Part D Control and Performance Measurement of Responsibilty Centres
4. Demand based approach
TQ could create a demand function much like that created from the second generation phones in part (a). This would represent a straight line relationship between price charged and quantity sold (P = a - bx) of the third generation phones, and allow us to find that price that we can charge that would maximise profits (MR = MC).
The main problem with this is that the quality of the market research to determine the demand function has to be very good, for it to have any real value.
It also assumes that price and quantity are the only factors in determining demand, but TQ must be mindful of other factors which are just as important such as quality, advertising, substitutes and brand loyalty. It is difficult to estimate the demand curve.
The demand function approach does give us a useful insight into the relationship between price and quantity and a basis to predict what strategy to take. It makes an attempt to incorporate demand into its calculations and is concerned with the marginal costs of making decision ignoring irrelevant costs.
The demand function also allows us to see at what price and quantity we would maximise profits and we can predict quantity sold given any selling price and vice versa.
I hope you have found this report useful but should you require any further assistance or have any questions please do not hesitate to contact me.
Signed : Management Accountant.
121 | P a g e A2 – 2 QP plc (CIMA P2 Nov 2005)
Part (a)
The theory of constraints is where a bottleneck exists (or limiting factor in production);
this therefore is a constraint on throughput. Throughput is the rate of production.
A manager’s aim in this situation would be to operate the bottleneck resource at 100%
capacity, whilst running non-bottleneck resources at a speed that matches this (which may not be at 100%). This would be efficient use of resources, but also would avoid the pile up of unnecessary work-in-progress in a JIT environment.
Throughput accounting aims to maximise contribution whilst minimising conversion (labour and overhead) cost.
Throughput contribution = Sales - material cost
It is assumed only materials and components are the variable cost.
Conversion cost = all other fixed cost
Return per factory hour is similar to the concept of contribution maximisation; you should notice the following calculation is similar to the contribution per unit of a limiting factor used in short-term decision-making.
Return per factory hour = Sales less material cost
Usage (in hours) of the bottleneck resource
TA ratio = Contribution (sales less material) per hour Conversion cost per hour (or cost per factory hour)
The above TA ratio can be used to assess the manager in terms of how well they have done maximising contribution, whilst eliminating the build up of stock.
Such a technique is similar to limiting factor analysis, as managers try to improve their TA Ratio they must concentrate on producing those products that generate the highest contribution per bottleneck resource (or limiting factor) in order to optimise contribution and therefore profit.
Traditionally when absorption costing was used, managers could improve results by setting production levels higher than sales (therefore the carry forward of fixed overhead this period to the next in the valuation of closing stock), however stock piling is not a good thing and such stock piling will not improve performance if you use the TA Ratio.
122 | P a g e Part (b)
We need to first identify the limiting factor and from the question it would seem it is only ingredient L. Ingredient M may be limited but it has a substitute being V which has unlimited supply. Having identified the limiting factor we must now work out the contribution we earn from each of the meals, then the contribution per kg of L, and then rank in order of production.
Throughput contribution 90 165 95
Kg of L used 7kg 9kg 4kg
Contribution per kg of L £90/7kg = £12.86 £165/9kg = £18.33 £95/4kg = £23.75
Rank in order of production 3 2 1
Total ingredient L available is 7,000kg, however we must make a minimum order first of 50 batches for each type of meal. The ingredients used for this must be deducted before working out the optimum production plan.
Minimum contract Kg of L per batch Ingredient L used
TR 50 7 350kg
PN 50 9 450kg
BE 50 4 200kg
Total 1,000kg
Amount of ingredient L available after the minimum contract is 6,000kg.
L used
Minimum contract Production Total
PN 50 350 400
BE 50 300 350
TR 50 236 286
123 | P a g e Part (c)
We need to interpret the linear programming solution that the computer has produced.
Objective function
This is £110,714 and is the maximum contribution that can be earned given the constraints.
TR, PN and BE values
These are the amounts we should produce in order to maximise contribution. Therefore we should make 500 batches of TR, 357 batches of PN and 71 batches of BE.
TR slack value
This is zero and represents the fact that we have produced up to the maximum demand of TR, this being 500 batches. There is no shortfall in demand.
PN and BE slack values
These values represent the fact that we have not met our maximum demands for PN and BE by 43 batches and 279 batches respectively. We are only producing 357 PN’s and 71 BE’s where our maximum demand is 400 and 350 batches respectively.
L and M values
These values represent shadow prices for ingredients L and M as they are both scarce resources. Ingredient M is now also scarce because it says in the question that substitute ingredient V is poisonous and therefore cannot be used.
The values show that for each kg of scarce resource we obtain at normal cost we can expect to earn £3 of contribution for each kg of L and £28 contribution for each kg of M.
Ingredient K does not have a shadow price because it is not a scarce resource; we have enough of K to produce our batches.
124 | P a g e A2 – 3 ZP plc (CIMA P2 Nov 2005)
Part (a)
Workings D E F Total
Consultants salary W1 40,000 140,000 60,000 240,000
Travel W2 4,000 7,000 4,000 15,000
Accommodation W3 nil 8,000 3,000 11,000
44,000 155,000 67,000 266,000
Workings
W1 - Consultants salary are direct costs for each client group, driven by chargeable hours.
Total cost = 4 x £60,000 = £240,000
Chargeable hours = (100 x 10) + (700 x 5) + (300 x 5) = 6,000 hours Rate per hour = £240,000 / 6,000 hours = £40 per hour
Cost for D = £40 x 100 x 10 = £40,000 Cost for E = £40 x 700 x 5 = £140,000 Cost for F = £40 x 300 x 5 = £60,000
W2 – Travel cost driven by number of miles.
Number of total miles = (50 x 3 x 10) + (70 x 8 x 5) + (100 x 3 x 5) = 5,800 miles Cost per mile = £15,000 / 5,800 miles = £2.59 per mile
Cost for D = £2.59 x 50 x 3 x 10 = £ 3,885 Cost for E = £2.59 x 70 x 8 x 5 = £7,252 Cost for F = £2.59 x 100 x 3 x 5 = £3,885
W3 – Accommodation costs are driven by visits to clients in excess of 50 miles.
Therefore not applicable to client D as distance to their clients is less than 50 miles.
Number of qualifying visits = (8 x 5) + (3 x 5) = 55 Cost per visit = £11,000 / 55 = £200
Cost for E = £200 x 8 x 5 = £8,000 Cost for F = £200 x 3 x 5 = £3,000
125 | P a g e
There is no obvious activity which directly drives these costs and therefore we must leave them out of our calculations as they would not add any further benefit if they were included.
Part (b)
Comparing the current system with the proposed ABC system
D E F Total
Chargeable hours 1,000 3,500 1,500 6,000
£ £ £ £
Current system (£75p/hr) 75,000 263,000 113,000 451,000
ABC 44,000 155,000 67,000 266,000
Difference 31,000 108,000 46,000 185,000
The difference is due to the unattributable costs of £185,000 as shown in part (a). We need to obtain a cost driver for these other costs to make the above comparison more meaningful.
We need to look at whether the same or similar figures can be arrived at by doing a rate per chargeable hour on the total costs for ABC.
Blanket rate on chargeable hours = £266,000 / 6,000 hrs = £44.33p/hr
D E F Total
Chargeable hours 1,000 3,500 1,500 6,000
£ £ £ £
Blanket (£44.33p/hr) 44,333 155,155 66,500 265,988
ABC 44,000 155,000 67,000 266,000
Difference 333 155 (500) (12)
It seems that ABC does not add much more value than the current system, as the current system gives similar figures.
In conclusion ABC is theoretically superior, but in this case perhaps not appropriate unless further costs drivers reveal different figures.
126 | P a g e Part (c)
Unit level costs
These are driven by the quantity of items produced. The more produced the lower the unit cost.
Example:
Consultants produce chargeable hours in exchange for their salary at work. We can work out a unit cost per chargeable hour. Cost per hour = £240,000 / 6,000 hours = £40 per hour
Batch level costs
These are costs incurred for every time a batch is processed for example administration costs maybe incurred when a batch of mugs are made in a factory.
Examples:
The cost incurred in visiting every client once.
The cost incurred in billing every client.
The cost incurred in chasing clients for outstanding monies.
The cost incurred in negotiating the fees on a contract with a client.
Product sustaining
These are costs needed to continue the product in the future, for example client care costs.
Examples:
The cost to employ administrative staff to organise, plan for clients service requirements.
The cost to entertain clients such as buying them lunch, evening meals and drinks or even tickets to see sports events.
Facility sustaining
These are fixed costs spent for the use of the company as a whole, for example warehouse or machinery costs.
Examples:
Telephone systems, fax machines, photocopiers and the canteen.
127 | P a g e A2 – 4 AVX plc (CIMA P2 May 2006)
Part (a) (i) (ii) November
1 batch made which took 50 hours which took as long as the standard and therefore no learning effect as the labour efficiency variance was nil.
December
1 batch was made which cost £500 – £170 = £330
Actual spend of standard cost is £330 / £500 x 100% = 66%
Actual hours taken = 66% x 50hrs = 33hrs
Average hours per batch = (50hrs +33hrs) / 2 = 41.5hrs Learning curve effect = 41.5 hrs / 50hrs = 83%
January
2 batches were made which cost £1,000 – £452.20 = £547.80 Actual spend of standard cost is £547.80 / £1,000 x 100% = 54.78%
Actual hours taken = 54.78% x 100hrs = 54.78hrs
Average hours per batch taken to date = (50hrs + 33hrs + 54.78hrs) / 4 = 34.45hrs Learning curve effect = 34.45hrs / 41.5hrs = 83%
February
4 batches were made which cost £2,000 – £1,089.30 = £910.70 Actual spend of standard cost is £910.70 / £2,000 x 100% = 45.53%
Actual hours taken = 45.53% x 200hrs = 91.06hrs
Average hours per batch taken to date = (50hrs + 33hrs + 54.78hrs + 91.06hrs) / 8 = 28.61hrs
Learning curve effect = 28.61hrs / 34.45hrs = 83%
128 | P a g e March
8 batches were made which cost £4,000 – £1,711.50 = £2,288.50 Actual spend of standard cost is £2,288.50 / £4,000 x 100% = 57.21%
Actual hours taken = 57.21% x 400hrs = 228.84hrs
Average hours per batch taken to date = (50hrs + 33hrs + 54.78hrs + 91.06hrs + 228.84hrs) / 16 = 28.61hrs
Learning curve effect = 28.61hrs / 28.61hrs = 100%
April
16 batches were made which cost £8,000 – £3,423 = £4,577
Actual spend of standard cost is (£4,577 / £8,000) x 100% = 57.21%
Actual hours taken = 57.21% x 800hrs = 457.68hrs
Average hours per batch taken to date = (50hrs + 33hrs + 54.78hrs + 91.06hrs + 228.84hrs + 457.68hrs) / 32 = 28.61hrs
Learning curve effect = 28.61hrs / 28.61hrs = 100%
The learning curve is 83% and ceases in March, when batches take 28.61 hours to make on average. The implications are that there are no further labour efficiencies to be had after the curve ceases and selling price and costs should be based on a batch taking 28.61 hrs.
Part (b)
Note: If Price (P) = a – bx then Marginal Revenue (MR) = a – 2bx 1. Determine the price function or demand function
The price or demand function formula is:
P = a - bQ P = Price
a = Price at which demand would be zero (i.e. the “p” when Q=0) b = The gradient of the demand curve
Q = Quantity sold at that price (P)
129 | P a g e P = 1,200
b = 20 Q = 16 a = ?
In order to determine the price function we need to first find the value of “a”. Substitute all known values into the price function formula to determine “a”.
1,200 = a – 20 (16) 1,200 = a – 320 1,200 + 320 = a 1,520 = a
Now we can construct the price function:
P = 1,520 – 20Q
2. Determine the marginal revenue function (MR)
The MR function is the price function itself, but it will have twice the value of whatever the ‘b’ value itself is, within the price function.
Therefore:
MR = 1,520 – 2 (20) Q MR = 1,520 - 40Q
3. Determine the marginal cost function (MC)
Marginal cost is given in the question as £672.72.
4. Equate MR = MC to obtain the units sold to maximise profits