ACCA - P5 Study text - Emile Woolf INT - 2010
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Answers
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$
Contribution from Product X: 8,000 × $6
48,000
Contribution from Product Y: 10,000 × $7
70,000
Total contribution 118,000
Fixed costs 90,000
Profit 28,000
(b) Throughput accounting is based on the view that value is not added to a
product until the product is eventually sold. There is no value in inventory.
When there is a limiting factor restricting production, all costs except for the
cost of bought-in materials (raw materials, purchased components) are fixed
costs in the short term, including direct labour costs and associated ‘variable’
overheads.
The aim should be to maximise throughput in a period, where throughput is
defined as sales minus the cost of bought-in materials.
The main difference between throughput accounting and marginal costing is
in the treatment of direct labour and variable overhead costs as a ‘fixed cost’ in
the short term. In throughput accounting, fixed costs are referred to as ‘factory
cost’.
(c) Throughput accounting ratio =
Return per bottleneck unit / Factory cost per bottleneck unit
Here, the bottleneck resource is machine time.
Product X
Product Y
$
$
Sales price 22
27
Materials cost 10
9
Throughput 12
18
Machine hours per unit 1.5 hours 2 hours
Throughput/return per machine hour $8 $9
To calculate the cost per factory hour, we need to make an assumption about
direct labour cost and variable overhead costs. It is assumed that the direct
labour cost and variable overhead cost in the answer to part (a) is fixed in the
short term.
$
Direct labour and variable overhead costs:
Product X: 8,000 × $6
48,000
Product Y: 10,000 × $11
110,000
Total contribution 158,000
Fixed costs 90,000
Factory cost in each period 248,000
Factory cost per machine hour = $248,000/32,000 hours = $7.75.
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Product X Product Y
Return per machine hour $8 $9
Factory cost per machine hour $7.75 $7.75
Machine hours per unit 1.5 hours 2 hours
Throughput accounting ratio 1.03 1.16
Priority for manufacture 2
nd
1
st
Tutorial note: The aim should be to maximise the throughput accounting
ratio, and to ensure that the ratio is higher than 1.0. The throughput
accounting ratio for both Product X and Product Y is low, close to the
minimum acceptable level.
(d) Profit will be maximised by making and selling 12,000 units of Product Y
(maximum sales demand). This will use up 24,000 machine hours. The
remaining 8,000 machine hours should be used to make 5,333.33 units of
Product X.
$
Return from Product Y: 12,000 × $18
216,000
Return from Product Y: 5,333.33 × $12
64,000
Total return/throughput 280,000
Fixed costs 248,000
Profit 32,000
4 Throughput ratio
Throughput per pallet = $3,000 – $2,000 = $1,000.
Throughput per inspection hour = $1,000/0.5 hours = $2,000.
Operating expenses per inspection hour = $300,000/200 = $1,500.
Throughput accounting ratio = $2,000/$1,500 = 1.33.
5 Backflush
Backflush accounting, with two trigger points
Raw materials inventory account
$
$
Creditors 5,000,000
Finished goods inventory 5,000,000
Finished goods inventory account
$
$
Raw materials
(100,000 × 50)
5,000,000
Income statement
(98,000 × 80)
7,840,000
Conversion costs
(100,000 × 30)
3,000,000
Balance c/f (2,000 × 80)
160,000
8,000,000
8,000,000
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Conversion costs account
$
$
Creditors (overheads) 3,000,000
Finished goods inventory 3,000,000
3,000,000
3,000,000
Sales
$
$
Income statement
(98,000 × 100) 9,800,000
Receivables
(98,000 × 100) 9,800,000
Income statement
$
$
Finished goods 7,840,000
Sales 9,800,000
Profit 1,960,000
9,800,000
9,800,000
6 Villaco
(a) Total machine hours required to meet sales demand = (2,000 × 4) + (3,000 × 1)
= 11,000. Since only 7,000 hours are available, machine hours are a limiting
factor.
Product A Product B
$ $
Sales price 20 10
Variable cost 8 6
Contribution 12 4
Machine hours per unit 4 1
Contribution per hour $3 $4
Priority for manufacture 2
nd
1
st
Decision: produce and sell the following products
Product
Units
Machine
hours
Contribution
per unit
Total
contribution
$
$
B 3,000 3,000
4
12,000
A (balance) 1,000 4,000
12
12,000
7,000
24,000
(b)
Product A Product B
$ $
Extra cost of external purchase 1 0.50
Machine hours saved by external purchase 4 1
Extra cost per machine hour saved $0.25 $0.50
Priority for manufacture 2nd 1st
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Item Number
of units
Machine
hours
Contribution
per unit
Contribution
Make
$ $
A 1,750
7,000
12 21,000
Buy
A (balance) 250
(12 – 1)
11 2,750
B 3,000
(4 – 0.5)
3.5 10,500
Total contribution
34,250
7 Shortages
Working: contribution per unit
A B C D
$/unit $/unit $/unit $/unit
Profit 35
55
30
55
Fixed costs:
Production 180
240
150
270
Selling 145
225
120
215
Contribution 360
520
300
540
Resources required for the priority order for the major customer
Casing
Units
required
Steel
Direct labour
per unit Total per unit Total
$
$
hours
hours
A 30 250
7,500
7.5
225.0
B 20 500
10,000
7.5
150.0
C 30 190
5,700
6.25
187.5
D 20 390
7,800
12.5
250.0
Total
31,000
812.5
(a) Steel in short supply and restricted to $250,000
Casing A B C D
$ $ $ $
Contribution/unit 360
520
300
540
Steel costs/unit 250
500
190
390
Contribution/$1 steel cost
1.44
1.04
1.58
1.38
Ranking for manufacture 2
n
d
4
th
1
s
t
3
r
d
It is assumed that the sales forecasts for the month are correct.
Profit-maximising production schedule
Steel used A B C D
$ units units units units
Priority order 31,000
30
20
30 20
Sales of C 51,300
270
Sales of A 67,500
270
Sales of D 70,200
180
220,000
Balance: Sales of B 30,000
60
Total steel available 250,000
Total production/sales
300
80
300 200
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(b) Components are in short supply and restricted to 400 units
A B C D
Contribution/unit $360 £520 $300 $540
Components/unit 1
1
1
1
Contribution/component £360
$520
$300
$540
Ranking for manufacture 3
r
d
2
n
d
4
th
1
s
t
Profit-maximising production schedule
Components used A B C D
units units units units units
Priority order 100
30
20
30 20
Sales of D 180
180
280
Balance: Sales of B 120
120
Total available 400
Total production/sales
30
140
30 200
(c) Labour is in short supply and restricted to 2,125 hours
Casing A B C D
Contribution/unit $360 $520 $300 $540
Labour hours/unit 7.5
7.5
6.25
12.5
Contribution per hour $48.00
$69.33
$48.00
$43.20
Ranking for manufacture 2
n
d
=
1
s
t
2
n
d
=
4
th
Profit-maximising production schedule
Labour hours A B C D
units units units units
Special order 812.5
30
20
30 20
Remaining hours 1,312.5
175
Total hours 2,125.0
Total production/sales
30
195
30 20
(d) Make or buy decision
A B C D
$ $ $ $
Contribution if made 360
520
300 540
Contribution if bought in 285
475
250 490
Extra contribution if made
75
45
50 50
Labour hours 7.5
7.5
6.25 12.5
Extra contribution per hour
$10
$6
$8 $4
Ranking/priority for making
1
s
t
3
r
d
2
n
d
4
th
Profit-maximising production schedule
Casing Hours A B C D
Special order 1,625 30 20 30 20
Remaining hours 2,625
175
Total hours 4,250
Made internally
205
20
30 20
Purchased externally
95
180
270 180
Total sales
300
200
300 200
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8 Product B22
Workings for relevant costs
Material X
The company has enough kilograms of material X in stock for the contract. When it
is used, the stocks of material X will not be replaced. The relevant cost of the
material is therefore its opportunity cost, not its replacement cost. The opportunity
cost is the higher of its current sale value ($7.50 per kg) or the net saving obtained if
it is used as a substitute for material Z ($9.50 – $1.50 = $8 per kg). The relevant cost
of material X is therefore $8 per kg.
Material Y
Material Y is in regular use, so its relevant cost is its current replacement cost.
kg
$
Total inventory 10,000 142,750
Purchased six months ago 3,000
(
×
$13.75)
41,250
Purchased last month 7,000
101,500
Purchase price last month = $101,500/7,000 kg = $14.50 per kg.
Current purchase price = 4% higher = $14.50 × 1.04 = $15.08.
Skilled labour
Skilled labour is in short supply. If it is used to make product B22, workers will
have to be taken off other work. The relevant cost of skilled labour is the wages for
the skilled workers for the time spent on B22, plus the lost contribution (net of
skilled labour cost) from not being able to make units of product B16.
Opportunity cost of skilled labour
Skilled labour cost per unit of Product B16 = $24
Number of hours per unit = 3 hours
Contribution per unit of B16 = $45
Contribution per skilled labour hour from B16 = $15
Opportunity cost of skilled labour if it is used to make B22 = (500 × 5) × $15 = $37,500
Unskilled labour
900 unskilled labour will be available at no incremental cost to the company (as it is
already being paid and is not fully employed). There is no relevant cost for these
hours. The additional 600 hours required will involve extra wage payments,
including overtime payments. The relevant cost of these 600 hours is $6 per hour ×
150% = $9 per hour, including the overtime premium.
Overheads
Variable overheads are included as relevant costs because they will be additional
costs if the units of B22 are made. The only incremental fixed costs, however, are the
extra cash costs of $4,000. The fixed overhead absorption rate is ignored. The
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additional costs of hiring special finishing machinery are also included as a relevant
cost.
Development costs
Those costs already incurred are past costs (sunk costs) and are not relevant. The
future development costs involve additional expenditure and are included as
relevant costs.
Minimum price for making 500 units of B22
Materials: £
X (500 units × 4kg) × $8 16,000
Y (500 units × 6kg) × $15.08
45,240
Labour:
Skilled wages
(500 units × 5 hours) × $8
20,000
Opportunity cost (500 units × 5 hours) × $15
37,500
Unskilled [(500 × 3)
–
900] x 6 × 1.5
5,400
Overheads:
Variable (500 units × 2 hours) × 8.75
8,750
Fixed Incremental spending
4,000
Machine hire (2 weeks × $2,650)
5,300
Development costs 1,750
Minimum price
143,940
9 Payoff table
(a)
Cost of buying Revenue from selling
Quantity $ Quantity $
20 2 20 6
40 4 40
12
60 6 60
18
Pay-off table, without perfect information
Sales demand per day
20 40 60
Purchases per day
$ $ $
20
4
4
4
(6
–
2)
(6
–
2)
(6
–
2)
40
2
8
8
(6
–
4)
(12
–
4)
(12
–
4)
60
0
6
12
(6
–
6)
(12
–
6)
(18
–
6)
EV of buying decision, without perfect information
Sales demand
EV of daily
profit
20 40 60 $
Probability 0.3
0.5
0.2
Purchases per day
$
$
$
20
4
4
4
EV
1.2
2.0
0.8
4.0
40
2
8
8
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EV
0.6
4.0
1.6
6.2
60
0
6
12
EV
0
3.0
2.4
5.4
On the basis of EV, and without perfect information about daily sales demand, the
decision should be to buy 40 buns per day, and the EV of daily profit will be $6.20.
(b)
With perfect information
With perfect information about daily sales demand, the baker will purchase the
exact number of buns to meet demand. Profit will be $4 when sales demand is 20, $8
when sales demand is 40 and $12 when sales demand is 60.
Sales and purchases Profit Probability EV
$ $
20 4
0.3
1.2
40 8
0.5
4.0
60 12
0.2
2.4
EV of profit with perfect information
7.6
EV of profit with perfect information
6.2
Value of perfect information 1.4
The value of having perfect information about sales demand each day is $1.40 per
day.
10 Grab Company
(a) Outcomes
Decision Outcome
Turnover
Variable
cost
Advance
hire
Conversion
premium
Profit
Low Low 4,000
2,800
1,000
0 200
Medium 8,500
5,950
1,000
850 700
High 15,000
10,500
1,000
2,150 1,350
Medium
Low 4,000
2,800
1,500
0 (300)
Medium 8,500
5,950
1,500
0 1,050
High 15,000
10,500
1,500
1,300 1,700
High Low 4,000
2,800
2,300
0 (1,100)
Medium 8,500
5,950
2,300
0 250
High 15,000
10,500
2,300
0 2,200
(b) Pay-off matrix
Low Medium High Expected value
Probability (p) 0.30 0.45 0.25
∑px
Decision
x =
x =
x =
Low 200
700
1,350 712.5
Medium
(300)
1,050
1,700 807.5
High (1,100)
250
2,200 332.5
The highest expected value is earned if the medium advance hire usage
contract is signed.
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(c) Risk preferences
The above decision assumes a neutral risk preference. It is possible the
organisation may adopt a different decision criterion than expected value.
Other decision criteria may be based on a risk-seeking approach or a risk-
averse approach.
Risk-seeking managers would prefer a maximax approach. This is to
maximise the highest possible outcome. In this example this would require a
high advance hire contract.
Risk-averse managers would prefer a maximin approach. This is to maximise
the lowest possible outcome of a course of action. This would require a low
advance hire contract.
(d) Value of perfect information
The maximum value to be paid for perfect information will be
EV
(perfect information)
– EV
(no information)
EV
(perfect information)
will ensure that the decision will always maximise the
EV of a given outcome.
Net profit Probability Expected value
$000 $000
High outcome
–
High advance hire
2,200
0.25 550.0
Medium outcome
–
Medium advance hire
1,050
0.45 472.5
Low outcome – Low advance hire
200
0.30 60.0
1,082.5
Value of perfect information = $1,082,500 – $807,500 = $275,000.
11 Learning
(a) (1)
hours
Average time for 1
st
2 units (200 hours × 80%)
160
Total time for 1
s
t
2 units (160 × 2)
320
Time for first unit 200
Time for second unit 120
Selling price for the second unit: $
Direct materials 2,000
Direct labour (120 hours
×
$15)
1,800
Fixed production overhead (120 hours
×
$20)
2,400
Full production cost 6,200
Profit margin (40%) 2,480
Selling price 8,680
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(2)
hours
Average time for 1
st
4 units (200 hours × 80% × 80%)
128
Total time for 1
s
t
4 units (128 × 4)
512
Time for 1
s
t
2 units
320
Time for 3
r
d
and 4
th
units
192
Average time per unit for 3
r
d
and 4
th
units
96
Average price for the 3
r
d
and 4
t
h
units: $
Direct materials 2,000
Direct labour (96 hours × $15)
1,440
Fixed production overhead (96 hours
×
$20)
1,920
Full production cost 5,360
Profit margin (40%) 2,144
Average selling price 7,504
(3)
hours
Average time for 1
st
8 units (200 hours × 80% × 80%× 80%)
102.4
Total time for 1
st
8 units (102.4
×
8)
819.2
Selling price for the first 8 units $
Direct materials ($2,000 × 8)
16,000.0
Direct labour (819.2 hours
×
$15)
12,288.0
Fixed production overhead (819.2 hours
×
$20)
16,384.0
Full production cost
44,672.0
Profit margin (40%)
17,868.8
Selling price 62,540.8
This gives an average selling price of $7,817.6 per unit.
(b) (1) It may be difficult to establish an expected learning rate. Reliable
statistical evidence of a constant learning rate (for example, as in the
aircraft manufacturing industry) is required.
(2) Learning curve theory is of little value for the development of low-cost
items where direct labour input is small. The benefits from the learning
curve would be small and fairly insignificant.
(3) Learning curve theory assumes that when the first unit has been made,
every other unit will be similar. It does not allow for changes in design
or other factors that could disrupt the learning effect and change the
learning rate.
12 Greenears
The cost of producing batches 6 – 12 is the difference between:
the cost of producing batches 1 – 5, and
the cost of producing batches 1 – 12.