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High/Low and Linear Regression Analysis Overview
The total costs associated with a business are the SUM of fixed costs and variable costs i,e. the total cost is semi-variable in nature.
Y=a+bx
where:
y= total cost in a period
a= the fixed costs in the period
b= the variable cost per unit of output or unit of activity
x= the number of output or the volume of activity in the period.
Methods for constructing Total cost function
The total cost function can be used to estimate costs associated with different levels of activities. Its useful for forecasting and decision making.
There are two methods for constructing the total cost function equation.
High/Low analysis;
can be used to estimate fixed costs and variable costs per unit, whenever:
The following circumstances are to be considered:
Step 1: Take activity level and cost for:
Step 2: Calculate variable cost per unit (b) as:
difference in total cost (highest minus lowest) divide by difference in no. of units (highest minus lowest).
Step 3: Now for fixed cost (a) put the variable cost per unit into one of the cost expressions (mostly high level).
Step 4: Construct total cost function for any activity level:
Total cost=a+bx
For Example:
Step 1
Highest level 7,000 (units) costs $38,800
Lowest level 4,500 (units) costs $30,400
Step 2: Difference
Therefore: variable cost per unit= 8400/2500 = $ 3.36
Step 3: Cost expressions: Total cost of 7,000 units
Fixed cost + variable cost= 38,800
Fixed cost + 7,000 x 3.36= 38,800
Fixed cost + 23,520= 38,800
Fixed cost=38,800–23,520=15,280
Step 4: Construct total cost function
Total cost=a+bx= 15,280+ 3.36x
Step 1: Take activity level and cost for:
Step 2: Make adjustment for the step in fixed cost:
Now calculate variable cost per unit (b) as:
difference in total cost (highest minus lowest) divide by difference in no. of units (highest minus lowest).
Step 3: Now for fixed cost (a) put the variable cost per unit into one of the cost expressions (mostly high level).
Step 4: Construct total cost function for any activity level:
Total cost=a+bx
For Example:
Step 1
Highest level 7,000 (units) costs $ 38,800
Lowest level 4,500 (units) costs $ 30,400
Step 2: Make an adjustment for step in fixed cost. For example fixed costs increase by $3,000 when the activity level exceeds or equals 10,000 units.
Add the increase in cost in lowest activity level.
Therefore: variable cost per unit= 5400/2500 = $ 2.16
Step 3: Cost expressions: Total cost of 7,000 units
Fixed cost + variable cost= 38,800
Fixed cost + 7,000 x 2.16= 38,800
Fixed cost + 15,120= 38,800
Fixed cost=38,800–15,120=23,680
Step 4: Construct total cost function (un-adjusted levels):
Total cost=a+bx= 23,680+ 2.16x
Total cost=a+bx=(23,680-3,000)+2.16x
Total cost=a+bx= 20,680+2.16x
When there is a percentage change after a particular level, this means there are TWO levels which share same fixed cost.
Step 1: Take activity level and cost for (3 levels):
Step 2: Choose the pair which is on the same side as the step.
Now calculate variable cost per unit (b) as:
difference in total cost divide by difference in no. of units.
Step 3: Now for fixed cost (a) put the variable cost per unit into one of the cost expressions (mostly high level).
Step 4: Construct total cost function for any activity level:
Total cost=a+bx
For Example:
Step 1
Step 2: Pair with same percentage change. (assume a 10% increase in fixed costs when the activity level exceeds or equals 5,500 units)
Therefore: variable cost per unit= 3800/1500 = $ 2.53
Step 3: Cost expressions: Total cost of 7,000 units
Fixed cost + variable cost= 38,800
Fixed cost + 7,000 x 2.53= 38,800
Fixed cost + 17,710= 38,800
Fixed cost=38,800–17,710=21,090
Step 4: Construct total cost function (un-adjusted levels):
Total cost=a+bx= 21,090+ 2.53x
Total cost=a+bx=(21,090 x 100/110)+2.53x
Total cost=a+bx= 19,173+2.53x
In summary, linear regression is a better technique then high/low analysis because;
Formula:
Line of best fit (y=a+bx) can be constructed by calculating values for “a” and “b” using:
a = ∑y – b∑x
n n
b= ∑xy – ∑x ∑y
n∑x2 – (∑x)2
where:
x = units
y = costs
Enter the values into the line of best fit (y=a+bx) and solve for b and then a .
The following table should be used for calculating values of “x” and “y”
Table
X | Y | X2 | XY |
Classification of cost Overview:
Introduction to cost and management accounting
ALL organizations needs to know:
Types of organizations
Manufacturing organizations
Types of costing systems they use:
Types of costing systems they use:
Any activity for which a separate measurement of costs is needed.
For Example
A unit of product or service for which costs are determined.
For Example
The cost incurred by a company to produce + store + sell one unit of a particular product.
Unit cost includes ALL fixed and variable costs involved in production.
Material costs are the costs of any material items purchased with the intention of using them in fairly short term future.
For example
The costs that are incurred in manufacturing finished products up to the time goods are completed.
Includes:
Includes:
Administrative costs
Cost of providing administrative services to entity, usually includes;
Selling and Distribution costs
The costs incurred in marketing and selling good or services to customers and costs of delivering the goods.
The costs of after-sales services such as customer support services are usually included in these costs.
They usually include;
Finance costs
These are the costs that are involved in financing the organization, e.g : Loan interest Bank O/D
* Some costs might be partly production, partly administration and selling & distribution e,g: salaries of managing director, building rental costs.
In such case costs are divided/ apportioned between function s on fair basis.
Costs that can be traced in FULL to a cost unit i,e. A direct cost can be attributed in its entirety to the cost of an item that is being produced.
The following are direct costs:
Direct Material
All the materials that are used directly in manufacturing a product or providing service.
Direct materials includes both raw materials and components.
Direct Labour
These are specific costs associated with labour-time spent directly on production of goods or services.
Direct Expenses
Expenses that can be attributed directly in full to a cost unit i,e. that have been incurred in full in making a unit of product/service .
* In manufacturing type organization direct expenses are not common.
Indirect Material
Indirect material are any materials that are used/consumed that cannot be attributed in full to the item. They are treated as overhead costs, maybe classified as production overheads, administration overheads, selling and distribution overheads.
For e.g. indirect production material includes some items of cleaning materials and any materials used by staff not engaged in production.
Indirect Labour
They mainly consists of the costs of indirect labour employees (who do not work directly on items that are produced) but may be necessary so that production takes place.
All employees in administration and marketing department including management are indirect labour.
Indirect Expenses
Many costs incurred cannot be directly linked to cost units e.g. Rental costs of factory.
In manufacturing company all costs of administration and selling & distribution are treated as indirect overheads.
Product Cost
Period Cost
Cost Behavior definition:
Cost Classification by behaviour;
These costs remain fixed/same in total during a period no matter how many units are produced and regardless the volume or scale of a activity.
However, the cost per unit falls because the cost is being spread over a greater number of units.
Semi-Variable cost
Stepped cost
Time Value of Money Overview
Discounted cash flow analysis
Present value Formulas
Discount factor = 1/(1+r)n
where
r = cost of capital
n = number of periods
Annuity factor = ( 1 – (1+r)-n /r)
Methods of Discounted Cash Flow
Net Present value (NPV)
Approach
Methods of incorporating Inflation
Real cash flows
The following steps are involved:
= money cost of capital – 1
inflation rate
This is the most common method used.
The following steps are involved:
*Both approaches give same solution, with a difference of rounding off.
Relevant costing and Decision Making Techniques Overview
Definitions:
Relevant cost
Incremental cost
Differential cost
Avoidable and unavoidable cost
Committed costs
Sink costs
Opportunity costs
When Material currently in inventory
Are material in regular use?
The relevant cost is the current Replacement cost.
The relevant cost is the current opportunity cost.
Opportunity cost is higher of;
When Material not currently in inventory
In this case the relevant cost is simply the purchase value.
Assumptions of limiting factors:
Make-or-buy decision non-financial considerations
Non-financial considerations will often be relevant to make-or-buy decision:
Example of such costs
Process Costing Overview
Normal loss = material input – expected output
Normal loss with recovery/scrap value
Cost of output = Total process cost – scrap value
Expected output
Expected output = material input – normal loss
Normal loss without recovery/scrap value
Cost of output = Total process cost – scrap value
Expected output
Cost of output = Total process cost – scrap value
Expected output
Abnormal Gain = Normal loss – Actual loss
Abnormal Gain where loss has NO scrap value
Cost of output = Total process cost – scrap value
Expected output
Abnormal Gain where loss has a scrap value
When loss occurs part-way through a process, the cost of any abnormal loss is calculated:
The same principles apply to the valuation of abnormal gain, where the gain occur part-way through the process as abnormal loss.
However there is one important difference, equivalent units of abnormal gain are given a Negative value and subtracted from the total equivalent units of output in the period.
Work in Progress Balance
Opening Work in Progress
weighted average cost method
FIFO cost method
Joint Products and By-Products
Joint Products
Joint products are two or more products generated simultaneously, by a singe manufacturing process, using common input, and being substantially equal in value.
Apportioning common processing costs
One of the following methods is used:
Units Basis
Common costs are apportioned on basis of total number of units produced.
Sales value at split-off point
Common costs are apportioned on basis of the sales value of Joint product produced when they are separated in process.
Net realizable value
Common costs are apportioned on basis of the sales value of Joint product produced when they are separated in process.
When two or more different products are produced. Any product that does not have a substantial sales value and relatively minor in quantity is called a by-product.
Treatment of By-Product
Any of following method is used:
Variances analysis Overview
Types
Types
Direct cost Variance
Indirect cost/overhead Variance
Direct material Variance
Total cost variance
The total direct material cost variance is the difference between actual material cost of actual units and the standard material cost of actual costs.
Standard material cost of actual production:
Actual material cost of actual production:
A price variance measures the difference between the actual paid for material and the price that should have been paid.
Standard material cost of actual production:
Actual material cost of actual production:
= Standard Price (standard quantity – Actual quantity)
Usage variance is further analysed into:
1. Material Mix Variance
= Standard Price (Total actual quantity x standard mix) – (Total actual quantity at actual mix)
2. Yield Variance
= Standard cost (standard output at actual mix) – (Actual output of actual mix)
Direct labour Variance
Total cost variance
The total direct labour cost variance is the difference between actual labour cost in producing units and the standard labour cost of producing those actual costs.
Standard actual cost of actual production:
Actual labour cost of actual production:
A rate variance measures the difference between the actual wage rate paid to per labour hour and the rate that should have been paid.
It looks at the hours paid.
Calculated as:
= Actual hrs (standard rate – actual rate)
An efficiency variance or productivity variance measures the difference between the time taken to make the production output and the time that should have been taken.
The difference is measured in hours and converted into a money value at the standard direct labour rate per hour.
It looks at the hours worked.
Calculated as:
= Standard rate per unit (standard hrs – actual hrs)
Idle time not part of standard cost
If idle time is not included in standard cost any idle time is unexpected and leads to an adverse variance.
Idle time included in standard cost
Include idle time as a separate element of standard cost so that standard cost of idle time is a part of total standard cost per unit ; or
Allow for a standard amount of idle time in standard hours per unit for each product. The standard hours per unit therefore include an allowance for expected idle time.
Variable Production Overhead variance
Total cost variance
Standard Cost
Actual Cost
It is the difference between actual variable overhead spending in hours worked and what the spending should have been (standard rate)
Similar to a material price variance or a labour rate variance.
= Actual hours (standard rate – actual rate)
The variable overhead efficiency variance in hours is same as the labour efficiency variance in hours (excluding any idle time variance) and is calculated in a very similar way.
= Standard Rate (standard hour – actual hours)
Fixed Production Overhead variance
Budgeted Cost
Actual Cost
= Budgeted F.OH – Actual F.OH
Can be measured in either units of output or standard hours.
= Standard cost (Budgeted Production – Actual Production)
Volume variance is further analyzed into:
Efficiency variance
Same as labour and variable production overhead variance in hours (worked/allowed).
= Standard Rate (standard hours – actual hours)
Capacity variance
= Standard Rate (budgeted hour – actual hour)
Excluding idle time.
Sales variance
Total sales variance
= Budgeted contribution – Actual Contribution
= Actual units sold (budgeted contribution – actual contribution)
Volume variance/ Volume profit variance
= Standard contribution or profit per unit (budgeted volume – Actual volume)
Standard Costing Overview
Standard cost
Standard costing
Types of Standard
Ideal Standard
This assumes perfect operating conditions.
No allowance for wastage is made.
Unlikely to be achieved.
Reported variance is always adverse
This assumes efficient but not perfect operating conditions.
An allowance for wastage is made.
Attainable targets.
These are based on current working conditions.
Includes an allowance for the expected wastage or idle time.
This remains unchanged over a long period of time.
Variances are calculated by comparing actual results with basic standard.
Methods of including idle time in standard costs
As a separate elements of standard cost
Allowance for expected idle time