COST FOR DECISION MAKING
1.1 Definition of Decision Making
Decision making is the essence of all management activity and naturally, accounting plays a
role in informing decisions. Making correct decisions is one of the most important tasks of a
successful
manager. Every
decision
involves
a
choice
between
at
least
two
alternatives. Decision making is a process of choosing among a set of alternative courses of
action with a view to attain the firm’s objectives. The costing system of any organisation is
integral in the decision making process. The costing system of the firm, for which the
accountant is responsible, has to report on the cost of products and services from which
decisions to discontinue redesign, make or buy, etc. have to be made. The quality of the
decision generally reflects the quality of the information provided to management by the
accountant.
Decision making is a future oriented activity; it involves forecasting and planning. What has
happened in the past is only of historical value. The function of decision making is to choose
alternatives for the future. There two perquisites for making efficient and effective decisions.
First, of all possible alternatives should be carefully delineated. A manager may choose a best
alternative form among the alternatives considered by him; but he may fail to consider some
other available alternatives which may be better than the chosen alternative. Second, the
objective should be correctly set. A wrong objective can lead to the adoption of undesirable
and unprofitable course of action.
The decision process may be complicated by volumes of data, irrelevant data, incomplete
information, an unlimited array of alternatives, etc. The role of the managerial accountant in
this process is often that of a gatherer and summarizer of relevant information rather than the
ultimate decision maker. In this regard, cost data are the most crucial quantitative factors
needed for making decisions. A distinction between relevant and irrelevant cost data should
be drawn. All costs are not relevant in decision making. A cost is relevant if it is pertinent to
the decision under consideration. A relevant cost is also a cost that differs between
alternatives. In other words, cost which varies as a consequence of the decision is a relevant
cost. A relevant cost for a particular decision is one that changes if an alternative course of
action is taken. Relevant costs are also called differential costs. Any cost that does not differ
between alternatives is irrelevant and can be ignored in a decision. Sunk costs (costs already
irrevocably incurred) are always irrelevant since they will be the same for any alternative. In
addition, an avoidable cost which can be eliminated (in whole or in part) by choosing one
alternative over another is a relevant cost. Relevant cost includes concepts such as differential
cost and marginal cost and contrition approach.
To identify which costs are relevant in a particular situation, take this three step approach:
1. Eliminate sunk costs
2. Eliminate costs that do not differ between alternatives
3. Compare the remaining costs and benefits that do differ between alternatives to make
the proper decision
1.1.1 Decision Making Process
A manager should take the following steps to make decision s intelligently and skilfully;
1. Definition of objectives/ Identification of problems: The first stage in decision making
process should be to specify the goal and objectives of the organisation. The basic
objective of most businesses is to maximise profit or shareholders’ wealth. Also, the firm
should recognise the problems for which the decisions have to be made.
2. Search for Alternatives: The firm must search for a range of possible alternatives or
courses of action that might help achieve the objectives of the firm or solve the problem
on hand. For decision making be successful, the firm must be able to identify all available
alternatives. It must have information in order to make a valid choice between the
alternative courses of action. The search for alternatives involves information concerning
future opportunities and environments
3. Evaluation of Alternatives: The firm should evaluate the alternatives by analysing the
costs and benefits. All alternatives should be assessed on their own merits to ascertain
their contribution to the attainment of the objectives of the firm. In this regard several
techniques or methodologies can be used to evaluate the viability of the various courses
of action available to the firm.
4. Selection of Alternative: Once alternative courses of action have been selected, they
should be implemented. Implementation forms a crucial aspect of the decision making
process in that no matter how good the decision is, if not implemented, it will not yield
the necessary results.
5. Comparison of Actual to Planned Outcome: After the selected alternative courses of
action have been implemented, the outcome of the implemented course of action is
compared to the planned to ascertain whether the alternative has generated the desired
results.
6. Taking Corrective Measures: The firm should take corrective actions to correct any
deviations in the implemented courses of action.
1.2 Relevant Information for Decision Making
Relevant costs are costs which are influenced by decisions taken. Therefore all other costs are
irrelevant. The same distinction can apply to information concerning revenues. Costs
generally fixed but variable for the period of the decision are relevant while all generally
variable but fixed for the period of the decision are irrelevant. It is important to appreciate
that all in all decision analysis economic values are used and not historical costs which mean
that it will not be possible to extract this data directly from the financial accounts. Some
values in the financial accounts will not be relevant.
1.2.1 Guidelines for Determining Relevant Costs
1. Materials: If raw materials has been acquired and held in the stock records at its
purchase cost this will be the purposes of the financial accounting records. This purchase
cost is not the relevant cost for material for any future decision. The relevant cost of the
material will be determined by whatever courses of action are opened to the firm. If the
material to be used in the production of a product is in regular use, the relevant cost is the
future replacement cost, on the basis that once applied to the chosen decision a further
material purchase will be needed to restore the company to its original state. If, on the
other hand the company cannot conceive of a use for the material except for its use on the
product then the relevant cost to be used is the anticipated disposal value of the material
(realisable value)when evaluating and costing the product. To incorporate this disposal
value into a costing of the product is to use it as an opportunity cost. Finally, if the
material cannot be disposed of and the only option is to use it on the product then the
relevant cost is zero, this material can be used for nothing. Incidentally, its use on the
product saved the company from having to pay for disposal of the material. Notice in no
case is the original acquisition cost used.
If any of the future costs and benefits have applying to them some contractual obligation
this is not relevant. In other words, the company is already committed to them, ay due to a
past contract of some kind, then these committed future costs and benefits are not relevant
to the decision at hand.
2. Labour: The principle here is if there is spare capacity then the labour cost will only be
relevant if either extra hand were contracted or overtime work was done by the workers.
If there is no spare capacity but the production of another product has to be abandoned to
create space, then the relevant cost is the contribution from alternative products which
must be abandoned to create spare capacity. This is against the backdrop that contracts of
employment and acknowledged social responsibility of employers it is possible that
reduction, removal or manipulation of a work force may not be easy or cost free.
3. Overheads: Only future costs and benefits are relevant. Hence only those overheads that
vary as a direct result of the decision taken are relevant overheads. For instance,
depreciation, an overhead cost is never relevant to a decision about its use or non-use.
Short-term management decisions can be made using full costing, variable costing, or
incremental analysis. Full costing often involves preparing side-by-side income statements
and identifying the differences. Incremental analysis is most often the straightest forward, the
shortest, the easiest, and the best approach to decision making because it helps managers
focus on the relevant parts of a decision. A manager that uses full or variable costing wastes a
lot of time capturing and listing costs that will not impact the decision at hand. This is
because they do not differ between decisions.
Two potential problems that should be avoided in relevant cost analysis are
(i) Do not assume all variable costs are relevant and all fixed costs are irrelevant.
(ii) Do not use unit cost data directly. It can mislead decision makers because
a. it may include irrelevant costs, and
b. comparisons of unit costs computed at different output levels lead to erroneous
conclusions
1.3 Types of Decisions
Relevant cost and revenue information can be used to make decisions with regards to;
a.
Make, lease or buy
b. Make special orders
c. Sell or process further
d. Keep or drop products
e. Multiple products and limited resources
1.3.1 Cost Analysis in Make, Lease or Buy Decisions
Management sometimes may have to make a choice between manufacturing the component
parts of a product, or buying them from outside. Such a situation of make or buy decision
may arise whenever the firm has the idle plant capacity and the technical capacity of
manufacturing the component parts. In a make or buy situation, the decision will hinge upon
both qualitative and quantitative factors qualitative consideration include product quality and
the necessity for long-run business relationships with subcontractors. The key quantitative
factors are the differential costs of the make and buy alternatives and the consequences of the
alternative uses of the idle facilities. These factors are best seen through the relevant cost
approach. The relevant cost of the buying alternative will include the purchase price and the
ordering costs. Costs relevant for the make alternative would include the variable costs, viz,
direct material, direct labour and variable overheads and those fixed costs which are
avoidable. If fixed costs are expected to remain unaltered, hey would be irrelevant in the
make or buy decision. The firm should also consider the alternative uses of the idle facilities.
If a more profitable use than manufacturing the parts exists, then the firm may procure the
parts from outside and use facilities for the more profitable alternatives.
Also, you can analyze the costs of the lease or buy problem through discounted cash flows
analysis. This analysis compares the cost of each alternative by considering the timing of the
payments, tax benefits, and interest rate on a loan, the lease rate, and other financial
arrangements. To make t analysis you must first make certain assumptions about the
economic life of the equipment, salvage value, and depreciation. A straight cash purchase
using the firm’s existing funds will almost be more expensive than the lease or loan/buy
options because of the loss of the use of funds.
Reasons to Buy from Outside

Flexibility to meet urgent demand of customers;

Overcome limiting factor problem




Concentrate on its own core competencies;
Take advantage of the specialist skill and expertise of the outsiders;
Overcome production bottleneck and
Solve seasonal demand problem
Illustration 1
Suppose a firm manufactures 1000 units of a part and has the following cost structure:
Cost
Per Unit Cost (GH¢)
Cost of 1000 units (GH¢)
Direct materials
2
2000
Direct labour
6
6000
Variable overheads
3
3000
Fixed Overheads
4
4000
Total
15
15000
An outside supplier offers to the firm to sell the parts for GH¢13 each. Should the company
accept the offer? One may argue that the answer is obvious. The cost of buying the part
GH¢1 is less than the cost of manufacturing the part (GH¢15), therefore, the part should be
bought. The comparison is not correct. To decide correctly, the differential manufacturing
cost of GH¢4000 should be considered, which may be unavoidable, that is, it will have to be
incurred whether the part is made or bought from outside. Then those fixed costs are not
relevant in making the comparison. The relevant cost of manufacturing part, thus, would be
GH¢11 only. If we assume that the idle facilities cannot be put to an alternative use, then the
firm should decide to me the part rather than buy it from outside.
Illustration 2
For many years Lansing Company has purchased the starters that it installs in its standard line
of garden tractors. Due to a reduction in output, the company has idle capacity that could be
used to produce the starters. The chief engineer has recommended against this move,
however, pointing out that the cost to produce the starters would be greater than the current
GH¢10.00 per unit purchase price. The company’s unit product cost, based on a production
level of 60,000 starters per year, is as follows:
Cost
Direct materials
Make (GH¢)
4
Direct labour
2.75
Variable manufacturing overheads
0.5
Fixed manufacturing overheads, traceable
(GH¢)
3
180,000
2.25
135,000
Fixed manufacturing overheads
(allocated based on direct labour hours)
12.5
An outside supplier has offered to supply the starter to Lansing for only GH¢10.00 per
starter. One-third of the traceable fixed manufacturing costs represent supervisory salaries
and other costs that can be eliminated if the starters are purchased. The other two-thirds of the
traceable fixed manufacturing costs is depreciation of special manufacturing equipment that
has no resale value. The decision would have no effect on the common fixed costs of the
company and the space being used to produce the parts would otherwise be idle.
Required: Should the company make or buy the starters?
Solution
Relevant Cost
Cost
Direct materials
Make (GH¢)
Buy(GH¢)
4
Direct labour
2.75
Variable manufacturing overheads
0.5
Fixed manufacturing overheads, traceable
1
Purchase Price
0
10
8.25
10
Units produced
60,000
60,000
Total cost
495,000
600,000
Total relevant cost
The two-thirds of the traceable fixed manufacturing overhead costs that cannot be eliminated,
and all of the common fixed manufacturing overhead costs, are irrelevant. The company
would save GH¢105,000 per year by continuing to make the parts itself. In other words,
profits would decline by GH¢105,000 per year if the parts were purchased from the outside
supplier.
Illustration 3
Jackson Company is now making a small part that is used in one of its products. The
company’s accounting department reports the following per unit costs of producing the part
internally.
Cost
(GH¢)
Direct materials
15
Direct labour
10
Variable manufacturing overheads
2
Fixed manufacturing overheads, traceable
4
Fixed manufacturing overheads(allocated)
5
Unit product cost
36
Depreciation of special equipment represents 75% of the traceable fixed manufacturing
overhead cost with supervisory salaries representing the balance. The special equipment has
no resale value and does not wear out through use. The supervisory salaries could be avoided
if production of the part were discontinued. An outside supplier has offered to sell the part to
Jackson Company for GH¢30 each, based on an order of 5,000 parts per year.
Should Jackson Company accept this offer, or continue to make the parts internally?
Solution
Cost
Make (GH¢)
Buy (GH¢)
Direct materials
15
Direct labour
10
Variable manufacturing overheads
2
Fixed manufacturing overheads, traceable
1
Purchase price
0
30
Unit product cost
28
30
5,000
5,000
140,000
150,000
Units produced
Unit product cost
Difference in favor of making: GH¢10,000. The depreciation on the equipment and common
fixed overhead are not avoidable costs. Hence, they are not relevant in the decision making.
Illustration 4
Moo Milk makes the 1-gallon plastic milk jugs used to package its premium goat’s milk. The
company has been approached by a plastic molding company with an offer to produce the
milk jugs at a cost of GH¢14.00 per thousand jugs. Moo’s president believes the company
should continue to produce the jugs and the plant manager has recommended accepting the
offer because the cost to produce the jugs is greater than the purchase price. The company’s
cost to produce one thousand jugs is as follows:
Cost
(GH¢)
Direct materials
4
Direct labour
2.75
Variable manufacturing overheads
3.5
Fixed manufacturing overheads, traceable
3
Fixed manufacturing overheads, common
2.25
Total Production Cost
15.75
One-half of the traceable fixed manufacturing costs represent supervisory salaries and other
costs that can be eliminated if the milk jugs are purchased. The balance of the traceable fixed
manufacturing costs is depreciation of manufacturing equipment that has no resale value.
Some of the space being used to produce the milk jugs could be used to store empty jugs,
eliminating a rented warehouse and reducing common fixed costs by 20%. The rest of the
space could be rented to another company for GH¢30,000 per year. Moo Milk produces
10,000,000 milk jugs per year.
Required: Should Moo Milk make or buy the milk jugs
Solution
Cost
Direct materials
Make (GH¢)
4
Direct labour
2.75
Variable manufacturing overheads
3.5
Fixed manufacturing overheads, traceable
1.5
Fixed manufacturing overheads, common
0.5
Purchase price
Buy (GH¢)
0
14
Unit product cost
12.25
14
Units produced (in thousands)
10,000
10,000
Sub-total
125,500
140,000
Opportunity cost
30,000
0
Product cost
152,500
140,000
Difference in favour of buying: GH¢12,500. The opportunity cost changed the decision from
making to buying the milk jugs.
1.3.2 Cost Analysis to Make Special Order Decisions
Special order decisions involve determining whether a special order from a customer should
be accepted. This type of decision is usually a one-time order that will not impact a
company’s regular sales. Before considered a special order, the company must have idle
capacity, i.e., it should have the ability to complete the special order without expanding its
operations. In other words, it must have capacity that is sitting idle and not being currently
used. The special order decision is based on the difference between the incremental revenue
and the incremental costs. The profit from a special order equals the incremental revenue less
the incremental costs. As long as the incremental revenue exceeds the incremental costs and
present sales are unaffected, the special order should be accepted.
Incremental revenues are the additional revenues generated from accepting the special order
that generates additional sales of the product or service. It does not affect current sales as they
will remain the same. Incremental costs are the additional costs incurred from accepting a
special order. Variable product costs will always be incremental and cause profits to decline.
Other variable costs of operations including selling costs like commissions and shipping costs
will be relevant as well. Rarely will cost savings be a consideration in special order decisions.
What Amounts Are Not Relevant in Special Order Decisions?
All costs that will be incurred regardless if a special order decision is accepted or not are not
relevant for special order decisions. Most often these will be fixed costs. Occasionally the
acceptance of a special order could cause a change in some fixed costs. However this will be
an obvious fact when you analyze the information concerning the special order. Sunk costs
are not relevant with any special order decision process.
When Should Special Orders Be Accepted?
Special orders should be accepted only if:

Incremental revenue exceeds incremental costs

Present sales are unaffected

The company has idle capacity to handle the order
Special orders which do not meet these criteria should generally not be accepted. Of course,
soft-benefits should be considered as well.
Accept or Reject?
If incremental revenues are less than incremental costs, reject the special order, unless
qualitative characteristics overwhelmingly impact the decision.
If incremental revenues are greater than incremental costs, accept the special order unless
qualitative characteristics overwhelmingly impact the decision.
If incremental revenues are equal to incremental costs, focus primarily on qualitative
characteristics to assess the decision.
Illustration 1
Tony’s T-shirts makes shirts for local soccer, baseball, basketball, and other sports teams.
The owner, Tony, purchases the shirts and prints graphics on the shirts for each team. The
graphics were designed several years ago, so design costs are no longer incurred. On average,
Tony sells 1,000 shirts each month. Typical monthly financial data follow:
Per Unit
Total Monthly Data for 1000
(GH¢)
Sales revenue
shirts (GH¢)
20
20,000
Variable Costs:
Direct materials
8
8,000
Direct labour
2
2,000
Manufacturing overhead
3
3,000
Total variable costs
13
13,000
Contribution margin
7
7,000
Fixed costs (rent, salaries etc)
4,000
Profit
3,000
The monthly information provided relates to the company’s routine monthly operations. A
representative of the local high school recently approached Tony to ask about a one-time
special order. The high school will be hosting a statewide track and field event and is willing
to pay Tony’s T-shirts GH¢17 per shirt to make 200 custom T-shirts for the event. Because
enough idle capacity exists to handle this order, it will not affect other sales. That is, Tony
has the factory space and machinery available to produce more T-shirts. Tony incurs the
same variable costs of GH¢13 per unit to produce the special order, and he will pay a firm
GH¢600 to design the graphics that will be printed on the shirts. This special order will have
no other effect on Tony’s monthly fixed costs. Should Tony accept the special order?
Solution
Reject Special Order
Accept Special Order
Differential GH¢
Sales revenue
20,000
23,400a
-
3,400
Variable costs
Contribution margin
13,000
7,000
15,600b
7,800
-
2,600
800
Fixed cost
4,000
4,600c
-
600
Profit
3,000
3,200
-
200
a= GH¢ 23,400 = GH¢20,000 + (GH¢17 per shirt × 200 shirts).
b= GH¢15,600 = GH¢13,000 + (GH¢13 × 200 shirts).
c= GH¢ 4,600 = GH¢4,000 + GH¢600 cost for special order design.
Result of Accepting Special Order
Sales revenue increase
3,400
Variable costs increase
Contribution margin increase
-2,600
800
Fixed cost increase: graphics design
-600
Profit increase from accepting special order
200
The table above shows the differential revenues and costs for the special order being
considered. If Tony’s T-shirts accepts the special order, sales revenue will increase GH¢
3,400 with a corresponding increase in variable costs of GH¢ 2,600. Fixed costs will increase
by GH¢ 600 because design work is required for the special order. Thus profit will increase
by GH¢ 200 (=GH¢ 3,400 − GH¢ 2,600 − GH¢ 600). Tony should therefore accept the
special order offer.
NB: In cases where the acceptance of the special order is going to affect the normal sales
of the firm negatively, then the fall in sales as a result of the special order should be
accounted for as opportunity cost.
Salient points on Qualitative factor to consider:
In the above case, we have assumed that there is spare capacity but it’s important to ensure
that there is really sufficient capacity before agreeing on special order;

ask whether there is any better alternative than accepting special order;

by accepting special order, needs to ensure that this special order does not affect
customer loyalty or affecting the status quo of the existing product, in the above case
is product X. Basically, we should not endanger the existing products by wanting to
utilize full production capacity.
Illustration 2
Trojan Company produces a single product. The cost of producing and selling a single unit of
this product at the company’s normal activity level of 8,000 units per year is:
GH¢
Direct materials
Direct labour
2.5
3
Variable manufacturing overheads
0.5
Fixed manufacturing overheads
4.25
Variable selling and administrative expense
1.5
Fixed selling and administrative expense
2
The normal selling price is GH¢15.00 per unit. The company’s capacity is 10,000 units per
month. An order has been received from an overseas source for 2,000 units at the special
price of GH¢12.00 per unit. This order would not affect regular sales.
Required:
a) If the order is accepted, how much will monthly profits increase or decrease? (The order
will not change the company’s total fixed costs.)
b) Assume the company has 500 units of this product left over from last year that are vastly
inferior to the current model. The units must be sold through regular channels at reduced
prices. What unit cost is relevant for establishing a minimum selling price for these units?
Explain.
Solution
a.
GH¢
Selling price
Direct materials
Direct labour
GH¢
12
2.5
3
Variable manufacturing overheads
0.5
Fixed manufacturing overheads
4.25
Variable selling and administrative expense
1.5
Total variable expenses
7.5
Contribution margin
4.5
Units sold
2000
Total Contribution margin
9000
b. The relevant cost is GH¢1.50 (the variable selling and administrative costs). All other
variable costs are sunk, since the units have already been produced. The fixed costs would
not be relevant, since they will not be affected by the sale of leftover units.
1.3.3 Cost Analysis in the Decision to Sell before or after Additional Processing
In some manufacturing processes, several intermediate products are produced from a single
input. A firm may manufacture and sell an intermediate product. If the facilities are
available,, it may want to process the product further d sell it as completely processed
product. To choose between sell and process further alternatives, the firm should see the
impact of differential cost of further processing on contribution. If the firm obtains more
contribution by selling the completed product, it should process further. In this sell or process
further decision making, joint costs are considered irrelevant since the joint costs have
already been incurred at the time of the decision and therefore represent sunk costs. The
decision will rely exclusively on additional revenue compared to the additional costs incurred
due to further processing.
Additional processing decisions are based on the differences between the incremental
revenues and the incremental costs. Incremental revenues represent the difference between
the revenues generated from selling the product 'as is,' often partially complete, and the
revenues generated after processing the product further to increase its saleability. Incremental
costs are the additional costs incurred from further processing. Costs associated with
producing the product up to the decision point are already incurred in the past and are
considered sunk. All sunk costs are irrelevant.
Evaluating the Decision
If incremental revenues are less than incremental costs, the product should be sold 'as is.' If
incremental revenues equal incremental costs, qualitative effects must be used to make the
decision. If incremental revenues are greater than incremental costs, the product should be
processed further. Regardless if the choice is to sell as-is or process further; a company
should always consider the 'touchy-feely' aspects of decision making effects. These
include employee morale, goodwill to the community, environmental effects, feasibility,
resource availability, etc.
A sell-or-process-further analysis can be carried out in three different ways:

Incremental (or Differential) Approach calculates the difference between the additional
revenues and the additional costs of further processing. If the difference is positive the
product must be processed further, otherwise not.

Opportunity Cost Approach calculates the difference between net revenue from further
processed product and the opportunity cost of not selling the product at split-off point. If
the difference is positive, further processing will increase profits.

Total Project Approach (or the comparative statement approach) compares the profit
statements of both options (i.e. selling or further processing) separately for each product.
The option generating higher profit is chosen
Illustration 1
Product A and B are produced in a joint process. At split-off point, Product A is complete
whereas product B can be process further. The following additional information is available:
Product
Quantity in Units
A
B
5000
10000
10
2.5
Selling Price per Unit:
At Split-Off
If Processed further
5
Costs After Split-Off
20000
Fixed selling and administrative expense
Perform sell-or-process-further analysis for product B.
Solution
Method 1 (Incremental Approach)
GH¢
Incremental Revenue
25,000
Incremental Costs
20,000
Increase in Profits Due to Further Processing
5,000
Method 2 (Opportunity Cost Approach)
GH¢
Sales in Case of Further Processing
50,000
Costs:
Additional Costs
20,000
Opportunity Cost of Not Selling at Split-Off
25,000
Gain on Further Processing
5,000
Method 3 (Total Approach)
Revenue
Split-Off
Further
Point
Processed
GH¢25,000
50,000
0
20,000
25,000
30,000
Costs
Net Revenue
Gain from Further Processing
5,000
Illustration 2
A market decline for staplers has caused Sobo Company to drop its selling price per stapler
from GH¢15 to GH¢12. There are 8,000 staplers in work in process (partially finished) that
have costs of GH¢7.80 per unit associated with them. Sobo can sell these units in their
current state for GH¢9.00 each. It will cost Sobo GH¢1.70 per unit to complete the staplers
in process, so that they can be sold for GH¢12 each.
a. How much is the incremental cost if processed further?
b. Use your answer to part A to calculate incremental profit or loss.
c. List any amounts given in the problem that Sobo should label as ‘sunk’ costs.
Solution
a. Incremental cost: 8,000 x GH¢1.70 = GH¢13,600
Incremental cost is the difference in cost if the staplers are 'processed further', i.e., completed.
The costs incurred in the past, the GH¢7.80 per stapler is not relevant because it will be the
same no matter if the staplers are processed further or sold as-is. This past cost is a sunk cost,
and sunk costs are never relevant because the cost cannot be changed and is the same
regardless if processed further or sold as-is.
b.
Incremental revenue (GH¢12 -9)*8,000
Incremental costs (part A)
Incremental profit if processed further
GH¢24,000
(13,600)
10,400
Because profits increase, the staplers should be processed further.
Revenue will increase by GH¢3 per unit and costs will increase by GH¢1.70 per unit netting
a profit increase of GH¢10,400. Because this is an incremental analysis, you must only
consider the incremental costs and incremental revenue.
c.
List any amounts given in the problem that Sobo should label as ‘sunk’ costs. Only one
amount is sunk, the GH¢7.80 cost of producing the products to their current state. This
amount has already been incurred and won't change regardless of the decision made.
1.3.4 Joint Product Cost Decisions
In some manufacturing processes, several end products are produced from a single input.
Such end products are known as joint products. The costs associated with making these
products up to the point where they can be recognized as separate products (the split-off
point) are called joint product costs.
Cost allocation problem
Joint product costs are really common costs that are incurred to simultaneously produce a
variety of end products. Unfortunately, these common costs are routinely allocated to the
joint products. Allocated joint product costs are often misinterpreted as costs that could
be avoided by producing less of one of the joint products. However, joint product costs
can only be avoided by producing less of all of the joint products simultaneously. If any of
the joint products is made, then all of the joint product costs up to the split-off point will have
to be incurred. Therefore, in deciding on whether to produce or not produce a particular
product that forms part of the joint products, we use only costs that are incurred in the
production of that product and the revenue generated after the spilt-off point. In this case, the
differential or incremental approach is widely used. Because the analysis is done by taking
account of only increases in revenue and cost after the split-off point.
1.3.5 Cost Analysis in the Decision to Keep or Drop Products or Services
Management is sometimes faced with the problem of dropping an unprofitable product or
department. The decision to drop an old product line or add a new one must take into account
both qualitative and quantitative factors. However, any final decision should be based
primarily on the impact the decision would have on contribution margin or net income.
Therefore the amount of common fixed costs typically continues regardless of the decision
thus cannot be saved by dropping the product line to which it is distributed
Just like other types of short term decisions, segment/product decisions can be made using
either full costing or incremental analysis. Full costing often involves preparing two side-byside income statements and looking at the differences. Incremental analysis is most often the
most straight-forward, the shortest, the easiest, and the best approach because it helps
managers focus on the relevant parts of a decision. A manager that uses full costing wastes a
lot of time looking at costs that will not differ between two decisions. We will focus
primarily on whether a product line or segment should be dropped.
Decisions
If the decrease in revenue > decrease in costs, do not drop the product line/services. If the
decrease in revenue < decrease in costs, drop the product line/services. If the decrease in
revenue = decrease in costs, consider qualitative issues alone.
Fixed Costs
Fixed costs in total remain the same regardless of activity. The same is generally true
regardless of how many product lines or segments a company has. Fixed costs fall into two
types that can help decide if they are relevant or not for add or drop decisions:
Common fixed costs

Costs that are not traceable to a particular product or segment;

Costs that benefit more than one product or segment; they are allocated/distributed
amongst a number of product/segments.

Not relevant because they continue whether the product or segment is dropped or not.

If one product or segment is dropped, total common fixed costs must be reallocated to
remaining products or segments.
Direct fixed costs

Costs that pertain specifically to one product or segment that are avoidable if that
product/segment is dropped

Relevant because they can be avoided if the product or segment is dropped
Approaches
Two basic approaches can be used to analyze data in this type of decision.
1. Compare contribution margins and fixed costs. A segment should be added only if the
increase in total contribution margin is greater than the increase in fixed cost. A segment
should be dropped only if the decrease in total contribution margin is less than the decrease in
fixed cost.
2. Compare net incomes. A second approach is to calculate the total net income under each
alternative. The alternative with the highest net income is preferred. This approach requires
more information than the first approach since costs and revenues that don't differ between
the alternatives must be included in the analysis when the net incomes are compared.
Beware of allocated common costs. Allocated common costs can make a segment look
unprofitable even though dropping the segment might result in a decrease in overall company
net operating income. Allocated costs that would not be affected by a decision are irrelevant
and should be ignored in a decision relating to adding or dropping a segment.
Illustration 1
A company has three products: Product A, Product B and Product C. Income statements of
the three product lines for the latest month are given below:
Product Line
A
B
C
GH¢467,000
GH¢314,000
GH¢598,000
Variable Costs
241,000
169,000
321,000
Contribution Margin
226,000
145,000
277,000
Direct Fixed Costs
91,000
86,000
112,000
Allocated Fixed Costs
93,000
62,000
120,000
Net Income
42,000
− 3,000
45,000
Sales
Use the incremental approach to determine if Product B should be dropped.
Solution
By dropping Product B, the company will lose the sale revenue from the product line. The
company will also obtain gains in the form of avoided costs. But it can avoid only the
variable costs and direct fixed costs of product B and not the allocated fixed costs. Hence:
If Product B is Dropped
Gains:
Variable Costs Avoided
GH¢169,000
Direct Fixed Costs Avoided
GH¢86,000
255,000
Less: Sales Revenue Lost
314,000
Decrease in Net Income of the Company
59,000
Illustration 2
B & B Inc., a retailing company has two departments, X and Y. A recent monthly
contribution format income state for the company follows.
X (GH¢)
Y (GH¢)
Total(GH¢)
Sales
3,000,000
1,000,000
4,000,000
Variable expenses
900,000
400,000
1,300,000
Contribution margin
2,100,000
600,000
2,700,000
Fixed expenses
1,400,000
800,000
2,200,000
Operating income(loss)
700,000
-200,000
500,000
A study indicates that GH¢340,000 of the fixed expenses being charged to Y are sunk costs
or allocated costs that will continue even if Y is dropped. In addition the elimination of Y will
result in a 10% decrease in the sales of X.
Required: If Department Y is discontinued, will this be a positive move or a negative move
for the company as a whole?
Solution
Contribution margin lost if Y is dropped:
(GH¢)
Department Y contribution margin
lost
-600,000
Department X contribution margin
lost
-210,000
Total contribution margin lost
-810,000
Avoidable fixed costs
460,000
Decrease in operating income
-350,000
1.3.6 Analyse Decision with Multiple Product and Limited Resources
Managers frequently confront the short-run problem of making the best use of scarce
resources that are essential to production activity or service provision but have limited
availability. Scarce resources include

machine hours,

skilled labour hours,

raw materials,

production capacity, and

Other inputs.
Whenever demand exceeds productive capacity, a production constraint (bottleneck)
exists. This means that the company is unable to fill all orders and some choices have to be
made concerning which orders are filled and which are not filled. Determining the best use
of a scarce resource requires management to identify company objectives. If an objective is to
maximize company profits, a scarce resource is best used to produce and sell the product
generating the highest contribution margin per unit of the scarce resource. This strategy
assumes that the company must ration only one scarce resource. Total contribution margin
will be maximized by promoting those products or accepting those orders that provide the
highest unit contribution margin in relation to the constrained resource.
Single Limiting Factor
Where a limiting factor exists, instead of concentrating on those products, which maximise
contribution, we do the following;
(a) Contribution will be maximised by earning the biggest possible contribution per unit of
scarce resource. Thus if Grade A labour is the limiting factor, contribution will be
maximised by earning the biggest contribution per hour of Grade A labour worked.
Similarly, if machine time is in short supply, profit will be maximised by earning the
biggest contribution per machine hour worked.
(b) The limiting factor decision therefore involves the determination of the contribution
earned by each different product per unit of scarce resource.
Steps
Step 1: Identify the scarce resource (limiting factor)
Step 2: Calculate the amount of the limiting factor needed by each product.
Step 3: Confirm that the amount of the limiting factor is insufficient to allow all products to
be produced.
Step 4: Calculate the contribution earned per unit of each product.
Step 5: Calculate the contribution of each product per unit of the limiting factor by dividing
step 4 by step 2
Step 6: Establish production priority by ranking products according to the contribution per
unit of the scarce resource.
Step 7: Allocate the available scarce resource according to the ranking.
Illustration
A company manufactures three products (X, Y and Z). All direct operatives are the same
grade and are paid at GH¢11 per hour. It is anticipated that there will be a shortage of direct
operatives in the following period, which will prevent the company from achieving the
following sales targets:
Product X 3,600 units
Product Y 8,000 units
Product Z 5,700 units
Selling prices and costs are shown below
Product X, Y, and Z Selling Prices and Costs per unit
Product X
Product Y
Product Z
100.00
69.00
85.00
Production*
51.60
35.00
42.40
Non-Production
5.00
3.95
4.25
Production
27.20
19.80
21.00
Non-Production
7.10
5.90
6.20
* includes the cost of direct operatives
24.20
16.50
17.60
Selling prices
Variable cost:
Fixed Costs:
The fixed costs per unit are based on achieving the sales targets. There would not be any
savings in fixed costs if production and sales are at a lower level
Solution
Step 1: Limiting factor if shortage of direct operatives
Step 2: Calculate the amount of the limiting factor needed by each product.
Product X GH¢24.20/unit ÷ GH¢11/hr = 2.2 hrs per unit × 3,600 units = 7,920 hrs
Product Y GH¢16.50/unit ÷ GH¢11/hr = 1.5 hrs per unit × 8,000 units = 12,000 hrs
Product Z GH¢17.60/unit ÷ GH¢11/hr = 1.6 hrs per unit × 5,700 units = 9,120 hrs
Total hours needed = 29,040 hrs
Step 3: Confirm that the amount of the limiting factor is insufficient to allow all products to
be produced.
Direct labour hours available are 2,640 less (26,400 - 29,040) than those required to achieve
the sales targets.
Step 4: Calculate the contribution earned per unit of each product.
Contribution is sales revenue less variable costs (both production and non-production). Thus:
Product X GH¢100.00 - GH¢56.60 (51.60 + 5.00) = GH¢43.40 per unit
Product Y GH¢69.00 - GH¢38.95 (35.00 + 3.95) = GH¢30.05 per unit
Product Z GH¢85.00 - GH¢46.65 (42.40 + 4.25) = GH¢38.35 per unit
Step 5: Calculate the contribution of each product per unit of the limiting factor by dividing
step 4 by step 2
The contribution per unit of scarce resource can be calculated either as a GH¢ contribution
per hour of direct operative time or as a GH¢ contribution per GH¢ cost of direct operatives.
Thus:
Product X GH¢43.40/unit ÷ 2.2 hrs/unit = GH¢19.73 per direct operative hour
Product Y GH¢30.05/unit ÷ 1.5 hrs/unit = GH¢20.03 per direct operative hour
Product Z GH¢38.35/unit ÷ 1.6 hrs/unit = GH¢23.97 per direct operative hour
Or
Product X GH¢43.40/unit ÷ GH¢24.20/unit = GH¢1.793 per GH¢ cost of direct operatives
Product Y GH¢30.05/unit ÷ GH¢16.50/unit = GH¢1.821 per GH¢ cost of direct operatives
Product Z GH¢38.35/unit ÷ GH¢17.60/unit = GH¢2.179 per GH¢ cost of direct operatives
Step 6: Establish production priority by ranking products according to the contribution per
unit of the scarce resource.
On the basis of the contribution per unit of the scarce resource, Product Z would be
manufactured as the first priority (GH¢23.97/hr or GH¢2.179/GH¢ cost), followed by
Product Y (GH¢20.03/hr or GH¢1.821/GH¢ cost) and finally Product X (GH¢19.73/hr or
GH¢1.793/GH¢ cost). The same conclusion would be reached whichever of the calculations
in stage 4 was used because the basis is the same.
Step 7: Allocate the available scarce resource according to the ranking.
The scarce resource of direct operative hours needs to be allocated according to the
production priority established in stage 5 above. Product Z has first priority and so the direct
operative hours will be allocated up to the limit required to achieve the sales target of 5,700
units. This was calculated in stage 1 to be 9,120 hours. The next priority is Product Y. The
allocation of the 26,400 hours available can be set out as follows:
Product Z= 9,120 hours 5,700 units
Product Y =12,000 hours 8,000 units
21,120 hours
Product X = 5,280 hours 2,400 units
(26,400 - 21,120) (5,280 hours ÷ 2.2 hours/unit) 26,400 hours
Multiple Limiting Factors-Linear Programming
When the production process requires two or more production constraints, the choice of sales
mix involves a more complex analysis, and in contrast to the case of one production
constraint which solves for a single product, the solution can include both products when two
constraints are involved. When there are more than one limiting factor, then a technique
known as linear programming is used. In formulating a linear programming problem the steps
involved are as follows;

Define the unknowns, i.e. the variables that need to be determined

Formulate the constraints, i.e. the limitation that must be placed on the variables

Formulate the objective function that needs to be maximised or minimised

Graph the constraints and objective functions

Determine the optimal solution to the problem by reading the graph.
Note that non-negativity constraints will be needed to ensure that there are no negative
values.
Linear programming problems could also be solved using algebra
Illustration 1
John manufactures chairs and tables. Each product passes through a cutting process and an
assembling process. One chair makes a contribution of GH¢50 and take 6 hours cutting time
and 4 hours assembly time. One table makes a contribution of GH¢40 and takes 3 hours
cutting time and 8 hours assembly time. There is a maximum of 36 cutting hours available
each week and 48 assembly hours. Find the output that maximises contribution.
Solution
Let x = number of chairs produced each week and y= number of tables produced each week.
Constraints are:
6x+3y = 36
4x+8y = 48
Solving for x and y simultaneously, x = 4 and y = 4
Thus maximum contribution = (4 * 50 ) + (4*40) = GH¢360
1.4 Behavioural, Implementation and Issues in Decision Making
A well-known problem in business today is the tendency of managers to focus on short-term
goals and neglect the long-term strategic goals because their compensation is based on short
term accounting measures such as net income. Many critics of relevant cost analysis have
raised this issue. As noted, it is critical that the relevant cost analysis be supplemented by a
careful consideration of the firm’s long-term, strategic goals. Without strategic
considerations, management could improperly use relevant cost analysis to achieve a shortterm benefit and potentially suffer a significant long-term loss. For example, a firm might
choose to accept a special order because of a positive relevant cost analysis without properly
considering that the nature of the special order could have a significant negative impact on
the firm’s image in the marketplace and perhaps a negative effect on sales of the firm’s other
products. The important message for managers is to keep the strategic objectives in the
forefront in any decision situation.
Further, people are affected by decisions. The people may be customers, or buyers for
corporate customers. They may also be suppliers. However, employees will be most affected
by decisions that a company takes. The decision would mean more overtime, redundancy or
changed work procedures. They have to be paid and then they are no longer employees. This
affects morale of the remaining employees. The morale of the employees affects the
productivity of the shop floor, the reject rate and the rate of labour turnover.
Trade union organisations may consider sending the company to court is the decision is to
render some staff members redundant. This might dent the image of the company which
could be translated into low demand for goods produced. Some customers regard certain
goods as jointly demanded and so its withdrawal will lead to the reduction in demand for the
other product. For instance, if the production of saucers is withdrawn, the demand for tea
cups will reduce.
1.5 Cost-Volume-Profit (CVP) Analysis
In any business, or, indeed, in life in general, hindsight is a beautiful thing. If only we could
look into a crystal ball and find out exactly how many customers were going to buy our
product, we would be able to make perfect business decisions and maximise profits. One of
the most important decisions that needs to be made before any business even starts is ‘how
much do we need to sell in order to break even?’ By ‘break even’ we mean simply covering
all our costs without making a profit.
CVP analysis is designed to illustrate the effects of changes in volume or output of work done
or sales made upon sales revenue and costs. As a consequence the effect upon profit is shown
as the difference between total revenue and total costs. CVP analysis looks primarily at the
effects of differing levels of activity on the financial results of a business. In performing this
analysis, there are several assumptions made, including:

Sales price per unit is constant.

Variable costs per unit are constant.

Total fixed costs are constant.

Everything produced is sold.

Costs are only affected because activity changes.

If a company sells more than one product, they are sold in the same mix.

The time scale necessary to implement any decision based upon the analysis is
relatively short.

Cost and revenue are linear

The contribution relationships are valid and constant

Either one product is made or a combination is made in the same proportion
throughout.

All costs behave in the manner assumed and can be split into fixed or variable.
Useful relationships
1. Profit = Revenue- Costs
2. Total Cost= Variable costs- Fixed costs
3. Profit = (Revenue – Variable costs)- Fixed costs
4. Contribution= Revenue – Variable costs
5. Total contribution = Quantity of sales * Contribution per unit
6. At Break-Even: Revenue =Total Costs
7. At Break-Even: Total contribution = Fixed costs and
8. Break-Even quantity = Fixed costs/Contribution per unit
Contribution margin and contribution margin ratio
Key calculations when using CVP analysis are the contribution margin and the
contribution margin ratio. The contribution margin represents the amount of income or
profit the company made before deducting its fixed costs. Said another way, it is the amount
of sales dollars available to cover (or contribute to) fixed costs. When calculated as a ratio, it
is the percent of sales dollars available to cover fixed costs. Once fixed costs are covered, the
next dollar of sales results in the company having income.
The contribution margin is sales revenue minus all variable costs. It may be calculated using
dollars or on a per unit basis. If The Three M's, Inc., has sales of GH¢750,000 and total
variable costs of GH¢450,000, its contribution margin is GH¢300,000. Assuming the
company sold 250,000 units during the year, the per unit sales price is GH¢3 and the total
variable cost per unit is GH¢1.80. The contribution margin per unit is GH¢1.20. The
contribution margin ratio is 40%. It can be calculated using either the contribution margin in
dollars or the contribution margin per unit. To calculate the contribution margin ratio, the
contribution margin is divided by the sales or revenues amount.
Contribution Margin
GH¢
750,000
450,000
300,000
Sales
Variable Costs
𝐶𝑜𝑛𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 𝑚𝑎𝑟𝑔𝑖𝑛 𝑟𝑎𝑡𝑖𝑜 =
𝐶𝑜𝑛𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 𝑚𝑎𝑟𝑔𝑖𝑛
𝑆𝑎𝑙𝑒𝑠
=
300,000
750,000
40% 𝑜𝑟
Per Unit (GH¢)
3
1.8
1.2
1.2
3
= 40%
Break-even point
The break-even point represents the level of sales where net income equals zero. In other
words, the point where sales revenue equals total variable costs plus total fixed costs, and
total contribution margin equals fixed costs.
𝐼𝑛 𝑡𝑒𝑟𝑚𝑠 𝑜𝑓 𝑠𝑎𝑙𝑒𝑠 𝑢𝑛𝑖𝑡𝑠 (𝑏𝑟𝑒𝑎𝑘 − 𝑒𝑣𝑒𝑛 𝑝𝑜𝑖𝑛𝑡 𝑖𝑛 𝑢𝑛𝑖𝑡𝑠) =
𝐹𝑖𝑥𝑒𝑑 𝑐𝑜𝑠𝑡
𝐶𝑜𝑛𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 𝑝𝑒𝑟 𝑢𝑛𝑖𝑡
𝐼𝑛 𝑡𝑒𝑟𝑚𝑠 𝑜𝑓 𝑠𝑎𝑙𝑒𝑠 𝑟𝑒𝑣𝑒𝑛𝑢𝑒 (𝑏𝑟𝑒𝑎𝑘 − 𝑒𝑣𝑒𝑛 𝑝𝑜𝑖𝑛𝑡 𝑖𝑛 𝑠𝑎𝑙𝑒𝑠) =
𝐹𝑖𝑥𝑒𝑑 𝑐𝑜𝑠𝑡
𝐶𝑜𝑛𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑖𝑜
Using the previous information and given that the company has fixed costs of GH¢300,000.
Break-even point in dollars: The break-even point in sales dollars of GH¢750,000 is
calculated by dividing total fixed costs of $300,000 by the contribution margin ratio of 40%.
𝐼𝑛 𝑡𝑒𝑟𝑚𝑠 𝑜𝑓 𝑠𝑎𝑙𝑒𝑠 𝑟𝑒𝑣𝑒𝑛𝑢𝑒 (𝑏𝑟𝑒𝑎𝑘 − 𝑒𝑣𝑒𝑛 𝑝𝑜𝑖𝑛𝑡 𝑖𝑛 𝑠𝑎𝑙𝑒𝑠) =
300,000
0.4
= GH¢750,000
Break-even point in units: The break-even point in units of 250,000 is calculated by
dividing fixed costs of GH¢300,000 by contribution margin per unit of GH¢1.20.
𝐼𝑛 𝑡𝑒𝑟𝑚𝑠 𝑜𝑓 𝑠𝑎𝑙𝑒𝑠 𝑢𝑛𝑖𝑡𝑠 (𝑏𝑟𝑒𝑎𝑘 − 𝑒𝑣𝑒𝑛 𝑝𝑜𝑖𝑛𝑡 𝑖𝑛 𝑢𝑛𝑖𝑡𝑠)
300,000
= 250,000 𝑢𝑛𝑖𝑡𝑠
1.2
Targeted income
CVP analysis is also used when a company is trying to determine what level of sales is
necessary to reach a specific level of income, also called targeted income. To calculate the
required sales level, the targeted income is added to fixed costs, and the total is divided by the
contribution margin ratio to determine required sales dollars, or the total is divided by
contribution margin per unit to determine the required sales level in units.
𝑅𝑒𝑞𝑢𝑖𝑟𝑒𝑑 𝑠𝑎𝑙𝑒𝑠 𝑖𝑛 GH¢ =
Fixed Cost + Targeted Income
Contribuion margin ratio
𝑅𝑒𝑞𝑢𝑖𝑟𝑒𝑑 𝑠𝑎𝑙𝑒𝑠 𝑖𝑛 units =
Fixed Cost + Targeted Income
Contribuion margin per unit
Using the data from the previous example, what level of sales would be required if the
company wanted GH¢ 60,000 of income? The GH¢60,000 required is called the targeted
income. The required sales level is GH¢900,000 and the required number of units is 300,000.
Remember that there are additional variable costs incurred every time an additional unit is
sold, and these costs reduce the extra revenues when calculating income.
𝑅𝑒𝑞𝑢𝑖𝑟𝑒𝑑 𝑠𝑎𝑙𝑒𝑠 𝑖𝑛 GH¢ =
300,000 + 60,000
= GH¢900,000
0.4
𝑅𝑒𝑞𝑢𝑖𝑟𝑒𝑑 𝑠𝑎𝑙𝑒𝑠 𝑖𝑛 units =
300,000 + 60,000
= 300,000 units
1.2
Note that this calculation of targeted income assumes it is being calculated for a division as it
ignores income taxes. If a targeted net income (income after taxes) is being calculated, then
income taxes would also be added to fixed costs along with targeted net income.
Margin of Safety
This is the amount by which the sales in units or a percentage of budgeted sales can fall
below before a loss is made.
𝑀𝑎𝑟𝑔𝑖𝑛 𝑜𝑓 𝑠𝑎𝑓𝑒𝑡𝑦 𝑖𝑛 units = Budgeted sales − Break − even sales
𝑀𝑎𝑟𝑔𝑖𝑛 𝑜𝑓 𝑠𝑎𝑓𝑒𝑡𝑦 𝑎𝑠 𝑎 % 𝑜𝑓 𝑠𝑎𝑙𝑒𝑠 =
Budgeted sales − Break − even sales
∗ 100% =
Budgeted sales
Using the data from the above example with additional information of budgeted sales for the
period of 350,000 units, calculate the margin of safety in units and calculate the margin of
safety as a % of budgeted sales.
𝑀𝑎𝑟𝑔𝑖𝑛 𝑜𝑓 𝑠𝑎𝑓𝑒𝑡𝑦 𝑖𝑛 units = 350,000 − 250,000 = 100,000 units
𝑀𝑎𝑟𝑔𝑖𝑛 𝑜𝑓 𝑠𝑎𝑓𝑒𝑡𝑦 𝑎𝑠 𝑎 % 𝑜𝑓 𝑠𝑎𝑙𝑒𝑠 =
350,000 − 250,000
∗ 100% = 40%
250,000
Sensitivity Analysis
A business environment can change quickly, so a business should understand how sensitive
its sales, costs, and income are to changes. Sensitivity analysis is a “what if” technique that
managers use to examine how an outcome will change if the original predicted data are not
achieved or if an underlying assumption changes. In the context of CVP analysis, sensitivity
analysis examines how operating income (or the breakeven point) changes if the predicted
data for selling price, variable cost per unit, fixed costs, or units sold are not achieved. The
sensitivity to various possible outcomes broadens managers’ perspectives as to what might
actually occur before they make cost commitments. CVP analysis using the break-even
formula is often used for this analysis. For example, marketing suggests a higher quality
product would allow The Three M’s Inc, to raise its selling price 10%, from GH¢ 3.00 to
GH¢ 3.30. To increase the quality would increase variable costs to GH¢ 2.00 per unit and
fixed costs to GH¢ 350,000. If The Three M's, Inc., followed this scenario, its break-even in
units would be 269,231.
𝐵𝑟𝑒𝑎𝑘 − 𝑒𝑣𝑒𝑛 𝑠𝑎𝑙𝑒𝑠 𝑢𝑛𝑖𝑡𝑠 =
𝐹𝑖𝑥𝑒𝑑 𝑐𝑜𝑠𝑡
350,000
=
= 269,231 𝑢𝑛𝑖𝑡𝑠
𝐶𝑜𝑛𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 𝑝𝑒𝑟 𝑢𝑛𝑖𝑡 (3.30 − 2)
These changes in variable costs and sales result in a higher break-even point in units than the
250,000 break-even units calculated with the original assumptions. The critical question is,
“Will the customers continue to purchase, and are new or existing customers identified that
will purchase the additional 19,231 units of the product required to break even at the higher
sales price?”
CVP with Multiple Product Mix
In cases where a company deals in multiple products, the analysis is similar to the single
product in that the concepts and formulae remain the unchanged. The only modification
however is that the analysis is performed by using weighted averages components. For
example, instead of contribution, weighted contribution margins and selling prices are used.
Limitation of CVP Analysis
1. Profits are calculated on a variable cost basis or, if absorption costing is used, it is
assumed that production volumes are equal to sales volumes.
2. Fixed costs remain constant over the ‘relevant range’ – levels of activity in which the
business has experience and can therefore perform a degree of accurate analysis. It will
either have operated at those activity levels before or studied them carefully so that it can,
for example, make accurate predictions of fixed costs in that range.
3. Costs can be divided into a component that is fixed and a component that is variable. In
reality, some costs may be semi-fixed, such as telephone charges, whereby there may be a
fixed monthly rental charge and a variable charge for calls made.
4. The total cost and total revenue functions are linear. This is only likely to hold true within
a short-run, restricted level of activity.
5. All other variables, apart from volume, remain constant, ie volume is the only factor that
causes revenues and costs to change. In reality, this assumption may not hold true as, for
example, economies of scale may be achieved as volumes increase. Similarly, if there is a
change in sales mix, revenues will change. Furthermore, it is often found that if sales
volumes are to increase, sales price must fall. These are only a few reasons why the
assumption may not hold true; there are many others.
Illustration 1
Ababio Plastic Company produces plastic buckets which are distributed all over the country.
During the years 2009 and 2010, the following data were extracted:
Sales (GHC)
Profits (GHC)
Year 2009
1,200,000
80,000
Year 2010
1,400,000
130,000
You are required to calculate the following:
i.
Profit –Volume Ratio (P/V Ratio)
ii.
Break – Even Point in Sales value
iii.
Profit when the sales value is GHC1,800,000
iv.
The Sales Value required to make a profit of GHC120,000
v.
The Margin of Safety in the Year 2010
Solution
Year 2009
Year 2010
Difference
(i)
P/V Ratio = 50,000 x 100
200,000
Less Profit
Fixed Cost
(iii)
(iv)
(v)
Profit (GHC)
1,200,000
1,400,000
200,000
80,000
130,000
50,000
= 25%
Contribution in 2009 (1,200,000 x 25%)
(ii)
Sales (GHC)
Break-even point in sales value:
Fixed Cost = 220,000
P/V Ratio
25%
300,000
80,000
220,000
= GHC880,000
Profit when sales is GHC1,800,000:
Contribution (GHC1,800,000 x 25%)
GHC
450,000
Less Fixed Cost
220,000
Profit
230,000
Sales to earn a profit of GHC120,000:
Fixed Cost + Target Profit =
P/V Ratio
=
Margin of safety in 2010:
Actual sales - Break-en sales
1,400,000
- 880,000
=
220,000 + 120,000
25%
GHC1,360,000
GHC520,000
Practice Questions
1. Dolow produces computer component A for sale at GH¢47 per unit to a Manufacturer of
computers. The company currently produces 15,000 units of the component per annum.
Total cost of production and unit cost are as follows:
Production Cost (GH¢)
Unit Cost (GH¢)
Direct Materials
210,000
14
Direct labour
180,000
12
Variable production cost
30,000
2
Fixed manufacturing overhead
150,000
10
Share of non-production overhead
105,000
7
675,000
45
A supplier has offered to supply 15,000 units of the components per annum at a price of
GH¢39 per unit over a four-year period without any change in price.
If Dolow accepts the offer, the following are the effects on current operation.
(1) Direct labour will be redundant but at a redundancy cost of GH¢5,000.
(2) Direct materials and variable production cost will be avoidable
(3) Fixed manufacturing cost will be reduced by GH¢18,750 per annum
(4) Share of non-production overhead cost will stay as it is.
Assuming further that, the extra capacity for accepting the contract offer from the supplier
can be used to produce and sell 15,000 units of component Z at a price of GH¢43 per unit
with the following assumptions:
(1) All of the labour force required to manufacture component A will be used to make
component Z.
(2) Variable manufacturing overhead will remain same.
(3) The fixed manufacturing overhead will remain same.
(4) Non-manufacturing overhead will be the same.
(5) The materials for component A will not be needed but additional materials at a cost of
GH¢15 per unit will be required for production.
Required:
(a) Should Dolow make or buy component A?
(b) Should Dolow accept the offer and use the available space to manufacture component
Z?
2. Xexe Ltd produces 4 products and is planning its production mix for the next period.
Estimated cost, sales and production data are shown below:
A
B
C
D
Selling price/unit (GH¢)
50
70
80
100
Materials @GH¢4/kg
12
36
20
24
Direct labour@GH¢2/hr
6
4
14
10
Maximum demand( units)
3000
3000
3000
3000
Required:
(i) Assuming labour hours is a limiting factor in the period, advise management on the most
appropriate mix if labour hours is limited to 45,000 hours.
(ii) Assuming, materials is a limiting factor in the period, advise management on the most
appropriate mix if materials is limited to 55,000 kgs in the period.
3. A Sports Kit manufacturer, in conjunction with a Software house, is considering the
launch of a new sporting simulator based on video-tapes that enables greater realism to be
achieved. Two proposals are being considered. Both use the same production facilities
and, as these are limited, only one product can be launched.
The following data are the best estimates the firm has been able to obtain:
Football Simulator
Cricket Simulator
Annual volume (units)
40,000
30,000
Selling price (per unit)
GH¢65
GH¢100
Variable cost of production
GH¢40
GH¢50
Fixed production cost
GH¢300,000
GH¢300,000
Fixed selling and administrative cost
GH¢225,000
GH¢675,000
The higher selling and administrative costs for the cricket simulator reflect the additional
advertising and promotion costs expected to be necessary to sell the more expensive cricket
system.
The firm has a minimum target of GH¢100,000 profit per year for new products. The
management recognizes the uncertainty in the above estimates and wishes to explore the
sensitivity of the profit on each product to changes in the values of the variables (volume,
price, variable cost per unit and fixed costs).
You are required to calculate for each of the products:
(a) The expected profit from each product
(b) (i) The units to be produced if the targeted profit is GH¢100,000
(ii) The unit selling price per product, if the expected profit per year is GH¢100,000