Ch18 Relevant costing and decision making
【Introduction】
Relevant costs
Choice of product ？product mix？ Make or buy
decisions decisions
Shut down decisions One-off contracts
1.Relevant Costs
？1？A relevant cost is a future cash flow arising as a direct consequence of a decision.
？2？Decision making should be based on relevant costs.
A.Relevant costs are future costs. A decision is about the future and it cannot alter what has been done already. Costs that have been incurred in the past are totally irrelevant to any decision n that is being made ‘now’.Such costs are past costs or sunk costs. Costs that have been incurred include not only costs that have already been paid, but also costs that have been committed. A committed cost is a future cash flow that will be incurred anyway, regardless of the decision taken now.
B.Relevant costs are cash flows. Only cash flow information is required. This means that costs or charges which do not reflect additional cash spending ？such as
depreciation and notional costs？ should be ignored for the purpose of decision
making.
C.Relevant costs are incremental costs.
？3？Other terms are sometimes used to describe relevant costs.
Avoidable cost: whether or not to discontinue a product
Differential cost is‘the difference on in total cost between alternatives.’
An opportunity cost is ‘The value of the benefit sacrificed when one course of action is chosen, in preference to an alternative’.
A sunk cost is a past cost which is not directly relevant in decision making.？The
principle underlying decision accounting is that management decisions can only affect the future. In decision making, managers therefore require information about future costs and revenues which would be affected by the decision under review. They must not be misled by events, costs and revenues in the past, about which they can do nothing.
Fixed and variable costs
？Variable costs will be relevant costs. Fixed costs are irrelevant to a decision.？
Controllable and uncontrollable costs
N.B.
Non-relevant variable costs
1.12 There might be occasions when a variable cost is in fact a sunk cost ？and
therefore a non-relevant variable cost？.For example,suppose that a company has some
units of raw material in stock.They have been paid for already,and originally cost
！2,000.They are now obsolete and are no longer used in regular production,and they have no scrap value.However,they could be used in a special job which the company is trying to decide whether to undertake.The special job is a ˊone-off ˊcustomer
order,and would use up all these materials in stock.
？a？In deciding whether the job should be undertaken,the relevant cost of the materials to the special job is nil.Their original cost of ！2,000 is a sunk cost,and
should be ignored in the decision.
b？However,if the materials did have a scrap value of,say, ！300,then their ？
relevant cost to the job would be the opportunity cost of being unable to sell them for scrap,ie ！300.
Attributable fixed costs
1.13 There might be occasions when a fixed cost is a relevant cost,and you must be aware of the distinction between ˊspecificˊor ˊdirectly attributableˊfixed
costs,and general fixed overheads.
1.14 Directly attributable fixed costs are those costs which,although fixed within a relevant range of activity level are relevant to a decision for either of the following reasons.
？a？They could increase if certain extra activities were undertaken.For example,it may be necessary to employ an extra supervisor if a particular order is accepted.The extra salary would be an attributable fixed cost.
General fixed overheads
1.15 General fixed overheads are those fixed overheads which will be unaffected by decisions to increase or decrease the scale of operations,perhaps because they are an apportioned share of the fixed costs of items which would be completely unaffected by the decisions.General fixed overheads are not relevant in decision making.
Absorbed overhead is a notional accounting cost and hence should be ignored for decision making purposes. It is overhead incurred which may be relevant to a decision.
1.16 Absorbed overhead is a notional accounting cost and hence should be ignored for decision-making purposes.It is overhead incurred which may be relevant to a decision.
？4？The relevant cost of materials
The relevant cost of raw materials is generally their current replacement cost, unless the materials have already been purchased and would not be replaced once used. In this case the relevant cost of using them is the higher of the following:
Their current resale value
The value they would obtain if they were put to an alternative use
If the materials have no resale value and no other possible use, then the relevant cost of using them for the opportunity under consideration would be nil.
Material B is used regularly by OˊReilly Ltd,and if units of B are required for
this job,they would need to be replaced to meet other production demand.
Materials C and D are in stock as the result of previous over-buying,and they have a restricted use.No other use could be found for material C,but the units of material D could be used in another job as substitute for 300 units of material E,which currently costs ！5 per unit？of which the company has no units in stock at the
moment？.
R equired
Calculate the relevant costs of material for deciding whether or not to accept the contract.
Answer
？a？Material A is not yet owned.it would have to be bought in full at the replacement cost of ！6 per unit.
？b？Material B is used regularly by the company.There are existing stocks ？600
units？but if these are used on the contract under review a further 600 units would be bought to replace them.Relevant costs are therefore 1,000 units at the replacement cost of ！5 per unit.
？c？1,000 units of material C are needed and 700 are already in stock.if used for
4 each.The existing stocks of 700 the contract,a further 300 units must be bought at ！
will not be replaced.if they are used for the contraci,they could not be sold at ！2.50
each.The realizable value of these 700 units is an opportunity cost of sales revenue forgone.
？d？The required units of material D are already in stock and will not be replaced.There is an opportunity cost of using D in the contract because there are alternative opportunities either to sell the existing stocks for ！6 per unit ？！1,200 in
total？ or avoid other purchases？of material E？,which would cost 300×！1,500.Since
substitution for E is more beneficial, ！1,500 is the opportunity cost.
？e？Summary of relevant costs
！
Material A？1,000×！6？ 6,000
Material B？1,000×！5？ 5,000
Material C？300×！4？plus？700×！2.50？ 2,950
Material D 1,500
Total 15,450
？5？Relevant cost of labor
1.19 EXAMPLE:RELEVANT COST OF LABOUR
LW plc is currently deciding whether to undertake a new contract.15 hours of labour will be required for the contract.LW plc currently produces product L,the standard cost details of which are shown below.
STANDARD COST CARD
PRODUCTL
！/unit
Direct materials？10kg，！2？ 20
Direct labour？5 hrs ，！6？ 30
50
Selling price 72
Contribution 22
？a？What is the relevant cost of labour if the labour must be hired from outside the organization?
？b？What is the relevant cost of labour if LW plc expects to have 5 hours spare capacity?
c？What is the relevant cost of labour if labour is in short supply? ？
1.20 SOLUTION
？a？Where labour must be hired from outside the organisation,the relevant cost of laboru will be the variable costs incurred.
？b？It is assumed that the 5 hours spare capacity will be paid anyway,and so if these 5 hours are used on another contract,there is no additional cost to LW plc.
Relevant cost of labour on new contract
！
Direct labour ？10 hours ，！6？ 60
5 hours ，！0？ 0 Spare capacity ？
60
？c？Contribution earned per unit of Product L produced=！22
If it requires 5 hours of labour to make one unit of product L,the contribution earned per labour hour=！22/5=！4.40.
Relevant cost of labour on new coutract ！
Direct labour ？15 hours ，！6？ 90
Contribution lost by not making product L？！4.40×15 hours？
66
156
1.21 It is important that you should be able to identify the relevant costs which are appropriate to a decision. In many cases,this is a fairly straightforward problem,but there are cases where great care should be taken.Attempt the following question.
？6？The deprival value of an asset
In simple terms, the deprival value of an asset represents the amount of money that a company would have to receive if it were deprived of an asset in order to be no worse off than it already is.
1.23 EXAMPLE:DFPRIVAL VALUE OF AN ASSET
A machine cost ！14,000 tne years ago.It is expected that the machine will generate future revenues of ！10,000.Alternatively,the machine could be scrapped
for ！8,000.An equivalent machine in the same condition would cost ！9,000 to buy
now.What is the deprival value of the machine?
1.24 SOLUTION
Firstly,let us think about the relevance of the costs given to us in the question.
Cost of machine=！14,000=past/sunk cost
Future revenues=！10,000=revenue expected to be generated
Net realizable value=！8,000=scrap proceeds
Replacement cost=！9,000
When calculating the deprival value of an asset,use the following diagram.
Therefore,the deprival value of the machine is the lower of the replacement cost
10,000.The deprival value is therefore ！9,000. and ！
2.Choice of Product ？Product Mix？Decisions
？1？A limiting factor is a factor which limits the organization’s activities.
2？It is assumed in limiting factor accounting that management wishes to ？
maximize profit and that profit will be maximized when contribution is maximized ？given no change in fixed cost expenditure incurred？. Marginal costing ideas are
applied.
？3？Contribution will be maximized by earning the biggest possible contribution from each unit of limiting factor.
？4？The limiting factor decision therefore involves the determination of the contribution earned by each different product from each unit of the limiting factor.
N.B.
In exam, five steps can be followed:
Step 1 Identify the limiting factor
Step 2 Calculate contribution per unit for each product
Step 3 Calculate contribution per unit of limiting factor
Step 4 Rank products ？make product with highest contribution per unit of
limiting factor first？
Step 5 Make products in rank order until scare resource is used up ？optimal
production plan？
2.6 EXAMPLE:LIMITING FACTOR
AB Ltd makes two products,the Ay and the Be.Unit variable costs are as follows.
Ay Be
！ ！
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 Ay and ！11 per Be.During July 20X2 the
available direct labour is limited to 8,000 hours.Sales demand in July is expected to be 3,000 units for Ays and 5,000 units for Bes.
Required
Determine the profit-maximising production mix,assuming that monthly fixed costs are ！20,000,and that opening stocks of finished goods and work in progress are nil.
2.7 SOLUTION
Step1. Confirm that the limiting factor is something other than sales demand.
Ays Bes Total
Labour hours per unit 2 hrs 1hr
Sales demand 3,000units 5,000units
Labour hours needed 6,000hrs 5,000hrs 11,000hrs
Labour hours available 8,000 hrs
Shortfall 3,000 hrs
Labour is the limiting factor on production.
Step2. Identify the contribution eamed by each product per unit of limiting factor,that is per labour hour worked.
Ays Bes
！ ！
Sales prict 14 11
Variable cost 8 7
Unit contribution 6 4
Labour hours per unit 2 hrs 1 hr
Contribution per labour hour？=unit
of limiting factor？ ！3 ！4
Although Ays have a higher unit contribution than Bes,two Bes can be made in the time it atkes to make one Ay.Because labour is in short supply is is more profitable to make Bes than Ays.
Step3. Determine the optimum production plan.Sufficient Bes will be made to meet the full sales demand,and the remaining labour hours available will then be used to make Ays.
Step 3. Determine the optimum production plan.Sufficient Bes will be made to meet the full sales demand,and the remaining labour hours available will then be used to make Ays.
？a？ Hours hours Priority of
product Demand required available manufacture
Bes 5,000 5,000 5,000 lst
Ays 3,000 6,000 3,000？bal？ 2nd
11,000 8,000
？b？ Hours Contribution
Product Units needed per unit Total
！ ！
Bes 5,000 5,000 4 20,000
Ays 1,500 3,000 6 9,000
8,000 29,000
Less fixed costs 20,000
Profit 9,000
3.Make or Buy Decisions
If an organization has the freedom of choice about whether to make internally or buy externally and has no scarce resources that put a restriction on what it can do itself, the relevant costs for the decision will be the differential costs between the two
options.
3.3 EXAMPLE:MAKE OR BUY
Buster Ltd makes four components,W,X,Y and Z,for which costs in the forthcoming year are expected to be as follows.
W X Y Z
units？ 1,000 2,000 4,000 3,000 Production？
Unit marginal costs ！ ！ ！ ！
Direct materials 4 5 2 4
9 4 4 Direct labour 8
Variable production overheads 2 3 1 2
14 17 7 12
Directly attributable fixed costs per annum and committed fixed costs are as follows.
！
Incurred as a direct consequence of making W 1,000
Incurred as a direct consequence of making X 5,000
Incurred as a direct consequence of making Y 6,000
Incurred as a direct consequence of making Z 30,000
Other fixed costs？committed？ 50,000
A subcontractor has offered to supply units of W,X,Y and Z for ！12, ！21,
！10 and ！14 respectively.
Required
Decide whether Buster Ltd should make or buy the components.
3.4 SOLUTION
？a？The relevant costs are the differential costs between making and buying,and they consist of differences in unit variable costs plus differences in directly attributable fixed costs.Subcontracting will result in some fixed cost savings.
W X Y Z
！ ！ ！ ！
Unit variable cost of making 14 17 7 12
Unit variable cost of buying 12 21 10 14
？2？ 4 3 2
W X Y Z
Annual requirements？units ？ 1,000 2,000 4,000 3,000
！ ！ ！ ！
Extra variable cost of
buying(pre annum) (2,000) 8,000 12,000 6,000
Fixed costs saved by buying (1,000)(5,000)(6,000) (8,000)
Extra total cost of buying (3,000) 3,000 6,000 (2,000)
手写板图示1402-01
？b？The company would save ！3,000 pa by subcontracting component W
？where the purchase cost would be less than the marginal cost per unit to make internally？and would save ！2,000 pa by subcontracting component Z ？because of
the saving in fixed costs of ！8,000？.
？c？In this example,relevant costs are the variable costs of in-house manufacture,the variable costs of subcontracted units,and the saving in fixed costs.
In a situation where a company must subcontract work to make up a shortfall in its own production capability, its total costs are minimized if those components/products subcontracted are those with the lowest extra variable cost of buying per unit of limiting factor saved by buying.
3.7 EXAMPLE:MAKE OR BUY AND LIMITING FACTORS
Green Ltd manufactures two components,the Alpha and the Beta,using the same machines for each.The budget for the next year calls for the production and assembly of 4,000 of each component.The variable production cost per unit of the final product,the gamma,is as follows.
Machine hours Variable cost
！
1 unit of Alpha 3 20
1 unit of Beta 2 36
Assembly 20
76
Only 16,000 hours of machine time will be available during the year,and a sub-contractor has quoted the following unit prices for supplying components:Alpha ！29;Beta ！40.Advise Green Ltd.
3.8 SOLUTION
？a？There is a shortfall in machine hours available,and some products must be sub-contracted.
Product Units Machine hours
Alpha 4,000 12,000
Beta 4,000 8,000
Required 20,000
16,000 Available
Shortfall 4,000
？b？The assembly costs are not relevant costs because they are unaffected by the make of buy decision.The units subcontracted should be those which will add least to the costs of Green Ltd.Since 4,000 hours of work must be sub-contracted,the cheapest policy is to subcontract work which adds the least extra costs？the least extra variable
costs？per hour of own-time saved.
？c？Alpha Beta
！ ！
Variable cost of making 20 36
29 40 Variable cost of buying
9 4
Machine hours saved by buying 3 hrs 2 hrs
Extra variable cost of buying,
per hour saved ！3 ！2
It is cheaper to buy Betas than to buy Alphas and so the priority for making the components in-house will be in the reverse order to the preference for buying them from a subcontractor.
？d？ Hrs per unit Hrs required Cumulative
Component to make in-house in total hours
Alpha 3hrs 12,000 12,000
Beta 2hrs 8,000 12,000
20,000
Hours available 16,000
Shortfall 4,000
There are enough machine hours to make all 4,000 units of Alpha and 2,000 units of Beta.4,000 hours production of Beta must be sub-contracted.This will be the cheapest production policy available
？e？ Number of Unit variable Total
Component Machine hours units cost variable cost
Make ！ ！
Alpha 12,000 4,000 20 80,000
Beta？balance？4,000 2,000 36 72,000
16,000
Buy Hours saved
Beta？balance？4,000 2,000 40 80,000
Total variable costs of components 232,000
Assembly costs？4,000×！20？ 80,000
Total variable costs 312,000
4.Shut down decisions
Shut down decisions involve thee following.
a.Whether or not to shut down a factory, department, or product line either because it is making a loss or it is too expensive to run;
b.If the decision is to shut down, whether the closure should be permanent or temporary.
4.2 EXAMPLE:SHUT DOWN DECISIONS
Suppose that a company manufactures three products, Corfus,Cretes and Zantes. The present net profit from these is as follows.
Corfus Cretes Zantes Total
！ ！ ！ ！
Sales 50,000 40,000 60,000 150,000
25,000 35,000 90,000 Variable costs 30,000
Contribution 20,000 15,000 25,000 60,000
Fixed costs 17,000 18,000 20,000 55,000
3,000 ？3,000？ 5,000 5,000 Profit/loss
The company is concerned about its poor profit performance,and is considering whether or not to cease selling Cretes.It is felt that selling prices cannot be raised or lowered without adversely affecting net income. ！5,000 of the fixed costs of Cretes
are attributable fixed costs which would be saved if production ceased.All other fixed costs would remain the same.
4.3 SOLUTION
？a？By stopping production of Cretes,the consequences would be a ！10,000 fall
in profits.
！
Loss of contribution ？15,000？
Savings in fixed costs 5,000
Incremental loss ？10,000？
？b？Suppose,however,it were possible to use the resources realized by stopping production of Cretes and switch to produing a new item.Rhodes,which would sell for ！50,000 and incur variable costs of ！30,000 and extra direct fixed costs of
！6,000.A new decision is now required.
Cretes Rhodes
！ ！
Sales 40,000 50,000
Less variable costs 25,000 30,000
Contribution 15,000 20,000
Less direct fixed costs 5,000 6,000