7
END-OF-CHAPTER CHAPTER PROBLEMS
7.5
utilization =
actual
5,000
=
= 0.7143 71%
design capacity 7,000
7.6
efficiency =
actual
4,500
=
= 0.9 or 90%
effective capacity 5,000
7.7
actual(planned) output
actual(planned) output
or 0.80 =
.
designed capacity
7,000
So, planned output = 5,600
7.8
effective capacity =
7.9
efficiency =
7.10
anticipated output = (Design capacity) (Effective capacity) (Efficiency)
= 108 0.80 0.90 = 77.76 78 chairs
effective capacity =
actual(planned) output
800
800
or 0.93 =
= 860
. Thus, design =
designed capacity
design
0.93
actual
500
or 0.80 =
.
effective capacity
effective capacity
500
effective capacity =
= 625
0.80
Thus,
7.12 Design: 93,600 0.92 0.95 = 81,806
Fabrication: 156,000 0.95 1.03 = 152,646
Finishing: 62,400 0.96 1.05 = 62,899
7.15
Sales
revenue
Large line
Hi
(2/3)
(200,000)
Lo
(1/3)
Expand
(2/3)
Hi
Small line
Lo
Cost for Extra cost
process to expand
Net
profit
600,000 300,000
= 300,000
300,000 300,000
=0
500,000 200,000 150,000 = 150,000
(200,000)
Do not expand
(100,000)
(1/3)
400,000 200,000
= 200,000
300,000 200,000
= 100,000
Prefer to build a large line. Large line has a payoff of $200,000. Small line has a payoff of
$133,333 + 33,333 = $166,666 .
7.16 (a)
Proposal A breakeven in units is:
Chapter 7: Process Strategy and Capacity Planning
1
Fixed cost 50,000 50,000
=
=
= 6,250 units
SP VC
20 12
8
(b)
Proposal B breakeven in units is:
Fixed cost 70,000 70,000
=
=
= 7,000 units
SP VC
20 10
10
7.17 (a)
Proposal A breakeven in dollars is:
Fixed cost 50,000 50,000
=
=
= $125,000
1 VC
1 12
0.40
SP
20
(b)
Proposal B breakeven in dollars is:
BEP$ =
Fixed cost 70,000 70,000
=
=
= $140,000
1 VC
1 10
0.50
SP
20
7.18 Set Proposal A = to Proposal B
(SPA VCA ) X A FA = (SPB VCB ) XB FB
(20 12) X 50,000 = (20 10) X 70,000
(8) X 50,000 = (10) X 70,000
(8) X + 20,000 = (10) X
20,000 = 10 X 8 X
20,000 = 2 X
10,000 = X
7.19 (a)
Proposal A: Profit at 8,500 units
Profit = ( SP VC ) X F
@ 8,500 for Proposal A: (20 12)8,500 50,000 = 18,000
@ 8,500 for Proposal B: (20 10 )8,500 70,000 = 15,000
Proposal A is best.
@ 15,000 units for Proposal A: (20 12)15,000 50,000 = $70,000
(b)
@ 15,000 units for Proposal B: (20 10)15,000 70,000 = $80,000
Proposal B is best.
7.20 Given:
Price ( P) = $8 unit
Variable cost (V ) = $4 unit
Fixed cost ( F) = $50,000
(a)
Breakeven in units is given by:
BEPx =
(b)
2
F
50,000 50,000
=
=
= 12,500 units
PV
84
4
Breakeven in dollars is given by:
Instructors Solutions Manual t/a Operations Management
BEP$ =
(c)
F
50,000 50,000
=
=
= $100,000
1 V
1 4
1 0.50
P
8
Profit is given by:
Profit = Volume Contribution Fixed cost
= 100,000 (8 4 ) 50,000
= 400,000 50,000 = $350,000
7.21 Given:
Price ( P) = $0.05 unit
Variable cost (V ) = $0.01 unit
Fixed cost ( F) = $12,000
Breakeven is given by:
BEP$ =
F
12,000 12,000
=
=
= $15,000
V
0 01
1 P 1 0..05 1 0.2
BEPx =
F
12,000
12,000
=
=
= 300,000 units
P V 0.05 0.01
0.04
7.22 Given:
Price ( P) = $30 unit
Variable cost (V ) = $20 unit
Fixed cost ( F ) = $250,000
Breakeven is given by:
BEP$ =
F
250,000 250,000
=
=
= $750,000
V
20
1 P
1 30
1 0.67
BEPx =
F
250,000 250,000
=
=
= 25,000 units
P V 30 20
10
7.23 Given:
Price ( P) = $30 unit
Variable cost (V ) = $20 unit
Fixed cost ( F) = $250,000 + $50,000
= $300,000
Breakeven is given by:
F
300,000 300,000
BEPx =
=
=
= 30,000 units
(a)
P V 30 20
10
F
300,000 300,000
BEP$ =
=
=
= $900,000
(b)
V
20
1 P
1 30
1 0.67
7.24 Option A: Stay as is
Option B: Add new equipment
Chapter 7: Process Strategy and Capacity Planning
3
Units ( Price VC ) FC = Profit
Profit A = 30000 (1.00 0.50 ) 14000 = $1,000
Profit B = 50000 (1.00 0.60 ) 20000 = $0
Therefore, the company should stay with the present equipment.
7.25 Option A: Stay as is
Option B: Add new equipment, raise selling price
Units ( Price VC ) FC = Profit
Profit A = 30000 (1.00 0.50 ) 14000 = $1,000
Profit B = 45000 (1.10 0.60 ) 20000 = $2,500
Therefore, the company should choose option B: add the new equipment and raise the selling
price.
7.26
0
3
Units
0
10,000
6
Qty
Mehras
15,000
33,200
9
Memphis Supply
0
40,000
at approximately 7,000 gears
4 x = 15,000 + 1.82 x
x = 6,881
7.27
(A)
(B)
(C)
4
Units
y = 600 + 1.10 = x
y 1100 + 0.70 x
y = 1800 + 0.4 x
0
600
1100
1800
4000
(arbitrary
number)
$5000 refurbish
$3900 modify
$3400 new
Instructors Solutions Manual t/a Operations Management
(a)
A
$5,000
4,000
B
3,000
C
2,000
1,000
0
0
(b)
(c)
1,000
2,000
Units
3,000
4,000
At 3,000, C is best.
Between 1600 and 2400, B is best.
7.31 Initial investment = $123,545
Salvage value: $44,560
Five-year return = $14,667
Cost of capital = 12%
NPV annuity factor 5 years @ 12% = 3.605 3.61
Present value = 3.61 14667 = 52948
Present value of salvage: 0.567 44560 = 25266
Net present value = 52948 + 25266 123545 = $45,331
7.32 Initial investment = $65,000
Eight-year return = $16,000 per year
Cost of capital = 10%
NPV annuity factor 8 years @ 10% = 5.33
Present value = 5.33 $16000 = $85,280
Net present value = $85,280 $65,000 = $20,280
7.33
P=
F
1000
1000
=
=
= $841.68
N
2
(1 + i )
(1 + 0.09 )
1.1881
or from Table 7.4
NPV = F PVF9%, 2 = 1000 0.842 = $842
7.34
P=
F
(1 + i ) N
=
5600
(1.08)15
=
5600
= $1,765.35
3.17
or from Table 7.4
NPV = F PVF8%, 15 = 5600 0.315 = $1,764
Chapter 7: Process Strategy and Capacity Planning
5
7.35 Expense
Original cost
Labor per year
Maintenance per year
Salvage value
Year
Now
1
2
3
3
Machine A
10000
2000
4000
2000
Machine A
Machine B
20000
4000
1000
7000
10000
6000
6000
6000
Expense
Expense
Expense
Expense
Salvage revenue
NPV Factor*
1.000
0.893
0.797
0.712
2000
0.712
NPV
10000
5358
4782
4272
24412
+ 1424
22988
* NPV factor from Table 7.4
Machine B
Year
Now
1
2
3
3
Expense
Expense
Expense
Expense
NPV Factor *
NPV
1.000
20000
0.893
4465
0.797
3985
0.712
3560
32010
7000
0.712
+ 4984
27026
20000
5000
5000
5000
Salvage revenue
* NPV factor from Table 7.4
NPV for machine A is $22,988; NPV for machine B is $27,026. Therefore, Machine A should
be recommended.
7.36 Expense
Original cost
Excess labor per year
Maintenance per year
Salvage value
Year
Now
1
2
3
4
5
5
Expense
Expense
Expense
Expense
Expense
Expense
Three Small Ovens Two Large Ovens
3750
5000
750
0
750
400
750
1000
Three Small Ovens
NPV Factor*
3750
1.000
1500
0.877
1500
0.769
1500
0.675
1500
0.592
1500
0.519
Salvage revenue
750
0.519
NPV
3750
1316
1154
1013
888
779
8900
+ 389
8511
* NPV factor from Table 7.4
6
Instructors Solutions Manual t/a Operations Management
Year
Now
1
2
3
4
5
5
Expense
Expense
Expense
Expense
Expense
Expense
Two Large Ovens
NPV Factor *
5000
1.000
400
0.877
400
0.769
400
0.675
400
0.592
400
0.519
Salvage revenue
1000
0.519
NPV
5000
351
308
270
237
208
6374
+ 519
5855
* NPV factor from Table 7.4
Chapter 7: Process Strategy and Capacity Planning
7
(a)
(b)
(c)
NPV of the three small ovens = $8,511; NPV of the two large ovens = $5,855.
Therefore, you should recommend that the firm purchase the two large ovens.
The basic assumptions made with regard to the ovens are:
n
The ovens are of equal quality
n
The ovens are of equivalent production capacity
The basic assumptions made with regard to methodology are:
n
Future interest rates are known
n
Payments are made at the end of each time period
7.37 Investment A net income, using Table 7.5
19000 PVF9%, 6 61000 = 19000 4.486 61000 = $24,234
Investment B Net Income
NPV Factor*
Expense
74,000
1.000
Revenue
19,000
0.917
Revenue
20,000
0.842
Revenue
21,000
0.772
Revenue
22,000
0.708
Revenue
21,000
0.650
Revenue
20,000
0.596
Revenue
11,000
0.547
Year
Now
1
2
3
4
5
6
7
NPV
74,000
+ 17,423
+ 16,840
+ 16,212
+ 15,576
+ 13,650
+ 11,920
+ 6,017
23,638
* From Table 7.4
Therefore, Investment A, with a payoff of $24,234, would be preferred over Investment B, with a
payoff of $23,638.
7.38 Initial investment = $ 20,000
NPV
Year
1
2
3
4
5
6
7
8
9
Factor
0.909
0.826
0.751
0.683
0.621
0.564
0.513
0.467
0.424
Cash Flow
1
$1,000
1,000
3,000
15,000
3,000
1,000
1,000
Cash Flows
Cash Flow
2
P
P
$ 909
$ 7,000
$ 6,363
826
6,000
4,956
2,253
5,000
3,755
10,245
4,000
2,732
1,863
4,000
2,484
564
4,000
2,256
4,000
2,052
467
2,000
934
$17,127
$25,532
Cash Flow
3
$ 10,000
5,000
3,000
2,000
1,000
1,000
1,000
1,000
P
$ 9,090
4,130
2,253
1,366
621
564
513
425
$18,962
The NPV from investment 2 is highest, at $5,532 (after initial investment of $20,000 is
subtracted).
8
Instructors Solutions Manual t/a Operations Management