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 9 Depreciation and Corporate Taxes Economic Depreciation Note: For most up-to-date depreciation and income tax information, consult the book’s website at http://www.prenhall.com http://www.prenhall.com a nd click on “Tax Information” 9.1
9.2
The loss of value is defined as the purchase price of an asset less its market value, also known as economic depreciation. Economic depreciation = $20,000 - $7, $7,00 000 0 = $13 $13,, 000 Economic depreciation = $20,000 - $14,000 = $6,000
Cost Basis 9.3 •
Total property value with the house: Original cost Add: New building Demolition expenses Property value
Land $155,000 $155,000
Building $245,000 $1,250,000 $15,000 $1,510,000
Total property value = $155,000+ $1,510,000= $1,665,000 Unrecognized loss (demolition of house) = $245,000
•
9.4
Cost basis for depreciation = $15,000+ $1,250,000 + $245,000 = $1,510,000 (Note: The demolition expense is treated as a site preparation expense) Cost basis for flexible manufacturing cells: Flexible Flexible Manufactur Manufacturing ing cells cells ($400,000 ($400,000 x 3) Freight charges Handling fee Site preparation costs Start-up and testing costs Special wiring and material costs Cost basis
$1,200,000 $1,200,000 $20,000 $15,000 $45,000 $24,000 $3,500 $1,307,500
(Note: start-up and testing costs = $20 x 40 x 6 x 5 = $24,000)
Page | 1
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.
9.5 •
•
Unrecognized profit Old drill press (Book value) Trade-in allowance Unrecognized loss
$46,220 $40,000 $6,220
Cost basis Cost of new drill Plus: unrecognized loss Cost basis of new drill
$148,000 $6,220 $154,200
Comments: If the old drill were sold sold on the market (instead (instead of trade-in), there there would be no unrecognized unrecognized loss. In that situation, the cost cost basis for the new drill would be $148,000.
9.6 •
•
Unrecognized profit Old lift truck (Book value) Trade-in allowance Unrecognized gains
$7,808 $9,000 $1,192
Cost basis Cost of new truck Minus: unrecognized gains Cost basis of new truck
$38,000 $1,192 $36,808
Comments: If the old truck were sold on the market (instead of trade-in), there would be no unrecognized unrecognized gains. In that situation, situation, the cost basis for the new drill would be $38,000.
Book Depreciation Methods 9.7 n
(a) SL Dn
(b) DDB Bn
Dn
Bn
1
$27,000
$138,000
$66,000
$99,000
2
$27,000
$111,000
$39,600
$59,400
3
$27,000
$84,000
$23,760
$35,640
4
$27,000
$57,000
$5,640
$30,000
5
$27,000
$30,000
0
$30,000 Page | 2
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.
9.8
Given: I = $125,000, n = 3 years, N = 8. α
D3
1 = 2( ) = 0.25 8 = 0.25 ×125, 000 × (1 − 0.25) 3−1
= $17,578
9.9
DDB switching to SL: n
Dn
Bn
1 2 3 4 5 6 7
$20,857 $14,898 $10,641 $7,601 $5,429 $5,287 $5,287
$52,143 $37,245 $26,603 $19,002 $13,573 $8,287 $3,000
9.10 Given: I = $88,000 , S = $13,000 , N = 6 years. (a) D1 = $29,333 , D2 = $19,556 , D3 = $13,037 , D4 = $8,691 (b) DDB Switching to SL n
Dn
Bn
1 2 3 4
$29,333 $19,556 $13,037 $8,691
$58,667 $39,111 $26,074 $17,383
5
$4,383
$13,000
6
$0
$13,000
Comments: If the regular DDB deduction were taken during the fifth year, B5 would be less than the salvage value. Therefore, it is necessary to adjust D5 . The number in the box represents the adjusted value. No switching is common for this type of situation whenever the salvage value is high.
Page | 3
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.
9.11 Given: I = $246,000, S = $36,000, N = 8 years Dn
n
1 2 3 4 5 6 7 8
$61,500 $46,125 $34,594 $25,945 $19,459 $14,594 $7,783 0
Bn
$184,500 $138,375 $103,781 $77,836 $58,377 $43,783 $36,000 $36,000
9.12
⎛1⎞ = ⎜ ⎟ 2 = 0.4 ⎝5⎠ (b) D2 = (0.4)(0.6)(36, 000) = $8, 640 (a)
α
(c)
B4
= (36, 000)(1 − 0.4) 4 = $4, 665.60
9.13 Given: I = $55,000, N = 5 years, n
(a) SL
1 2 3 4 5
S =
$5,000
(b) DDB
$10,000 $10,000 $10,000 $10,000 $10,000
$22,000 $13,200 $7,920 $4,752 $2,128
9.14 Given: I = $56,000, S = $6,500, N = 12 years $56,000 − $6,500 = $4,125 12
(a)
D
=
(b)
D3
= $6,481
Page | 4
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.
Units-of-Production Method 9.15 Allowed depreciation amount D
=
$90,000 − $5,000 (30,000) = $10,200 250,000
9.16 D5,000 hours
$68,000 − $7,500 (5,500) 50,000 = $6,655 =
9.17 (a) Straight line: D1 = (b) UP: D1 =
157,000 − 27,000 = 13, 000; B1 = $144, 000 10
157,000 − 27,000 (23, 450) = 12,194; B1 = $144, 806 250,000
(c) Working hours: D1
=
157,000 − 27,000 (2, 450) = 10, 616.67; B1 = $146, 383.33 30,000
(d) DDB(without conversion to SL): D1 = 0.2(157, 000) = 31, 400; B1 = $125, 600 (e) DDB(with conversion to SL): D1 = 0.2(157, 000) = 31, 400; B1 = $125, 600 Note that: (d) and (e) are indifferent in year 1.
Tax Depreciation 9.18 Given: I = $265,000, Delivery and installment costs =$46,000, N = 12 years, and 7-year MACRS (a) Cost basis = $265,000 + $46,000 = $311,000
Page | 5
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.
(b) n
MACRS Depreciation
1 2 3 4 5 6 7 8
$44,442 $76,164 $54,394 $38,844 $27,772 $27,741 $27,772 $13,855
9.19 Given: I = $35,000, S = $6,000, N = 8 years, and 5-year MACRS n
Book Depreciation
MACRS Depreciation
1 2 3 4 5 6 7 8
$3,625 $3,625 $3,625 $3,625 $3,625 $3,625 $3,625 $3,625
$7,000 $11,200 $6,720 $4,032 $4,032 $2,016 -
9.20 (a) Cost basis: $190,000 + $25,000 = $215,000 (b) D1
= $30, 723.5, D2 = $52, 653.5, D3 = $37, 603.5, D4 = $26,853.5
D5
= D7 = $19,199.5, D6 = $19,178, D8 = $9, 589
9.21 Given: I = $100,000, S = $20,000, N = 7 years (a) MACRS-7 year class: B3 = $100,000 − (0.1429 + 0.2449 + 0.1749)($100,000) =$43,730
⎡ $100,000 − $20,000 ⎤ (b) SL: B3 = $100, 000 − 3 ⎢ ⎥⎦ = $65, 714.29 7 ⎣ The Difference is $21,984.29. Page | 6
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.
9.22 Let I d enote the cost basis for the equipment. B3 = I − ( D1 + D2 + D3 ) I
= I − (0.1429 + 0.2449 + 0.1749) I = I − 0.5627 I = 0.4373($185,000) = $80,901 9.23 Given: I = $92,000, S = $12,000, N = 5 years, 7-year MACRS depreciation class D1 D2 D3 D4 D5
= $13,147 = $22,531 = $16,091 = $11,491 = $8,216
9.24 Given: I = $50,000, tax depreciation method = 6-year MACRS property class with half-year convention 200% DB n
Bn −1
Dn
1 2 3 4
$50, 000 $41, 667 $27, 778 $18,519
$8, 333 $13,889 $9, 259 $6,173
5 6 7
$12,346
$4,115
SL
MACRS
life Dn Dn 6.5 $7692 $8,333 5.5 $7, 576 $13,889 4.5 $6,173 $9, 259 3.5 $5, 291 $6,173 2.5 $4, 938 1.5 $4, 938 0.5 $2, 46 9
$4,938 $4, 938 $2, 469
: Optimal time to switch
9.25 Since the land is not depreciable, just consider the building depreciations. Given: I = $250,000, tax depreciation method = 27.5-year MACRS property
Page | 7
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.
n
1 2 3 4 5
Depreciation Allowed rate depreciation 2.5758% $6,439 3.6364% $9,091 3.6364% $9,091 3.6364% $9,091 3.1818% $7,955
9.26 Given: I = $33,000 and 7-year MACRS property n
Dn
1 2 3 4 5 6 7 8
$4, 716 $8, 082 $5, 772 $4,122 $2,947 $2, 944 $2,947 $1, 472
9.27 Given: Residential real property (27.5-year), I = $270,000 (a) ⎛ 100% ⎞ 2.5 D1 = ⎜ ⎟ ⎝ 27.5 ⎠ 12 = (0.00758)($270, 000) = $2, 045 (b) Total amount of depreciation over the 4-year ownership, assuming that the asset is sold at the end of 4thc alendar year: n
1 2 3 4
Rate 0.7576% 3.6364% 3.6364% 3.4848%
Dn
$2,045 $9,818 $9,818 $9, 049
Total amount of depreciation allowed = $31,091. Note that the 4 th year depreciation reflects the mid-month convention (11.5 months). B4
= $270,000 − $31,091 = $238,909
Page | 8
Contemporary Engineering Economics, Fifth Edition, by Chan S. Park. ISBN: 0-13-611848-8 © 2011 Pearson Education, Inc., Upper Saddle River, NJ. All rights reserved. This material is protected by Copyright and written permission should be obtained from the publisher prior to any prohibited reproduction, storage in a retrieval system, or transmission in any form or by any means, electronic, mechanical, photocopying, recording, or likewise. For information regarding permission(s), write to: Rights and Permissions Department, Pearson Education, Inc., Upper Saddle River, NJ 07458.
9.28 Types of Asset Depreciating Methods End of year Initial Cost ($) Salvage value ($) Book value ($) Depreciation life Depreciable Amount ($) Accumulated Depreciable ($)
I SL 6 30,000 6,000 12,000 8 yr 3,000 18,000
II DDB 3 25,000 5,000 5,400 5 yr 3,600 19,600
III UP 3 41,000 5,000 20,500 90,000 mi 6,000 18,000
IV MACRS 4 20,000 2,000 3,456 5 yr 2,304 16,544
9.29 (a) Book depreciation methods: • Straight-line method: n
1 2 3 4 5
•
Dn
Bn
Cum. Dn
$15,800
$73,200
$15,800
$15,800 $15,800
$57,400 $41,600
$31,600 $47,400
$15,800
$25,800
$63,200
$15,800
$10,000
$79,000
DDB method: n
1 2 3 4 5
Dn
Cum. Dn
Bn
$35,600
$53,400
$35,600
$21,360 $12,816 $7,690 $1,534
$32,040 $19,224 $11,534 $10,000
$56,960 $69,776 $77,466 $79,000
(b) Tax depreciation: 7-year MACRS n
1 2 3 4 5 6 7 8
Dn
Cum. Dn
Bn
$12,718
$76,282
$12,718
$21,796 $15,566
$54,486 $38,920
$34,514 $50,080
$11,116
$27,804
$61,196
$7,948 $7,939
$19,856 $11,917
$69,144 $77,083
$7,948
$3,969
$85,031
$3,969
$0
$89,000
Page | 9
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.
(c) Trade-in allowance Book value of the old equipment ( B3)
$38,920
Less: Trade-in allowance
$20,000
Unrecognized loss
($18,920)
Cost of new equipment Plus: Unrecognized loss on trade-in Cost basis of new equipment
$92,000 $18,920 $110,920
Comments: If the old equipment were sold on the market (instead of trade-in), there would be no unrecognized loss. In that situation, the cost basis for the new equipment would be just $92,000. No half-year convention is assumed in this analysis.
Depletion 9.30 (a)
Ore mine: Depletion rate per ton =
$8,900,000 − $1,500,00 = $1.85 per ton 4,000,000
Mining equipment: Depreciation rate per ton =
$2,500,000 = $0.625 per ton 4,000,000
(b)
For tax year 2009: Depletion expense = $1.85(550,000) = $1,017,500 Depreciation expenses = $0.625(550,000) = $343,750
For tax year 2010: Depletion expense = $1.85 (688,000) = $1,272,800 Depreciation expenses = $0.625 (688,000) = $430,000
9.31
• •
$600,000 = $88, 235.29 per MBF 6.8 Total depletion allowance = $88, 235.29(1.5) = $132, 352.94
Depletion allowed per MBF =
Page | 10
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.
9.32 Percentage depletion versus cost depletion: Gross Income Depletion Computed % depletion
•
$48,365,000 × 15% $7,254,750
Percentage depletion: Gross Income Expenses
$48,365,000 $22,250,000
Taxable income Deduction limit
$26,115,000 50% $13,057,500 ×
Maximum depletion deduction The allowable percentage deduction is $7,254,750.
•
Cost depletion =
$80,000,000 (52,000) = $8,320,000 500,000
T he cost depletion is more advantageous than the percentage depletion.
∴
9.33 (a) Cost basis:
Parcel A:
$39,000,000 = $4.33 per bbl 9,000,000
Parcel B:
$24,000,000 = $4.80 per bbl 5,000,000
(b) Depletion charge for parcel A: Cost depletion: $4.33(1, 200, 000) = $5, 200, 000
Percentage depletion: Gross income = $60 × 1,200,000 = $72,000,000 Gross Income $72,000,000 Depletion × 15% Computed % depletion $10,800,000 Gross Income Expenses
$72,000,000 $3,600,000
Taxable income Deduction limit
$68,400,000
Maximum depletion deduction
$34,200,000
50%
×
Page | 11
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.
The allowable percentage deduction is $10,800,000. (c) Percentage depletion versus cost depletion for parcel A in year 2010: Cost depletion: $4.33(1, 000, 000) = $4,330, 000
Percentage depletion: - Gross income = $75 × 1,000,000 = $75,000,000 Gross Income Depletion Computed % depletion
$75,000,000 × 15% $11,250,000
Gross Income Expenses
$75,000,000 $3,600,000
Taxable income Deduction limit
$71,400,000 50%
×
Maximum depletion deduction
$35,700,000 The allowable percentage deduction is $11,250,000. (d) Percentage depletion versus cost depletion for parcel B in year 2010 Cost depletion: $4.80(800, 000) = $3,840, 000
Percentage depletion: Gross income = $75 × 800,000 = $60,000,000 Gross Income Depletion Computed % depletion
$60,000,000 × 15% $9,000,000
Gross Income Expenses
$60,000,000 $3,000,000
Taxable income Deduction limit
$57,000,000 50%
×
Maximum depletion deduction
$28,500,000 The allowable percentage deduction is $9,000,000. During year 2010, Oklahoma Oil claimed its depletion deduction in the amount of $9,000,000 from parcel B. Page | 12
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.
Book value of $15,000,000 ($24,000,000-$9,000,000) is at the beginning of year 2011. The revised cost per bbl is $15,000,000 = $3.75 per bbl 4,000,000 Since no gross income figure is available during year 2011, we may calculate the depletion charge based on unit cost $3.75(1, 000,000) = $3, 750,000
9.34 (a) Cost depletion: $30,000,000 = $4.6154 per ton 6,500,000 Depletion cost = $4.6154(1, 000,000) = $4, 615,400 Cost per ton =
(b) Percentage depletion: Gross Income Depletion Computed % depletion
$15,000,000 × 10% $1,500,000
Gross Income Expenses
$15,000,000 $1,850,000
Taxable income Deduction limit
$13,150,000
Maximum depletion deduction
50%
×
$6,575,000
The allowable percentage deduction is $1,500,000.
Revision of Depreciation Rates 9.35 (a) (b)
D = $800,000/ 25
= $32,000
B = $400,000 + $125,000
(c) n=
= $525,000
$800,000 − $400,000 = 12.5 $32,000 Page | 13
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.
Remaining years = (25 - 12.5) + 10 = 22.5 years D = $525,000 / 22.5
= $23,333 (d) Depreciation rate for 12.5 years (June of 12 thy ear) : 2.5641% D12.5
= ( $800,000 + $125,000 )(0.025641) = $23,718
9.36 (a) Book depreciation amount for 2010:
= $180, 000 − 3($18,000) = $126,000 revised depreciation basis = $126,000 + $45,000 = $171,000 revised useful life = 12 years D2010 = $171,000 /12 = $14,250 B2008
(b) Tax depreciation amount for 2010:
Depreciation schedule for the original machine: D2010
= $180, 000(0.0892) = $16, 056
Depreciation schedule for the improvement (treated as a separate MACRS property):
D2010
= $45, 000(0.1749) = $7,870.5
T otal tax depreciation for 2006:
∴
D2010
= $16,056 + $7,870.5 = $23,926.5
9.37 Given: Cost basis = $85,000 + $4,500 = $89,500 (a) Book depreciation schedule (Depreciation basis = $89,500) n
2008 2009 2010 2011
Dn
Bn
Cum. Dn
$10,688
$78,813
$10,688
$10,688 $10,688 $10,688
$68,125 $57,438 $46,750
$21,375 $32,063 $42,750
Page | 14
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.
(b) Tax depreciation schedule (Depreciation basis = $89,500) n
2008 2009 2010 2011
Dn
Cum. Dn
Bn
$12,790
$76,710
$12,790
$21,919 $15,654 $11,179
$54,792 $39,138 $27,960
$34,708 $50,362 $61,540
Comments: The accessories costing $5,000 that were incurred in 2006 do not change the depreciation schedule, because these neither extended the machine’s life nor resulted in any additional salvage value.
Corporate Tax Systems 9.38 Net income calculation: Gross income Expenses: Salaries Wages Depreciation Loan interest Taxable income Income taxes
$
35,000,000
$ $ $ $ $ $
6,000,000 7,000,000 800,000 150,000 21,050,000 7,367,499
Net income
$
13,682,501
Note: Income taxes = $6,416,666+0.35(21,050,000-$18,333,333) = $7,367,499 9.39 (a) Taxable income = $8,500,000 - $2,280,000 - $456,000 = $5,764,000 (b) Income tax calculation using tax formula (c) Income taxes = $113,900 + 0.34(5,764,000 - 335,000) = $1,959,760
Page | 15
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.
9.40 (a) Income tax liability: Gross revenues Expenses: Manufacturing Operating Interest
$ 3,500,000
Taxable operating income Adjustment: loss
$ 2,490,000 $ 15,000
Taxable income Income taxes
$ 2,475,000 $ 841,500
Net income
$ 1,633,500
$ $ $
650,000 320,000 40,000
Note 1: Book loss = $60,000 - $75,000 = ($15,000) Note 2: Income taxes = $113,900+0.34($2,475,000-$335,000) = $841,500 (b) Operating income: Taxable operating income Income taxes
$ 2,490,000 $ 846,600
Net operating income
$ 1,643,400
Gains or Losses 9.41
Allowed depreciation = $200,000(0.1429 + 0.2449 + 0.1749 +0.1249 / 2) = $125,030 Book value = $200,000 − $125,030 = $74,970 Gain = $120, 000 − $74, 970 = $45, 030 Net proceeds = $120,000 − $45,030(0.4) = $101,988
9.42 (a) Disposed of in year 3: Allowed depreciation = $80,000(0.20 + 0.32 + 0.192 / 2) = $49,280 Book value = $80,000 − $49,280 = $30,720 Loss = $40, 000 − $30, 720 = $9, 280
Page | 16
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.
(b) Disposed of in year 5: Allowed depreciation = $80,000(0.20 + 0.32 + 0.192 + 0.1152 + 0.1152 / 2) = $70,7848 Book value = $80,000 − $70,7848 = $9,216 Taxable gains = $30,000 − $9,216 = $20,784 (c) Disposed of in year 6: Allowed depreciation = $80,000 Book value = $0 Taxable gains = $10,000
9.43
Allowed depreciation = $350,000(0.1429 + 0.2449 + 0.1749 +0.1249 + 0.0893/ 2) = $256,288 Book value = $350,000 − $256,288 = $93,713
(a) If sold at $20,000: Loss = $20, 000 − $93, 713 = ($73, 713) Loss credit = $73,713(0.34) = $25,062 (b) If sold at $99,000: Gain = $99, 000 − $93, 713 = $3, 713 Gains tax = $3,713(0.34) = $1,262
9.44 Allowed depreciation = $50,000(0.2 + 0.32 + 0.192 + 0.1152 / 2) = $38,480 Book value = $50,000 − $38,480 = $11,520
Page | 17
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.
9.45 Given: I = $80,000, S = $20,000, N = 8 years. (a) Book value on December 31, 2012 using SL depreciation method n
2010 2011 2012
Dn
Bn
Cum. Dn
$7,500
$72,500
$7,500
$7,500 $7,500
$65,000 $57,500
$15,000 $22,500
(b) Depreciation amount for 2012 using DDB n
2010 2011 2012
Dn
Bn
Cum. Dn
$20,000
$60,000
$20,000
$15,000 $11,250
$45,000 $33,750
$35,000 $46,250
(c) Optimal time to switch: year 2014. SL Method n
2010 2011 2012 2013 2014
Dn
Bn
Cum. Dn
$7,500
$72,500
$7,500
$7,500 $7,500 $7,500
$65,000 $57,500 $50,000
$15,000 $22,500 $30,000
$7,500
$42,500
$37,500
DDB Method n
2010 2011 2012 2013 2014
Dn
Bn
Cum. Dn
$20,000
$60,000
$20,000
$15,000 $11,250 $8,438
$45,000 $33,750 $25,313
$35,000 $46,250 $54,688
$6,328
$18,984
$61,016
Page | 18
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.
(d) Taxable gain Allowed depreciation = $80,000(0.1429 + 0.2449 + 0.1749 + 0.1249 / 2) = $50,012 Book value = $80,000 − $50,012 = $29,988 Taxable gains = $38,000 − $29,988 = $8,012
Marginal Tax Rate in Project Evaluation 9.46 (a) Economic depreciation for the milling machine $200,000 − $50,000 = $150,000 (b) Marginal tax rates with the project:
1
$80,000
$28,580
Taxable income $51,420
2
$80,000
$48,980
$31,020
$456,020
34%
3
$80,000
$34,980
$45,020
$470,020
34%
4
$80,000
$24,980
$55,020
$480,020
34%
5
$80,000
$17,860
$62,140
$487,140
34%
6
$80,000
$8,920
$71,080
$496,080
34%
n
Revenue
Dn
Combined income $476,420
Marginal rate 34%
(c) Average tax rates n
1 2 3 4 5 6
Combined income $476,420 $456,020 $470,020 $480,020 $487,140 $496,080
Combined income taxes $161,982.80 $155,046.80 $159,806.80 $163,206.80 $165,627.60 $168,667.20
Average tax rate 34% 34% 34% 34% 34% 34%
9.47 Incremental tax rate calculation:
Revenue Operating costs Depreciation Taxable income
Year 1 $220,000 $150,000 $12,000 $58,000
Year 2 $220,000 $150,000 $19,200 $50,800 Page | 19
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.
Year 1 $650,000 $221,000
Year 2 $650,000 $221,000
Taxable income with project Income taxes
$708,000 $240,720
$700,800 $238,272
Incremental taxable income Incremental income taxes Incremental tax rate (%)
$58,000 $19,720 0.34
$50,800 $17,272 0.34
Taxable income without project Income taxes
Comment: Note that the marginal tax rates over the project life remain unchanged because the additional income from the new project is not large enough to push the company into a higher tax bracket.
9.48
Good
Economic condition Fair
Taxable income Before expansion Due to expansion After expansion
$ $ $
2,500,000 2,000,000 4,500,000
Income Taxes
$
1,530,000 $
$ $ $
2,500,000 500,000 3,000,000
Poor
$ $ $
2,500,000 (100,000) 2,400,000
1,020,000 $
816,000
(a) Marginal tax rate
34%
34%
34%
(b) Average tax rate
34%
34%
34%
9.49 Incremental tax calculations: (a) Additional taxable income due to project: Year 1
Year 2
Year 3
Annual revenue
$80,000
$80,000
$80,000
Operating cost
$20,000
$20,000
$20,000
Depreciation
$16,665
$22,225
$3,703
Taxable income
$43,335
$37,775
$56,298
Page | 20
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.
(b) Additional income tax calculation: Year 1
Year 2
Year 3
$350,000
$350,000
$350,000
$119,000
$119,000
$119,000
Taxable income with project Income taxes
$393,335 $133,734
$387,775 $131,844
$406,298 $138,141
Incremental taxable income Incremental income taxes Incremental tax rate
$43,335 $14,734 34%
$37,775 $12,844 34%
$56,298 $19,141 34%
Taxable income without project Income taxes
(c) Gain taxes: Total depreciation = $42,593 Book value = $50, 000 − $42, 593 = $7, 408 Taxable gains = $10, 000 − $7, 408 = $2, 593 Gain taxes = (0.34)($2,593) = $881
Combined Marginal Income Tax Rate 9.50 (a) Explicit calculation of state income taxes: State taxable income = $3,500,000 − $1,800,000 = $1,700,000 State income taxes = $1, 700, 000(0.05) = $85,000 Federal taxable income = $1,700,000 − $85,000 = $1,615,000 Federal income taxes = $1, 615, 000(0.34) = $549,100 Combined taxes = $85,000+549,100=$634,100
(b) Tax calculation based on the combined tax rate: Combined tax rate = 0.34 + 0.05 − (0.05)(0.34) = 37.3% Combined taxes = (0.373)($1,700,000) = $634,100
Page | 21
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.
9.51 (a) Marginal tax rates: State taxable income = $6,500,000 − $3,450,000 − $650,000 = $2,400,000 $193,120 = 8.05% State tax rate = $2,400,000 Federal taxable income = $2, 400,000 − $193,120 = $2, 206,880 $332,000 Federal tax rate = = 15.04% $2,206,880 (b)
Combined marginal tax rate = 0.0805 + 0.1504 − (0.0805)(0.1504) = 21.88%
9.52 (a) Additional annual taxable income due to expansion = $30,000 Taxable income in year 1 = $170,000 + $30,000 = $200,000 The marginal tax rate after business expansion is 39%.
(b) Average tax rate after business expansion $61,250/ $200,000 = 30.63% Note: Income taxes = $22,250+0.39($200,000-$100,000)=$61,250 (c) PW of income taxes:
Depreciation schedules: depreciation base = $20,000 n
1 2 3 4
MACRS $ 6,666 $ 8,890 $ 2,962 $ 1,482
Page | 22
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.
Incremental income taxes under 3-year MACRS
Revenue Expense Depreciation Taxable income Income taxes PW(10%)=
Operating Year Year 1 Year 2 $50,000 $50,000 $20,000 $20,000 $6,666 $8,890
Year 3 $50,000 $20,000 $2,962
$23,334
$21,110
$27,038
$9,100 $22,999
$8,233
$10,545
9.53 n
Dn
(a) Bn−1
1 2 3 4 5 6 7 8
$ 500,150 $ 857,150 $ 612,150 $ 437,150 $ 312,550 $ 312,200 $ 312,550 $ 156,100
$3,500,000 $299,850 $2,142,700 $1,530,550 $1,093,400 $780,850 $468,650 $156,100
(b) Taxes $42,000 $35,998 $25,712 $18,367 $13,121 $9,370 $5,624 $1,873
Short Case Studies ST 9.1 Given: I = $82,000 + $3,000 = $85,000, • Book depreciation expenses for 2004: $85,000 − $3,000 D2004 = = $8,200 10
N = 10 years, S =
n
Dn
Bn
2004 2005 2006
$8,200 $8,200 $8,200
$76,800 $68,600 $60,400
$3,000
Page | 23
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.
•
Book depreciation expenses for 2007: basis = $60,400 + $8,000 = $68,400 Remaining useful life=10 years Salvage value = $3,000
N ew depreciation
∴
•
D2007
=
$68,400 − $3,000 = $6,540 10
n
Dn
Bn
2007 2008 2009
$6,540 $6,540 $6,540
$61,860 $55,320 $48,780
Book depreciation expenses for 2010: New depreciation basis = $48,780 + $5,000 = $53, 780 Remaining useful life=7 years Salvage vlaue = $6,000 ∴
D2010
=
$53,780 − $6,000 = $6,825.71 7
ST 9.2 (a) Depletion basis = $32.5 million - $3 million = $29.5 million $29,500,000 = $4.54 per bbl 6,500,000 Cost depletion for 2009 = $4.54 / bbl × 420,000bbl = $1,906,800 Cost depletion for 2010 = $4.54 / bbl ×510, 000 bbl = $2,315, 400 Depletion allowance per bbl =
(b) Depreciation basis = equipment cost + pipeline cost = $3,360,000 $3,360,000 = $0.517per bbl 6,500,000 Cost depreciation for 2009 = $0.517 / bbl × 420, 000 bbl = $217,140 Cost depreciation for 2010 = $0.517 / bbl ×510, 000 bbl = $263, 670 Depreciation allowance per bbl =
Page | 24
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.
ST 9.3 (a) Incremental Operating income: Year
1
Revenue Mfg. Cost Depreciation O&M
2
3
4
5
$15,000,000 $15,000,000 $15,000,000 $15,000,000 $15,000,000 6,000,000 6,000,000 6,000,000 6,000,000 6,000,000 714,500 1,224,500 874,500 624,500 223,250 1,200,000 1,200,000 1,200,000 1,200,000 1,200,000
Taxable Income Income Tax
7,085,500 2,479,925
6,575,500 2,301,425
6,925,500 2,423,925
7,175,500 2,511,425
7,576,750 2,651,863
Net Income
4,605,575
4,274,075
4,501,575
4,664,075
4,924,888
(b) Gains or losses: Total depreciation = $3, 661, 250 B5 = $5,000,000 − $3,661, 250
= $1,338,750 Taxable gains = $1,600,000 − $1,338,750 = $261,250
ST 9.4 (a) If Diamond invests in the facilities and markets the product successfully, the expected tax rate in each year will remain at 34%. Since the local and state taxes are tax-deductible expenses on federal tax calculation purpose, the combined marginal tax rate is
t m
= 0.34 + 0.05 − (0.05)(0.34) = 37.3%
(b) Gains or losses
•
Plant (39-year MACRS):
Total depreciation = (2.4573% + 2.5641% + + 2.4573%)($10,000,000) = $2,029,913 B8 = $10,000,000 − $2,029,913
= $7,970,087 Losses = $6,000,000 − $7,970,087 = ($1,970,087) Page | 25
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.
•
Equipment (7-year MACRS): Total depreciation = $40,000,000 B8 = 0
•
Ordinary gains = $4, 000, 000 Net gains:
Net gains = $4,000,000 − $1,970,087 = $2,029,913 Gains tax(37.3%) = $2,029,913 × 0.373 = $757,158 Net proceeds from sales = $9,000,000 − $757,158 = $8,242,842 (c) Net operating income Income Statement (all units in thousand dollars) n
1 $30,000
2 $30,000
3 $30,000
4 $30,000
5 $30,000
6 $30,000
7 $30,000
8 $30,000
9,000 12000
9,000 12000
9,000 12000
9,000 12000
9,000 12000
9,000 12000
9,000 12000
9,000 12000
246 5716
256 9796
256 6996
256 4996
256 3572
256 3568
256 3572
246 1784
Taxable Income for State State Income taxes (5%) Taxable Income for Federal Federal Income taxes (34%)
$3,038 152 $2,886 981
($1,052) -53 ($999) -340
$1,748 87 $1,661 565
$3,748 187 $3,561 1,211
$5,172 259 $4,913 1,671
$5,176 259 $4,917 1,672
$5,172 259 $4,913 1,671
$6,970 349 $6,622 2,251
Net Income
$1,905
($660)
$1,096
$2,350
$3,243
$3,245
$3,243
$4,370
Revenue Expenses : Mfg. cost Operating cost Depreciation Building Equipment
Corporate operating losses: Ordinary operating losses (say, year 2) can be carried back to each of the preceding 3 years and forward for the following 15 years, and can be used to offset taxable income in those years. In our example, the taxable income during the first year is large enough to offset the operating loss during the second year, so that the corporation wil get a federal tax refund in the amount of $ 340,000 plus $53,000 (state tax refund) at the end of year 2.
Page | 26