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 8 Cost Concepts Relevant to Decision Making Classifying Cost 8.1
• Storage and material handling costs for raw materials: product cost (indirect costs)
• Gains or loss on disposal of factory equipment: period costs • Lubricants for machinery and equipment used in production: product cost (mfg. overhead)
• Depreciation of a factory building: product product cost (mfg. overhead) • Depreciation of manufacturing equipment: product cost (mfg. overhead) • Depreciation of the company president’s automobile: period cost • Leasehold costs for land on which factory buildings stand: period cost • Inspection costs of finished goods: product cost • Direct labor cost: product cost • Raw materials cost: product cost • Advertising expenses: period cost Cost behavior 8.2
• Wages paid to temporary workers: Variable cost • Property taxes on factory building: Fixed cost • Property taxes on administrative administrative building: Fixed cost • Sales commission: Variable cost • Electricity for machinery and equipment in the plant: Variable cost • Heat and air-conditioning for the plant: Fixed cost • Salaries paid to design engineers: Fixed cost • Regular maintenance on machinery and equipment: Fixed cost • Basic raw materials used in production: Variable cost • Factory fire insurance: Fixed cost 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.
8.3 (a)
C (301) − C (300)
= 12, 519.01 −12, 500
= $19.01 C ′( x) = 0.0003 x 2
(b)
− 0.16 x + 40
C ′(200) = $20 C ′′( x ) = 0.0006 x − 0.16 C ′′(200) = −0.04 < 0 → Decreasing
(c)
Average unit cost =
C ( x) x
= 0.0001 x 2 − 0.08 x + 40 +
5, 000 x
Average C (300) = $41.67 8.4 Output level 1,000 units 2,000 Units
Question (a) Total manufacturing cost (b) Manufacturing cost per unit (c) Total variable costs (d) Total variable costs per unit (e) Total costs to be recovered
$98,000 $98 $67,000 $67 $125,000
$130,000 $65 $104,000 $52 $162,000
Cost-Volume-Profit Relationships 8.5 (a) Total unit manufacturing costs if 30,000 units are produced:
($150,000 + $300,000 + $100,000 + $80,000)/ 30,000 = $21 (b) Total unit manufacturing costs if 40,000 units are produced:
⎛ ⎞ 40,000 $150,000 $300,000 $100,000 $80,000 / 40,000 = $20.33 + + + ⎜⎝ 300000 ⎠⎟
(
)
(c) Break-even price with 30,000 units produced: $21 + $150,000 / 30,000 = $26
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.
8.6 (a) Break-even sales volume: $200,000 (b) Marginal contribution rate =
$20,000 = 0.2 $300,000 − $200,000
(c) Let R = break-even sales dollars; F = total fixed cost; V = variable cost per unit; Q = sales price per unit
R =
F
1 − V Q V
1−
=
F MCR
= 1−
; 1−
V 1
V Q
= 1−
Q 0.95 0.95Q $40,000 = $253,333 R = 0.1579
= 0.2;
V Q
= 0.8;
0.8 = 0.1579; 0.95
The break-even sales volume would increase by $53,333. (d) F
= 1.1F = $44, 000
$44,000 = $220,000 0.2 The break-even sales volume would increase by $20,000.
R =
(e) 1− 1−
V Q
= 0.2;
1.06V Q
V Q
= 0.8;
= 1 − 1.06(0.8) = 0.1520;
$40,000 = $263,158 0.1520 The break-even sales volume would increase by $63,158.
R =
(f)
$40,000 − $20,000 = $100,000 0.2
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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.
8.7 (a)
Since belt A has the maximum contribution margin, we choose to first produce belt A at its maximum demand. Then the fixed cost remains at $255,000 − $3(20,000) = $195,000 and we calculate the break-even $195,000 = 97,500 units. The demand for belt B volume for belt B: V b = $2 is 100,000 units, which past the break-even point. Therefore, we opt to produce belt B for up to 97,500 units. Then, the policy is to produce 20,000 units of belt A and 97,500 units of belt B, respectively in order to break-even.
(b)
The total contribution margin when 200,000 units are sold is $3(20,000) + $2(100,000) + $1(80,000) = $340,000. And the operating income is $340,000 − $255,000 = $85,000 .
(c)
Operating income = $3(20,000) + $2(80,000) + $1(100,000) −$255,000 =$65,000 . Once again, we choose to produce belt A at its maximum demand. Then the new fixed cost is $255,000 − 20,000($3) = $195,000 . Then, we choose belt B based on the contribution margin. Note that the break-even volume $195,000 = 97,500 units. However, since the new for belt B is V b = $2 demand for belt B is only 80,000 units, which is less than the break-even point, we can only produce belt B at its maximum demand; 80,000 units. The new fixed cost is $195,000 - $2(80,000) = $35,000. Then we proceed to produce belt C. The break-even point for belt C is $35,000 = 35,000 units. Thus, the new break-even is 20,000 units of V b = $1 belt A, 80,000 units of belt B, and 35,000 units of belt C.
8.8 (a) Total fixed cost to be recovered (b) Sales volume & Profit/Loss (c) Profit = 0 (d) Contribution margin per unit (e) Volume
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.
8.9 (a) No. 1. 2. 3. 4. 5.
Description Profit (Loss) Sales volume Total manufacturing cost Variable costs Fixed costs
No. 6. 7. 8. 9. 10.
Description Break-even Loss Profit Total revenue Marginal contribution
(b) Case
Unit Sold
Sales
Variable Expenses
Contribution Margin per Unit
Fixed Expenses
A B C D
9,000 14,000 20,000 5,000
$270,000 $350,000 $400,000 $100,000
$162,000 $140,000 $280,000 $30,000
$12
$90,000 $170,000 $85,000 $82,000
$15 $6 $14
Net Income (Loss) $18,000
$40,000 $35,000 ($12,000)
Cost Concepts Relevant to Decision Making 8.10 Additional order units = 100 Labor cost = ($12)(5)(100) = $6,000 Material cost = ($14)(100) = $1,400 Overhead cost = (50%)($6,000) = $3,000 Total cost = $6,000 + $1,400 + $3,000 = $10,400 Profit margin = (30%)($10,400) = $3,120 Unit price to quote = $10,400 + $3,120 = $13,520
8.11 (a) Product mix that must satisfy: 4A = 3B or B = 0.75A Break-even formula: Total revenue = Total cost: 10A + 12(1.25)A = 5A + 10(1.25)A + 2,600; 7.5A = 2,600; A = 347 units and B =462 units (b) 10A + 12A = 5A + 10A + 2,600; A = 371 units (c) Compute the marginal contribution rate (MCR) for each product: Product A = $5, Product B = $2; with the assumption A > 0 and B > 0, more weight should be given to product A. 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.
(d) Product A: MCR = $5 per unit; Production time = 0.5 hour per unit; profit per hour = $10 Product B: MCR = $2 per unit; Production time = 0.25 hour per unit; profit per hour = $8 Product A is still more profitable, so it should be pushed first.
8.12 (a) Incremental cost In-house Outscoring Option O ption $4.80 $7.50 $6.00 $5.00 $4.25 $4.00 $3.40 $0.20 $0.20 $16.70 $18.65
Description Soldering operation Direct m aterials Direct labor M fg. O v erhead Fixed cost Unit cost
The outsourcing option would cost $1.95 more for each unit. The company should not accept the supplier’s offer at the stated price. Note that the fixed cost of $20,000 (or $0.20 per unit based on 100,000 production volume) remains unchanged under either option. (b) Break-even price = $4.80 - $1.95 = $2.85 per unit
Short Case Studies ST 8.1 (a) Break-even volume:
• 6-day operation: capacity
6,000 cwt/day, 6 days, Q = $12.40 / cwt F = ($4,200)(6 days) = $25,200, V = [$0.34+($4.34)(2.35)] = $10.539 / cwt F
→
+ NV = NQ N b
=
F Q − V
• 7-day operation: capacity
=
$25,200 = 13,541 $12.40 − $10.539
6,000 cwt/day, 7 days, Q = $12.40 / cwt F = ($4,200)(6 days) + $4,620 = $29,820, V = [$0.34(6/7) + $0.66(1/7) + ($4.34)(2.35)] = $10.585 / cwt →
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.
F
+ NV = NQ N b
=
F Q − V
=
$29,820 = 16,427 $12.40 − $10.585
(b)
• 6-day operation: MCR = 1 −
V Q
=1−
10.539 = 0.1501 12.40
• 7-day operation: MCR = 1 −
V Q
=1−
10.585 = 0.1464 12.40
(c) 6-day operation
• Average total cost per cwt = unit F + V =
$25,200 + $10.539 = $11.239 / cwt (6000)(6)
• Net profit margin before taxes MC = Q - V = $12.4 - $10.539 = $1.861/cwt,
$25,200 = $0.7/ cwt (6000)(6) Net profit margin before taxes per cwt=MC-unit F = 1.161/cwt unit F =
(d) 7-day operation
• Net profit margin before taxes MC = Q - V = $12.4 - $10.585=$1.815/cwt $29,820 = $0.71/ cwt (6000)(7) Net profit margin before taxes per cwt=MC-unit F = $1.105/cwt unit F =
• Total profit for each operation: • 6- day operation case Total profit =1.161(6,000)(6) = $41,796
•
7- day operation case: Total profit =1.105(6,000)(7) = $46,410
Total profit of 7 days’ operation is much more than the total profit of 6 days’ operation, so it would be economical for the mill to operate on Sunday. 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.
ST 8.2 (a) OP1 :5 x1 = 0 OP2 : −5 M + 10 x2 = 0 OP3 : −30 M − 60 x3 + 100 x3 = 0 x1 = 0 x2 = 0.5 M x3 = 0.75 M
(b)
−5 M + 10 x = −30 M − 60 x + 100 x x = 0.833 M
(c)
5 x = −30 M − 60 x + 100 x x = 0.857 M ∴
Use option 1 below 857,000 barrels and option 3 above 857,000 barrels.
ST 8.3 (a) Make
Buy
Variable Costs
Direct materials Direct manufacturing labor Variable manufacturing overhead (power & utilities) Inspection, setup, material handling Cost to purchase chains
$40,000.00 $20,000.00 $15,000.00 $2,000.00 $0.00
$82,000.00
Fixed Costs
Machine lease Allocated fixed plant admin, taxes, & insurance Total Cost Unit Cost
$3,000.00 $30,000.00
$30,000.00
$110,000.00 $112,000.00 $11.00 $11.20
Ace should not accept the offer, since the unit cost is slightly more when ACE buys chains. 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.
(b) Make
Buy
Variable Costs
Direct materials Direct manufacturing labor Variable manufacturing overhead (power & utilities) Inspection, setup, material handling Cost to purchase chains Cost to upgrade the bike
$40,000.00 $20,000.00 $15,000.00 $2,000.00 $0.00
$82,000.00 $180,000.00
Fixed Costs
Machine lease Allocated fixed plant admin, taxes, & insurance Fixed costs of upgrades (10,000 units) Profit by upgrading the bike Total Cost Unit Cost
$3,000.00 $30,000.00
$30,000.00 $16,000.00
$110,000.00 $11.00
$200,000.00 $108,000.00 $10.80
Buying option is better. (c) Make
Buy
Variable Costs
Direct materials Direct manufacturing labor Variable manufacturing overhead (power & utilities) Inspection, setup, material handling (8 batches) Cost to purchase chains (6200 units)
$24,800.00 $12,400.00 $9,300.00 $1,600.00 $0.00
$50,840.00
Fixed Costs
Machine lease Allocated fixed plant admin, taxes, & insurance
$3,000.00
$0.00
$30,000.00
$30,000.00
Total Cost Unit Cost
$81,100.00 $13.08
$80,840.00 $13.04
It seems the buying option appears to be marginally better. Page | 9