Part D Control and Performance Measurement of Responsibilty Centres
5. Use the price function to determine the selling price that would maximise profits We can substitute in 21.182 units into the price function we created before to determine
the selling price that will maximise profits.
130 | P a g e P = 1,520 – 20Q
P = 1,520 – 20 (21.182) P = 1,520 – 423.64 P = 1,096.36
The selling price that will maximise profits is £1,096.36.
Part (c) (i)
Standard costing
A standard cost is a planned or forecast unit cost for a product or service, which is assumed to hold good given expected efficiency and cost levels within an organisation. It represents a target cost and is useful for planning, controlling and motivating within an organisation.
Under a standard costing system an organisation can value stock at standard cost, incorporating this within the ledger or cost accounts of the organisation, the budget or forecasts being a memorandum kept outside the ledger accounts.
Target costing
Market price to achieve desired market share XX
TARGET COST (Balance) (XX)
Desired profit XX
Used by Nissan, Sony and Toyota and many other Japanese companies, who sought not what a product ‘does’ cost (which is what most UK companies used as the method of pricing) but rather what it ‘should’ cost.
The idea is that the product price is determined by the market place, a desired level profit is decided upon and the balance is the costs to manufacture the products through improved processes to be able to reduce costs to sell at the market price. Target costing seeks to continually improve the manufacturing process by the use of JIT, TQM, cost reduction, value analysis and benchmarking.
Standard costing develops a product, determines its cost and adds a mark up to determine a price. This was very much an internal process ignoring competition or demand. Target costing starts with the external market price and works backwards to deicide on levels of cost and profit.
131 | P a g e Part (c) (ii)
AVX Plc sells the CB45 circuit board which is a high technology product and has been able to charge a premium price for these products.
AVX Plc has used this approach and has enjoyed good product volume as little competition exists initially, however it seems that competitors have now managed to create a close substitute to this circuit board and so customers are choosing the cheaper alternative.
This indicates that AVX Plc must look to reducing the price of the circuit board in order to sustain the volume of sales they expect, and use economies of scale to reduce costs. If a price reduction is not made then we could find continuation of falling volumes sold and the CB45 falling out of favour with customers who have bought the cheaper alternative.
It also shows that these circuit boards have a short lifecycle as in six months it seems that the CB45 is already into its maturity stage and perhaps heading towards decline. AVX Plc can no longer set its own price and must accept the market price.
If AVX Plc wanted to sustain the same price for these circuit boards then they to be modified to provide additional functions that customers value which the competitor’s circuit boards do not provide.
A2 – 5 GHK (CIMA P2 May 2006) Part (a)
Workings
W1 – Direct Material A
We know that they used $5 per kg in the budgets. This is in correct as they should have used $7 per kg as the material is in regular use and is not scarce.
Material A cost percentage change = ($7 per kg / $5 per kg) x 100% = 140%
Therefore increase the budgets by 140% to obtain a basis on $7 per kg, and then divide by the number of units budgeted for to obtain a cost per unit.
Product Relevant cost Budgeted units Cost per unit
G $9,000 x 140% = $12,600 3,000 $12,600 / 3,000 = $4.20 H $12,000 x 140% = $16,800 3,000 $16,800 / 3,000 = $5.60 J $4,500 x 140% = $6,300 3,000 $6,300 / 3,000 = $2.10 K $18,000 x 140% = $25,200 3,000 $25,200 / 3,000 = $8.40
132 | P a g e W2 – Direct Material B
This is used when required and the cost of $10 per kg is used in the budgets.
Therefore on a per unit basis:
G: $6,000 / 3,000 units = $2 H: $6,000 / 3,000 units = $2 J: $13,500 / 3,000 units = $4.50 K: $36,000 / 3,000 units = $12 W3 – Direct Labour
This is used when required and the cost of $10 per hour is used in the budgets.
Therefore on a per unit basis:
G: $6,000 / 3,000 units = $2 H: $24,000 / 3,000 units = $8 J: $22,500 / 3,000 units = $7.50 K: $9,000 / 3,000 units = $3 W4 – Overhead
We need to look at the change in overhead costs between different levels of units. This will be our relevant cost for overheads.
3,000 units 5,000
133 | P a g e Part (b)
We need to work out how much extra contribution we can make if we did not supply the major customer.
All resources are available except material B. Let’s find out how much of the scarce resource material B will be released if the major customer was not supplied.
Product Units in contract Material B cost per unit contribution. Therefore we should make product K with the released material B.
We should only produce another 4,000 – 2,017 = 1,983 units of K as demand would be satisfied then. With 1,260 kg of material B we can make another 1,260 kg / 1.20 kg per unit = 1,050 units of K.
The extra contribution from K = 1,050 units x $3.60 per unit = $3,780. As a result of stopping the contract to the major customer it means that we will be stopping the production of J which is loss making, and therefore we will be saving on it’s the specific fixed costs of $1,000. Therefore the extra contribution will be from K = £4,780.
Product Units Contribution per unit Total contribution
G 500 $0.80 $400
H 1,600 $1.40 $2,240
J 800 ($2.10) ($1,680)
K 400 $3.60 $1,440
Total $2,400
More contribution is earned if the contract is ignored. The extra amount of contribution that is earned is $4,780 - $2,400 = $2,380. GHK would be indifferent meeting the contract or paying the penalty if the penalty was $2,380.
134 | P a g e Part (c)
Product Selling Price per unit Contribution per unit C/S ratio
G $10 $0.80 0.80/10 = 0.08
H $20 $1.40 1.40/20 = 0.07
J $15 ($2.10) (2.10)/15 = 0.14
K $30 $3.60 3.60/30 = 0.21
Part (d)
We need to see how fixed costs are covered by the sales of each of these products first, if we are to sketch a profit volume chart. Specific fixed costs can be avoided by not undertaking a product but non-specific or general fixed costs are unavoidable. We need to work out how much non-specific fixed costs we have.
Workings
Product G – for 5,000 units Overhead costs = $8,000
We know that the variable element of this is $1 per unit x 5,000 units = $5,000 We also know that product specific fixed cost is $1,000
Therefore the non-specific fixed cost = $8,000 - $5,000 - $1,000 = $2,000 Product H – for 5,000 units
Overhead costs = $19,000
We know that the variable element of this is $3 per unit x 5,000 units = $15,000 We also know that product specific fixed cost is $1,000
Therefore the non-specific fixed cost = $19,000 - $15,000 - $1,000 = $3,000 Product J – for 5,000 units
Overhead costs = $17,000
We know that the variable element of this is $3 per unit x 5,000 units = $15,000 We also know that product specific fixed cost is $1,000
Therefore the non-specific fixed cost = $17,000 - $15,000 - $1,000 = $1,000 Product K – for 5,000 units
Overhead costs = $17,000
We know that the variable element of this is $3 per unit x 5,000 units = $15,000 We also know that product specific fixed cost is $1,000
Therefore the non-specific fixed cost = $17,000 - $15,000 - $1,000 = $1,000
135 | P a g e Specific fixed costs for all four products 4,000
Total 11,000
We need to now introduce each of the products and noting the cumulative profit or loss figure. We would obviously make the product which gives the most contribution first.
Remember the requirement says that we have no longer any restrictions on resources and make as many as we desire, and we should make up to the demand we have which would of course include the one off contact to a major customer.
Cumulative Profit Cumulative Sales No products sold
(only non-specific costs) -$7,000 Nil
Specific fixed costs of K -$7,000 - $1,000
136 | P a g e Part (e)
The chart illustrates the profit that could be earned by the 4 products. It assumes that we will earn profits in line with contribution and assumes that the products are manufactured in the order of highest contribution earners first.
It also shows which products are earning more contribution as the more steep the line is the more contribution is earned, clearly here we can see that K is the most steep and earns the most contribution then G and then H. J slopes downwards and shows that it is making a negative contribution per unit. J should not be manufactured on these grounds.
We can also see the specific fixed costs for each product on the chart by the initial reduction of profit by £1,000 at the start of each separate product line. The specific fixed would not be spent if the product was not made.
5,000 0
10,000 10,000
5,000 20,000
15,000
50 100 150 200 250 300 350
K
G
H J
Sales ($’000)
Profit/Loss ($’000)
Profit volume chart for products G, H, J, and K
137 | P a g e A2 – 6 H (CIMA P2 May 2007)
Part (a) Relevant costs
Workings $
Technical report W1 0
Material A W2 15,000
Material B W3 2,000
Direct labour W4 500
Supervision W5 0
Machine A W6 240
Machine B W7 100
Despatch W8 400
Fixed overhead costs W9 0
Profit mark-up W10 0
Total costs 18,240
Workings
W1 – Technical report
The cost of the technical report has already been spent and so should not be included. It is a sunk cost.
W2 – Material A
It is a direct material which is regularly used and therefore we would need to use the replacement cost to value it. 10,000 sheets x $1.50 = $15,000.
W3 – Material B
We need 200 litres of ink specifically for the job but we can only buy in order sizes of 250 litres. There is also no certainty of any value for the remaining ink therefore the full amount should be included. $8 x 250 litres = $2,000.
W4 – Direct labour
The cost for direct labour is the overtime = 50hrs x $10p/h = $500.
W5 – Supervision
The cost for the supervisor should be zero as currently she is able to include the additional duties within her current hours.
W6 – Machine A
Lost contribution of machine A hours = 20 hrs x $12per hr = $240.
138 | P a g e W7 – Machine B
These are the extra running costs = 25 machine hrs x $4 per hr = $100.
W8 – Despatch
Delivery cost necessary for the catalogues of $400.
W9 – Fixed overhead costs
These costs are ignored as they are not incurred as result of this job.
W10 – Profit
The profit mark up should be ignored as we are working out the lowest possible quote for this job.
Part (b)
In the case of short-term pricing it is appropriate to look at relevant costing. This is because relevant costing takes into account the true costs and benefits that would occur as a result of selling at a price today. It ignores those costs that have already been spent such as fixed overheads as these would not be incurred now if the product was sold.
In the case of long-term pricing it is appropriate to include these fixed overheads as they have not being occurred yet and would be as result of the manufacture of the product in question. As a result of this the long-term price maybe higher than the short-term price, and may mean that the price is no longer competitive.
Traditional absorption costing systems tries to include an element of fixed overhead costs in the unit cost of products; this would be based on an activity basis that best represents how the fixed overheads will be used. However fixed overheads do not increase or decrease on a per unit basis they change when capacity is reached for a facility in the organisation. This makes the inclusion of fixed overheads arbitrary and the true profitability of the different products distorted.
Relevant costing would ignore the fixed overheads when trying to understand the profitability of the different products because it would show the true contribution to fixed overheads without any arbitrary distortions.
139 | P a g e A2 – 7 DFG (CIMA P2 Nov 2007)
Part (a)
Define the key variables - this is the assigning of letters to the products and services that are needed to be made and then using these letters to represent the amount that should be made at the optimum point.
Let: D = number of D units produced G = number of G units produced
Construct the objective function – this is looking at identifying the main objective that is trying to be achieved. Here we are trying to maximise the contribution for D and G, so we need to work this out first and then construct the objective function.
D per unit ($) G per unit ($)
Selling price 115 120
Direct material A 20 10
Direct material B 12 24
Skilled labour 28 21
Variable overhead 14 18
Contribution 41 47
Objective function:
C = 41D + 47G
Set up the constraints – these show the limits of resources available to us to try and meet the conditions of the objective function and they are usually described as linear equations.
D per unit G per unit Usage of material A 20 / 5 = 4kg 10 / 5 = 2kg Usage of material B 12 / 3 = 4kg 24 / 3 = 8kg Usage of skilled labour 28 / 7 = 4hrs 21 / 7 = 3hrs Usage of machine 14 / 2 = 7hrs 18 / 2 = 9hrs 4D + 2G ≤ 1,800 (Material A constraint)
4D + 8G ≤ 3,500 (Material B constraint)
4D + 3G ≤ 2,500 (Skilled labour hours constraint) 7D + 9G ≤ 6,500 (Machine hours constraint) D ≤ 400, G ≤ 400 (Maximum demand constraints)
140 | P a g e Logic or non-negativity constraints – these are constraints which will ensure that the answer obtained in the solution is sensible in that only zero or positive values are in the answer.
D ≥ 0, G ≥ 0 (Non-negativity constraints)
All constraints are plotted on to a graph and then moving away from the origin a solution is sought where all constraint conditions are met and maximises the objective function.
Material A (4D + 2G = 1,800) If D = 0 then:
4(0) + 2G = 1,800 2G = 1,800 G = 1,800 / 2 G = 900 If G = 0 then:
4D + 2(0) = 1,800 4D = 1,800 D = 1,800 / 4 D = 450
Material B (4D + 8G = 3,500) If D = 0 then:
4(0) + 8G = 3,500 8G = 3,500 G = 3,500 / 8 G = 438 If G = 0 then:
4D + 8(0) = 3,500 4D = 3,500 D = 3,500 / 4 D = 875
141 | P a g e Skilled labour (4D + 3G = 2,500)
If D = 0 then:
4(0) + 3G = 2,500 3G = 2,500 G = 2,500 / 3 G = 833 If G = 0 then:
4D + 3(0) = 2,500 4D = 2,500 D = 2,500 / 4 D = 625
Machine hours (7D + 9G = 6,500) If D = 0 then:
7(0) + 9G = 6,500 9G = 6,500 G = 6,500 / 9 G = 722 If G = 0 then:
7D + 9(0) = 6,500 7D = 6,500 D = 6,500 / 7 D = 929
142 | P a g e Through observing the graph the solution appears to be to make 290 units of G and 315 units of D. This however is only as accurate as the graph drawn. The solution can also be derived through simultaneous equations which is far more accurate than using the graph or graphical method.
We know that our solution is where “material A constraint” intersects with the “material B constraint”.
Material A 4D + 2G = 1,800 Equation 1 Material B 4D + 8G = 3,500 Equation 2
We can use the subtraction method or substitution method to solve. We will use the subtraction method.
Therefore subtract equation 2 from equation 1 4D + 2G = 1,800 Equation 1
143 | P a g e 6G = 1,700
G = 1,700 / 6 G = 283
Substitute G =283 into equation 1 4D + 2(283) = 1,800
4D + 566 = 1,800 4D = 1,800 – 566 4D = 1,234 D = 1,234 / 4 D = 308.5
Therefore to maximise contribution we should make:
308 units of D and 283 units of G.
Part (b)
The shadow price is the extra contribution earned if one more unit of the scarce resource was made available. A shadow price only exists for scarce resource. Skilled labour has a nil shadow price because at the optimal solution it is not fully utilised as there are some skilled labour hours left. This can be seen in the graph in that the optimal solution lies below the skilled labour constraint indicating that there are excess skilled labour hours available.
Direct material A is a scarce resource because at the optimal solution in the graph we are on the constraint itself and so we have fully utilised all this resource. This is further indicated by the value of £5.82 above. If we were to obtain another unit of direct material A then we would earn a contribution of £5.82. Also as a result of this our optimal solution would change.
Part (c)
If the selling price of product D increased then this would have direct impact on the objective function or iso-contribution line. It would change how the objective function sloped.
In order to calculate how much the selling price would have to rise before the optimal solution would change we would have to identify the extreme points of the feasible region and the relative unit contributions of D and G that would cause a change in choice of optimal solution in the objective function.
144 | P a g e A2 – 8 Highly skilled workers (CIMA P2 May 2008)
Part (a)
The limiting factor is material M1 and the most profitable course action would be to make those products that will maximise the contribution earned per square metre of M1.
Amount of M1 available is 1,000 square metres.
M1 used may go to other suppliers who provide both P6 and P4 and not just P6.
Exam tip: The examiner is only after three other factors, however we have given you other factors that could be equally valid to discuss.
145 | P a g e
P6 and P4 maybe complimentary products and so the non- production of P4 may reduce the sales of P6.
The fixed overheads may have a variable element varying with production; if this is the case then contribution will change for some of the products and therefore the optimum production plan.
The stability of the cost of material M1 as if this increases then it may not be beneficial to make C3 and C5 but to buy them in.
The future market of the products if they are going to continue to be popular with customers or whether they are starting to fall out of favour because of better products coming on to the markets to replace them.
The elasticity of demand of the products and in particular how sensitive demand would be to changes in prices.
Part (b)
If we had more material M1 available then we would make a further 750 units of C5 and then 2,000 units of P4.
The amount of M1 needed to make 750 units of C5:
750 units x 0.50 = 375 square metres
This would save $100 per square metre of M1 and so therefore the maximum price would be $120 including the cost of M1.
The amount of M1 needed to make 2,000 units of P4:
2,000 units x 0.75 = 1,500 square metres
This would give contribution of $93.33 per square metres of M1 and so therefore the maximum price would be $113.33 including the cost of M1.
After satisfying these requirements there is no further need for M1 and so therefore the maximum price to be paid for M1 is zero.
Part (c)
If we were to supply this contract and we have no more M1 then we have to stop the production of some or all of C5, C3 and P6. We should stop the production of those products which give us the least amount of contribution per square metre of M1 first.
500 units of P4 would need 500 x 0.75 = 375 square metres of M1.
146 | P a g e Therefore take material M1 as follows to fulfil the new order:
125 square metres from C5 125 square metres from C3 125 square metres from P6 Lost contribution:
C5 125 x $100 $12,500 C3 125 x $124 $15,500 P6 125 x $200 $25,000
Total $53,000
Contribution from the 500 units = 500 x $70 = $35,000
Net benefit from doing the 500 units = $53,000 - $35,000 = $18,000 Therefore the minimum financial penalty must be $18,000.
A2 – 9 RT (CIMA P2 May 2010) Part (a)
In order to find the optimum production plan we must first establish what the scarce resource is that is restricting production to meet all demand. We will work out the total amount of resources needed to meet maximum demand and then compare this to the resources that we have available to us to determine any scarce resources.
R T Total
Total demand 750 1,150
Direct labour (hours) 2,250 5,750 8,000 Material A (kg) 3,750 4,600 8,350 Material B (litre) 1,500 1,150 2,650 Machine hours 2,250 4,600 6,850
Direct labour hours is the scarce resource or limiting factor as we only have available to us 7,500 hours and we need 8,000 hours.
147 | P a g e
Contribution per labour hour 47/3 = 15.67 61/5 = 12.20
Rank in order of production 1 2
Total labour hours available is 7,500 hrs, however we must fulfil a commercial customer order first of 250 R’s and 350 T’s before working out the optimum production plan.
Commercial
Amount of labour hours available after commercial contract is 5,000 hrs.
Labour
Commercial contract Production Total
R 250 500 750
T 350 700 1,050
Contribution per unit from commercial contract
Product R T
148 | P a g e
$6,100. This is less than the financial penalty of $10,000 if the commercial contract was not met, so therefore it is better at least from a financial perspective to fulfil the Objective function = 47R + 61T
Constraints: answer obtained in the solution is sensible in that only zero or positive values are in the answer.
R ≥ 0, T ≥ 0 (Non-negativity or logic)
All constraints are plotted on to a graph and then moving away from the origin a solution is sought where all constraint conditions are met and maximises the objective function.
149 | P a g e (Labour) 3R + 5T = 4,250
If R = 0 then:
3(0) + 5T = 4,250 5T = 4,250 T = 4,250 / 5 T = 850 If T = 0 then:
3R + 5(0) = 4,250 3R = 4,250 R = 4,250 / 3 R = 1,417
(Material A) 5R + 4T = 5,000 If R = 0 then:
5(0) + 4T = 5,000 4T = 5,000 T = 5,000 / 4 T = 1,250 If T = 0 then:
5R + 4(0) = 5,000 5R = 5,000 R = 5,000 / 5 R = 1,000
(Material B) 2R + T = 1,850 If R = 0 then:
2(0) + T = 1,850 T = 1,850 If T = 0 then:
2R + 0 = 1,850 2R = 1,850 R = 1,850 / 2 R = 925
150 | P a g e
The optimal solution is the furthest point away from the origin within the feasible region;
therefore the optimal production plan is make 500 units of R and 550 units of T in
151 | P a g e Part (d)
If there is an increase in optimism by mangers then the constraints would all move to the right illustrating the availability of more resources and production would increase.
Currently the most constraining lines are labour hours and maximum demand for R.
If labour hours were increased then there would be further production of T as the labour constraint would move to the right. This would continue up until the labour constraint intersects with the material A constraint and maximum demand for R, it is at this point material A also becomes a constraining resource and would need to be increased if production were to further increase.
If labour hours were increased then there would be further production of T as the labour constraint would move to the right. This would continue up until the labour constraint intersects with the material A constraint and maximum demand for R, it is at this point material A also becomes a constraining resource and would need to be increased if production were to further increase.