COST ESTIMATION

It is the process of determining in advance the amount of cost to be incurred when a given activity is
undertaken. It assumes that the total cost is made up of both fixed and variable cost.

Total cost = Fixed cost + variable cost

Y= a + bx

Where:
Y=Total cost
a = Fixed cost
b=Variable cost per unit
x = number of units/hours/periods.

STEPS IN ESTIMATION
1. Identify the dependent variable/item to be predicted (Y)
2. Identify the cost driver of the cost to be predicted/independent variable (x)
3. Gather data for both x and y
4. Analyze the data above and observe the trend.
5. Develop an estimation equation using appropriate method.
METHODS OF COST ESTIMATION
1. Industrial engineering method
2. Accounts analysis
3. High – low method
4. Simple regression/least square method.
5. Scatter diagram method

1. Industrial engineering method

This is where a professional engineer applies his skills, knowledge and experience to
determine the relationship between inputs and outputs in physical quantities. This method
is preferred where:
The item is new and unique.
The item is of construction nature.
The relationship can be expressed in physical quantities.
This method is easier to understand, economical and time effective. However the method is
subjective/biased, therefore it cannot be used for general estimation.
2. Accounts analysis method
It involves the examining of cost drivers and classifying them as either fixed or variable
costs. This costs are then used to establish an estimation equation inform of:

Y= a + bx

Where:
Y=Total cost
a = Fixed cost

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b=Variable cost per unit
x = number of units/hours/periods.

Example: The following information has been extracted from the books of kk Ltd
Total
Direct Materials All variable 600,000
Labor cost 10% fixed 500,000
Maintenance cost 50% fixed 900000
Rent All fixed 540000
Overheads 30% fixed 840,000

The number of the units manufactured during the period were 2088 units
Required:
1. Determine the cost estimation equation using the accounts analysis in the form of Y= a + bx
2. Using the equation above estimate the total cost of manufacturing 3500units
3. Using the equation in (I ) above determine the number of units manufactured if the company
had budgeted the total cost sh. 4.8 million
Fixed Variable
Direct material 600000
Labor 50000 450000
Maintenance 450000 450000
Rent 540000 -
Overheads 252000 588000

(i) Where:
Y=Total cost
a = Fixed cost
a = 1292000
bx = 2088000
b = 2088000/2088 = 1000units
Y=1292000+1000x

(ii) Y=1292000+1000x
= 1292000 + 1000(3500) = 4792000
(iii) Y =4.8m
4800000 = 1292000+1000x
4800000-1292000=3508000/1000 =3508units

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CPA
June 2009 5(b)
Good Health care Hospital has prepared a schedule of estimated overhead costs for its blood test unit, on
the assumption that production will be 80,000 tests. Overheads costs have been classified as fixed costs
and variable costs.
Overheads Cost (sh)
Supplies 375000 (all variable)
Indirect labour 1,942,000 (1,710,000 fixed)
Rent 2,364,200 (all fixed)
Utilities 272,100 (all variable)
Depreciation 810,000 (all fixed)
Maintenance 243,300 (85000 fixed)
Data processing 253,200 (158,200 fixed)
Technical support 169,400 (all fixed)

Required:
(i) A cost estimation equation using the account analysis approach taking the number of tests as
the only cost driver (6 marks)
(ii) Using the equation in (b) (i) above estimate the total cost given that the anticipated number of
tests are 90,000. ( 2 marks )

Overheads Cost Fixed Variable

Supplies 375,000 - 375000
Indirect labour 1,942,000 1,710,000 232000
Rent 2,364,200 2,364,200 -
Utilities 272,100 - 272100
Depreciation 810,000 810,000 -
Maintenance 243,300 85,000 158300
Data processing 253,200 158,200 9500
Technical support 169,400 169,400 -
5,296,800 1,132,400
a. 𝑦 = 𝑎 + 𝑏𝑥
- 𝑎 = 5,296,800
- 𝑏𝑥 = 1,132,400
𝑏𝑥 1,132,400
- 𝑏= 𝑥
= 800,000
- = 14.155
- 𝑦 = 5,296,800 + 14.155𝑥
b. 𝑥 = 90,000
𝑦 = 5,296,800 + 14.155(90,000) =6570750
Disadvantages of accounts analysis method
- Classification of cost into fixed and variable component is based on individual judgement which
might be subjective.
- The result of this method cannot be defined using a statistical method since there is no procedure of
distinguishing variable and fixed cost.
- Can be time consuming and expensive to perform
- May not be suitable to small business with limited resources

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 3 HIGH LOW METHOD
It involves taking the highest and the lowest level of activity and using this two points to develop
an estimation equation in form: y = a + bx

Where;
Y – Total production Cost
a- Fixed cost
b- Variable cost
c- x- units manufactured
E.g., The following was extracted from the books of K Ltd
Period Machine hrs. X Maintenance cost Y
1 80 200
2 120 300
3 40 150
4 160 400
Required:
a) Determine the relationship between the machine hours and maintenance cost in the form of 𝑦 =
𝑎 + 𝑏𝑥 using the high low method
b) Estimate the maintenance cost for 900 units

(a) High Low (b) 900 units

X 160 40 Y = 80 + 2(900) = 1880
Y 400 150
b= 400 – 150 = 2
160-40

Using the highest point to determine the value of

a
Y = a + bx
400 = a + 2(160)
400 -320 = 80
Y = 80 + 2x

Example 2
Kenya Auto Assemblers Ltd cars from imported knocked –down-kits. The company has been operating at
60% capacity, assembling 3,000 cars per year.
The following information relates to the company’s operations at two different levels of capacity

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 Level of activity
Costs 60% 80%
Direct materials 600,000 800,000
Direct labour 150,000 200,000
Indirect labour 200,000 240,000
Factory fuel and power 100,000 130,000
Factory repairs 130,000 155,000
Total cost 1,180,000 1,525,000

Required:
Using the high- low method, establish the cost equations of the company for Y=a+bx for each of the
following costs for the company
(i) Direct Materials
(ii) Direct labour
(iii) Indirect labour
(iv) Factory fuel and power
(v) Factory repairs
(b) Using the results obtained in (a) above, estimate the total costs at 120% level of operation
showing clearly the variable and fixed components of mixed costs.
60% =3000cars 2.direct labour 4. factory fuel and power
80% = 3000*80% =4000cars b =130000-100000 =30
60% 4000-3000
130000=a+30(4000)
a = 130000 -120000 = 10000
y =10000+30x

1. Direct materials High Low 5 factory repairs

High Low X 4000 3000 b 155000-130000 =25
4000-3000
155000 = a + 25(4000)
a = 155000-100000 = 55000
y = 55000+25x

X 4000 3000 Y 200000 150000

Y 800000 600000 b = 200000-150000 =50
4000-3000
b = 800000-600000 = 200 Y = a +bx
4000 - 3000 200000=a+50(4000)
a=0
y=50b
Use the highest points to 3 indirect labour cost
obtain the value of a
Y = a + bx b = 240000-200000 =40
800000 = a + 200(4000) 4000-30000
a=0 240000=a+40(4000)
y =200b a = 240000-160000 = 80000
y = 80000+40x
At 120% level of operation the 120% x3000 = 6000 cars
output level is 60%

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 60% = 3000
120% =?
KENYA AUTO ASSEMBLERS LTD COST STATEMENT FOR 6000 CARS

VARIABLE COSTS SH. SH

Direct materials 200 x 6000 1200000

Direct labour 50 x6000 300000

Indirect labour 40 x6000 240000
Factory fuel power 30 x 6000 180000
Factory repairs 25 x6000 150000
2070000
FIXED COSTS
Indirect labour 80000
Factory fuel and power 10000
Factory repairs 55000 145000
2215000

y = a + bx
High low
X 600 200
Y 23,600 19,500
b = 23,600 – 19,500 = 410 = 10.25
600- 200 400
a = Use the highest points
y = a + bx
23,600 = a + 10.25(600)
23,600 = a + 6150
a = 23,600 – 6150
= 17450
Y = 17450 + 10.25X

Advantages of high-low method

1. Easy to use.
2. It is a faster method of cost estimation.
Disadvantage
1. It uses only two data values and ignore the rest. These values may not develop a reliable
equation.
2. The equation developed cannot be appraised for efficiency and reliability

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 4 Regression analysis/Least square method
This is a statistical method which is used to determine the nature of the relationship existing
between variables. The values of b and a are determined using the formulae below.
i) b = n∑xy - ∑x∑y
n∑x2 – (∑x)2

a = ∑y - b∑x
n

CPA DECEMBER 2012 Q 1b,

The information given below relates to Brutex Ltd which manufacturers a single type of
chemical. Overheads processing costs for the last 8 months have been as follows;
Month Machine hours Overhead costs
Sh “000”
1 10600 120
2 17000 180
3 4000 70
4 21000 184
5 19000 178
6 7800 100
7 14000 172
8 12000 154

Required: Equation in the form of Y = a + bx using:

i) High – low method ( 2 mks )
ii) Regression analysis method ( 6 mks )
X y xy (‘000’) x2
10,600 120 1272,000 112300,000
17,000 180 3060,000 239,000,000
4000 70 280,000 16,000,000
21,000 184 3864,000 441,000,000
19,000 178 3382,000 361,000,000
7,800 100 780,000 60,840,000
14,000 172 2408,000 196,000,000
12,000 154 1848,000 144,000,000
x=105,400 y=1158 xy=16,894,000 x2=1620, 200,000

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 ii) b = n∑xy - ∑x∑y
n∑x2 – (∑x)2

b = 8 x 16,894,000 – 105,400 x 1158

8 x 1,620,200,000 – (105,400)2

b = 7.07

a = ∑y - b∑x
n

= 1,158,000 – 7.07 x 105,400 =51602.75

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y = 51,602.75 + 7.07x

CPA MAY 2015 Q 1b

The following details have obtained from the records of King pin Ltd, a firm dealing in computer
repairs and maintenance.
week Number of computer Total cost incurred
purchased
1 310 23200
2 200 19500
3 600 23600
4 480 20220
5 400 23600
6 440 18480
7 440 16200
8 330 20200
Required: Formulate the cost function in the form of Y = a + bx using least square method
X y xy x2
310 23,200
200 19,500
600 23,600
480 20,220
400 23,600
440 18,480
440 16,200
330 20,200
∑x=3200 165,000 ∑xy=66,322,800 ∑x2=1382,600

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 b = n∑xy - ∑x∑y
n∑x2 – (∑x)2
= 8 x 66,322,800 – 3200 x 165,000
8 x 1382,600 – (3200)2

b = 3.1462

a = ∑y - b∑x
N
a = 165,000 – 3 x 3200
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= 19,366.5
y = 19,366.5 + 3.1462x

Advantages of regression analysis

1. It uses all the data values and therefore the equation developed is more accurate.
2. The equation developed can be evaluated for reliability and efficiency.
Disadvantages/Assumptions
1. It assumes that all the variables are linear i.e. there is linearity before the variables.
2. There is only one factor affecting activity level i.e. the only variable which causes
changes in the total cost are the units of production.
3. It uses historical data which may not predict future accurately

ASSUMPTION OF LINEAR REGRESSION MODEL

(i) The chosen sample is representative of population
(ii) There is a linear relationship between the independent variable and the dependent
variable.
(iii) All the variable are normally distributed

SCATTER DIAGRAM/ VISUAL FIT METHOD

- Under this method, a scatter diagram is constructed and two points from the diagram are picked
which are used to drive an estimation equation inform of Y = a + bx.

Y2

Y1

X2
 X1 =100 Y1 =1000
X2 =150 Y2 =1500

Y= a + bx
1500 = a + 150b
1000= a+ 100b
500 = 50b
b =10
1000 = a + 100(10)
a =0
Y =10x

Advantages
1. It’s easy to understand and operate since the values of x & y are plotted on the diagram
2. It takes into account all the observation available.
Disadvantages
1. It can’t be used if these are more than one independence variables
2. It is subjective since some of the observation are not used in making the conclusion.

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