Cost behaviour marginal costing in investments

1. New Module Topic-3 COST BEHAVIOUR
• Direct and Indirect Costs
• Fixed Costs
• Variable and semi-variable costs
• Marginal Costing
• Operational Gearing or Leverage
Costing: Is the process of determining the cost of doing something e.g. the cost of
manufacturing an article.
3.0 Classification of costs:
Costs can be classified as:
(i) Direct costs, and (ii) Indirect costs
(i) Direct Costs:
These costs comprising direct material, direct labour and direct expenses
and are those which can be directly identified with a job, a product or a
service.
Direct materials: consist of all those materials, which can be physically
identified with a specific product e.g. timber in case of a chair.
Direct labour: Consist of those labor costs which can be specifically
traced to a particular product e.g. wages of carpenter in manufacturing a
chair.
Direct expenses: Cost of raising a machine for producing a specific
product is an example of direct expense
Direct material + direct labour + direct expenses = Prime Cost
(ii) Indirect costs:
All material, labour and expense expenditure which cannot be identified
with the particular product are termed as indirect costs. The total of
indirect costs is known as overhead which is normally separated into
categories such as production overheads, Administrative overheads,
selling and distribution overheads.
• Prime cost + Production overheads = Factory cost
• Factory cost + Administrative overheads + Selling and distribution
overheads = Total cost
1

2. Elements of manufacturing cost
In a manufacturing organization product costs consist of direct material,
direct labour, direct expenses and manufacturing overheads.
Manufacturing overhead: Include indirect material, indirect labour &
indirect expenses such as depreciation of machinery, Rent, etc
Indirect overheads are allocated to various products on some sensible
basis.
Indirect materials: If the materials are used for several products and is
not identifiable with the specific product, it is known as indirect material
such as welding rod. (It forms part of manufacturing overhead cost)
Indirect labour: can not be specifically assigned to product such as
foreman wages/salaries. This forms part of manufacturing overhead.
Prime cost + manufacturing overhead= Total manufacturing cost
Classification of costs on the basis of cost object(ive):
1. Costs for Stock Valuation
2. Cost for Decision-making and Planning
3. Cost for Control
Costs for Stock Valuation:
Un-expired costs are the resources acquired to contribute to future revenue. These are
recorded as assets in the Balance Sheet.
Expired costs: are expenses, which have been consumed in generating revenue and are
shown in the P & L Account.
Period costs: are those expenses (administration, selling & distribution) which are not
included in the stock valuation and are treated as expenses in the period in which they are
incurred.
All non-manufacturing costs are period costs.
Product costs: are those costs which are identified with goods produced / purchased and
are attached to the product and are included in the stock valuation.
All fixed costs are recorded as product cost.
Classification for Decision–making and Planning
Cost & Revenues behavior: Knowledge of how cost and revenues will vary with
different levels of volume is essential for decision making.
How costs react to changes in volume? Variable cost, fixed cost, semi–variable costs,
semi– fixed costs, terms are used.
2

3. Variable cost: vary in direct proportion to the volume of activity
Total variable costs are linear.
A unit variable cost is constant
Fixed costs: remain constant over wide ranges of activity for specified time period.
Dep. on factory Building, lease charges, supervisors Salaries etc..
Unit fixed cost: decrease proportionality with the level of activity increased.
Semi – Variable cost: include a cost which has both elements, a fixed and a variable, e.g.
Hiring a loader, telephone expense etc.
3
2500
2000
1500
1000
500
Total
variable cost
1000 2000 3000 4000
Level of Activity
Unit variable
cost
10
50
1000 2000 3000 4000
Level of Activity
Total fixed
cost
Unit fixed cost

4. Semi–fixed or Step Costs: Are fixed for a given level of activity but eventually increase
at same critical point
Relevant and Irrelevant Costs & Revenues.
Costs & revenues can be classified for decision – making as Relevant or
Irrelevant. Relevant cost or revenues are those future cost / revenues which will be
changed by decision making.
Irrelevant cost & revenues are those which will not be affected by the decision, e.g.
journey by car or by public transport-- road tax and insurance of car is irrelevant for
taking decision, it is the fuel cost & wear & tear of the car vs. transport charges should be
taken into account.
Sunk costs:
These are the costs, which have already incurred by a decision made in the past,
which cannot be changed e.g. investment in machinery.
Opportunity cost: Measuring benefits forgone in order to take alternative course of
action.
Incremental cost / revenues: There are additional costs/ revenue which arise from the
production/ sale of additional units, called Incremental or differentiall cost / revenues.
Marginal cost / revenues: Marginal cost / revenue represent the additional cost / revenue
of one extra unit of output.
Thus, the above classification of cost is helpful to the management in decision
making.
Classification of Costs for Control:
The allocation of cost to products is inappropriate for cost control purposes. For control
purposes costs and revenues are allocated to the individuals who are responsible for their
performance. The system is known as responsibility accounting. It is based on the
4
Level of activity
Total fixed
cost (step)

5. recognition of individual areas of responsibility as specified in the firm’s organization
structure. There are three types of responsibility centre:
1. Cost centre: where the manager is responsible for the expenses under his
control
2. Profit Centre: where a manger is accountable for the sales revenue,
expenses and profit.
3. Investment Centre: where a manager is responsible for capital
investment decisions.
Controllable and Non–controllable cost / Revenues
Cost / Revenues allocated to responsibilities centre should be classified into
controllable and non–controllable by the responsibility centre manager.
A controllable cost: is one which is reasonably subject to regulation by the responsibility
centre manager. In this the difference between budgeted and actual results is emphasized
and corrective measures are taken.
Non–controllable cost: is one for which the responsibility centre manager is not
responsible as they are under the decision of his superiors.
The comparison of budgeted costs and actual costs is made for the same level of
activity. If it is different, the budget cost first be revised to the actual level of activity for
comparison purposes, for this the understanding of behaviour of cost (variable, fixed) is
important.
Method of Isolating the variable and fixed component of Semi–variable cost
1. William’s Method or High – low Method
The following steps are taken:-
(i) A minimum and maximum volume of production is determined along with
the total costs of each level
(ii) The difference in total costs of minimum and maximum level is
ascertained along with difference in minimum and maximum volume.
(iii) Following formula is applied
Variable cost per unit = Difference in total cost
Difference in volume
This is multiplied with the units of volume which will give total variable cost of each
level, if deducted from the total semi–variable cost of that level will give the fixed cost of
that level.
5

6. Example 3.1
Isolate the variable and fixed component of Semi – variable cost by Williams’s
method.
Volume of Production Semi – variable cost
in unit Shs
100 8,300
200 12,300
300 16,300
400 20,300
500 24,300
Solution
Minimum volume of Production 100
Maximum volume of Production 500
Total cost at minimum level 8,300 shs
Total cost at maximum level 24,300 shs
Difference in volume 500 – 100 = 400 units
Difference in total cost 24,300 – 8,300 = Shs. 16,000
Variable cost per unit = 16,000 or shs 40/=
400
Units x variable Variable Semi-Variable Fixed cost i.e
cost per unit cost Semi-variable minus Variable
100 x 40 4000 8300 4300
200 x 40 8000 12300 4300
300 x 40 12000 16300 4300
400 x 40 16000 20300 4300
500 x 40 20000 24300 4300
6

7. This method is not scientific as it assumes that observing the two extreme limits
can draw straight line and the cost of the volumes of production between these two limits
would lie on this straight line.
The accurate result should not be expected from this method as there is a possibility of
negative value of fixed costs, which would never be found in practice? This would
change with the volume of production to the next level.
Marginal Costing:
Change in total cost on account of adding or subtracting one unit is known as marginal
cost.
Marginal cost is also known as variable cost.
Variable cost = Direct material + Direct Labor + Variable direct expenses
+ variable indirect expenses
We know that
TC = VQ + F
TC = Total costs
VQ = Variable costs at a given Quantity
Marginal cost per unit = V = TC – F
Q
Determination of Profit under marginal costing
C = S – Vc
C = Contribution
S = Sales
Vc = Variable cost
Where:
C = F + Pt
F = Fixed cost
Pt = Profit
or
S – Vc = F + Pt
or
S = F + Pt + Vc or F = C – Pt
or
S = C + Vc
7

8. Remember:
Fixed costs under marginal costing are regarded as period cost (charged against
the profit immediately rather than as a product cost (assigned to units produced)
Procedure for Profit determination under marginal costing:
(i) Sales value is compared to it variable costs and the difference between the
two is called contribution. Only variable costs of units sold are taken into
account.
(ii) Fixed cost for the period is deducted from the contribution and the balance
is known as profit.
(iii) Units remaining unsold (i.e. stock) are valued at marginal cost. No portion
of fixed cost is carried over to the next period through inventory valuation
Example: 3.2
Guru Engineering Co. is manufacturing two products – A & B.
The costs of manufacturing are as under:-
A B
Shs Shs
Direct material per unit 60 80
Direct labour per unit 40 60
Selling price per unit 200 300
Output 2000 units 2000 units
Total overheads are Shs 160,000 out of which Shs 120,000 are fixed and the rest are
variable. The overheads are to be apportioned in the ratio of output. The closing stock is
of 200 units in case of product A and 300 units in case of Product B.
Find profit under Marginal costing
8

9. Solution
Statement of cost and Profit
(Marginal Approach)
Sales A 1800 unit x 200 Sh 360,000 Sh 510,000 Sh 870,000
B 1700 unit x 300
Product A Product B Total
Direct material 120,000 160,000 280,000
Direct Labour 80,000 120,000 200,000
Variable overheads 20,000 20,000 40,000
Total Variable Costs 220,000 300,000 520,000
Less: Closing stock 22,000 45,000 67,000
220,000 = Shs110 x 200
2000
300,000 = Shs 150 x 300
2000
Total Marginal Cost 198,000 255,000 453,000
Contribution 162,000 255,000 417,000
S-V
Less: Fixed cost 120,000
Profit 297,000
9

10. Uses of Marginal Costing
Example 3.3
Dropping a line or Product or Department
These are three lines of production and their production cost
per unit & selling price per unit is given below:-
X Y Z
£ £ £
Materials 20 25 40
Wages 15 19 24
Variable overheads 20 30 36
Fixed overheads 50 80 90
_______________________________
Total costs 105 154 190
Selling Price 125 220 290
________________________________
Net Profit £ 20 66 100
________________________________
Production in units 3000 2000 2500
The production manager wants to discontinue one line and
guarantees that the production of other two lines shall rise by 50%.
He wants to discontinue X as it is least profitable.
(a) Do you agree to the scheme in principle?
(b) If yes, do you think that line X should be discontinued?
10

11. Workings
Fixed overheads
X 3000 x £ 50 150,000
Y 2000 x £ 80 160,000
Z 2500 x £ 90 225,000
£ 535,000
Marginal cost per unit in £
X Y Z
Materials 20 25 40
Wages 15 19 24
Variable overheads 20 30 36
______________________________
Marginal cost 55 74 100
Selling Price 125 220 290
______________________________
Contribution 70 146 190
===========================
Contribution Ratio 56.0% 66.36% 65.52%
Now Let us consider the alternative arrangements:-
(i) If all lines are continued
Sales Marginal Contribution
Cost
Lines X 375,000 165,000 210,000
Y 440,000 148,000 292,000
Z 725,000 250,000 475,000
977,000
Less: Fixed cost 535,000
Profit £ 442,000
11

12. (ii) When X line is dropped the production of Y and Z would rise by 50%
Sales Marginal Contribution
£ £ £
Y 3000 x 220 660,000 222,000 438,000
Z 3750 x 290 1,087,500 3,750,000 712,500
1,150,500
Less: Fixed cost 535,000
Profit £ 615,500
(iii) When Y line is dropped, the production of X and Z would rise by 50%
Units Sales Marginal Contribution
X 4500 562,500 247,500 315,000
Z 3750 1,087,500 375,000 712,500
1,027,500
Less: Fixed cost 535,000
Profit 492,500
(iv) When Z lines is dropped the production X & Y would rise by 50%
Units Sales Marginal Contribution
X 4500 562,500 247,500 315,000
Y 3000 660,500 222,000 438,500
753,500
Less: Fixed cost 535,000
Profit 218,000
It is not true by dropping any one line the profit would rise, however by dropping X line the
profit would rise from £ 442,000 to £ 615,500.
Example 3.4
Introducing a New product / Line
DSM Ltd. Produce a product X. Present level of production is 2000 units as against the
installed capacity of 3000 units. The present cost structure is as under
Materials Shs 200,000
Labour 100,000
Variable overheads 20,000
12

13. Fixed overheads including Dep 150,000
Fixed overheads include Shs 40,000 for depreciation. Product X is sold at Shs 300 per
unit. It is proposed to manufacture product Y along with product X.
The installed capacity of product Y will be 1500 unit. This will require a additional
investment of Shs. 250,000 in machine over and above existing investment of Shs
500,000. At the start 1,000 units will be manufactured & sold at a price of Shs 200 each.
Fixed overheads would be Shs 15,000 apart from 10% depreciation on machine. Shs.
50,000 will be required for working capital.
The cost estimates of Y product
Material Shs 100
Labour Shs 30
Variable overheads Shs 10
Is it advisable to introduce product Y?
Solution
Statement of Profitability of Each Product
2000 units 1000 units
Existing product X New product Y Total
Sales 600,000 200,000 800,000
Less: Marginal cost
Material 200,000 100,000 300,000
Labour 100,000 30,000 130,000
Variable overheads 20,000 10,000 30,000
________________________________________________________
Marginal cost 320,000 140,000 460,000
Contribution 280,000 60,000 340,000
Less: Fixed overheads
including Dep. 150,000 40,000 190,000
___________________________________________________
Net Profit 130,000 20,000 150,000
================================================
Contribution Ratio 46.67% 30% 42.5%
===============================================
Net Profit on Investment 26% 6.67% 18.75%
Introduction of New product will not improve the profitability in terms of contribution
ratio & Net Profit on Capital Employed.
Example 3.5
Optimum Sales Mix
13

14. The directors of TAN PLANT Ltd. are considering the sales budget for the next year.
You are required to present to the Board a Statement showing the Marginal Cost of each
product and also to recommend which of the following sales – mix should be adopted:
(i) 900 units of X and 600 units of Y
(ii) 2000 units of X only
(iii) 1500 units of Y only
(iv) 1200 units of X and 600 units of Y.
You are given the following information
Product X Product Y
Direct labour per hour @ Shs 50 20 hour 30hour
Direct material Shs.2000 Shs.2500
Selling Price Shs.7000 Shs.10, 000
Overheads
Fixed Shs1, 000, 000
Variable overheads 100% of Direct labour.
Statement of Marginal cost per unit
Product X Product Y
Direct material 2000 2500
Direct labour 50 x 20 1000 ------
50 x 30 ------ 1500
Variable overheads 1000 1500
Marginal cost 4000 5500
Selling price 7000 10,000
Contribution 3000 4500
Profitability of various Sales Mix
(i) X 900 units and Y 600 units
Product Sales Marginal Contribution
X 6,300,000 3,600,000 2,700,000
Y 6,000,000 3,300,000 2,700,000
5,400,000
Less: fixed costs 1,000,000
Profit 4,400,000
14

15. (ii) 2000 units of X only
Product Sales Marginal Contribution
X 14,000,000 8,000,000 6,000,000
Less: fixed cost 1,000,000
Profit 5,000,000
(iii) 1500 units of Y only
Product Sales Marginal Contribution
Y 15,000,000 8,250,000 6,750,000
Less: fixed cost 1,000,000
Profit 5,750,000
(iv) 1200 units of X and 600 units of Y
Product Sales Marginal Contribution
X 8,400,000 4,800,000 3600,000
Y 6,000,000 3,300,000 2,700,000
6,300,000
Less: fixed costs 1,000,000
Profit 5,300,000
Sales mix (iii) is best however if the product X is discontinued and the demand for Y is
reduced, the firm would have changed its sales mix. It is better to continue with both
products and option (iv) is near to the best solution.
Example 3.6
Use of marginal costing in achieving profit target
A Co. has invested Shs.100, 000,000 in its factory and sets a goal of 15% annual
return on investment. Fixed costs in the factory at present are Sh. 40,000,000 and variable
cost is Shs 1500. In the past the firm produced and sold 50,000 units at shs. 2500 each
and earned a net profit of shs 10,000,000.
How can the management achieve their target profit by making changes in fixed
costs, variable costs, quantity sold or increasing the selling price per unit?
15

16. Solution
Target Profit = 100,000,000 x 15
100
= Shs. 15,000,000
(i) Change in fixed costs:
S = Vc + C
C = S – Vc
F = C – Pt
Vc = 50,000 units x 1500 = 75,000,000
S = 50,000 units x 2500 = 125,000,000
C = 125,000,000 – 75,000,000 = 50,000,000
F = 50,000,000 – 15,000,000 = 35,000,000
Present Fixed costs are 40,000,000. The management can achieve the target profit by
reducing the Fixed cost by Shs 5,000,000
(ii) Change in Variable cost
Vc = S – C
C = F + Pt
C = 40,000,000 + 15,000,000 = 55,000,000
Vc = 125,000,000 – 55,000,000 = 70,000,000
Variable cost per unit = 70,000,000 = Shs. 1400
50,000
It should be reduced to Shs 1400 per unit from Shs 1500 per unit
(iii) Change in Quantity sold
S – Vc = F + Pt
S = P x Q
Vc = V x Q
Q (P – V) = C
Q (2500 – 1500) = 55,000,000
16

17. Q = 55,000,000 or 55,000 units
1000
(iv) Change in selling price
S = Vc + C
PQ = Vc + C
P = Vc + C
Q
P = 75,000,000 + 55,000,000
50,000
= 130,000,000
50,000
= Shs 2600
If the selling price could be raised to Shs 2600
Example 3.7
Dropping a line or a product
There are three lines of product and their product cost per unit and selling price
per unit are given below:
X Y Z
Material 180 260 300
Wages 70 90 100
Variable overheads 20 30 30
Fixed overheads 50 80 90
320 460 520
Selling price 400 600 610
Net profit 80 140 90
Production in units 4000 2000 5000
The manager wants to discontinue one line and guarantees that the production of other
two lines shall rise by 50%. He wants to discontinue line X as it is least profitable
Solution
Total fixed cost
X 4000 x 50 = 200,000
Y 2000 x 80 = 160,000
Z 500 x 90 = 450,000
810,000
17

18. (i) When all lines are continued
Sales Marginal
Contribution
X 1,600,000 1,080,000 520,000
Y 1,200,000 760,000 440,000
Z 3,050,000 2,150,000 900,000
5,850,000 3,990,000 1,860,000
Less fixed cost
810,000
_____
Profit 1,050,000
=======
(ii) When line X is dropped the production in Y & Z will increase by 50%
Product Sales M.C Contribution
Y 1,800,000 1,140,000 660,000
X 4,575,000 3,225,000 1,350,000
2,010,000
Less fixed cost 810,000
______
Profit 1,200,000
=====
(iii) When line Y is dropped the production of X & Z will increase by 50%
Product Sales M.C Contribution
X 2,400,000 1,620,000 780,000
Z 4,575,000 3,225,000 1,350,000
2,130,000
Less fixed cost 810,000
Profit 1,320,000
(iv) If Z line is dropped the production of X & Y will increase by 50%
Product Sales M.C Contribution
Y 2,400,000 1,620,000 780,000
X 1,000,000 1,140,000 660,000
1,440,000
Less fixed cost 810,000
18

19. Profit 630,000
To maximize profit, Y line should be dropped.
Example 3.8
Introducing a New Product or line
Simba Plastic limited produces a product X. The capacity of the plant is to
produce 30,000 units. However at present 20,000 units are produced. The present cost is
as under:
Material Shs. 200,000,000
Labour 100,000,000
Variable overheads 20,000,000
Fixed overheads 150,000,000
Product X is sold at Shs 30,000 per unit. It is proposed to manufacture product Y along
with product X. This will require additional investment of Shs. 250,000,000 to
manufacture 15000 units of Y. Initially 10,000 units of Y can be manufactured and sold
for 20,000 each.
The cost estimates of Y product are:-
Material Shs. 10,000 per unit,
Labour Shs. 3000 per unit
Variable overheads Shs. 1000per unit
Fixed overheads Shs. 35,000,000
Is it advisable to introduce product Y?
Solution:
Existing Product New Product Total
Sales 600,000,000 200,000,000 800,000,000
Less: Marginal costs
Material 200,000,000 100,000,000 300,000,000
Labour 100,000,000 30,000,000 130,000,000
Variable overheads 20,000,000 10,000,000 30,000,000
Total marginal cost 320,000,000 140,000,000 460,000,000
______________________________________________
Contribution 280,000,000 60,000,000 340,000,000
19

20. Less: fixed overhead 150,000,000 35,000,000 185,000,000
Net profit 130,000,000 25,000,000 155,000,000
Contribution ratio = C x 100 46.6% 30% 42.5%
S
Contribution ratio will decline. However total profit will increase. It would be better to
increase the production of X product.
Example 3.9
Accepting Special offer / Exploring new market.
The Zenith Plastic is operating at 60% of it capacity. The cost position is as
follows for producing 15000 units:-
Material Shs 30,000 per unit
Labour Shs. 15,000 per unit
Variable overheads Shs. 5,000 per unit
Fixed overheads Shs. 20,000 per unit or shs.300,000,000 Total FC
70,000
Profit 20,000 per unit
Selling price Shs 90,000 per unit
The import duty in the EA region has been abolished. A company in Kenya is willing to
buy 10,000 units at a price of Shs. 60,000 each. However the extra production can not be
sold in Tanzania. Would you recommend that the company should accept this offer?
Solution:
Statement of Marginal cost & contribution
Existing Kenya order Total
15,000 unit 10,000 unit 25,000 unit
Material 450,000,000 300,000,000 750,000,000
Labour 225,000,000 150,000,000 375,000,000
Variable overheads 75,000,000 50,000,000 125,000,000
Marginal cost 750,000,000 500,000,000 1,250,000,000
Sales 1,350,000,000 600,000,000 1,950,000,000
20

21. Contribution 600,000,000 100,000,000 700,000,000
Les: fixed cost 300,000,000 ---------- 300,000,000
Profit 300,000,000 100,000,000 400,000,000
Contribution ratio 44.44% 16.66% 35.89%
Contribution ratio will decline after accepting the Kenya’s offer. However
in absolute terms the profit margin will increase by Shs 100,000,000 so the Kenya’s offer
should be taken on board, as this will help us to operate at full capacity.
Operating Leverage
Operating leverage influences the net operating income of the firm due to investing
decision. The investments are made in fixed assets incurring fixed costs and incurring
variable costs. In many cases due to investments in fixed assets, the variable costs are
reduced considerably. So how much investment is to be made in each category is a
planning function, which should be looked into carefully.
Operating leverage is the extent to which a firms fixed costs contribute to total
operating costs at different level of sales.
The DOL measures the % change in NOI (%∆NOI) for a given % in change in sales
(%∆S).
The DOL is a Magnification factor. DOL exists because of fixed costs and fixed costs
amplify changes in NOI for small changes in sales.
DOL = Total Sales – Total Variable Costs or
Total Sales – Total Variable Costs –Total Fixed Costs
= Q (P-V)
Q (P-V) – F
DOL = %∆NOI
%∆S
Example 3.10
You have been provided with the following information concerning X Company
and Y Company.
X Company Shs Y Company Shs
Sales 100,000 Sales 100,000
Fixed costs 50,000 per year Fixed costs 20,000 per year
Variable costs 30% of sales Variable costs 60% of sales
Compute
21

22. i. The degree of Operating Leverage
ii. If the sales increase by 10% what would be the impact on NOI?
X Company Y Company
DOL = TS –TV DOL = TS –TV
TS – TV– TF TS – TV– TF
= 100,000 – 30,000 = 100,000 – 60,000
100,000 – 30,000 – 50,000 100,000 – 60,000 – 20,000
= 70,000 = 40,000
20,000 20,000
= 3.5 = 2.0
DOL = %∆NOI DOL = %∆NOI
%∆S %∆S
3.5 = %∆NOI 2.0 = %∆NOI
10% 10%
35% = %∆NOI
20% = %∆NOI
To Prove NOI of X C0.
NOI=TS-VC-FC (before change in NOI)
= 100,000-30,000-50,000
= 20,000
NOI= TS-VC-FC(new NOI)
= 110,000-33,000-50,000
=27,000
∆NOI =27,000-20,000
=7,000
%∆NOI=7,000 X 100
20,000
=35%
Example 3.11
Light source makes bulbs and has F = shs.1, 000,000, V = shs.5 and P = shs.10 at
a given Q = 250,000 units. Calculate the DOL and %∆NOI if the sales go up by
5%.
DOL = Q (P-V)
22

23. Q (P-V) – F
= 250,000 (10 – 5)
250,000 (10 – 5) – 1,000,000
= 5.0
DOL = %∆NOI
%∆S
5.0 = %∆NOI
5%
5 x 5% = %∆NOI
25% = %∆NOI
The DOL is a Magnification factor. DOL exists because of fixed costs and fixed costs
amplify changes in NOI for small changes in sales.
Example 3.12
A small company in Morogoro has a current NOI of shs. 200,000. Next year NOI
is expected to be shs. 300,000 as sales are expected to go up by 25%, what is its
DOL.
%∆NOI = New NOI- Old NOI
Old NOI
= 300,000 – 200,000 X 100
200,000
= 50%
DOL = %∆NOI
%∆S
= 50%
25%
= 2.0
Example 3.13
Chagga Bros. make seat covers for cars and sell at shs.20,000 each with a variable
cost of shs.12,000 each. Next year he expects 20% drop in sales and 50% drop in
NOI due to lack of demand. Current level of sales is 112 set of seat covers. What
is the level of fixed cost?
23

24. %∆S = - 20%; %∆NOI = - 50%
DOL = %∆NOI
%∆S
= -50%
-20%
= 2.5
DOL = Q (P – V)
Q (P – V) – F
2.5 = 112(20,000 – 12,000)
112(20,000 – 12,000) – F
2.5 = 896,000
896,000 – F
-2.5F + 2.5 x 896,000 = 896,000
-2.5F + 2,240,000 = 896,000
-2.5F = -2,240,000 + 896,000
-2.5F = -1,344,000
F = 537,600
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