Sol INDR202_WS6

(1)

INDR 202 – Engineering Economics

Solutions for Problem #6

9.9)

1 2 0 , 0 0 0 3 0 , 0 0 0 9 0 , 0 0 0

( ) $ 1 8 , 0 0 0

5 5

1 .5 ( ) A s s u m i n g 1 5 0 % D B m e t h o d , 0 .3

5

1 $ 1 2 0 , 0 0 0 0 .3 3 6 , 0 0 0 $ 1 2 0 , 0 0 0 3 6 , 0 0 0 8 4 , 0 0 0

2 8 4 , 0 0 0 0 .3 2 5 , 2 0 0 8 4 , 2 0 0 2 5 , 2 0 0 5 8 , 8 0 0

3 5 8 , 8 0 0 0 .3 1 7 , 6 4 0 5 8 , 8 0 0 1 7 , 6

n

n n

I S

a D p e r y e a r

N b

E O Y D B

                

   4 0 4 1, 1 6 0

4 4 1, 1 6 0 0 .3 1 2 , 3 4 8 1 1, 1 6 0 4 1, 1 6 0 1 1, 1 6 0 3 0 , 0 0 0

5 0 3 0 , 0 0 0 0 3 0 , 0 0 0

T o t a l d e p r e c i a t i o n $ 9 0 , 0 0 0



    

 



9.12 DDB switching to SL in year 5:

With switching

n

D

n

B

n

0 $38,000

1 $12,667

$25,333

2 $8,444

$16,889

3 $5,630

$11,259

4 $3,753

$7,506

5 $3,753

$3,753

(2)

9.29)

Given:

Im a c h in e to o l  $ 5, 0 0 0 ,IC N C m a c h in e $ 1 2 5, 0 0 0 , a n d Iw a r e h o u s e  $ 3 3 5, 0 0 0



Machine tool

n

Dep. Rate

D

n

B

n

0 $5,000

1 0.3333

$1,667

$3,333

2 0.4444

$2,222

$1,111

3 0.1481

$741

$370

4 0.0741

$370

$0



CNC machine

n

Dep. Rate

D

n

B

n

0 $125,000

1 0.1429

$17,857

$107,143

2 0.2449

$30,612

$76,531

3 0.1749

$21,866

$54,665

4 0.1249

$15,618

$39,046

5 0.0892

$11,156

$27,890

6 0.0892

$11,156

$16,734

7 0.0892

$11,156

$5,578

8 0.0446

$5,578

$0



Warehouse

N

Dep. Rate

D

n

B

n

0 $335,000

1 0.0139

$4,653

$330,347

2 0.0256

$8,590

$321,757

3 0.0256

$8,590

$313,168

…….

…

..

39 0.0256

$8,590

$3,937

(3)

9.31)

Given: Residential real property (27.5 year),

I

= $150,000

(a)

1

1 0 0 % 2 .5

( $ 1 5 0 , 0 0 0 ) 2 7 .5 1 2

( 0 .0 0 7 5 7 6 ) ( $ 1 5 0 , 0 0 0 ) $ 1, 1 3 6 D   _

 

 

(b)

Total amount of depreciation over the 4-year ownership, assuming that the

asset is sold at the end of the 4

th

_{calendar year:}

n

Dep. Rate

D

n

B

n

0 $150,000

1 0.00757

$1,136

$148,864

2 0.03636

$5,455

$143,409

3 0.03636

$5,455

$137,955

4 0.03485

$5,227

$132,727

Total amount of depreciation allowed = $17,271. Note that the 4

th

_{year depreciation reflects the}

mid-month convention (11.5 months).





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

$ 1 3 2 , 7 2 9

B    

 



9.41)

(4)

Revenues:

Gross income $ 4,250,000 Expenses:

Labor $ 1,550,000

Materials $ 785,000 Depreciation $ 332,500 Office supplies $ 15,000 Interest $ 42,200

Rental $ 45,000

Taxable income $ 1,480,300 Taxable income $ 1,480,300 Income taxes $ 503,302

Net income_{Net income} $ _$976,998

-(b)

Taxable gains:

$43,000 - $30,000 = $13,000

(c)

Total taxes:

in c o m e ta x e s  $ 1 1 3, 9 0 0 0 .3 4 ($ 1, 4 8 0 , 3 0 0 $ 3 3 5 , 0 0 0 )  $ 5 0 3, 3 0 2

g a in ta x e s  ( 0 .3 4 )($ 1 3, 0 0 0 )  $ 4 , 4 2 0

(5)

10.16)

(a), (b), and (c)

Input Output

Tax Rate(%)= 40 PW(i) = $299,551 >0, acceptable

MARR(%)= 12 IRR(%) = 97%

0 1 2 3 4 5 6

Income Statement

Revenues (savings) $300,000 $300,000 $300,000 $300,000 $300,000 $300,000

Expenses:

Labor $100,000 $100,000 $100,000 $100,000 $100,000 $100,000

Materials 50,000 50,000 50,000 50,000 50,000 50,000

Depreciation 20,000 32,000 19,200 11,520 11,520 5,760

Taxable Income $130,000 $118,000 $130,800 $138,480 $138,480 $144,240

Income Taxes (40%) 52,000 47,200 52,320 55,392 55,392 57,696

Net Income $78,000 $70,800 $78,480 $83,088 $83,088 $86,544

Cash Flow Statement Operating Activities:

Net Income $ 78,000 $ 70,800 $ 78,480 $ 83,088 $ 83,088 $ 86,544

Depreciation $ 20,000 $ 32,000 $ 19,200 $ 11,520 $ 11,520 $ 5,760

Investment Activities:

Investment $ (100,000)

Salvage 0

Gains Tax 0

(6)

10.17)

Investment in industrial robot:

0 1 2 3 4 5

Revenues (savings) $125,000 $125,000 $125,000 $125,000 $125,000

Expenses:

Depreciation 35,725 61,225 43,725 31,225 11,163

Taxable Income $89,275 $63,775 $81,275 $93,775 $113,838

Income Taxes (35%) 31,246 22,321 28,446 32,821 39,843

Net Income $58,029 $41,454 $52,829 $60,954 $73,994

Cash Flow Statement

Operating Activities:

Net Income $58,029 $41,454 $52,829 $60,954 $73,994

Depreciation $35,725 $61,225 $43,725 $31,225 $11,163

Investment ($250,000)

Salvage $50,000

Gains Tax $5,928

Net Cash Flow ($250,000) $93,754 $102,679 $96,554 $92,179 $141,085

PW(15%)= $95,498 Accept the investment

IRR= 29% >15%(MARR)

10.25)

Investment in 3-D computerized car-styling system

Input Output

Tax Rate(%) = 40 PW(i) = $459,071

MARR(%) = 12 IRR(%) = 95.53%

0 1 2 3 4 5

Revenues (savings) $350,000 $350,000 $350,000 $350,000 $350,000

Expenses:

O&M costs $80,000 $80,000 $80,000 $80,000 $80,000

Depreciation 36,000 57,600 34,560 20,736 10,368

Taxable Income $234,000 $212,400 $235,440 $249,264 $259,632

Income Taxes (40%) 93,600 84,960 94,176 99,706 103,853

Net Income $140,400 $127,440 $141,264 $149,558 $155,779

Net Income $ 140,400 $ 127,440 $ 141,264 $ 149,558 $ 155,779 Depreciation $ 36,000 $ 57,600 $ 34,560 $ 20,736 $ 10,368 Investment Activities:

Investment $ (180,000)

Salvage $ 5,000

Gains Tax $ 6,294

(7)

10.34)

(a) and (b)

Input Output

Tax Rate(%) = 40 PW(i) = $75,616

MARR(%) = 14 IRR(%) = 43.24%

0 1 2 3 4 5 6 7 8

Revenues (savings) $60,000 $60,000 $60,000 $60,000 $60,000 $60,000 $60,000 $60,000

Expenses:

O&M cost 8,000 8,000 8,000 8,000 8,000 8,000 8,000 8,000

Depreciation 15,719 26,939 19,239 13,739 9,823 9,812 9,823 4,906

Debt interest (10%) 4,000 3,650 3,265 2,842 2,377 1,865 1,301 682

Taxable Income 32,281 21,411 29,496 35,419 39,800 40,323 40,876 46,412

Income Taxes (40%) 12,912 8,564 11,798 14,168 15,920 16,129 16,350 18,565

Net Income $19,369 $12,846 $17,697 $21,251 $23,880 $24,194 $24,525 $27,847

Net Income 19,369 12,846 17,697 21,251 23,880 24,194 24,525 27,847

Depreciation 15,719 26,939 19,239 13,739 9,823 9,812 9,823 4,906

Investment (110,000)

Salvage 10,000

Gains Tax (4,000)

Financing Activities:

Borrowed funds 40,000

Principal repayment (3,498) (3,848) (4,232) (4,656) (5,121) (5,633) (6,196) (6,816)

(8)

10.50)

(a) & (b) Actual and constant dollar analysis:

0 1 2

Income Statement

Revenue $126,000 $132,300

Expenses:

O&M 62,400 64,896

Depreciation 12,000 9,600

Taxable Income 51,600 57,804

Income Taxes 15,480 17,341

Net Income 36,120 40,463

Cash Flow Statement Cash from operation

Net Income 36,120 40,463

Depreciation 12,000 9,600

Investment / Salvage (60,000) 40,000

Working capital (5,000) (200) 5,200

Gains Tax (480)

Net Cash Flow (actual) ($65,000) $47,920 $94,783

Net Cash Flow (constant) ($65,000) $44,370 $81,261

IRR'(%) = 51.04%

(b)

Given

f 8 % , i1 5 %

0 .1 5 0 .0 8

6 .4 8 % 1 0 .0 8

i   



(Inflation-free MARR)

(9)

12.11) At

i 1 2 %

, the economic service life is 1 year.

Interest rate

12%

n

Market ValueO&M Costs CR(12%)

OC(12%)

AEC(12%)

0 $30,000

1 $25,800

$5,000

$7,800

$5,000

$12,800

2 $16,000

$6,500

$10,204

$5,708

$15,911

3 $10,000

$10,000

$9,527

$6,980

$16,507

4 $5,000

$12,500

$8,831

$8,135

$16,966

(10)

12.27)

At

i1 0 %

and tax rate = 40%, the economic service life is 1 year.

Tax Rate 40%

MARR 10%

Permitted Annual Depreciation Amounts over the

Holding Holding Period Total Book

Period 1 2 3 4 5 6 7 8 Depreciation Value

0 $30,000

1 $4,287 $4,287 $25,713

2 $4,287 $3,674 $7,961 $22,040

3 $4,287 $7,347 $2,624 $14,258 $15,743

4 $4,287 $7,347 $5,247 $1,874 $18,755 $11,246

5 $4,287 $7,347 $5,247 $3,747 $1,340 $21,968 $8,033

Annual O&M Costs over the Holding Period Total PW

Holding Total PW of of A/T

Period 1 2 3 4 5 6 7 8 O&M CostsO&M Costs

0 `

1 $5,000 $4,545 $2,727

2 $5,000 $6,500 $9,917 $5,950

3 $5,000 $6,500 $10,000 $17,431 $10,458

4 $5,000 $6,500 $10,000 $12,500 $25,968 $15,581

5 $5,000 $6,500 $10,000 $12,500 $14,800 $35,158 $21,095

Expected Net A/T A/T Operating Costs (in PW) Total

Holding Market Taxable Gains Market over the Holding Period OC(10%) CR(10%)AEC(10%)

Period Value Gains Tax Value O&M CostsTax Shield Total OC

0

1 $25,800 $87 $35 $25,765 $2,727 $1,559 $1,168 $1,285 $7,235 $8,520

2 $16,000 ($6,040) ($2,416) $18,416 $5,950 $2,773 $3,177 $1,831 $8,516 $10,347

3 $10,000 ($5,743) ($2,297) $12,297 $10,458 $4,776 $5,682 $2,285 $8,348 $10,633

4 $5,000 ($6,246) ($2,498) $7,498 $15,581 $6,076 $9,505 $2,998 $7,848 $10,847

(11)

12.35)



Defender:

Tax Rate

35%

Investment

$12,725

MARR

18%

Book value

$15,000

Permitted Annual Depreciation Amounts over the

Holding

Holding Period

Total

Book

Period

1

2

3

4

5

6

7

8 Depreciation

Value

0 $15,000

1

$4,000

$11,000

2

$4,000 $4,000

$8,000

$7,000

3

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

$12,000

$3,000

Annual O&M Costs over the Holding Period

Total PW

Holding

Total PW of

of A/T

Period

1

2

3

4

5

6

7

8 O&M Costs O&M Costs

0 `

1 $4,500

$3,814

$2,479

2 $4,500

$5,300

$7,620

$4,953

3 $4,500

$5,300

$6,100

$11,333

$7,366

Expected

Net A/T

A/T Operating Costs (in PW)

Total

Holding

Market

Taxable

Gains

Market

over the Holding Period

OC(18%)

CR(18%)

AEC(18%)

Period

Value

Gains

Tax

Value

O&M Costs Tax Shield Total OC

0

1

$5,200

($5,800)

($2,030)

$7,230

$2,479

$1,186

$1,292

$1,525

$7,786

$9,311

2

$3,500

($3,500)

($1,225)

$4,725

$4,953

$2,192

$2,761

$1,764

$5,960

$7,724

3

$1,200

($1,800)

($630)

$1,830

$7,366

$3,044

$4,322

$1,988

$5,340

$7,328

Note: The opportunity cost of retaining the defender is as follows:



Current market value = $11,500



Current book value = $15,000



Losses = ($11,500 - $15,000) = ($3,500)



Loss tax credit = $3,500(0.35) = $1,225

(12)



Challenger:

Financial Data n 0 1 2 3 4 5

Depreciation $6,216 $10,653 $7,608 $5,433 $3,885

Book value $43,500 $37,284 $26,631 $19,023 $13,589 $9,705

Salvage value

O&M cost $1,500 $1,500 $1,500 $1,500 $1,500

-(0.65)*(O&M cost) ($975) ($975) ($975) ($975) ($975)

+(.35)*(Depreciation) $2,176 $3,729 $2,663 $1,902 $1,360

Investment ($43,500)

Net proceeds from sale

Net Cash Flow ($43,500) $1,201 $2,754 $1,688 $927 $385

Financial Data n 6 7 8 9 10

Depreciation $3,880 $3,885 $1,940 $0 $0

Book value $5,825 $1,940 ($0) ($0) ($0)

Salvage value $3,500

O&M cost $1,500 $1,500 $1,500 $1,500 $1,500

-(0.65)*(O&M cost) ($975) ($975) ($975) ($975) ($975)

+(.35)*(Depreciation) $1,358 $1,360 $679 $0 $0

Investment

Net proceeds from sale $2,275

Net Cash Flow $0 $383 $385 ($296) ($975) $1,300

PW (18%) = ($38,619)

AEC(18%) = $8,593