Short Term Decision Making

MA2 · Chapter 9

Short Term Decision Making

1 Introduction

The previous chapter looked at the importance of contribution when working out break even points and deciding what quantities had to be made and sold to make target profits. This chapter looks at other decisions that contribution analysis can be used for. It also introduces the concept of relevant costs.

2 Limiting factors

Limiting factors are also sometimes known as key factors or restricted resources.

A limiting factor is whatever restricts an organisation’s activities. It could be a limitation on the amount of materials, labour or machine time available. It might be that no more units can be sold because all demand has been met. Occasionally, there might be production quotas restricting output.

Usually in questions the limiting factor is whatever first prevents more profits being made.

Look at this example:

	Product A	Product B
Maximum demand	12,000 units	10,000 units
	$	$
Selling price	30	40
Material	10	16
Labour	8	8
Variable overhead	6	8
Fixed overhead	4	5
Total absorption cost	28	37
Profit	2	3

Both products use the same material, of which there is only $200,000 available

Step 1 – identify the limiting factor

Here, if the maximum units demanded were made, the material needed would be;

12,000 x 10 + 10,000 x 16 = $280,000.

Only $200,000 is available, so material is a limiting factor.

Step 2 – calculate the contribution per unit of limiting factor used

We have identified material as the limiting factor. This means that material is particularly precious and we have to take care when deciding how to use it: each unit of material be used in the way that will earn most.

As in all decision-making, profits are usually irrelevant (because the fixed costs are fixed) and what we need to concentrate on are the contributions.

	Product A	Product B
Maximum demand	12,000 units	10,000 units
	$	$
Selling price	30	40
Material	10	16
Labour	8	8
Variable overhead	6	8
Marginal cost	24	32
Contribution	6	8

So, every unit of Product A made and sold makes the company $6 richer and every unit of Product B made and sold makes the company $8 richer.

However, this does not mean that Product B should be made in preference to Product A. Different amounts of material are needed for each and we need to make sure that each precious unit of material is used wherever it earns most. That can be found by working out:

Contribution per unit/Material needed per unit

or more generally:

Contribution per unit of limiting resource

The higher this is the better: it gives an earning rate per unit of the restricted resources used

	Product A	Product B
Maximum demand	12,000 units	10,000 units
	$	$
Material	10	16
Contribution	6	8
Contribution/$ of material needed	6/10 = 0.6	8/16 = 0.5
Ranking	1	2

Therefore, make Product A in preference, then turn to Product B and make as much of that as possible with any material left.

Step 3 – calculate the production plan

The production plan would be:

	Material used $		Units made		Contribution made
Product A	120,000 (12,000 x $10)	@ $10/unit	12,000 (maximum demand)		72,000 (12,000 x $6)
Product B	80,000 (balance of material)	@ $16/unit	5,000		40,000 (5,000 x $8)
Maximum material	200,000			Total contribution	112,000
				Fixed costs 4 x 12,000 + 5 x 10,000	(98,000)
				Profit	14,000

Note: the fixed costs are based on the absorption rates in the original budget.

Material available = 1200 kgs

Product A: contribution/unit = $24; uses 10 kg/unit; maximum demand = 80 units

Product B: contribution/unit = $15; uses 5 kg/unit; maximum demand = 200 units

What is the production plan that would maximise contribution and what is that contribution?

Example 1

Product A: contribution/kg = 24/10 = 2.4

Product B: contribution/kg = 15/5 = 3

Therefore make B in preference.

200 units (maximum demand) of B will consume 1000kg and generate $3,000

200 kgs of material left, which is enough to allow 20 units. These will generate $480.

Therefore, total maximum contribution = $3,480

Practice question

A company makes three products, X, Y and Z,

Their contributions per unit are: X $25; Y $45; Z $30

The manufacturing hours for each are: X 5; Y 10; Z 4

If manufacturing hours are a limiting resource, in what order of preference should the units be made?

X, Y, ZY, Z, XZ, X, YY, X, Z

Practice question

A company makes two products, P and Q

Their contributions per unit are: P $25; Q $45. The materials needed for each are P $5; Q $10. A contract means that a minimum of 1,000 units of Q have to be made. Maximum demands are P: 2,000 units and Q: 3,000.

Material available = $16,000

How many units of Q will be made if contribution is to be maximised?

1,0003,0001,6002,000

	Product R	Product S
Selling price per unit	$60	$32
Variable cost per unit	$45	$20
Material used per unit	6 kgs	3 kgs
Maximum demand	500	1,200

Practice question

A company makes two products, R and S. The products use the same material, which is limited to 3,900 kgs.

Details are as follows:

	Product R	Product S
Selling price per unit	$60	$32
Variable cost per unit	$45	$20
Material used per unit	6 kgs	3 kgs
Maximum demand	500	1,200

How many units of R and S should be made to maximise contribution?

500 R and 300 S1,200 S and 50 R1,200 units of S and 500 units of R500 units of R and 150 of S

3 Limiting factors with make-buy decisions

If production capacity is limited then it is sometimes possible to buy in some of what’s needed so that higher sales levels can be achieved. For example:

Material available = 1200 kgs

Product A: manufacturing cost/unit = $20; buy-in cost /unit = $25; uses material at the rate of 10 kg/unit; maximum demand = 80 units

Product B: manufacturing cost/unit = $25; buy-in cost = $35; uses material at the rate of 5 kg/unit; maximum demand = 200 units

Step 1 identify the limiting factor

If maximum demand for each product were manufactured then the material used would be:

80 x 10 + 200 x 5 = 1,800 kgs.

As only 1,200 are available, material is a limiting resource.

Step 2 identify which product should be bought in by calculating the extra cost of buying over making per unit of scarce resource

Product A: buying for $25 rather than making for $20 costs $5 per unit

Product B: buying for $35 rather than making for $25 costs $10 per unit.

However, buying a unit of A instead of making it saves 10kg material

and buying a unit of B instead of making it saves 5kg material

Additional cost per kg of material saved:

Product A: 5/10 = 0.5 Product B: $10/5 = 2.0

Therefore, make Product B in preference as that is a much more expensive way of saving material.

Step 3 The production plan

The production plan would be:

	Material used kg		Units made	Costs
Product B	1,000	@ 5 kgs/unit	200 (maximum demand)	5,000 (200 x$25)
Product A	200 (balance of material)	@ 10 kgs/unit	20	400 (20 x $20)
Maximum material	1,200
			Product A to be bought in
Product A to be bought in			60 (to make up to maximum demand)	1,500 (60 x 25)
			Total costs	6,900

The availability of Material M is limited to 32,000 kg

Product	Azed	Byoz
Demand (units)	5,000	7,000
Variable cost to make ($ per unit)	22	30
Buy-in price ($ per unit)	38	34
Kg of M required per unit	4	2

Calculate how much of each product should be made and how much should be bought in.

Example 2

	Azed	Byoz
Buy-in price	38	34
Cost to make	22	30
Saving per unit of making rather than buying	16	4
Kg of scarce resource M used/unit	4	2
Saving per Kg of scarce resource made by making rather than buying	4	2
Ranking	1	2

Make as much as possible of the products with the higher rank:

Product Azed: make 5,000 units, consuming	20,000 kgs
Product Byoz: make 6,000 units, consuming	12,000 kgs	(Balance)
	32,000 kgs

Buy in the remaining 1,000 units of Byoz

Product	Unit contribution	Maximum demand (units)	Machine hours per unit
P	18	500	6
Q	48	250	12

Practice question

A company makes 10,000 units of a component for a variable cost of $25,000. This takes all of the 6,000 production hours available.

The components (essential for other production) could be bought for $55,000 and the machine hours released could then be spent on making:

Product	Unit contribution	Maximum demand (units)	Machine hours per unit
P	18	500	6
Q	48	250	12

Contribution will be maximised if the company:

Buys 10,000 units and makes PBuys 10,000 units and makes QBuys 10,000 units and makes P and QManufactures 10,000 units

4 Discontinuing operations

Sometimes a company might want to look at the effect of discontinuing a product or a whole division. What it must compare is the revenue lost and the costs saved from the closure.

Illustration

$	Division A	Division B
Sales	250,000	600,000
Variable costs	(120,000)	(350,000)
Fixed costs	(150,000)	(200,000)
Divisional profit	(20,000)	50,000

The company is worried about Division A, which reports a loss of $20,000, and is considering closing down that division.

Fixed costs of only $100,000 would be saved if A were closed.

Advise the company on whether Division A should be closed.

Solution:

If A is closed down, revenue will fall by $250,000 and costs of $220,000 will be saved ($120,000 + $100,000 = $220,000).

Revenue falls more than costs, so closing the division will make the company worse off.

Therefore do not close down Division A

Trio Ltd operates three divisions. The latest profit statements and is concerned that division Gamma is making a loss.

Advise Gamma whether or not to close down division C.

Division	Alpha	Beta	Gamma
	(000s)	(000s)	(000s)
Sales	150	120	60
Variable costs	90	75	45
Fixed costs	30	30	20
Profit/(loss)	30	15	(5)

You are also informed that 50% of the fixed costs are division specific. The rest of the fixed costs are allocated arbitrarily to the divisions from head office.

Should division Gamma be shut down?

Example 3

If Gamma is closed:

Revenue will decrease by $60,000
Costs will decrease by $45,000 + $20,000 x 50% = $55,000

Therefore the division should not be closed. If it were, contribution would be reduced.

	Product A	Product B
Sales revenue	200,000	300,000
Variable costs	170,000	150,000
Divisional fixed costs	100,000	100,000
Profit	(70,000)	50,000

Practice question

A company division makes two products. Details are as follows:

	Product A	Product B
Sales revenue	200,000	300,000
Variable costs	170,000	150,000
Divisional fixed costs	100,000	100,000
Profit	(70,000)	50,000

The divisional fixed costs are arbitrarily split (equally) between the products. These costs can be avoided if the division is shut down. No fixed costs are avoided by discontinuing one product.

The action needed to maximise profits is:

Discontinue product ADiscontinue product BKeep production as it is at presentShut down the whole division.

5 Relevant costs

The costs relevant to decision making are those which are:

Affected by the decision. Therefore they are future incremental costs.
Cash flows

Some examples should make these points clear.

Illustration 1

A company has spent $100,000 acquiring patent rights to manufacture a product. It hopes to sell 30,000 units at a selling price of $10 each and the variable costs of production will be $7 per unit.

Should the company proceed with production?

Solution

$100,000 is known as a past cost or a sunk cost. That money is gone and what the company has to do is to concentrate on future cash flows. The future cash flows will generate a contribution of:

30,000 x ($10 - $7) = $90,000

Therefore, proceeding with production will increase the company’s wealth, so it should proceed.

[Note: The incorrect approach would be to look at all costs: 30,000 ($10 - $7) - $100,000 = -$10,000. This is incorrect because the business has no control over the past cost of $100,000. The company has to make the best of what can be done in the future.]

Illustration 2

A company rents a factory for $100,000 per year. Half of the factory is already occupied by a machine. The company is considering installing an additional machine which would produce 20,000 units for a variable cost of $5 per unit. These units would sell for $7 each. Half of the factory rent would be apportioned to the new machine.

Should the company purchase new machine?

Solution

The factory rent of $100,000 will be paid irrespective of whether the factory is empty, has one machine or two machines. It is a fixed cost, is non-incremental and is therefore irrelevant to the decision.

The new machine will generate a contribution of 20,000 x ($7 - $5) = $40,000

The new machine should therefore be purchased.

Illustration 3

A company is considering installing a machine which would produce 20,000 units for a variable cost of $5 per unit. These units would sell for $7 each. Additional space would have to be rented at a cost of $50,000.

Should the company take on this project?

Solution

Here the rent of $50,000 is an incremental cost and is therefore relevant to the decision.

The new machine will generate a contribution of 20,000 x ($7 - $5) - $50,000 =

- $10,000.

Therefore, the project should not be taken on.

Illustration 4

A company has some inventory that was bought for $10,000.

It could be sold for $4,000 or used to make a product that would sell for $15,000. There is no other use for the inventory.

Additional costs needed to convert the inventory into the product are $9,000. The material could be bought now for $8,000

What should the company do?

Solution

The $10,000 cost of the inventory is irrelevant: it is a sunk or past cost.

The $8,000 current price is irrelevant because the company has no use for the material so would not buy more.

The $4,000 resale value of the inventory is relevant as the company could receive that cash by selling the inventory. Therefore, $4,000 is a future incremental cash flow. If the company keeps the inventory and produces the product $4,000 will not be obtained and the $4,000 is known as an opportunity cost.

If the company proceeds with the new product, the incremental cash flows will be:

	$
Sales revenue	15,000
Conversion costs	(9,000)
Opportunity cost of not selling the material	(4,000)
Contribution	2,000

Illustration 5

A company has some inventory that was bought for $10,000. The inventory is used on a day to day basis for normal production. It could be sold for $4,000 or used to make a special product that would sell for $15,000. Additional costs needed to convert the inventory into the product are $9,000. The material could be bought now for $11,000

What should the company do?

Solution

The $10,000 cost of the inventory is irrelevant: it is a sunk or past cost.

The $11,000 current price is relevant because the company uses the material every day. If some of the material is used to make the special product, it will have to be replaced, at a cost of $11,000, to allow ordinary production to be carried on.

The $4,000 is irrelevant as the company would not sell material for $4,000 only to have to replace it for $11,000.

If the company proceeds with the special product, the incremental cash flows will be:

	$
Sales revenue	15,000
Conversion costs	(9,000)
Opportunity cost of the material	(11,000)
Negative contribution	(5,000)

Therefore, the special product should not be made.

Illustration 6

A company can make 1,000 units of a product for $12 material per unit and $15 per unit for labour costs. The product sells for $20 per unit.

There is enough spare (currently idle) labour capacity to make the 1,000 units. These employees are paid but are not working on any product.

Should the product be made?

Solution

The labour cost is irrelevant: these employees are being paid anyhow and all the new product does is to require them now to work for their wages.

		$
Sales revenue	1,000 x $20	20,000
Material costs	1,000 x $12	(12,000)
Contribution		8,000

Therefore the product should be made.

Illustration 7

A company can make 1,000 units of a product for $12 material per unit and 2 hours per unit for labour. The product sells for $22 per unit.

Employees are paid at $15 per hour and are currently employed on the production of another product that takes 3 hours of labour and which generates a contribution of $12/unit. Extra employees cannot be recruited and would have to be transferred from current work.

Should the new product be made?

Solution

Note: this is quite a difficult problem

If employees are transferred from current work to the new product, each 2 hours needed to make the new product will mean that 2/3 of an existing product cannot be made. This will cause a contribution loss of $12 x 2/3 = $8 per new unit made.

You will be tempted to set out the effect of the new product as:

		$
Sales revenue	1,000 x $22	22,000
Material costs	1,000 x $12	(12,000)
Contribution forgone	1,000 x $8	(8,000)
Contribution		2,000

However, this would be incorrect.

The problem is that the contribution that is being given up on existing production $12/unit (or $4/hour) implies that sales revenue is lost and that material and labour costs are saved (contribution is revenue less costs). If they simply sacked employees from the existing production the company would lose $12/unit of old production no longer manufactured. But here, the employees are still employed and are still being paid at $15/hour.

Therefore, the correct calculation is:

		$
Sales revenue	1,000 x $22	22,000
Material costs	1,000 x $12	(12,000)
Contribution forgone	1,000 x $8	(8,000)	[if employees no longer employed]
Labour costs	1,000 x 2 x $15	(30,000)
Contribution		(28,000)

The new product should not be made.

A company will make a new product that takes 2,000 kg of material. 1,200 kg is already in inventory, bought some time ago for $3,600 and with a sales value of $1,600.

The current purchase price of the material is $1.20/kg.

The company has no use for this material other than making the new product, which uses 2kg/unit.

Market research of $1,500 has already been carried out and this indicates that the product would sell for $4/unit. Fixed costs of $4,000 will be apportioned to the new product.

Should production commence?

Example 4

Incremental revenue	= $4 x 2,000/2 =	4,000
Incremental costs	800 kg bought @1.20	(960)
Opportunity cost of not selling existing inventory		(1,600)
Increase in contribution =		1,440

[Note irrelevant: $3,600 = sunk; $1,500 market research = sunk/past; $4,000 not incremental, merely reapportioned.]

Material	Quantity needed per unit of the new product (kg)	Original cost ($/kg)	Current purchase price ($/kg)	Sale price ($/kg)
G	6	3.00	4.00	2.00
H	9	2.00	3.50	0.60

Practice question

To make a product a business needs to use two materials, G and H. These materials are in inventory. G is used on a day-to-day basis in the business; H has no uses other than in the new product.

Information about the two materials is as follows:

Material	Quantity needed per unit of the new product (kg)	Original cost ($/kg)	Current purchase price ($/kg)	Sale price ($/kg)
G	6	3.00	4.00	2.00
H	9	2.00	3.50	0.60

What cost should be included for materials per unit of the new product?

$55.50$29.40$43.50$36.00

Practice question

Gizmo Incorporated needs to work out the cost of a new contract. The contract requires two sorts of employee:

Programmers: time needed = 2,000 hours @$30/hour

Analysts: time needed = 900 hours @ $50/hour

There is currently a shortage of analysts and if this contract is accepted, analysts will have to be moved from other work where they generate a contribution of $80/hour, after charging their salaries.

There is sufficient idle time amongst programmers to provide the time needed for this project. Because programmers are skilled and scarce, the company has no intention of removing programmers from the workforce.

What is the incremental and opportunity costs of labour that should be assigned to this contract?

117,00072,000177,000132,000

Answer the questions one at a time. Your progress is saved so you can leave and come back.

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