 year. Its annual equivalent cost is $1,666. When the defender is replaced now by the challenger, its equivalent annual cost is $2,191, indicating that the defender should be kept for now. (a) Economic service life = one year Tax Rat e MARR

30% 12%

Hol di ng Per i od 0 1 2 3 4 5

1

I nvest ment $1, 050 Book val ue $0 Permi t t ed Annual Depreci at i on Amount s over t he Hol di ng Per i od 3 4 5 6 7

2

Tot al epr eci at i o

8

$0 $0 $0 $0 $0 Annual O&M Cost s over t he Hol di ng Per i od



Book Val ue

1

2

3

4

5

6

7

8

$0 $0 $0 $0 $0

Tot al PW of O&M Cost s

Tot al PW of A/ T O&M Cost s

$1, 696 $3, 530 $5, 452 $7, 422 $9, 351

$1, 188 $2, 471 $3, 816 $5, 195 $6, 546

` $1, 900 $1, 900 $1, 900 $1, 900 $1, 900 Expect ed Mar ket Val ue $1, 200 $1, 000 $500 $0 $0

$2, 300 $2, 300 $2, 300 $2, 300

Taxabl e Gai ns $1, 200 $1, 000 $500 $0 $0

$2, 700 $2, 700 $2, 700

$3, 100 $3, 100 Net A/ T Mar ket Val ue

Gai ns Tax $360 $300 $150 $0 $0

$840 $700 $350 $0 $0

$3, 400 A/ T Oper at i ng Cost s ( i n PW) over t he Hol di ng Per i od O&M Cost s ax Shi el d Tot al OC $1, 188 $2, 471 $3, 816 $5, 195 $6, 546

$0 $0 $0 $0 $0

OC( 12%)

$1, 188 $2, 471 $3, 816 $5, 195 $6, 546

Tot al AEC( 12%)

CR( 12%)

$1, 330 $1, 462 $1, 589 $1, 710 $1, 816

$336 $291 $333 $346 $291

$1, 666 $1, 753 $1, 922 $2, 056 $2, 107

(b) Replace the defender Financial Data

n

Depreciation Book value Salvage value Operation Cost

0 $6,000

1 $1,200 $4,800

2 $1,920 $2,880

3 $1,152 $1,728

4 $691 $1,037

$1,100

$1,300

$1,500

$1,700

5 $346 $691 $1,000 $1,800

360 (770)

576 (910)

346 (1,050)

207 (1,190)

907 104 (1,260)

($410)

($334)

($704)

($983)

($249)

AEC(12%) =

$2,191

Cash Flow Statement

Investment Net proceeds from sale +(.30)*(Depreciation) -(1-0.30)*(Operation cost)

(6,000)

Net Cash Flow

($6,000) PW (12%) =

($7,899)

Page | 46


14.48 Option 1 : Keep the defender n

Depreciation Book value Market value Operating cost Cash Flow Statement +(.3)*(Depreciation) -(1-0.30)*(Operating cost) Opportunity cost Net proceeds from sale

0 $5,120 $7,680 $12,000

1 $3,072 $4,608

2 $1,843 $2,765

3 $1,843 $922

4 $922 $0

5

6

$4,000

$4,000

$4,000

$4,000

$4,000

$0 $0 $2,000 $4,000

$922 ($2,800)

$553 ($2,800)

$553 ($2,800)

$276 ($2,800)

$0 ($2,800)

$0 ($2,800)

$0 $0

($11,472) $1,400

Net Cash Flow

($11,472)

PW (11%) = ($20,703)

($1,878) AEC(11%) =

($2,247)

($2,247)

($2,524)

($2,800)

($1,400)

$4,894

Option 2 : Replace the defender n

Depreciation (First Cycle) Book value (First Cycle) Depreciation (Second Cycle) Book value (Second Cycle) Salvage value Operating cost Cash Flow Statement +(.3)*(Depreciation) -(1-0.30)*(Operating cost) Investment Net proceeds from sale Net Cash Flow PW (11%) = ($15,583)

0 $10,000

1 $2,000 $8,000

2 $3,200 $4,800

$2,000

$2,000

$600 ($1,400)

$960 ($1,400)

($10,000)

($10,000)

($800) AEC(11%) =

($440)

3

4

5

6

$2,000 $8,000

$3,200 $4,800

$2,000

$2,000

$960 $3,840 $4,000 $2,000

$288 ($1,400) ($10,000) $3,952

$600 ($1,400)

$960 ($1,400)

$288 ($1,400)

($7,160)

($800)

$960 $3,840 $10,000 $4,000 $2,000

$3,952 ($440)

$2,840

$3,683

∴ Decision:

Replace the defender now with the current challenger. Then, replace the current challenger at the end of 3 years with a similar challenger.

Page | 47


Short Case Studies ST 14.1 (a) The following assumptions were made: (1) Depreciable life for the challenger = 12 years (2) the challenger will be obsolete after 10 years with zero salvage value. (3) Kazakhstan’s tax rate = 40%. (5) No market value for a leaky oil system (defender). With these assumptions, the defender wins. Do not replace the defender. Option 1 : Upgrade the defender Financial Data

0

n

Depreciation Book value Market value Operating cost

$104,000

1 $10,400 $93,600

2 $10,400 $83,200

3 $10,400 $72,800

4 $10,400 $62,400

5-9 $10,400 $52,000

10 $10,400 $0

$41,000

$41,000

$41,000

$41,000

$41,000

$41,000

4,160

4,160

4,160

4,160

4,160

4,160

(24,600)

(24,600)

(24,600)

(24,600)

(24,600)

(24,600)

($20,440)

($20,440)

($20,440)

($20,440)

($20,440) ($20,440)

AE (20%) =

($45,246)

1 $27,083 $297,917

2 $27,083 $270,833

3 $27,083 $243,750

4 $27,083 $216,667

5-9 $27,083 $189,583

$12,000

$12,000

$12,000

$12,000

$12,000

10 $27,083 $54,167 $0 $12,000

Cash Flow Statement

+(.4)*(Depreciation) Opportunity cost Net proceeds from sale

(104,000)

Net Cash Flow

($104,000)

PW (20%) = ($189,694) Option 2 : Replace the defender Financial Data

n

Depreciation Book value Salvage value Operating cost

0 $325,000

Cash Flow Statement

Investment Net proceeds from sale +(.4)*(Depreciation) -(1-0.40)*(Operating cost) Net Cash Flow

(325,000)

($325,000) PW (20%) =

10,833 (7,200)

10,833 (7,200)

10,833 (7,200)

10,833 (7,200)

10,833 (7,200)

21,667 10,833 (7,200)

$3,633

$3,633

$3,633

$3,633

$3,633

$25,300

($306,268)

AE (20%) =

($73,052)

(b) If environmental impact is taken into account, it might be better to install the new facility. It is also quite possible that the government of Kazakhstan would impose some huge fines upon discovering the environmental damage caused by the defending facility. Such issues need to be addressed before making any final decision. Page | 48


ST 14.2 (a) The current FMS manufacturing technology would prevail for several years with no major cost and productivity improvement. Therefore, if the present system is kept for the remaining useful life, it will be replaced by the current FMS technology with the same investment and O&M costs. (b) Decision: The challenger should be adopted. Option1: Keep the defender 0

n

Operating cost Current market value

2 3 4 $115,000 $125,000 $135,000

5 $145,000

$140,000

Cash Flow Statement -(.6)*(O&M) Opportunity cost

($84,000)

Net Cash Flow

($84,000)

PW (15%) =

1 $105,000

($63,000) ($69,0 00) ($75,0 00) ($81,0 00) ($87,0 00)

($329,837)

($63,000)

($69,000) ($75,0 00) ($81,000) ($87,0 00)

AEC(15%) =

$98,395

1 $185,770 $1,114,230 $664,243 $45,0 00

2 3 4 $318,3 70 $227,3 70 $162,370 $795,860 $568,490 $406,120 $664,243 $664,243 $664,243 $47,000 $49,000 $51,000


Depreciation Book value Savings Operating cost

$1,300,000

Cash Flow Statement +(.4)*(Depreciation) +(0.60)*(Savings) -(.6)*(O&M) Investment Net proceeds


0

$74,3 08 $127,348 $90,948 $64,948 $46,4 36 $46,384 $46,436 $23,192 $398,546 $398,546 $398,546 $398,546 $398,5 46 $398,546 $398,546 $398,546 $398,5 46 $398,5 46 ($27,000) ($28,200) ($29,4 00) ($30,600) ($31,800) ($33,000) ($34,2 00) ($35,400) ($36,6 00) ($37,800) ($1,300,000) ($1,3 00,0 00)

$888,146

5 6 7 8 9 10 $116,0 90 $115,9 60 $116,090 $57,9 80 $290,030 $174,070 $57,9 80 $664,2 43 $664,2 43 $664,243 $664,243 $664,243 $664,243 $53,0 00 $55,0 00 $57,000 $59,000 $61,0 00 $63,0 00

$445,854

$497,694 $460,094 $432,8 94

$72,000 $413,182

$411,930 $410,782 $386,3 38 $361,946 $432,746

AEC(15%) = ($176,965)

Page | 49


ST 14.3 (a) Decision: Replace the defender now. (b) The optimal time to replace the defender is “now.” If the AE cost for the defender were smaller than that of the challenger, we would need to perform the marginal analysis, i.e., calculating the incremental cost of operating the defender for just 1 more year. Option1: Keep the defender 1 $65,000 $2,500

2 $65,000 $2,875

Cash Flow Statement -(.6)*(O&M) Opportunity cost

($40,5 00)

($40,725) ($40,9 84) ($41,281) ($41,624)

Net Cash Flow

($40,5 00)

($40,725) ($40,9 84) ($41,281) ($41,624)

n

0

Operating cost Maintenance

PW (16%) =

($134,052)

3 $65,000 $3,306

4 $65,000 $3,802

5 $65,000 $4,373

AEC(16%) =

$40,941

1 $1,160 $46,040 $18,777 $112,623 $57,895 $35,000

2 $1,210 $44,830 $32,180 $80,443 $57,895 $35,000

$7,975 $34,737 ($21,000)

$13,356 $9,677 $7,049 $5,178 $34,737 $34,737 $34,737 $34,737 ($21,000) ($21,0 00) ($21,000) ($21,000)


Depreciation(Building) Book value (Building) Depreciation(Equipment) Book value (Equipment) Savings O&M cost Cash Flow Statement +(.4)*(Depreciation) +(0.60)*(Savings) -(.6)*(O&M) Investment Net proceeds


0 $47,2 00 $131,400

4 $1,210 $42,410 $16,412 $41,049 $57,895 $35,000

5 $1,210 $41,200 $11,734 $29,315 $57,895 $35,000

6 $1,210 $39,990 $11,721 $17,594 $57,895 $35,000

7 $1,210 $38,780 $11,734 $5,860 $57,895 $35,000

8 $1,210 $37,570 $5,860

9 $1,210 $36,360

10 $1,160 $35,2 00

$57,895 $35,000

$57,895 $35,000

$57,895 $35,000

$5,172 $5,178 $2,828 $484 $464 $34,737 $34,737 $34,737 $34,737 $34,737 ($21,000) ($21,0 00) ($21,000) ($21,0 00) ($21,000)

($178,600) ($178,600)

($72,819)

3 $1,210 $43,620 $22,982 $57,461 $57,895 $35,000

$21,712

$27,093

AEC(16%) =

$15,066

$23,414

$21,964 $20,786

$18,915

$18,909

$18,915

$16,565

$14,221

$36,165

Page | 50


ST 14.4 (a) Development of a combined productivity index: Combined productivity means “inherent productivity” × relative hours for challenger. Operating hours

n

Ratio Combined productivity index

Defender

Challenger

1

1,800

2,500

1.389

1.667

2

1,800

2,400

1.333

1.600

3

1,700

2,300

1.353

1.624

4

1,700

2,100

1.235

1.482

5

1,600

2,000

1.250

1.500

(b)

• Adjusted annual O&M costs for Defender n

Operating HR Maintenance

Wages

Fuel

Total

1

1,800

$46,800

$42,120

$24,408

$113,328

2

1,800

$46,800

$42,120

$24,408

$113,328

3

1,700

$46,800

$39,780

$23,052

$109,632

4

1,700

$46,800

$39,780

$23,052

$109,632

5

1,600

$46,800

$37,440

$21,696

$105,936

• Adjusted annual O&M costs for Challenger Operating n HR

M

L

F

Combined Productivity index

M

Adjusted L

F

Total

1

2,500

$35,000 $58,500 $48,000

1.667

$21,000

$35,100 $28,800 $84,900

2

2,400

$38,400 $56,160 $46,080

1.600

$24,000

$35,100 $28,800 $87,900

3

2,300

$43,700 $53,820 $44,160

1.624

$26,917

$33,150 $27,200 $87,267

4

2,100

$48,300 $49,140 $40,320

1.482

$32,583

$33,150 $27,200 $92,933

5

2,000

$58,000 $46,800 $38,400

1.500

$38,667

$31,200 $25,600 $95,467

Page | 51


(c) Replacement analysis • Defender analysis Market Dep. n value 0 1 2 3 4 5

$75,000 $60,000 $50,000 $30,000 $30,000 $10,000

0 0 0 0 0

O&M Cost

After tax Salvage

Dep. Tax credit

A/T O&M cost

$113,328 $113,328 $109,632 $109,632 $105,936

$36,000 $30,000 $18,000 $18,000 $6,000

0 0 0 0 0

$67,997 $67,997 $65,779 $65,779 $63,562

Equivalent Annual Cost Net Cumulative Net n O&M cost O&M cost Investment Capital cost Operating Total cost 0 1 2 3 4 5

$67,997 $67,997 $65,779 $65,779 $63,562

$59,128 $110,543 $153,794 $191,403 $223,005

$13,696 $22,316 $33,165 $34,708 $42,017

$15,750 $13,726 $14,526 $12,158 $12,534

$67,997 $67,995 $67,362 $67,049 $66,522

$83,747 $81,721 $81,888 $79,207 $79,056

Dep.

O&M Cost

After tax Salvage

Dep. Tax credit

A/T O&M cost

$80,000 $128,000 $76,800 $46,080 $46,080

$84,900 $87,900 $87,267 $92,933 $95,467

$308,000 $220,800 $160,080 $117,648 $78,216

$32,000 $51,200 $30,720 $18,432 $18,432

$50,940 $52,740 $52,360 $55,760 $57,280

• Challenger analysis n

Market value

0 1 2 3 4 5

$400,000 $300,000 $240,000 $190,000 $150,000 $115,000

Equivalent Annual Cost Net Cumulative Net n O&M cost O&M cost Investment Capital cost Operating Total cost 0 1 2 3 4 5

$18,940 $1,540 $21,640 $37,328 $38,848

$16,470 $17,634 $31,863 $53,205 $72,519

$132,174 $233,043 $294,745 $332,734 $361,113

$152,000 $143,345 $129,098 $116,557 $107,720

$18,940 $10,847 $13,956 $18,638 $21,633

$170,940 $154,192 $143,054 $135,195 $129,352

∴ Decision:

The economic service life for the defender is 5 years with AE(15%) = $79,060. On the other hand, the economic service life for the challenger is 5 years with AE(15%) = $129,352. Even though the challenger is a better

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machine in terms of operating efficiency, its initial cost is too high to justify its purchase at this point. (d) Replacement analysis under inflation

• Adjusted operating and maintenance cost by inflation: Sample calculation for fuel cost – Defender for Year 2: Fuel cost before inflation = $24,408 Price index for fuel for year 2 = 120 Fuel cost after inflation = $24,408(1.2) = $29,290 Other inflation-adjusted operating and maintenance cost elements can be calculated in a manner similar to the fuel cost. The following table summarizes these calculations. All cost figures are in actual dollars. Defender n

Maintenance

Wage

Fuel

Total

1

$50,544

$48,438

$26,849

$125,831

2

$54,288

$52,650

$29,290

$136,228

3

$58,032

$51,714

$29,968

$139,714

4

$58,968

$53,703

$32,273

$144,944

5

$59,904

$52,416

$32,544

$144,864

Challenger n

Maintenance

Wage

Fuel

Total

1

$22,680

$40,365

$31,680

$94,725

2

$27,840

$43,875

$34,560

$106,275

3

$33,377

$43,095

$35,360

$111,832

4

$41,055

$44,753

$38,080

$123,888

5

$49,493

$43,680

$38,400

$131,573

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