Chapter 18 - Answer
Content
MANAGEMENT ACCOUNTING - Solutions Manual
CHAPTER 18
APPLICATION OF QUANTITATIVE TECHNIQUES IN
PLANNING, CONTROL AND DECISION MAKING II
I.
Questions
1. PERT is superior to Gantt Charts in complex projects because:
a. PERT charts are flexible and can reflect slippage or changes in plans,
but Gantt charts simply plot a bar chart against a calendar scale.
b. PERT charts reflect interdependencies among activities; Gantt charts
do not.
c. PERT charts reflect uncertainties or tolerances in the time estimates
for various activities; Gantt charts do not.
2. The use of PERT provides a structured foundation for planning complex
projects in sufficient detail to facilitate effective control.
A workable sequence of events that comprise the project are first
identified. Each key event should represent a task; then the interdependent
relationships between the events are structured.
After the network of events is constructed, cost and time parameters are
established for each package. Staffing plans are reviewed and analyzed.
The “critical path” computation identifies sequence of key events with
total time equal to the time allotted for the project’s completion. Jobs
which are not on the critical path can be slowed down and the slack
resources available on these activities reallocated to activities on the
critical path.
Use of PERT permits sufficient scheduling of effort by functional areas
and by geographic location. It also allows for restructuring scheduling
efforts and redeployment of workers as necessary to compensate for
delays or bottlenecks. The probability of completing this complex project
on time and within the allotted budget is increased.
3. Time slippage in noncritical activities may not warrant extensive
managerial analysis because of available slack, but activity cost usually
increases with time and should be monitored.
18-1
Chapter 18 Application of Quantitative Techniques in Planning, Control and Decision Making II
4. The critical path is the network path with the longest cumulative expected
activity time. It is critical because a slowdown along this path delays the
entire project.
5. Crashing the network means finding the minimum cost for completing the
project in minimum time in order to achieve an optimum tradeoff between
cost and time. The differential crash cost of an activity is the additional
cost of that activity for each period of time saved.
6. Slack is the amount of time an event can be delayed without affecting the
project’s completion date. Slack can be utilized by management as a
buffer against bottlenecks that may occur on the critical path.
7. Unit gross margin are typically computed with an allocation of fixed
costs. Total fixed costs generally will not change with a change in volume
within the relevant range. Unitizing the fixed costs results in treating them
as though they are variable costs when, in fact, they are not. Moreover,
when multiple products are manufactured, the relative contribution
becomes the criterion for selecting the optimal product mix. Fixed costs
allocations can distort the relative contributions and result in a suboptimal
decision.
8. This approach will maximize profits only if there are no constraints on
production or sales, or if both products use all scarce resources at an
equal rate. Otherwise management would want to maximize the
contribution per unit of scarce resource.
9. The opportunity cost of a constraint is the cost of not having additional
availability of the constrained resources. This is also called a shadow
price.
10. The feasible production region is the area which contains all possible
combinations of production outputs. It is bounded by the constraints
imposed on production possibilities. The production schedule which
management chooses must come from the feasible production region.
11. The accountant usually supplies the contribution margin data that is used
in formulating a profit-maximizing objective function. In addition, the
accountant participates in the analysis of linear programming outputs by
assessing the costs of additional capacity or of changes in product mix.
12. a.
b.
c.
d.
e.
Hourly fee for inventory audit
Salary of purchasing supervisor
Costs to audit purchase orders and invoices
Taxes on inventory
Stockout costs
18-2
(C)
(N)
(P)
(C)
(P)
Application of Quantitative Techniques in Planning, Control and Decision Making – II Chapter
18
f.
g.
h.
i.
j.
Storage costs charged per unit in inventory
Fire insurance on inventory
Fire insurance on warehouse
Obsolescence costs on inventory
Shipping costs per shipment
(C)
(C)
(N)
(C)
(P)
13. Although the inventory models are developed by operations researchers,
statisticians and computer specialists, their areas of expertise do not
extend to the evaluation of the differential costs for the inventory models.
Generally, discussions of inventory models take the costs as given. It is
the role of the accountant to determine which costs are appropriate for
inclusion in an inventory model.
14. Cost of capital represents the interest expense on funds if they were
borrowed or opportunity cost if funds were provided internally or by
owners. It is included as carrying cost of inventory because funds are tied
up in inventory.
15. Costs that vary with the average number of units in inventory:
Inventory insurance
Inventory tax
Total
P 2.80
2.05 (P102.25 x 2%)
P 4.85
Costs that vary with the number of units purchased:
Purchase price
Insurance on shipment
Total
P102.25
1.50
P103.75
Total carrying cost = (25% x P103.75) cost of capital + P4.85 = P25.94 +
P4.85 = P30.79
Order costs:
Shipping permit
Costs to arrange for the shipment
Unloading
Stockout costs
Total
II. Problems
Problem 1 (Solution is found on the next page.)
18-3
P201.65
21.45
80.20
122.00
P425.30
Chapter 18 Application of Quantitative Techniques in Planning, Control and Decision Making II
Problem 2
Requirement (a)
The critical path through each of the three alternative paths calculated as the
longest is 0 - 1 - 6- 7- 8.
0-1-2-5-8
0-1-3-4-7-8
0-1-6-7-8
________
2 + 8 + 10 + 14
2+8+7+5+3
2 + 26 + 9 + 3
=
=
=
34
25
40*
* critical
Requirement (b)
40 - 3 - 5 = 32
Requirement (c)
If path 4 - 7 has an unfavorable time variance of 10, this means it takes a total
time of 15 to finish this activity rather than 5. This gives the path 0 - 1 - 3 - 4
- 7 - 8 a total time of 35, but since this is less than the critical path of 40, it
has no effect.
Requirement (d)
The earliest time for reaching event 5 via 0 - 1 - 2 - 5 is 20, the sum of the
expected times.
Problem 3
No, they didn’t make a right decision, since they included fixed costs which do
not differ in the short run. If they had used contribution margin instead of
gross margin, they would have had P5 for G1 and P6.50 for G2, therefore they
would have decided to produce G2 exclusively.
18-4
Application of Quantitative Techniques in Planning, Control and Decision Making – II Chapter 18
Problem 1
Requirement (a)
TASKS
Hobbing
1
2
3
4
Order 1
Machining X X X X
5
6
7
8
9
10
11
12
Order 3
Order 1
X X
13
14
15
16
17
Order 4
Order 3
18
19
20
21
22
23
24
25
26
27
28
Order 2
X
___________
X Dead Time
Requirement (b)
28 days are required for the four orders.
18-5
X
X
Order 4
Order 2
Chapter 18 Application of Quantitative Techniques in Planning, Control and Decision Making II
Problem 4
Order costs
P
Carrying costs
S
=
Insurance
+
Other order costs
=
P860
+
=
Out-of-pocket
costs
+
Cost of capital
on inventory
=
P65
+
20% x P222
P18
=
P878
=
P119.40
a. Carrying costs:
QS
2
=
Order costs:
AP
=
Q
250 x P109.40
2
=
P13,675.00
1,500 x P878
250
=
P 5,268.00
P18,943.00
Total
b. Economic order quantity:
Q* =
2 x 1,500 x P878
P109.40
= 24,077
Carrying costs:
QS
2
=
155 x P109.40
2
=
P 8,478.50
Order costs:
AP
=
Q
1,500 x P878
155
=
P 8,496.77
P16,975.27
Total
Problem 5
18-6
=
155 units
Application of Quantitative Techniques in Planning, Control and Decision Making – II Chapter
18
It is necessary to evaluate the annual carrying costs and expected stockout
costs at each safety-stock level. The carrying cost will be P24.40 for each
unit in safety stock. With the given order size, there are 15 orders placed a
year (i.e., 39,000/2,600 = 15). Based on these computations, we prepare the
following schedule:
Safety
Stock
0
150
175
250
Carrying Costs
of Safety Stock
0
150 x P24.40 = P3,660
175 x P24.40 = P4,270
250 x P24.40 = P6,100 b
Expected Stockout
Costs
0.50 x 15a x P1,650 = P12,375
0.20 x 15a x P1,650 = P 4,950
0.05 x 15a x P1,650 = P 1,273.5
0.01 x 15a x P1,650 = P 247.5
Total
Costs
P12,375
8,610
5,507.5 (optional)
6,347.5
Additional computations:
a
b
15 is the number of orders per year.
It should be evident that at this level the carrying costs alone exceed the total
costs at a safety stock of 175 units. Therefore, it is not possible for this or any
safety-stock level larger than 250 to be less costly than 175 units. Indeed, given a
total cost at 175 units of P5,507.5, stockout costs would have to occur with
probability zero for any safety stock greater than 225.72 units (i.e., P5,507.5 /
P24.40 = P225.72).
III. Multiple Choice Questions
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
C
B
D
B
D
C
A
A
A
C
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
D
C
A
A
A
C
C
D
C
D
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
18-7
D
C
C
D
D
B
D
E
B
A
31.
32.
33.
34.
35.
36.
37.
38.
C
D
A
C
D
C
D
D
CHAPTER 18
APPLICATION OF QUANTITATIVE TECHNIQUES IN
PLANNING, CONTROL AND DECISION MAKING II
I.
Questions
1. PERT is superior to Gantt Charts in complex projects because:
a. PERT charts are flexible and can reflect slippage or changes in plans,
but Gantt charts simply plot a bar chart against a calendar scale.
b. PERT charts reflect interdependencies among activities; Gantt charts
do not.
c. PERT charts reflect uncertainties or tolerances in the time estimates
for various activities; Gantt charts do not.
2. The use of PERT provides a structured foundation for planning complex
projects in sufficient detail to facilitate effective control.
A workable sequence of events that comprise the project are first
identified. Each key event should represent a task; then the interdependent
relationships between the events are structured.
After the network of events is constructed, cost and time parameters are
established for each package. Staffing plans are reviewed and analyzed.
The “critical path” computation identifies sequence of key events with
total time equal to the time allotted for the project’s completion. Jobs
which are not on the critical path can be slowed down and the slack
resources available on these activities reallocated to activities on the
critical path.
Use of PERT permits sufficient scheduling of effort by functional areas
and by geographic location. It also allows for restructuring scheduling
efforts and redeployment of workers as necessary to compensate for
delays or bottlenecks. The probability of completing this complex project
on time and within the allotted budget is increased.
3. Time slippage in noncritical activities may not warrant extensive
managerial analysis because of available slack, but activity cost usually
increases with time and should be monitored.
18-1
Chapter 18 Application of Quantitative Techniques in Planning, Control and Decision Making II
4. The critical path is the network path with the longest cumulative expected
activity time. It is critical because a slowdown along this path delays the
entire project.
5. Crashing the network means finding the minimum cost for completing the
project in minimum time in order to achieve an optimum tradeoff between
cost and time. The differential crash cost of an activity is the additional
cost of that activity for each period of time saved.
6. Slack is the amount of time an event can be delayed without affecting the
project’s completion date. Slack can be utilized by management as a
buffer against bottlenecks that may occur on the critical path.
7. Unit gross margin are typically computed with an allocation of fixed
costs. Total fixed costs generally will not change with a change in volume
within the relevant range. Unitizing the fixed costs results in treating them
as though they are variable costs when, in fact, they are not. Moreover,
when multiple products are manufactured, the relative contribution
becomes the criterion for selecting the optimal product mix. Fixed costs
allocations can distort the relative contributions and result in a suboptimal
decision.
8. This approach will maximize profits only if there are no constraints on
production or sales, or if both products use all scarce resources at an
equal rate. Otherwise management would want to maximize the
contribution per unit of scarce resource.
9. The opportunity cost of a constraint is the cost of not having additional
availability of the constrained resources. This is also called a shadow
price.
10. The feasible production region is the area which contains all possible
combinations of production outputs. It is bounded by the constraints
imposed on production possibilities. The production schedule which
management chooses must come from the feasible production region.
11. The accountant usually supplies the contribution margin data that is used
in formulating a profit-maximizing objective function. In addition, the
accountant participates in the analysis of linear programming outputs by
assessing the costs of additional capacity or of changes in product mix.
12. a.
b.
c.
d.
e.
Hourly fee for inventory audit
Salary of purchasing supervisor
Costs to audit purchase orders and invoices
Taxes on inventory
Stockout costs
18-2
(C)
(N)
(P)
(C)
(P)
Application of Quantitative Techniques in Planning, Control and Decision Making – II Chapter
18
f.
g.
h.
i.
j.
Storage costs charged per unit in inventory
Fire insurance on inventory
Fire insurance on warehouse
Obsolescence costs on inventory
Shipping costs per shipment
(C)
(C)
(N)
(C)
(P)
13. Although the inventory models are developed by operations researchers,
statisticians and computer specialists, their areas of expertise do not
extend to the evaluation of the differential costs for the inventory models.
Generally, discussions of inventory models take the costs as given. It is
the role of the accountant to determine which costs are appropriate for
inclusion in an inventory model.
14. Cost of capital represents the interest expense on funds if they were
borrowed or opportunity cost if funds were provided internally or by
owners. It is included as carrying cost of inventory because funds are tied
up in inventory.
15. Costs that vary with the average number of units in inventory:
Inventory insurance
Inventory tax
Total
P 2.80
2.05 (P102.25 x 2%)
P 4.85
Costs that vary with the number of units purchased:
Purchase price
Insurance on shipment
Total
P102.25
1.50
P103.75
Total carrying cost = (25% x P103.75) cost of capital + P4.85 = P25.94 +
P4.85 = P30.79
Order costs:
Shipping permit
Costs to arrange for the shipment
Unloading
Stockout costs
Total
II. Problems
Problem 1 (Solution is found on the next page.)
18-3
P201.65
21.45
80.20
122.00
P425.30
Chapter 18 Application of Quantitative Techniques in Planning, Control and Decision Making II
Problem 2
Requirement (a)
The critical path through each of the three alternative paths calculated as the
longest is 0 - 1 - 6- 7- 8.
0-1-2-5-8
0-1-3-4-7-8
0-1-6-7-8
________
2 + 8 + 10 + 14
2+8+7+5+3
2 + 26 + 9 + 3
=
=
=
34
25
40*
* critical
Requirement (b)
40 - 3 - 5 = 32
Requirement (c)
If path 4 - 7 has an unfavorable time variance of 10, this means it takes a total
time of 15 to finish this activity rather than 5. This gives the path 0 - 1 - 3 - 4
- 7 - 8 a total time of 35, but since this is less than the critical path of 40, it
has no effect.
Requirement (d)
The earliest time for reaching event 5 via 0 - 1 - 2 - 5 is 20, the sum of the
expected times.
Problem 3
No, they didn’t make a right decision, since they included fixed costs which do
not differ in the short run. If they had used contribution margin instead of
gross margin, they would have had P5 for G1 and P6.50 for G2, therefore they
would have decided to produce G2 exclusively.
18-4
Application of Quantitative Techniques in Planning, Control and Decision Making – II Chapter 18
Problem 1
Requirement (a)
TASKS
Hobbing
1
2
3
4
Order 1
Machining X X X X
5
6
7
8
9
10
11
12
Order 3
Order 1
X X
13
14
15
16
17
Order 4
Order 3
18
19
20
21
22
23
24
25
26
27
28
Order 2
X
___________
X Dead Time
Requirement (b)
28 days are required for the four orders.
18-5
X
X
Order 4
Order 2
Chapter 18 Application of Quantitative Techniques in Planning, Control and Decision Making II
Problem 4
Order costs
P
Carrying costs
S
=
Insurance
+
Other order costs
=
P860
+
=
Out-of-pocket
costs
+
Cost of capital
on inventory
=
P65
+
20% x P222
P18
=
P878
=
P119.40
a. Carrying costs:
QS
2
=
Order costs:
AP
=
Q
250 x P109.40
2
=
P13,675.00
1,500 x P878
250
=
P 5,268.00
P18,943.00
Total
b. Economic order quantity:
Q* =
2 x 1,500 x P878
P109.40
= 24,077
Carrying costs:
QS
2
=
155 x P109.40
2
=
P 8,478.50
Order costs:
AP
=
Q
1,500 x P878
155
=
P 8,496.77
P16,975.27
Total
Problem 5
18-6
=
155 units
Application of Quantitative Techniques in Planning, Control and Decision Making – II Chapter
18
It is necessary to evaluate the annual carrying costs and expected stockout
costs at each safety-stock level. The carrying cost will be P24.40 for each
unit in safety stock. With the given order size, there are 15 orders placed a
year (i.e., 39,000/2,600 = 15). Based on these computations, we prepare the
following schedule:
Safety
Stock
0
150
175
250
Carrying Costs
of Safety Stock
0
150 x P24.40 = P3,660
175 x P24.40 = P4,270
250 x P24.40 = P6,100 b
Expected Stockout
Costs
0.50 x 15a x P1,650 = P12,375
0.20 x 15a x P1,650 = P 4,950
0.05 x 15a x P1,650 = P 1,273.5
0.01 x 15a x P1,650 = P 247.5
Total
Costs
P12,375
8,610
5,507.5 (optional)
6,347.5
Additional computations:
a
b
15 is the number of orders per year.
It should be evident that at this level the carrying costs alone exceed the total
costs at a safety stock of 175 units. Therefore, it is not possible for this or any
safety-stock level larger than 250 to be less costly than 175 units. Indeed, given a
total cost at 175 units of P5,507.5, stockout costs would have to occur with
probability zero for any safety stock greater than 225.72 units (i.e., P5,507.5 /
P24.40 = P225.72).
III. Multiple Choice Questions
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
C
B
D
B
D
C
A
A
A
C
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
D
C
A
A
A
C
C
D
C
D
21.
22.
23.
24.
25.
26.
27.
28.
29.
30.
18-7
D
C
C
D
D
B
D
E
B
A
31.
32.
33.
34.
35.
36.
37.
38.
C
D
A
C
D
C
D
D
