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  • High/Low and Linear Regression Analysis

    High/Low and Linear Regression Analysis


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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.

    • Total costs can be divided into fixed costs /variable cost per unit of output.
      Formula for total costs:

    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.

    Constructing Total cost function

    High/Low and Linear Regression Analysis


    Methods for constructing Total cost function

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    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.

    1. High/Low Analysis.
    2. Linear Regression Analysis.

    High/Low and Linear Regression Analysis



    High/Low Analysis

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    High/Low analysis;

    can be used to estimate fixed costs and variable costs per unit, whenever:

    • figures available for total costs at two different level of output.
    • it can be used that fixed costs are same and variable cost per unit is constant at both levels of activity.
    • the different between the total costs at high level and low level of output is entirely variable cost.

    The following circumstances are to be considered:

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    When No Change

    Step 1: Take activity level and cost for:

    • Highest level
    • Lowest level

    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

    A step change in fixed costs as money value And the amount is known

    Step 1: Take activity level and cost for:

    • Highest level
    • Lowest level

    Step 2: Make adjustment for the step in fixed cost:

    • add the step in fixed cost in lower level; or
    • deduct it from higher level

    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):

    • Above 10,000 units

    Total cost=a+bx= 23,680+ 2.16x

    • Below 10,000 units

    Total cost=a+bx=(23,680-3,000)+2.16x
    Total cost=a+bx= 20,680+2.16x

    A step change in fixed costs is given as a Percentage amount

    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):

    • Highest level
    • Middle level
    • Lowest level

    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

    • Highest level 7,000 (units) costs $ 38,800
    • Middle level 5,500 (units) costs $ 35,000
    • Lowest level 4,500 (units) costs $ 30,400

    Step 2: Pair with same percentage change. (assume a 10% increase in fixed costs when the activity level exceeds or equals 5,500 units)

    • Highest level 7,000 (units) costs $ 38,800
    • Middle level 5,500 (units) costs $ 35,000

    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):

    • Above 5,500 units

    Total cost=a+bx= 21,090+ 2.53x

    • Below 5,500 units

    Total cost=a+bx=(21,090 x 100/110)+2.53x
    Total cost=a+bx= 19,173+2.53x

    A step change in variable costs (is given as a Percentage/money amount)

    • When there is a step change in variable cost per unit as money value the same approach is needed as for a step change in fixed cost. (above)
    • When the change in variable cost per unit is given as a percentage amount, then variable cost(s) per unit should be calculated for TWO levels:
      • variable cost per unit used above change ; and
      • variable cost per unit used below change.

    High/Low and Linear Regression Analysis



    Linear Regression Analysis

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    In summary, linear regression is a better technique then high/low analysis because;

    • it is more reliable ; and
    • it’s reliability can be measured.

    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
  • Introduction to Cost and Management Accounting

    Introduction to Cost and Management Accounting


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    Classification of cost Overview

    Introduction to cost and management accounting

    • Cost Accounting (classification of cost in cost accounting)
      • ​Cost Accounting involves the calculation and measurement of the resources used by a business in undertaking its various activities and is concerned with identifying cost of various things ( i.e. gathering data about cost of ‘products’ or ‘services’ and ‘cost of activities’).
    • Management Accounting (cost classification in management accounting)
      • Management accounting  includes cost accounting as one of its discipline but is wider in scope.
      • Management accounting provides information to management that helps it to run the business:
      1. it provides detailed financial information so that they plan and control the activities or operation for which they are responsible.
      2. this information helps managers to make other decisions i,e. planning, controlling and taking one-off decisions.

    ALL organizations needs to know:

    • how much it costs to make the products or provide its services.
    • to make sure product/services is sold at a Profit.
    • to control the entity.
    • to measure to what extent it is achieving its objectives.
    • to plan expenditure for future.

    Introduction to Costs


    Types of organizations

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    Manufacturing organizations

    Types of costing systems they use:


    Service organizations

    Types of costing systems they use:

    • Standard costing.
    • Job costing.


    Key Terminology

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    Cost object

    Any activity for which a separate measurement of costs is needed.

    For Example

    • cost of a department.
    • cost of a project.


    Cost unit

    A unit of product or service for which costs are determined.

    For Example

    • cost of A car.
    • cost of bread items.
    • cost of An item.


    Unit cost

    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.

    Types of Cost Classification

    Classification of Cost by Type

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    Material costs

    Material costs are the costs of any material items purchased with the intention of using them in fairly short term future.

    For example

    • Raw material that go into the production process.
    • Cost of stationary, cartridges replacement.


    Labour costs

    • Labour costs are the employees remuneration costs paid by the entity and includes;
      • wages and salaries of part-time workers, bonuses, pension contribution etc.


    Other expenses

    • That costs which are not Material/ Labour costs and includes;
      • cost of services provided by external suppliers, telephone cost, rental costs, depreciation charges.

    Classification of Cost by Function

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    Production costs

    The costs that are incurred in manufacturing finished products up to the time goods are completed.

    Includes:

    • Material costs: of raw materials and components used in production.
    • Labour costs: of all employees working for the manufacturing function.
      Other Expenses.


    Non-Production costs

    Includes:

    Administrative costs

    Cost of providing administrative services to entity, usually includes;

    • Salaries to staff in administration.
    • Cost of office space (rent)
    • Other expense incurred for administration only.

    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;

    • Salaries to staff in selling and distribution.
    • Advertising costs and other marketing costs
    • Operating costs for delivery vehicles such as fuel costs and repairs.
    • Other costs incurred for selling and distribution department.

    Finance costs

    These are the costs that are involved in financing the organization, e.g : Loan interest Bank O/D

    • They are generally included in administration costs ; or
    • alternatively finance costs might be excluded from cost accounting system.

    * 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.

    Cost classification by Nature

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    Direct costs

    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 costs (overheads)

    • An indirect cost (overhead cost) is any cost that is not a direct costs.
    • Indirect costs cannot be attributed directly and full to a cost unit.
    • Indirect costs include production overheads and non-production overheads. Each of these might include the following:

    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

    • Product cost include the prime cost Plus production overhead.
    • Product cost are associated with goods that are produced or purchased for resale.
    • They are inventory and only expensed out when sold.

    Period Cost

    • The costs that do not contribute towards the value of inventory.
    • These are expensed in the period in which they occur.

    Cost Behavior

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    Cost Behavior definition:

    • Cost behavior refers to the way in which costs changes as volume of the activity changes.
    • As a general rule, total costs are expected to increase as volume of activity rises.
    • Understanding of cost behavior helps to;
      • forecast/plan what costs ought to be.
      • compare actual cost with budgeted.

    Cost Classification by behaviour;

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    Fixed costs

    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

    • A semi-variable cost is a cost that is partly fixed and partly variable.
    • It is often assumed that total costs of an activity are mixed.

    Stepped cost

    • A cost which is fixed within a limited range of activity and goes up or down in steps when the volume of activity rises above or falls below certain levels.


    Variable costs

    • These costs increase usually by the same amount for each additional unit of product or service provided.
    • The variable cost of a cost unit is also called marginal cost of unit.
    • This means that total variable costs increase in direct proportion to the volume of output or activity.
    • The cost per unit remains fixed . However, total cost increase as more units are made.
  • Time Value of Money (TVM) – formula with examples

    Time Value of Money (TVM) – formula with examples


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    Time Value of Money Overview

    Discounted cash flow analysis

    • It is a technique for evaluating the proposed investments to decide whether thy are financially worthwhile.
    • The expected future cash flows (inflows/outflows) from the investment are all converted to a present value by discounting them at the cost of capital ‘r’
    • Taking into account the concept of relevant cost.
    • It is usually assumed that cash flow early during a year should be treated as a cash flow as at the end of the previous year.

    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)

    Discounted Cash Flow

    Time Value of Money


    Methods of Discounted Cash Flow

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    Net Present value (NPV)

    • In Net present value (NPV) analysis, all future cash flows from a project are converted into a present value.
    • NPV is the difference between present value of all costs incurred and present value of all benefits received.

    Approach

    1. List all cash flows from the project (initial investments, future cash inflows/outflows).
    2. Discount these cash flows to present value using ‘cost of capital’ as discount rate.
    3. If present value of Benefits exceeds the present value of costs, the NPV is positive and if present value of benefits is less, then NPV is negative.
    • A project is worthwhile if NPV is positive.
    • The project commences at time ‘0’ where the cash flows are already at present value.
    • Changes in working capital included as cash flows. An increase usually at the beginning of the project in time ‘0’ is a cash outflow and reduction is a cash inflow.


    Internal Rate of Return (IRR)

    • It is the discounted rate of return on investment.
    • It is the average annual investment return from the project.
    • The NPV of the projected cash flows is ‘zero‘ when those cash flows are discounted at IRR.
    • A company might establish the minimum rate of return that it wants to earn on an investment:
      • If a project’s IRR is equal or higher than minimum acceptable rate of return, it should be undertaken.
      • If IRR is lower than the minimum required return, it should be rejected.
    • The following step are involved for calculation of a reliable Internal rate of return (IRR):
      1. Calculate NPV of the project at TWO different rates. One of the NPV should be positive and the other should be negative.
      2. Put the NPVs in the formula:

    IRR formula

    Discounted Cash Flow and Inflation

    Time Value of Money


    Methods of incorporating Inflation

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    Real cash flows

    • The cash flows expressed in today’s price terms.
    • They ignore the expectations of inflation.
    • In order to incorporate real cash flows in NPV calculation, real cash flows should be discounted at the real cost of capital.

    The following steps are involved:

    • Calculate real discount rate

    = money cost of capital – 1
    inflation rate

    • Calculate net cash flows at today’s prices.
    • Discount them using real discount rate.


    Money cash flows

    This is the most common method used.

    • Money (nominal) cash flows are cash flows that include expected inflation.
    • Money cash flows should be discounted at the money cost of capital.

    The following steps are involved:

    1. Calculate net cash flows at today’s price.
    2. Make adjustment for inflation (by doing this they will be converted into money cash flows).
    3. Use money cost of capital as discount rate.

    *Both approaches give same solution, with a difference of rounding off.

  • Relevant costing and Decision Making Techniques

    Relevant costing and Decision Making Techniques


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    Relevant costing and Decision Making Techniques Overview

    Definitions:

    Relevant cost

    • A relevant cost is a future cash flow that will occur as a direct consequence of making a particular decision.
    • They cannot include any cost occurred in past.
    • Costs that occur whether or not a particular decision is taken are not relevant costs.
    • Relevant costs are cash flows. Notional costs such as depreciation, interest costs and absorbed fixed cost are not relevant cost.

    Incremental cost

    • Any incremental cost, if a particular decision is taken, results in cash flow are relevant cost.

    Differential cost

    • A differential cost is an amount by which future costs will be higher or lower. A differential cost is a relevant cost.

    Avoidable and unavoidable cost

    • Avoidable costs are relevant costs
    • Unavoidable costs are not relevant.

    Committed costs

    • Committed costs are unavoidable costs, therefore not relevant for decision making.

    Sink costs

    • Cost that are already incurred/or committed by an earlier decision. Such costs are not relevant costs.

    Opportunity costs

    • The relevant cost is the benefit that would be lost by switching to other work.

    Identifying Relevant costs


    Relevant costs of:

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    Materials

    When Material currently in inventory

    Are material in regular use?

    • Yes

    The relevant cost is the current Replacement cost.

    • No

    The relevant cost is the current opportunity cost.
    Opportunity cost is higher of;

    1. Net disposal/sales value/scrap value or;
    2. Net benefit from alternative use.

    When Material not currently in inventory

    In this case the relevant cost is simply the purchase value.


    Labour

    • If the cost of labour is a variable cost and labour is not in restricted supply: The relevant cost is its variable cost.
    • If labour is a fixed cost and there is spare labour time available: The relevant cost of using labour is ‘zero‘. The spare time would otherwise be paid for idle time.
    • If labour is in unlimited supply: Relevant cost includes the opportunity cost of using the labour time for the decision instead of next most profitable way.


    Overheads

    • Normal rules of relevant costs are applied i,e Relevant costs are future cash flows.
    • Fixed overheads absorption rate are irrelevant. However the variable overhead hourly rate is treated as relevant cost.
    • The only overhead fixed costs that are relevant costs are the extra cash spending.

    Decision Making Techniques


    Types of Decisions

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    • The concept of relevant costs can be applied for both ‘long term’ and ‘short term’ decisions.
    • The application is same for both types of decisions except for long term decisions ‘time value of money’ should be considered.

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    Such Types of Decisions are:

    Limiting Factor Decisions

    • Limiting factor are the factors that ‘restricts‘ operational capabilities, sales demand is normally the factor that sets a limit on volume of production. However the availability of scarce resources such as Direct material, skilled labour or machine capacity could be the limiting factor.
    • If the company makes just one product and a production resource is in limited supply, profit is maximized by making as many units of product as possible with limited resources.
    • However, if the company produces more than one product with same scarce resources then a budgeting problem is to decide how many of each product to make and sell in order to maximize Profit. In Such case select products for manufacture and sale according to the contribution per unit. The following steps are involved:
    1. Calculate the contribution per unit of each good produced.
    2. Identify scarce resources (e,g labour hours).
    3. Calculate the amount of scarce resources used by each good produced (e,g ‘X’ no. of labour hours)
    4. Now divide the contribution earned by each good by scarce resources used by that good to give the contribution per unit of scarce resources for that good.
    5. Rank each good in order of contribution per unit per scarce resources (highest contribution is ranked 1st).
    6. Construct a production plan based on ranking.

    Assumptions of limiting factors:

    • Profit is maximized by maximizing contribution.
    • Variable costs are only the relevant costs.
    • Fixed cost will be the same whatever decision is taken. Therefore are not relevant.

    One-off contractual decisions

    • The contract where the Job is once only and will not be repeated in future.
    • The one-off contract is under taken if extra revenue is higher than relevant costs.
    • The decision is to whether agree to do the Job at a Price offered by customer or decide a selling price (base on relevant costs).
    • Profit = Revenue – Relevant cost
    • One-off contract decisions might occur when a company has spare capacity and an opportunity arises to earn some extra profit.

    Make-or-Buy decisions

    • A decision whether: to make an item internally or buy it externally. The decision should be based on relevant cost, the preferred option from a financial view point is the one with the lowest relevant costs.
    • A financial assessment of a make or buy decision involves a comparison of:
      • cost that would be saved; and
      • incremental cost of outsourcing
    • A situation may arises where entity is operating in full capacity, in order to overcome some restrictions on its output and sales, the entity may outsource some products.
    • The decision is about which item to outsource and which to retain in-house.
    • The profit maximizing decision is to which items to outsource.
    • Those items are outsource where cost of outsourcing is least.
    • To identify the Least-cost of outsourcing, it is necessary to compare:
      • additional cost of outsourcing; with
      • amount of resources need to make product in-house.

    Make-or-buy decision non-financial considerations

    Non-financial considerations will often be relevant to make-or-buy decision:

    • When work is outsourced, the entity loses some control over the work. It will rely on the external supplier. There may be some risk that external supplier will:
      • provide a lower quality.
      • fail to meet delivery on said dates.
    • The entity will lose some flexibility. If it needs to increase or reduce supply of the outsourced item at short notice.
    • Redundancy of employees may occur as a consequence of outsourcing affecting relations between management and other employees.

    Shut-down Decisions

    • A shutdown decision is whether or not to shut down a part of the operations of a company.
    • From a financial view an operation should be shutdown if the benefits of shutdown exceeds relevant costs.

    Example of such costs

    • Fixed costs may be saved, Employee redundancy cost.

    Joint Product further processing decisions

    • Joint products are product manufactured from a common process.
    • The entity has a choice whether:
      1. selling joint product as soon as it is output; or
      2. processing it further before selling (at a higher price).
    • This is a short-term decision and financial assessment should be made using relevant cost and revenues. The financial assessment should compares:
      1. Revenue (less) selling cost from joint product as soon as it is output.
      2. The revenue that will be obtained if Joint product is processed further (less) incremental cost of further processing.
  • Standard Costing – Types, Meaning and Objectives

    Standard Costing – Types, Meaning and Objectives


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    Standard Costing Overview

    Standard cost

    • A standard cost is an estimated/predetermined unit cost of performing an operation or producing a good or services under normal conditions.
    • The predetermined unit cost (standard cost) is based on expected direct materials quantities and expected direct labour time and priced at a predetermined rate per unit of direct materials and rate per direct labour hour and rate per hour of overhead.
    • Overheads are normally absorbed at direct labour hour.

    Standard costing

    • Standard costing is a control technique that report variances by comparing actual cost to pre-set standards. Standard costing may use; absorption or marginal costing.

    Types of Standard


    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


    Attainable Standard

    This assumes efficient but not perfect operating conditions.

    An allowance for wastage is made.

    Attainable targets.


    Current Standard

    These are based on current working conditions.

    Includes an allowance for the expected wastage or idle time.


    Basic Standard

    This remains unchanged over a long period of time.

    Variances are calculated by comparing actual results with basic standard.


    Idle Time

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    • Idle time are the hours for which the direct labour employees are paid for no work.
    • Idle time is recorded and the hours lost due to idle time are measured.

    Methods of including idle time in standard costs

    As a separate elements of standard cost

    • Standard of idle time is a part of Total standard cost per unit.

    Allowance for expected idle time

    • Allows for a standard amount (pre-set amount) of idle time in standard hours per unit of each product, therefore including an allowance for expected idle time.

    Budget

    • Budget: A budget is a formal plan (for a specified time period) covering all the activities of the entity.
    • It is a statement of what the entity is going to strive to achieve in future.
    • Standard costing is a component of budgeting.
    • Standard costs for a unit are often set out in record called a standard cost card.


    Types of Budget

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    Fixed Budget

    • It is the original budget prepared at the beginning of a budget period.
    • It is prepared for a specific volume of output and sales activity.
    • It is the master plan for the financial year that company tries to achieve.
    • Variances are NOT calculated by comparing actual results to fixed budget directly.


    Flexed Budget

    • It is drawn-up at the end of the period.
    • It is based on the actual levels of activity and standard revenue and standard costs.
    • This shows the amount that the company would have received for the actual number of units sold if they had been sold at the budgeted revenue per item.
    • Variances are calculated by comparing actual results with flexed budget.