# Limiting Factors and Throughput Accounting

## Limiting Factors and Throughput Accounting

### Limiting Factors and Throughput Accounting

Chapter 5 Limiting Factors and Throughput Accounting

1.       Objectives

1.1       Identify limiting factors in a scarce resource situation and select an appropriate technique.
1.2       Determine the optimal production plan where an organization is restricted by a single limiting factor.
1.3       Explain the concept of optimized production technology.
1.4       Explain the theory of constraints.
1.5       Explain the concept of throughput accounting.
1.6       Calculate and interpret a throughput accounting ratio (TPAR).
1.7       Compare the techniques of limiting factors and throughput accounting in the determination of optimal production.

2.       Limiting Factors

 2.1 Limiting Factors A limiting factor is any factor that is in scarce supply and that stops the organisation from expanding its activities further, that is, it limits the organisations activities.

2.2       An organisation might be faced with just one limiting factor (other than maximum sales demand) but there might also be several scarce resources, with two or more of them putting an effective limit on the level of activity that can be achieved.
2.3       Examples of limiting factors include sales demand and production constraints.
(a)        Labour. The limit may be either in terms of total quantity or of particular skills.
(b)        Materials. There may be insufficient available materials to produce enough units to satisfy sales demand.
(c)        Manufacturing capacity. There may not be sufficient machine capacity for the production required to meet sales demand.
2.4       It is assumed in limiting factor analysis that management would make a product mix decision or service mix decision based on the option that would maximise profit and that profit is maximized when contribution is maximised (given no change in fixed cost expenditure incurred). In other words, marginal costing ideas are applied.
(a)        Contribution will be maximised by earning the biggest possible contribution per unit of limiting factor. For example if grade A labour is the limiting factor, contribution will be maximised by earning the biggest contribution per hour of grade A labour worked.
(b)        The limiting factor decision therefore involves the determination of the contribution earned per unit of limiting factor by each different product.
(c)        If the sales demand is limited, the profit-maximising decision will be to produce the topranked product(s) up to the sales demand limit.
2.5       In limiting factor decisions, we generally assume that fixed costs are the same whatever product or service mix is selected, so that the only relevant costs are variable costs.
2.6       When there is just one limiting factor, the technique for establishing the contribution-maximising product mix or service mix is to rank the products or services in order of contribution-earning ability per unit of limiting factor.

2.7

# Example 1

Sausage makes two products, the Mash and the Sauce. Unit variable costs are as follows.

 Mash Sauce \$ \$ Direct materials 1 3 Direct labour (\$3 per hour) 6 3 Variable overhead 1 1 8 7

The sales price per unit is \$14 per Mash and \$11 per Sauce. During July the available direct labour is limited to 8,000 hours. Sales demand in July is expected to be as follows.

 Mash 3,000 units Sauce 5,000 units

Required:

Determine the production budget that will maximize profit, assuming that fixed costs per month are \$20,000 and that there is no opening inventory of finished goods or work in progress.

Solution:

1. Determine the limiting factor

 Mash Sauces Total Labour hours per unit 2 hrs 1 hr Sales demand 3,000 units 5,000 units Labour hours needed 6,000 hrs 5,000 hrs 11,000 hrs Labour hours available 8,000 hrs Shortfall 3,000 hrs

Labour is the limiting factor on production.

2. Identify the contribution earned by each product per unit of scarce resource, that is, per labour hour worked.

 Mash Sauce \$ \$ Sales price 14 11 Variable cost 8 7 Unit contribution 6 4 Labour hour per unit 2 hrs 1 hr Contribution per labour hour (= per unit of limiting factor) \$3 \$4 Ranking 2 1

3. Determine the budgeted production and sales.

 Product Units Hours needed Contribution per unit Total \$ \$ Sauces 5,000 5,000 4 20,000 Mashes (Bal.) 1,500 3,000 6 9,000 8,000 29,000 Less: fixed costs 20,000 Profit 9,000

Conclusion:
(1)       Unit contribution is not the correct way to decide priorities.
(2)       Labour hours are the scarce resource, therefore contribution per labour hour is the correct way to decide priorities.
(3)       The Sauce earns \$4 contribution per labour hour, and the Mash earns \$3 contribution per labour hour. Sauces therefore make more profitable use of the scarce resource, and should be manufactured first.

Question 1
Triproduct Limited makes and sells three types of electronic security systems for which the following information is available.

Standard cost and selling prices per unit

 Product Day scan Night scan Omni scan \$ \$ \$ Materials 70 110 155 Manufacturing labour 40 55 70 Installation labour 24 32 44 Variable overheads 16 20 28 Selling price 250 320 460

Fixed costs for the period are \$450 000 and the installation labour, which is highly skilled, is available for 25 000 hours only in a period and is paid £8 per hour.

Both manufacturing and installation labour are variable costs.

The maximum demand for the product is:

 Day scan Night scan Omni scan 2,000 units 3,000 units 1,800 units

Required:

(a)      Calculate the shortfall (if any) in hours of installation labour.                          (2 marks)
(b)      Determine the best production plan, assuming that Triproduct Limited wishes to maximise profit.                                                                                                 (5 marks)
(c)      Calculate the maximum profit that could be achieved from the plan in part (b) above.
(3 marks)
(d)      Having carried out an investigation of the availability of installation labour, the firm thinks that by offering \$12 per hour, additional labour would become available and thus overcome the labour shortage.

Required:
Based on the results obtained above, advise the firm whether or not to implement the
proposal.                                                                                                             (5 marks)
(Total 15 marks)

3.       Throughput Accounting (產量會計)

3.1       Optimized production technology (OPT)

3.1.1    During the 1980s Goldratt and Cox (1984) advocated a new approach to production management called OPT. OPT is based on the principle that profits are expanded by increasing the throughput of the plant. The OPT approach determines what prevents throughput being higher by distinguishing bottleneck and non-bottleneck resources.
3.1.2    A bottleneck might be a machine whose capacity limits the throughput of the whole production process. The aim is to identify bottlenecks and remove them or, if this is not possible, ensure that they are fully utilized at all times.
3.1.3    Non-bottleneck resources should be scheduled and operated based on constraints within the system, and should not be used to produce more than the bottlenecks can absorb. The OPT philosophy therefore advocates that non-bottleneck resources should not be utilized to 100% of their capacity, since this would merely result in an increase in inventory.

3.2       Theory of constraints

3.2.1    Goldratt and Cox (1992) describe the process of maximizing operating profit when faced with bottleneck and non-bottleneck operations as the theory of constraints (TOC).
3.2.2    The TOC aims to increase throughput contribution while simultaneously reducing inventory and operational expenses. However, the scope for reducing the latter is limited since they must be maintained at some minimum level for production to take place at all. In other words, operational expenses are assumed to be fixed costs.
3.2.3    The TOC adopts a short-run time horizon and treats all operating expenses (including direct labour but excluding direct materials) as fixed, thus implying that variable costing should be used for decision-making, profit measurement and inventory valuation.
3.2.4    It emphasizes the management of bottleneck activities as the key to improving performance by focusing on the short-run maximization of throughput contribution.

3.2.5

# Example 1 – Illustration of the TOC

Machine X can process 1,000 kg of raw material per hour, machine Y 800 kg. Of an input of 900 kg, 100 kg of processed material must wait on the bottleneck machine (machine Y) at the end of an hour of processing.

The traditional view is that machines should be working, not sitting idle. So if the desired output from the above process were 8,100 kgs, machine X would be kept in continual use and all 8,100 kgs would be processed through the machine in nine hours. There would be a backlog of 900 kgs [8,100 – (9 hrs × 800)] of processed material in front of machine Y, however. All this material would require handling and storage space and create the additional costs related to these non-value added activities. Its processing would not increase throughput contribution.

3.3       Throughput Accounting (TA)

3.3.1    Galloway and Waldron (1988) advocate an approach called throughput accounting to apply the TOC philosophy.

 3.3.2 Throughout Accounting Throughput accounting is a product management system which aims to maximise throughput, and therefore cash generation from sales, rather than profit. A just in time (JIT) environment is operated, with buffer inventory kept only when there is a bottleneck resource.

3.3.3    TA for JIT is said to be based on three concepts.
(a)        Concept 1
In the short run, most costs in the factory (with the exception of materials costs) are fixed (the opposite of ABC, which assumes that all costs are variable). These fixed costs include direct labour. It is useful to group all these costs together and call them Total Factory Costs (TFC).
(b)        Concept 2
In a JIT environment, all inventory is a 'bad thing' and the ideal inventory level is zero. Products should not be made unless a customer has ordered them. When goods are made, the factory effectively operates at the rate of the slowest process, and there will be unavoidable idle capacity in other operations.

Work in progress should be valued at material cost only until the output is eventually sold, so that no value will be added and no profit earned until the sale takes place. Working on output just to add to work in progress or finished goods inventory creates no profit, and so should not be encouraged.
(c)        Concept 3
Profitability is determined by the rate at which 'money comes in at the door' (that is, sales are made) and, in a JIT environment, this depends on how quickly goods can be produced to satisfy customer orders. Since the goal of a profit-orientated organisation is to make money, inventory must be sold for that goal to be achieved. The bottleneck resource slows the process of making money.

3.3.4

Throughout Accounting and Decision Making

In a throughput environment, production priority must be given to the products best able to generate throughput, that is those products that maximize throughput per unit of bottleneck resource.

The TA ratio can be used to assess the relative earning capabilities of different products and hence can help with decision making.

 TA ratio = Return per factory hour Total conversion cost per factory hour

Where:

 Return per factory hour = Sales – direct material costs Usage of bottleneck resource in hours (factory hours)
 Total conversion cost per factory hour = Total factory Total time available on bottleneck resource

3.3.5

# Example 2 – Throughput accounting

A Ltd produces three products, X, Y and Z. The capacity of A Ltd’s plant is restricted by process alpha. Process alpha is expected to be operational for eight hours per day and can produce 1,200 units of X per hour, 1,500 units of Y per hour, and 600 units of Z per hour.

Selling prices and material costs for each product are as follows.

 Product Selling price \$ per unit Material cost \$ per unit Throughput contribution \$ per unit X 150 80 70 Y 120 40 80 Z 300 100 200

Conversion costs are \$720,000 per day.

Required:

(a)       Calculate the profit per day if daily output achieved is 6,000 units of X, 4,500 units of Y and 1,200 units of Z.
(b)       Calculate the TA ratio for each product.
(c)       In the absence of demand restrictions for the three products, advise A Ltd’s management on the optimal production plan.

Solution:

(a)       Profit per day = throughput contribution – conversion cost
= [(\$70 x 6,000) + (\$80 x 4,500) + (\$200 x 1,200)] – \$720,000
= \$300,000
(b)       TA ratio = throughput contribution per factory hour / conversion cost per factory hour

Conversion cost per factory hour = \$720,000 / 8 = \$90,000

 Product Throughput contribution per factory hour Cost per factory hour TA ratio X \$70 x 1,200 = \$84,000 \$90,000 0.93 Y \$80 x 1,500 = \$120,000 \$90,000 1.33 Z \$200 x 600 = \$120,000 \$90,000 1.33

(c)       An attempt should be made to remove the restriction on output caused by process alpha's capacity. This will probably result in another bottleneck emerging elsewhere. The extra capacity required to remove the restriction could be obtained by working overtime, making process improvements or product specification changes. Until the volume of throughput can be increased, output should be concentrated upon products Y and Z (greatest TA ratios), unless there are good marketing reasons for continuing the current production mix.

Product X is losing money every time it is produced so, unless there are good reasons why it is being produced, for example it has only just been introduced and is expected to become more profitable, A Ltd should consider ceasing production of X.

3.3.6    How can a business improve a throughput accounting ratio?

 Measures Consequences Increase sales price per unit Demand for the product may fall Reduce material cost per unit, e.g. change materials and/or suppliers Quality may fall and bulk discounts may be lost Reduce operating expenses Quality may fall and/or errors increase

 3.3.7 Throughput and limiting factor analysis The throughput approach is very similar to the approach of maximising contribution per unit of scarce resource. Throughput is defined as sales less material costs whereas contribution is defied as sales less all variable costs. Throughput assumes that all costs except materials are fixed in the short run.

Question 2 – Throughput Accounting
Yam Co is involved in the processing of sheet metal into products A, B and C using three processes, pressing, stretching and rolling. Like many businesses Yam faces tough price competition in what is a mature world market.

The factory has 50 production lines each of which contain the three processes: Raw material for the sheet metal is first pressed then stretched and finally rolled. The processing capacity varies for each process and the factory manager has provided the following data:

 Processing time per metre in hours Product A Product B Product C Pressing 0.50 0.50 0.40 Stretching 0.25 0.40 0.25 Rolling 0.40 0.25 0.25

The factory operates for 18 hours each day for five days per week. It is closed for only two weeks of the year for holidays when maintenance is carried out. On average one hour of labour is needed for each of the 225,000 hours of factory time. Labour is paid \$10 per hour.

The raw materials cost per metre is \$3.00 for product A, \$2.50 for product B and \$1.80 for product C. Other factory costs (excluding labour and raw materials) are \$18,000,000 per year. Selling prices per metre are \$70 for product A, \$60 for product B and \$27 for product C.

Yam carries very little inventory.

Required:

(a)        Identify the bottleneck process and briefly explain why this process is described as a ‘bottleneck’.                                                                                                    (3 marks)
(b)        Calculate the throughput accounting ratio (TPAR) for each product assuming that the bottleneck process is fully utilised.                                                                 (8 marks)
(c)        Assuming that the TPAR of product C is less than 1:
(i)         Explain how Yam could improve the TPAR of product C.                 (4 marks)
(ii)        Briefly discuss whether this supports the suggestion to cease the production of product C and briefly outline three other factors that Yam should consider before a cessation decision is taken.                                                   (5 marks)
(Total 20 marks)
(ACCA F5 Performance Management June 2009 Q1)

Question 3 – Limiting Factor
Red Hot Ltd manufactures electronic components in the Mainland of China and exports to the US market. In the past few years, demand for the components has increased dramatically. The company is currently preparing various business plans for its investments and operations for the next year. At a recent board meeting, the management discussed how to determine an economical sales and production mix in the business plans. Below is the estimated data and information for next year:

 Product Demand (units) Selling price per unit (\$) Direct materials (\$) Direct labour (\$) A 5,000 135 43 32 B 4,200 55 11 20 C 3,500 210 65 56 D 4,000 100 20 40 E 32,500 80 32 16

The direct labour rate of \$80 per hour is expected to remain unchanged during the coming year. The company’s plant has a maximum capacity of 13,000 direct labour hours per year on a single-shift basis. Overtime work is paid at a premium of 50%. The company’s present facilities and resources including employees and equipment can produce all the five products. Fixed manufacturing costs total \$320,000 per year and variable overhead costs are \$20 per direct labour hour. Selling and administrative costs are fixed at an estimated amount of \$200,000 per year. Having adopted the just-in-time inventory management system, the company’s finished goods inventory is negligible and can be ignored.

Required:

(a)        Assuming there is no overtime work, determine the optional production mix of the five products to maximize the profit for next year and calculate the amount of maximum profit. Show all supporting calculations.                                                                                                      (15 marks)
(b)       What is the highest price (in terms of a rate per hour) that the company would be willing to pay for additional direct labour time? Suggest whether it is justified to work overtime to satisfy any unmet demand.                                                                                                               (5 marks)
(Total 20 marks)
(HKIAAT PBE Paper II Management Accounting June 2007 Q1)

# Question 4 – Limiting Factor and Throughput Accounting

Ride Ltd is engaged in the manufacturing and marketing of bicycles. Two bicycles are produced. These are the ‘Roadster’ which is designed for use on roads and the ‘Everest’ which is a bicycle designed for use in mountainous areas. The following information relates to the year ending 31 December 2005:

(1)        Unit selling price and cost data is as follows:

 Roadster Everest \$ \$ Selling price 200 280 Material cost 80 100 Variable production conversion costs 20 60

(2)        Fixed production overheads attributable to the manufacture of the bicycles will amount to \$4,050,000.
(3)        Expected demand is as follows:

 Roadster 150,000 units Everest 70,000 units

(4)        Each bicycle is completed in the finishing department. The number of each type of bicycle that can be completed in one hour in the finishing department is as follows:

There are a total of 30,000 hours available within the finishing department.
(5)        Ride Ltd operates a just in time (JIT) manufacturing system with regard to the manufacture of bicycles and aims to hold very little work-in-progress and no finished goods stocks whatsoever.

Required:

(a)        Using marginal costing principles, calculate the mix (units) of each type of bicycle which will maximise net profit and state the value of that profit.                                                       (6 marks)
(b)        Calculate the throughput accounting ratio for each type of bicycle and briefly discuss when it is worth producing a product where throughput accounting principles are in operation. Your answer should assume that the variable overhead cost amounting to \$4,800,000 incurred as a result of the chosen product mix in part (a) is fixed in the short-term.                                             (5 marks)
(c)        Using throughput accounting principles, advise management of the quantities of each type of bicycle that should be manufactured which will maximise net profit and prepare a projection of the net profit that would be earned by Ride Ltd in the year ending 31 December 2005.       (5 marks)
(d)        Explain two aspects in which the concept of ‘contribution’ in throughput accounting differs from its use in marginal costing.                                                                                           (4 marks)
(Total 20 marks)
(ACCA Paper 3.3 Performance Management December 2004 Q2)

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#### Limiting Factors and Throughput Accounting

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##### Limiting Factors and Throughput Accounting

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