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Watch Free ACCA/CA/CIMA/ICAEW video lectures.These simplified video tutorials will make you understand lengthy and complex things in a better way.

Externally oriented Cost Management Techniques
The value chain

The sequence of business activities by which, from the perspective of the end user, value is added to the products and services produced by an entry’.

Activities

Activities are the means by which an organisation creates value in its products.

According to Porter, the activities of any organisation can be divided into nine types and analysed into a value chain. A firm which performs the value chain activities more efficiently, and at a lower cost, than its competitors will gain competitive advantage.

It is necessary to understand how value chain activities are performed and how they interact with each other. The activities are not just a collection of independent activities but a system of interdependent activities in which the performance of one activity affects the performance of other activities

The activities which comprise the value chain are as follows:

Primary activities

Primary activities are directly related to production, sales, marketing, delivery and service.
1. Inbound logistics – which entail receiving, storing, materials handling, warehousing, inventory control, vehicle scheduling, returns to suppliers.
2. Operations – which entail transferring inputs into final product form (e.g. machining, packaging, assembly, equipment maintenance, testing, printing and facility operations).
3. Outbound logistics – which entail distributing the finished product (e.g. finished goods warehousing, material handling, operation of delivery vehicles, order processing and scheduling).
4. Marketing and sales – which entail inducing and facilitating buyers to purchase the product, e.g. advertising, activities of sales personnel, preparation of quotations, channel selection, channel relations, pricing of goods and services.
5. After sales service – which entails maintaining or enhancing the value of the product after the sale has taken place, installation, commissioning, repair, training, parts supply and product adjustment.
Support activities

Support activities provide purchased inputs, human resources, technology and infrastructural functions to support the primary activities.
1. Procurement – Acquiring the resource inputs to the primary activities (such as purchase of materials, subcomponents equipment)
2. Technology development – Designing products, improving processes and/or resource utilization
3. Human resource management – Recruiting, training, developing and rewarding people
4. Firm infrastructure – Planning, finance, quality control (Porter believes they are crucially important to an organisation’s strategic capability in all primary activities.)
Method of value analysis
- Determine the function of the product and each component that is used within the product.
- Determine the existing costs associated with individual components.
- Develop alternative solutions to the needs met by the components. This may involve design changes, manufacturing method, materials used, etc.
- Evaluate the alternatives and their anticipated effect.
- Implement the recommendations.
Value analysis will often lead to the reduction of components used in a product, the use of alternative, cheaper components and the standardisation of parts across several product lines.

Supply chain management

Supply chain management is often explained with reference to Porter’s value chain and value systems. A supply chain is the network of customers and suppliers that a business deals with.

Supply chain management considers logistics but also relationships between members of the supply chain, identification of end-customer benefit and the organisational consequences of greater inter-firm integration to form ‘network organisations’.

A longer supply chain often results in a lengthening of order-to-delivery lead times.

Purchasing

It is important for a company to work closely with its suppliers. A true partnership will enable a better, faster and more reliable service.

Stocks

Efficient stock control relies upon accurate customer records, well-managed customer information and effective stock-control information systems. A close collaboration with suppliers and customers will enable stock levels to be kept to a minimum.

Customer ordering

From the customer’s perspective the ordering process should be fast, flexible (meet individual customer needs) and efficient. A satisfied customer is more likely to return for repeat orders.

Gain – Sharing Arrangements

In simple terms, gain-sharing is a program that returns cost savings to the employees.

While risk-sharing/gain-sharing arrangements can take different forms, companies typically guarantee their customers that they will achieve a certain amount of cost savings or top-line improvement. If targets are not met, the company commits to making up the difference in cash. If however targets are exceeded, the supplier may also receive a pre-specified percentage of the gains.

Gain sharing is an approach to the review and adjustment of an existing contract, or series of contracts, where the adjustment provides benefits to both parties. It is a mutual activity requiring the agreement of both parties to the contract adjustment. Consideration of a gain-sharing proposal will be limited to just that area affected by the proposal.

The sharing of benefits provides an incentive to both parties to a contract to explore gain-sharing possibilities. The gain, benefit or advantage to be shared might not be financial in nature, though financial benefits are likely to feature strongly.

A gain-sharing arrangement must possess the following components:
1. Mutual interdependence and trust between the parties (as opposed to a blame culture).
2. Identification of common goals for success.
3. Agreed decision-making and problem-solving procedures.
4. Commitment to continuous improvement.
5. Team working down the entire product and supply chain.
February 12, 2022
Pricing decisions and Pricing strategies
Transfer Pricing

A transfer price is the ‘Price at which goods or services are transferred between different units of the same company’. These transfer pricing notes are prepared by mindmaplab team and covering introduction to transfer pricing, transfer costs, international transfer pricing, market-based transfer pricing, cost-based transfer pricing, the minimum transfer pricing and methods of transfer pricing management. transfer pricing short note are also available in pdf version too download.

Demand base Pricing

Elastic and inelastic demand

The value of demand elasticity may be anything from zero to infinity.

Demand is referred to as INELASTIC if the absolute value is less than 1 and ELASTIC if the absolute value is greater than 1.
- Where demand is inelastic, the quantity demanded falls by a smaller percentage than the percentage increase in price.
- Where demand is elastic, demand falls by a larger percentage than the percentage rise in price.
There are two extremes in the relationship between price and demand. A supplier can either sell a certain quantity, Q, at any price (as in graph (a)). Demand is totally unresponsive to changes in price and is said to be completely inelastic. Alternatively, demand might be limitless at a certain price P (as in graph (b)), but there would be no demand above price P and there would be little point in dropping the price below P. In such circumstances, demand is said to be completely elastic.

A more normal situation is where the downward-sloping demand curve shows the inverse relationship between unit selling price and sales volume. As one rises, the other falls. Demand is elastic because demand will increase as prices are lowered.

Price elasticity of demand

Price elasticity of demand is a measure of the extent of change in market demand for a good in response to a change in its price, is measured as:

The change in quantity demanded, as a % of demand

The change in price, as a % of the price

* it is usual to ignore the any minus sign

Example

The price of a good is $1.20 per unit and annual demand is 800,000 units. Market research indicates that an increase in price of 10 pence per unit will result in a fall in annual demand of 75,000 units. What is the price elasticity of demand?

Solution

Annual demand at $1.20 per unit is 800,000 units.

Annual demand at $1.30 per unit is 725,000 units.

% change in demand = (75,000/800,000) x 100% = 9.375% %

change in price = (10p/120p) x 100% = 8.333%

Price elasticity of demand = (–9.375/8.333) = –1.125

Ignoring the minus sign, price elasticity is 1.125.

The demand for this good, at a price of $1.20 per unit, would be referred to as elastic because the price elasticity of demand is greater than 1.

Elasticity and the pricing decision
1. With inelastic demand, increase prices because revenues will increase and total costs will reduce (because quantities sold will reduce).
2. With elastic demand, increases in price will bring decreases in revenue and decreases in price will bring increases in revenue.
3. In situations of very elastic demand, overpricing can lead to massive drops in quantity sold and hence profits, whereas underpricing can lead to costly inventory outs and, again, a significant drop in profits. Elasticity must therefore be reduced by creating a customer preference which is unrelated to price (through advertising and promotion).
4. In situations of very inelastic demand, customers are not sensitive to price. Quality, service, product mix and location are therefore more important to a firm’s pricing strategy.
Economic theory (Demand-based approaches) suggests that the volume of demand for a good in the market as a whole is influenced by a variety of variables such as:
- The price of the good, Tastes and fashion
- The price of other goods
- The perceived quality of the product, Expectations
- The size and distribution of household income, Obsolescence
The volume of demand for one organisation’s goods rather than another’s is influenced by three principal factors:
1. product life cycle (It is characterised by defined stages including research, development, introduction, maturity, decline and abandonment)
2. quality (the better quality good will be more in demand)
3. marketing (including the ‘four Ps’ of the marketing mix: Price, Product, Place, Promotion)
Other (Non-financial) issues that influence pricing decisions

Non-financial issues that influence pricing decisions, include competition, quality, price sensitivity and the market in which an organisation operates.

Markets

The price that an organisation can charge for its products will be determined to a greater or lesser degree by the market in which it operates.

Competition

In established industries dominated by a few major firms, it is generally accepted that a price initiative by one firm will be countered by a price reaction by competitors. In these circumstances, prices tend to be fairly stable, unless pushed upwards by inflation or strong growth in demand.

Fighting a price war

Ways to fight a price war include:
1. Sell on value, not price – where value is made up of service, response, variety, knowledge, quality, guarantee and price.
2. Use ‘package pricing’ to attract customers
3. Build up key accounts – as it is cheaper to get more business from an existing customer than to find a new one. Customer profitability analysis (CPA)
4. Explore new pricing models
A range of other issues influence pricing decisions, including the market in which an organisation operates, competition, quality and price sensitivity, Inflation, Compatibility with other products, Competition from substitute products etc.

Deriving the demand curve

The demand curve shows the relationship between the price charged for a product and the subsequent demand for that product.

Demand curve equations

Example:

Deriving the demand curve

The current price of a product is $12. At this price the company sells 12,000 items a month. One month the company decides to raise the price to $13, but only 9,500 items are sold at this price. Determine the demand equation.

Solution

Step 1 – Find the gradient of the line (b) b = 1/2,500 = 0.0004

Step 2 – Extract figures from the question

The demand equation can now be determined as P = a – bx

b = 0.0004 x = 12,000 (number of units sold at current selling price)

P = a – (0.0004 x 12,000)

12 = a – 4.80

a = 16.80

∴ P = 16.80 – 0.0004x

Step 3 – Check your equation

We can check this by substituting $12 and $13 for P.

12 = 16.80 – 0.0004x = 16.80 – (0.0004 x 12,000)

13 = 16.80 – 0.0004x = 16.80 – (0.0004 x 9,500)

Example:

Profit maximisation and the demand curve

The profit-maximising price/output level

The overall objective of an organisation should be profit maximisation.

In microeconomics theory, Profits will continue to be maximised only up to the output level where marginal cost has risen to be exactly equal to the marginal revenue.

Determining the profit-maximising selling price: using equations (Algebraic Approach)

The optimal selling price can be determined using equations (ie when MC = MR).

In an exam question you could be provided with equations for marginal cost and marginal revenue and/or have to devise them from information in the question. By equating the two equations you can determine the optimal price.

Marginal revenue may not be the same as the price charged for all units up to that demand level, as to increase volumes the price may have to be reduced.

Procedure for establishing the optimum price of a product

This is a general set of rules that can be applied to most questions involving algebra and pricing.
1. Establish the linear relationship between price (P) and quantity demanded (Q). The equation will take the form: P = a – bQ
2. Double the gradient to find the marginal revenue: MR = a − 2bQ.
3. Establish the marginal cost MC. This will simply be the variable cost per unit.
4. To maximise profit, equate MC and MR and solve to find Q.
5. Substitute this value of Q into the price equation to find the optimum price.
6. It may be necessary to calculate the maximum profit.
Example 1 – Algebraic Approach

At a price of Rs 200 a company will be able to sell 1,000 units of its product in a month. If the selling price is increased to Rs 220, the demand will fall to 950 units. The product has a variable cost of Rs 140 per unit, and company’s fixed costs will be Rs 36,000 per month.

Required:
1. Find an equation for the demand function (that is, price as a function of quantity demanded).
2. Write down the marginal revenue function.
3. Write down the marginal cost.
4. Find the quantity that maximises profit.
5. Calculate the optimum price.
6. What is the maximum profit?
Solution

(1). b = (220 – 200) ÷ (950 – 1,000) = –0.4

200 = a – 0.4 × 1,000

a = 200 + 400 = 600

So the demand function is: P = 600 – 0.4Q

(2). To find MR, just double the gradient, so that

MR = 600 – 0.8Q

(3) MC = 140

(4) To maximise profit, MC = MR

140 = 600 – 0.8Q

Q = (600 – 140) ÷ (0.8) = 575

(5). = 600 – 0.4 × 575 = Rs 370

(6). Revenue = Price × Quantity = Rs 370 × 575 = 212,750

Less Cost = 36,000 + Rs 140 × 575 = 116,500

Profit = 96,250

Example 2

The total fixed costs per annum for a company that makes one product are Rs. 100,000 and a variable cost of Rs. 64 is incurred for each additional unit produced and sold over a very large range of outputs. The current selling price for the product is Rs 160, and at this price 2,000 units are demanded per annum. It is estimated that for each successive increase in price of Rs. 5 annual demand will be reduced by 50 units. Alternatively, for each Rs. 5 reduction in price demand will increase by 50 units.

Required:
1. Calculate the optimum output and price assuming that if prices are set within each Rs. 5 range there will be a proportionate change in demand.
2. Calculate the maximum profit.
Solution

(1). Let Q = quantity produced/sold

Demand curve

Price = a – 0.1Q

160 = a – 0.1 (2,000)

a = 360

P = 360 – 0.1Q

MR = 360 – 0.2Q

MC = 64

(2). To maximise profit: MR = MC

360 – 0.2Q = 64

P = 360 – 0.1 (1,480) = Rs 212

Revenue Rs 212 × 1,480 Rs 313,760

Less costs Rs 64 × 1,480 + Rs 100,000 Rs (194,720)

Maximum profit Rs. 119,040

Example 3

Ltd makes and sells a single product. It has been estimated that at a selling price of Rs 20, demand would be 10,000 units. It is further estimated that for every 10p drop in selling price, demand would increase by 100 units and that for every 10p increase in selling price demand would fall by 100 units. Variable costs are Rs. 8 per unit and fixed costs are Rs. 50,000.

Required: Calculate the optimum selling price.

Solution

Demand curve: p = a – bQ

b = –0.1 ÷ 100 = –0.001

P = a – 0.001Q

20 = a – 0.001 x 10,000

20 = a – 10, therefore a = 30

Demand curve is: P = 30 – 0.001Q

Marginal revenue (MR) = 30 – 0.002Q

Marginal cost (MC) = 8

Profit is maximised when MC = MR, when: 8 = 30 – 0.002Q

0.002Q = 22

Q = 11,000 units

Selling price, P = 30 – 0.001Q; at 11,000 units:

P = 30 – 0.001 × 11,000 = Rs 19

Determining the profit-maximising selling price: The tabular approach

A tabular approach to price setting involves different prices and volumes of sales being presented in a table. To determine the profit-maximising selling price:
1. Work out the demand curve and hence the price and the total revenue (PQ) at various levels of demand
2. Calculate total cost and hence marginal cost at each level of demand
3. Finally calculate profit at each level of demand, thereby determining the price and level of demand at which profits are maximized
Example

Solution

The profit is maximised at 7 units of output and a price of $32,000, when MR is most nearly equal to MC.

Cost-based approaches to pricing

Full cost-plus pricing

Full cost-plus pricing adds a percentage onto the full cost of the product to arrive at the selling price.

The traditional approach to cost plus pricing is to take the full absorption cost of a product or service and to add on a predetermined percentage mark-up to arrive at the selling price. Full cost may comprise production costs only, or it may include some absorbed administration, selling and distribution overhead as well.

Advantages
1. Widely used and accepted.
2. Simple to calculate if costs are known.
3. Selling price decision may be delegated to junior management.
4. Justification for price increases.
5. May encourage price stability – if all competitors have similar cost structures and use similar mark-up.
Disadvantages
1. Ignores the economic relationship between price and demand.
2. No attempt to establish optimum price.
3. This structured method fails to recognise the manager’s need for flexibility in pricing.
4. Different absorption methods give rise to different costs and hence different selling prices.
5. Does not guarantee profit – if sales volumes are low fixed costs may not be recovered.
Marginal cost-plus (mark-up) pricing

A marginal (variable) cost-plus approach to pricing draws attention to gross profit and the gross profit margin, or contribution.

Marginal cost-plus pricing/mark-up pricing – is a method of determining the sales price by adding a profit margin on to either marginal cost of production or marginal cost of sales.

Advantages
1. It is simple to operate.
2. It draws management attention to contribution and the effects of higher or lower sales volumes on profit. In this way, it helps to create a better awareness of the concepts of marginal costing and break-even analysis.
3. In practice, it is used in businesses where there is a readily identifiable basic variable cost, e.g. retail industries.
Disadvantages
1. Although the size of the mark-up can be varied in accordance with demand conditions, it is not a method of pricing which ensures that sufficient attention is paid to demand conditions, competitors’ prices and profit maximisation.
2. It ignores fixed overheads in the pricing decision, but the sales price must be sufficiently high to ensure that a profit is made after covering fixed costs. Pricing cannot ignore fixed costs altogether.
Pricing based on mark-up per unit of limiting factor

It demonstrates how to calculate a price based on mark-up per unit of a limiting factor.

Another approach to pricing might be taken when a business is working at full capacity and is restricted by a shortage of resources from expanding its output further. By deciding what target profit, it would like to earn, it could establish a mark-up per unit of limiting factor.

Example

Different Pricing strategies for new products

When a new product is launched, it is essential that the company gets the pricing strategy correct, otherwise the wrong message may be given to the market (if priced too cheaply) or the product will not sell (if the price is too high).

A new product pricing strategy will depend largely on whether a company’s product or service is the first of its kind on the market.
- If the product is the first of its kind, there will be no competition yet, and the company, for a time at least, will be a monopolist. A monopolist’s price is likely to be higher, and its profits bigger, than those of a company operating in a competitive market.
- If the new product being launched by a company is following a competitor’s product onto the market, the pricing strategy will be constrained by what the competitor is already doing. The new product could be given a higher price if its quality is better, or it could be given a price which matches the competition.
Two pricing strategies for new products are market penetration pricing and market skimming pricing.

Market penetration pricing

Market penetration pricing is a policy of low prices when the product is first launched in order to obtain sufficient penetration into the market.

Circumstances in which a penetration policy may be appropriate.
1. If the firm wishes to discourage new entrants into the market.
2. If the firm wishes to shorten the initial period of the product’s life cycle in order to enter the growth and maturity stages as quickly as possible.
3. If there are significant economies of scale to be achieved from a high volume of output, so that quick penetration into the market is desirable in order to gain unit cost reductions.
4. If demand is highly elastic and so would respond well to low prices.
Penetration prices are prices which aim to secure a substantial share in a substantial total market. A firm might therefore deliberately build excess production capacity and set its prices very low. As demand builds up, the spare capacity will be used up gradually and unit costs will fall; the firm might even reduce prices further as unit costs fall. In this way, early losses will enable the firm to dominate the market and have the lowest costs.

Market skimming pricing

Market skimming pricing involves charging high prices when a product is first launched and spending heavily on advertising and sales promotion to obtain sales.

As the product moves into the later stages of its life cycle, progressively lower prices will be charged and so the profitable ‘cream’ is skimmed off in stages until sales can only be sustained at lower prices. The aim of market skimming is to gain high unit profits early in the product’s life. High unit prices make it more likely that competitors will enter the market than if lower prices were to be charged.

Circumstances in which such a policy may be appropriate.
1. Where the product is new and different, so that customers are prepared to pay high prices so as to be one up on other people who do not own it.
2. Where the strength of demand and the sensitivity of demand to price are unknown.
3. Where high prices in the early stages of a product’s life might generate high initial cash flows.
4. Where products may have a short life cycle, and so need to recover their development costs and make a profit relatively quickly.
Price Discrimination

Price discrimination is the practice of charging different prices for the same product to different groups of buyers when these prices are not reflective of cost differences.

Conditions required for a price-discrimination strategy:
1. The seller must have some degree of monopoly power, or the price will be driven down.
2. Customers can be segregated into different markets.
3. Customers cannot buy at the lower price in one market and sell at the higher price in the other market.
4. Price discrimination strategies are particularly effective for services.
5. There must be different price elasticities of demand in each market so that prices can be raised in one and lowered in the other to increase revenue.
Dangers of price-discrimination as a strategy:
1. A black market may develop allowing those in a lower priced segment to resell to those in a higher priced segment.
2. Competitors join the market and undercut the firm’s prices.
3. Customers in the higher priced brackets look for alternatives and demand become more elastic over time.
Premium pricing

This involves making a product appear ‘different’ through product differentiation so as to justify a premium price. The product may be different in terms of, for example, quality, reliability, durability, after sales service or extended warranties. Heavy advertising can establish brand loyalty, which can help to sustain a premium, and premium prices will always be paid by those customers who blindly equate high price with high quality.

Product bundling

Product bundling is a variation on price discrimination which involves selling a number of products or services as a package at a price lower than the aggregate of their individual prices. This might encourage customers to buy services that they might otherwise not have purchased.

The success of a bundling strategy depends on the expected increase in sales volume and changes in margin. Other cost changes, such as in product handling, packaging and invoicing costs, are possible. Longer-term issues, such as competitors’ reactions, must also be considered.

Loss leader pricing

A loss leader is when a company sets a very low price for one product intending to make customers buy other products in the range which carry higher profit margins. People will buy many of the high-profit items but only one of the low-profit items, yet they are ‘locked in’ to the former by the latter.

Discount pricing

Discount pricing is where products are priced lower than the market norm, but are put forward as being of comparable quality. The aim is that the product will procure a larger share of the market than it might otherwise do, thereby counteracting the reduction in selling price.

Reasons for using discounts to adjust prices:
1. To get rid of perishable goods that have reached the end of their shelf life
2. To sell off seconds
3. Normal practice (e.g. antique trade)
4. To increase sales volumes during a poor sales period without dropping prices permanently
5. To differentiate between types of customer (wholesale, retail and so on)
6. To get cash in quickly
February 12, 2022
Multi-product Break-even (CVP) analysis
Drawing a Basic Break-even Chart

A basic Break-even chart records costs and revenues on the vertical axis (y) and the level of activity on the horizontal axis (x). Lines are drawn on the chart to represent costs and sales revenue.

A break-even chart or graph shows:
- total costs, analyzed between variable costs and fixed costs
- sales
- profit (= the difference between total sales and total costs)
- the break-even point (where total costs = total sales revenue, and profit = 0).
The concept of a break-even chart is similar to a cost behavior chart, but with sales revenue shown as well. If the chart also indicates the budgeted volume of sales, the margin of safety can be shown as the difference between the budgeted volume and the break-even volume of sales.

The Break-even point can be read off where the total sales revenue line cuts the total cost line.

Drawing a Basic Profit/volume chart (P/V chart)

A profit volume chart (or P/V chart) is an alternative to a break-even chart for presenting CVP information. It is a chart that shows the profit or loss at all levels of output and sales. This chart plots a single line depicting the profit or loss at each level of activity.

The vertical axis shows profits and losses and the horizontal axis is drawn at zero profit or loss.

At Rs.0 sales, there is a loss equal to the total amount of fixed costs. The loss becomes smaller as sales volume increases, due to the higher contribution as sales volume increases. Break-even point is then reached and profits are made at sales volumes above the break-even point. The Break-even point is where this line cuts the horizontal axis.

Multi-product Break-even analysis

CVP Analysis assumes that, if a range of products is sold, sales will be in accordance with a pre-determined sales mix.

When a pre-determined sales mix is used, it can be depicted in the CVP Analysis by assuming average revenues and average variable costs for the given sales mix. However, the assumption has to be made that the sales mix remains constant. This is defined as the relative proportion of each product’s sale to total sales. It could be expressed as a ratio such as 2:3:5, or as a percentage as 20%, 30%, 50%.

This assumption allows us to calculate a weighted average contribution per unit or batch and/or CS ratio which can be used to solve Break-even, margin of safety and target profit problems.

Break-even analysis – C/S ratio

In multi-product situations, a weighted average C/S ratio is calculated by using the formula:

Weighted average C/S ratio = Total contribution

Total revenue

The weighted average C/S ratio is useful in its own right, as it tells us what percentage each $ of sales revenue contributes towards fixed costs.

Margin of safety – Multi product

The margin of safety is the difference between:
- the budgeted sales (in units or Rs.) and
- the break-even amount of sales (in units or Rs.).
It is usually expressed as a percentage of the budgeted sales. However, it may also be measured as:
- a quantity of units (= the difference between the budgeted sales volume in units and the break-even sales volume), or
- an amount of sales revenue (= the difference between the budgeted sales revenue and the total sales revenue required to break even).
It is called the margin of safety because it is the maximum amount by which actual sales can be lower than budgeted sales without incurring a loss for the period. A high margin of safety therefore indicates a low risk of making a loss.

For Multi-product margin of safety, the break-even point can be compared to the budgeted activity level using batches, units or revenue.

Establishing a target profit for multiple products

Management might want to know what the volume of sales must be in order to achieve a target profit. CVP analysis can be used to calculate the volume of sales required.

The necessary contribution to earn the target profit is the target profit plus the fixed costs. The activity level required to achieve the necessary contribution may be found using contribution per unit, contribution per batch or the CS ratio.

Advantages of Break – Even Analysis
1. The major benefit of using Break-even analysis is that it indicates the lowest amount of activity necessary to prevent losses.
2. Break-even analysis aids Decision Marking as it explains the relationship between cost, production volume and returns.
3. It can be extended to show how changes in fixed costs – variable costs relationships or in revenues will affect profit levels and Break-even points.
Limitations of break-even analysis

The following underlying assumptions will limit the precision and reliability of a given cost-volume-profit analysis.
1. The behaviour of total cost and total revenue has been reliably determined and is linear over the relevant range.
2. All costs can be divided into fixed and variable elements.
3. Total fixed costs remain constant over the relevant volume range of the CVP analysis.
4. Total variable costs are directly proportional to volume over the relevant range.
5. Selling prices are to be unchanged.
February 12, 2022
Linear programming: Graphical method
Linear programming: Graphical method

If faced with two or more limiting factors, then the situation is more complicated and linear programming techniques must be used (and the limiting factors are now called constraints). These linear programming notes are prepared by mindmaplab team and covering the linear programming introduction, theory, the first step in formulating a linear programming problem, the shadow price and slack concept with examples. These summary notes are actually the linear algebra full course for dummies. These linear programming questions and answers are also available in pdf too. We have also prepared the linear programming pdf version download.

Introduction

In decision making when faced with one limiting factor, we calculate the contribution per unit of the limiting factor and rank the products, allocating the scarce resource to the best product and then the next best product and so on until the resource is fully utilised.

If faced with two or more limiting factors, then the situation is more complicated and linear programming techniques must be used (and the limiting factors are now called constraints).

Firms face many constraints on their activity and plan accordingly:
- limited demand
- limited skilled labour and other production resources
- limited finance (‘capital rationing’).
Planning with one limiting factor

The usual objective in questions is to maximise profit. Given that fixed costs are unaffected by the production decision in the short run, the approach should be to maximise the contribution earned.

If there is one limiting factor, then the problem is best solved using key factor analysis:

Step 1: identify the scarce resource.

Step 2: calculate the contribution per unit for each product.

Step 3: calculate the contribution per unit of the scarce resource for each product.

Step 4: rank the products in order of the contribution per unit of the scarce resource.

Step 5: allocate resources using this ranking and answer the question.

Several limiting factors – linear programming

Where there are two or more resources in short supply which limit the organisation’s activities, then linear programming is required to find the solution.

linear programming is used to:
- maximise contribution and/or
- minimise costs
The steps involved in linear programming are as follows:

Example

Solution

Limiting factor analysis – Assumptions
- There is a single quantifiable objective – e.g. maximise contribution. In reality there may be multiple objectives such as maximising return while simultaneously minimising risk.
- Each product always uses the same quantity of the scarce resource per unit. In reality this may not be the case. For example, learning effects may be enjoyed.
- The contribution per unit is constant. In reality this may not be the case:
  - the selling price may have to be lowered to sell more
  - there may be economies of scale, for example a discount for buying in bulk.
- Products are independent – in reality:
  - customers may expect to buy both products together
  - the products may be manufactured jointly together.
- The scenario is short term. This allows us to ignore fixed costs.
The assumptions apply to the analysis used when there is one limiting factor or if there are multiple limiting factors.

Shadow prices and slack

Slack

Slack refers to the amount of a constraint that is not used in the optimal solution to a linear programming problem.

Only non-limiting resources have slack. Limiting resources are fully utilised so never have any slack.

The amount of slack in any non-limiting resources is easily found by substituting the optimum product mix into the equation for that resource. This would show how much of that resource was needed for the optimum solution. This could then be compared to the amount of resource available to give the slack.

Shadow prices

The shadow price or dual price of a limiting factor is the increase in contribution created by the availability of one additional unit of the limiting factor at the original cost.
- The shadow price of a resource can be found by calculating the increase in value (usually extra contribution) which would be created by having available one additional unit of a limiting resource at its original cost.
- It therefore represents the maximum premium that the firm should be willing to pay for one extra unit of each constraint. This aspect is discussed in more detail below.
- Non-critical constraints will have zero shadow prices as slack exists already.
Calculating shadow prices

The simplest way to calculate shadow prices for a critical constraint is as follows:

Step 1: Take the equations of the straight lines that intersect at the optimal point. Add one unit to the constraint concerned, while leaving the other critical constraint unchanged.

Step 2: Use simultaneous equations to derive a new optimal solution.

Step 3: Calculate the revised optimal contribution and compare to the original contribution calculated. The increase is the shadow price.
February 12, 2022
Linear programming the simplex method
The Simplex Method – using computer

The simplex method is of particular use because it is able to consider more complex problems involving more than two output variables. This is an iterative (or repetitive) process that calculates the contribution at each vertex of the feasible region, starting with the origin. The process is normally carried out by a computer which will provide not only an optimal solution but also a sensitivity analysis for the data.

There are three stages:
1. Preparing the input for the computer (or a manual solution). We do this in the form of a table or tableau, known as the initial tableau.
2. The computer processes the data by means of a series of matrix multiplications.
3. The computer produces the output in the form of a final tableau and we have to interpret the information.
Setting up the initial tableau

The initial tableau shows the production problem when the output of all the products is zero. It is like considering the origin of the graph. In order to produce the first tableau it is necessary to convert each inequality into an equation. This is done by introducing a slack variable for each constraint.

Let S1 = Slack in Department A

Let S2 = Slack in Department B

Let S3 = Slack in Department C

Having written the equations, it is now possible to produce the initial tableau:

Variable X Y S₁ S₂ S₃ Solution

S1

S2

S3

Contribution

The contributions per unit should be entered as negative numbers. This is just a feature of the mathematics and has to be remembered as a rule.

Interpreting the final tableau

The computer processes the data contained in the initial tableau and it produces the final tableau.

*In the examination, the final tableau will always be given. You must be able write a full interpretation of the output.

Test your understanding

Solution

(c) The optimum monthly production plan is: 4,000 tonnes of X1 and 8,000 tonnes of X2. Zero tonnes of X3 should be produced.

The maximum monthly contribution is Rs 284,000. This contribution would fall by Rs 22 for each tonne of X3 that was produced.

The nitrate and phosphate are both fully utilised, their slack is zero. If additional tonnes of these chemicals could be obtained then contribution would increase by Rs 170 per tonne of nitrate and by Rs 40 per tonne of phosphate. There is slack of 600 tonnes of potash.

Additional information revealed by this final tableau:
- If one additional tonne of nitrate were to become available production of X1 should increase by 20 tonnes and production of X2 should decrease by 10 tonnes. This alteration to the mix will increase contribution by Rs 170. The slack of potash will fall by 3 tonnes.
- If one additional tonne of phosphate were to become available production of X1 should decrease by 10 tonnes and production of X2 should increase by 10 tonnes. This alteration to the mix will increase contribution by Rs 40. The slack of potash will increase by 1 tonne.
- If one tonne of X3 must be manufactured contribution will decrease by Rs 22. The mix must be altered in order to make one tonne of X3; Production of X1 must decrease by 3 tonnes and production of X2 must increase by 1 tonne. The slack of potash will increase by 0.4 of a tonne.
February 12, 2022
Risk and uncertainty in decision making
Risk and uncertainty in decision making

All businesses face risk. Risk is the variability of possible returns.

Risk management is important in a business. It is the process of understanding and managing the risks that an organisation is inevitably subject to.

Investment projects are long-term projects, often with a time scale of many years. When the cash flows for an investment project are estimated, the estimates might be incorrect. Estimates of cash flows might be wrong for two main reasons:
- Risk in the investment, and
- Uncertainty about the future
Risk – there are a number of possible outcomes and the probability of each outcome is known.

Uncertainty – there are a number of possible outcomes but the probability of each outcome is not known.

Methods of assessing risk and uncertainty

There are several methods of analysing and assessing risk and uncertainty. In particular:
1. Sensitivity analysis
2. Risk modelling and simulation
3. Probability analysis and Expected values
4. Maximax, maximin and minimax regret
5. Decision Trees.
Risk attitudes

The selection criterion applied by the manager will often depend upon the manager’s attitude towards risk. It is common to recognise three different attitudes:
1. Risk neutral –This person considers all possible outcomes and will select the strategy that maximises the expected value of benefit.
2. Risk seeker – The decision maker is likely to select the strategy with the best possible outcomes, regardless of the likelihood that they will occur. This person will apply the maximax criterion
3. Risk averse – This person will consider the worst outcome each time. They will apply the maximin criterion or the minimax regret approach.
Responding to risk and uncertainty

Risk is considered by using probability distribution, expected values, simulation, or CAPM (for adjusting discount rate for every project). Uncertainty is considered using the following measures:
1. setting a minimum payback period for projects;
2. increasing the discount rate to provide a more pessimistic measure of npv;
3. making prudent / conservative estimates to assess the worst outcomes possible;
4. performing scenario analysis to analyse the best and the worst possible situations and a range of outcomes; or
5. using sensitivity analysis to measure the “margin of safety” on input data.
Probabilities and Expected values (EV)

An expected value is a weighted average value, calculated using probability estimates of different possible outcomes. To calculate an expected value, the probability of each possible outcome is estimated, and the mean (average) outcome is calculated.

In other words, it is obtained by multiplying the value of each possible outcome (x), by the probability of that outcome (p), and summing the results.

Formula: Expected value

Expected value = Σpx

Where:

p = the probability of each outcome

x = the value of each outcome

When expected values are used to assess the risk in capital investment appraisal, x would be the NPV for each possible outcome, and the EV would be the expected value of the project net present value (the EV of the NPV).

*The basic decision rule is that an investment project should be undertaken if the expected value of its NPV is positive.

However, a project with a positive EV of NPV might not be undertaken if the risk involved seems too great in relation to the amount of the return expected.

Advantages and disadvantages of using expected values

Advantages
1. Takes uncertainty into account by considering the probability of each possible outcome and using this information to calculate an expected value.
2. The information is reduced to a single number resulting in easier decisions.
3. Calculations are relatively simple.
Disadvantages
1. The probabilities used are usually very subjective.
2. The EV is merely a weighted average and therefore has little meaning for a one-off project.
3. The EV gives no indication of the dispersion of possible outcomes about the EV, i.e. the risk.
4. The EV may not correspond to any of the actual possible outcomes.
Data tables

Data tables are often produced using spreadsheet packages and show the effect of changing the values of variables.

A one-way or one-input data table shows the effect of a range of values of one variable. For example, it might show the effect on profit of a range of selling prices.

A two-way or two-input data table shows the results of combinations of different values of two key variables. The effect on contribution of combinations of various levels of demand and different selling prices would be shown in a two-way data table.

Any combination of variable values can therefore be changed and the effects monitored.

Data tables and probability

If a probability distribution can be applied to either or both of the variables in a data table, a revised table can be prepared to provide improved management information.

The maximin, maximax and minimax regret bases for decision making

When probabilities are not available, there are still tools available for incorporating uncertainty into decision making.

Maximin

The ‘play it safe‘ basis for decision making is referred to as the maximin basis. This is short for ‘maximise the minimum achievable profit‘. (It might also be called ‘minimax’ which is short for ‘minimise the maximum potential cost or loss’). Maximin decisions are taken by risk-averse decision makers.

Playing safe, and choosing the option with the least damaging results if events were to turn out badly.

The maximin rule involves selecting the alternative that maximises the minimum pay-off achievable. The investor would look at the worst possible outcome at each supply level, then selects the highest one of these. The decision maker therefore chooses the outcome which is guaranteed to minimise his losses. In the process, he loses out on the opportunity of making big profits.

The main weakness of the maximin basis for decision making is that it ignores the probabilities that various different outcomes might occur, and so in this respect, it is not as good as the EV basis for decision making.

Maximax

A basis for making decisions by looking for the best outcome is known as the maximax basis, short for ‘maximise the maximum achievable profit‘. (It can also be called the minimin cost rule – minimise the minimum costs or losses.) Maximax decisions are taken by risk-seeking decision makers.

The Minimax Regret rule

The ‘opportunity loss’ basis for decision making is known as minimax regret.

The minimax regret strategy is the one that minimises the maximum regret. It is useful for a risk-averse decision maker. Essentially, this is the technique for a ’sore loser’ who does not wish to make the wrong decision.

Minimax regret considers the extent to which we might come to regret an action we had chosen.

An alternative term for regret is opportunity loss. We may apply the rule by considering the maximum opportunity loss associated with each course of action and choosing the course which offers the smallest maximum. If we choose an action which turns out not to be the best in the actual circumstances, we have lost an opportunity to make the extra profit we could have made by choosing the best action.

Using the standard deviation to measure risk

Risk can be measured by the possible variations of outcomes around the expected value. One useful measure of such variations is the standard deviation of the expected value.

The decision maker can then weigh up the EV of each option against the risk (the standard deviation) that is associated with it.

Decision trees

Decision trees are diagrams which illustrate the choices and possible outcomes of a decision.

A Decision tree is ‘A pictorial method of showing a sequence of interrelated decisions and their expected outcomes. Decision trees can incorporate both the probabilities of, and values of, expected outcomes, and are used in decision-making.’

A decision tree is a diagrammatic representation of a decision problem, where all possible courses of action are represented, and every possible outcome of each course of action is shown. Decision trees should be used where a problem involves a series of decisions being made and several outcomes arise during the decision-making process.

A complex problem is broken down into smaller, easier-to-handle sections. Only relevant costs and revenues are considered, and that all cash is expressed in present value terms.

A decision tree is drawn from its “root” up to its “branches” and then, once drawn, analysed from its “branches” back to its “root”.

Exactly how does the use of a decision tree permit a clear and logical approach?
- All the possible choices that can be made are shown as branches on the tree.
- All the possible outcomes of each choice are shown as subsidiary branches on the tree.
Constructing a decision tree

Three-step method

Step 1 – Draw the tree from left to right showing appropriate decisions and events/outcomes.

There are two different types of branching point in the tree:
- Decision points – as the name suggests this is a point where a decision is made
- Outcome points – an expected value is calculated here.
The following symbols are used for decision points and outcome points:

Square is used to represent a decision point (i.e. where a choice between different courses of action must be taken. A circle is used to represent a chance point. The branches coming away from a Circle with have probabilities attached to them. All probabilities should add up to ‘1’.

Step 2 – Evaluate the tree from right to left carrying out these two actions:
1. Calculate an EV at each outcome point.
2. Choose the best option at each decision point.
Step 3 – Recommend a course of action to management.

Evaluating the decision with a decision tree

Rollback analysis evaluates the EV of each decision option. You have to work from right to left and calculate EVs at each outcome point.

The EV of each decision option can be evaluated, using the decision tree to help with keeping the logic on track. The basic rules are as follows:
1. We start on the right-hand side of the tree and work back towards the left-hand side and the current decision under consideration. This is sometimes known as the ‘rollback’ technique or ‘rollback analysis’.
2. Working from right to left, we calculate the EV of revenue, cost, contribution or profit at each outcome point on the tree.
Evaluating decisions by using decision trees has a number of limitations:
1. The time value of money may not be taken into account.
2. Decision trees are not very suitable for use in complex situations.
3. The outcome with the highest EV may have the greatest risks attached to it. Managers may be reluctant to take risks which may lead to losses.
4. The probabilities associated with different branches of the ‘tree’ are likely to be estimates, and possibly unreliable or inaccurate.
The value of information

Perfect information is guaranteed to predict the future with 100% accuracy.

Perfect information removes all doubt and uncertainty from a decision, and enables managers to make decisions with complete confidence that they have selected the optimum course of action.

The forecast of the future outcome is always a correct prediction. If a firm can obtain a 100% accurate prediction they will always be able to undertake the most beneficial course of action for that prediction.

Imperfect information is better than no information at all, but could be wrong in its prediction of the future. The forecast is usually correct, but can be incorrect.

Imperfect information is not as valuable as perfect

The value of perfect information

The value of perfect information is the difference between the EV of profit with perfect information and the EV of profit without perfect information.

Step 1 – If we do not have perfect information and we must choose between two or more decision options, we would select the decision option which offers the highest EV of profit. This option will not be the best decision under all circumstances. There will be some probability that what was really the best option will not have been selected, given the way actual events turn out.

Step 2 – With perfect information, the best decision option will always be selected. The profits from the decision will depend on the future circumstances which are predicted by the information; nevertheless, the EV of profit with perfect information should be higher than the EV of profit without the information.

Step 3 – The value of perfect information is the difference between these two EVs.

The value of imperfect information

Perfect information is only rarely accessible. In fact, information sources such as market research or industry experts are usually subject to error. Market research findings, for example, are likely to be reasonably accurate – but they can still be wrong. Therefore, our analysis must extend to deal with imperfect information.

Sensitivity analysis

Sensitivity analysis is a useful but simple technique for assessing investment risk in a capital expenditure project when there is uncertainty about the estimates of future cash flows. It is recognised that estimates of cash flows could be inaccurate, or that events might occur that will make the estimates wrong.

The purpose of sensitivity analysis is to assess how the NPV of the project might be affected if cash flow estimates are worse than expected.

Sensitivity analysis takes each uncertain factor in turn, and calculates the change that would be necessary in that factor before the original decision is reversed. By using this technique, it is possible to establish which estimates (variables) are more critical than others in affecting a decision.

There are two main methods of carrying out sensitivity analysis on a capital expenditure project.

Method 1

Sensitivity analysis can be used to calculate the effect on the NPV of a given percentage reduction in benefits or a given percentage increase in costs. For example:
- What would the NPV of the project be if sales volumes were 10% below estimate?
- What would the NPV of the project be if annual running costs were 5% higher than estimate?
The percentage variation in the expected cash flows should be an amount that might reasonably occur, given the uncertainty in the cash flow estimates.

There are also forms of ‘stress testing’, similar to sensitivity analysis, that might be used to assess the investment risk. An assessment could be made to estimate the effects of:
- Of an unexpected event occurring in the future that would make the cash flow estimates for the project wrong; or
- The effect of a delay so that the expected cash inflows from the project occur later than planned.
This sort of analysis is sometimes called “what if?” analysis.

Method 2

Alternatively, sensitivity analysis can be used to calculate the percentage amount by which a cash flow could change before the project NPV changed. For example:
- By how much (in percentage terms) would sales volumes need to fall below the expected volumes, before the project NPV became negative?
- By how much (in percentage terms) would running costs need to exceed the expected amount before the NPV became negative?
Estimating the sensitivity of a project to changes in the cost of capital

The sensitivity of the project to a change in the cost of capital can be found by calculating the project IRR. This can be compared with the company’s cost of capital.

Strengths of sensitivity analysis
1. There is no complicated theory to understand.
2. Information will be presented to management in a form which facilitates subjective judgement to decide the likelihood of the various possible outcomes considered.
3. It identifies areas which are crucial to the success of the project. If the project is chosen, those areas can be carefully monitored.
Weaknesses of sensitivity analysis
1. It assumes that changes to variables can be made independently, e.g. material prices will change independently of other variables. Simulation allows us to change more than one variable at a time.
2. It only identifies how far a variable needs to change; it does not look at the probability of such a change.
3. It provides information on the basis of which decisions can be made but it does not point to the correct decision directly.
Simulation models

Simulation is computer-based risk adjustment model which overcomes the problem of having a large number of possible outcomes and correlation between them.

Sensitivity analysis considers the effect of changing one variable at a time. Simulation improves on this by looking at the impact of many variables changing at the same time.

Using mathematical models, it produces a distribution of the possible outcomes from the project. The probability of different outcomes can then be calculated.

Steps in simulation
1. Specify major variables, e.g.: market size, selling price, market growth rate, market share.
2. Specify the relationships between variables to calculate an NPV.
3. Simulate the environment:
  - assign random numbers to represent the probability distribution for each variable
  - draw a random number for each variable
  - select the value of each variable corresponding with the selected random number and compute an NPV
  - repeat the process many times to create a probability distribution of returns.
4. The results of a simulation exercise will be a probability distribution of NPVs.
Advantages of simulation

The major advantages of simulation are as follows:
1. it includes all possible outcomes in the decision-making process.
2. it is a relatively easily understood technique.
3. it has a wide variety of applications (inventory control, component replacement, corporate models, etc.).
Drawbacks of simulation
1. models can become extremely complex and the time and costs involved in their construction can be more than is gained from the improved decisions.
2. probability distributions may be difficult to formulate.
February 12, 2022
Relevant costs and revenues
Relevant costs and revenues

Management make decisions about the future. When they make decisions for economic or financial reasons, the objective is usually to increase profitability or the value of the business, or to reduce costs and improve productivity.

Relevant costs should be used for assessing the economic or financial consequences of any decision by management. Only relevant costs and benefits should be taken into consideration when evaluating the financial consequences of a decision.

As a relevant cost is a future cash flow that will occur as a direct consequence of making a particular decision, it is used for target profit analysis as well.

The key concepts in this definition of relevant costs are as follows:
- Relevant costs are costs that will occur in the future. They cannot include any costs that have already occurred in the past.
- Relevant costs of a decision are costs that will occur as a direct consequence of making the decision. Costs that will occur anyway, no matter what decision is taken, cannot be relevant to the decision.
- Relevant costs are cash flows. Notional costs, such as depreciation charges, notional interest costs and absorbed fixed costs, cannot be relevant to a decision.
Several terms are used in relevant costing, to indicate how certain costs might be relevant or not relevant to a decision.

Incremental cost

An incremental cost is an additional cost that will occur if a particular decision is taken. Provided that this additional cost is a cash flow, an incremental cost is a relevant cost.

Differential cost

A differential cost is the amount by which future costs will be different, depending on which course of action is taken. A differential cost is therefore an amount by which future costs will be higher or lower, if a particular course of action is chosen. Provided that this additional cost is a cash flow, a differential cost is a relevant cost.

Avoidable and unavoidable costs

An avoidable cost is a cost that could be saved (avoided), depending whether or not a particular decision is taken. An unavoidable cost is a cost that will be incurred anyway.

Avoidable costs are relevant costs and Unavoidable costs are not relevant to a decision.

Committed cost

Committed costs are a category of unavoidable costs. A committed cost is a cost that a company has already committed to or an obligation already made, that it cannot avoid by any means. Committed costs are not relevant costs for decision making.

*Leases normally represent a committed cost for the full term of the lease, since it is extremely difficult to terminate a lease agreement.

Sunk costs

Sunk costs are costs that have already been incurred (historical costs) or costs that have already been committed by an earlier decision. Sunk costs must be ignored for the purpose of evaluating a decision, and cannot be relevant costs.

Opportunity costs

Relevant costs can also be measured as an opportunity cost. An opportunity cost is a benefit that will be lost by taking one course of action instead of the next-most profitable course of action.

This cost should be taken into consideration as a cost that would be incurred as a direct consequence of a decision. The opportunity cost is a relevant cost.

Relevant cost of materials

Relevant costs of materials are the additional cash flows that will be incurred (or benefits that will be lost) by using the materials for the purpose that is under consideration.

If none of the required materials are currently held as inventory, the relevant cost of the materials is simply their purchase cost.

If the required materials are currently held as inventory, the relevant costs are identified by applying the following rules:

Relevant cost of labor

The relevant cost of labor for any decision is the additional cash expenditure (or saving) that will arise as a direct consequence of the decision.
- If the cost of labor is a variable cost, and labor is not in restricted supply, the relevant cost of the labor is its variable cost.
- If labor is a fixed cost and there is spare labor time available, the relevant cost of using labor is 0. The spare time would otherwise be paid for idle time, and there is no additional cash cost of using the labor to do extra work.
- If labor is in limited supply, the relevant cost of labor should include the opportunity cost of using the labor time for the purpose under consideration instead of using it in its next-most profitable way.
Relevant cost of overheads

Relevant costs of expenditures that might be classed as overhead costs should be identified by applying the normal rules of relevant costing. Relevant costs are future cash flows that will arise as a direct consequence of making a particular decision.

Fixed overhead absorption rates are therefore irrelevant, because fixed overhead absorption is not overhead expenditure and does not represent cash spending.

However, it might be assumed that the overhead absorption rate for variable overheads is a measure of actual cash spending on variable overheads. It is therefore often appropriate to treat a variable overhead hourly rate as a relevant cost, because it is an estimate of cash spending per hour for each additional hour worked.

The only overhead fixed costs that are relevant costs for a decision are extra cash spending that will be incurred, or cash spending that will be saved, as a direct consequence of making the decision.

Relevant costs associated with non-current assets (Machinery)

Typical relevant cash flows
1. The purchase price of any new machinery that needs to be bought.
2. If an existing machine is to be used in the project that would otherwise have been sold, then there is an opportunity cost equal to the proceeds foregone.
3. Scrap/disposal proceeds on new assets bought.
4. If we need to take an existing machine from another department and it is not replaced (either by choice or because a replacement is not available), then there is an opportunity cost equal to the lost contribution from the other department would need to be included.
Items that are not relevant
1. Depreciation is not a cash flow so is never relevant.
2. Profit or loss on disposal incorporates accumulated depreciation so is not relevant – instead look at the cash element only – i.e. the scrap proceeds.
3. The original purchase price of existing machinery is a sunk cost.
4. The NBV of existing machinery is a combination of the original price (sunk) and accumulated depreciation (not a cash flow).
February 12, 2022
Activity based costing | Customer Profitability Analysis
Activity based costing (ABC)

Activity based costing (ABC) has been developed as an alternative costing system to traditional overhead absorption costing. ABC was developed to improve the cost allocation process as traditional techniques assumed that costs were only driven by volume.

Definition – Activity Based Costing (ABC) is ‘An approach to the costing and monitoring of activities which involves tracing resource consumption and costing final outputs. Resources are assigned to activities and activities to cost objects based on consumption estimates. It uses cost drivers to attach activity costs to outputs.

Production overheads are not necessarily driven by volume, therefore allocation using traditional methods is not necessarily meaningful. With ABC, multiple overhead absorption rates (OARs) are calculated based on the different activities that cause the costs to change.

Cost drivers and cost pools

A cost driver is a ‘factor influencing the level of cost. Examples of cost drivers:
- Set-up costs – Number of production runs
- Production scheduling – Number of production runs
- Inspection costs – Number of inspections or inspection hours
- Despatch costs – Number of customer orders delivered
All of the costs associated with a particular cost driver (for example production runs) would be grouped into cost pools.

Types of cost driver
1. Resource cost driver – is a measure of the quantity of resources consumed by an activity. It is used to assign the cost of a resource to an activity or cost pool.
2. Activity cost driver – is a measure of the frequency and intensity of demand placed on activities by cost objects. It is used to assign activity costs to cost objects.
In traditional absorption costing, overheads are first related to cost centres and then to cost objects (products). In ABC, overheads are first related to activities or grouped into cost pools (depending on the terminology preferred) and then related to the cost objects.

Like traditional absorption costing rates, ABC rates are calculated in advance, usually for a year ahead.

Stages in ABC calculations
1. Group overheads into cost pools, according to how they are driven. This involves gathering overheads that are caused by the same activity into one group and is done by means of resource cost drivers.
2. Identify the cost drivers for each activity
3. Calculate a cost per unit of cost driver (Cost driver rate = total cost of activity / Cost driver)
4. Absorb activity costs into production based on the usage of cost drivers.
*ABC traces the appropriate amount of input to each product. However, it is important to realise that although ABC should be a more accurate way of relating overheads to products, it is not a perfect system and product costs could still be inaccurate, as ABC is based on a number of assumptions.

A summary of benefits and limitations

Benefits
1. Provides more accurate product-line costings particularly where non-volume-related overheads are significant and a diverse product line is manufactured.
2. Is flexible enough to analyse costs by cost objects other than products such as processes, areas of managerial responsibility and customers.
3. Provides a reliable indication of long-run variable product cost which is particularly relevant to managerial decision making at a strategic level.
4. Provides meaningful financial (periodic cost driver rates) and non-financial (periodic cost driver volumes) measures which are relevant for cost management and performance assessment at an operational level.
5. Aids identification and understanding of cost behaviour and thus has the potential to improve cost estimation.
6. Provides a more logical, acceptable and comprehensible basis for costing work.
Limitations
1. Little evidence to date that ABC improves corporate profitability.
2. ABC information is historic and internally orientated and therefore lacks direct relevance for future strategic decisions.
3. Practical problems such as cost driver selection.Its novelty is questionable. It may be viewed as simply a rigorous application of conventional costing procedures.
Many of ABC’s supporters claim that it can assist with decision making because it provides accurate and reliable cost information. ABC establishes a long-run product cost and because it provides data that can be used to evaluate different business possibilities and opportunities, it is particularly suited for the types of decision such as:
1. Pricing
2. Make or buy decisions
3. Promoting or discontinuing products or parts of the business
4. Developing and designing changed products
* An ABC cost is an average cost, but it is not always a true cost because some costs, such as depreciation, are usually arbitrarily allocated to products. An ABC cost is therefore not a relevant cost for all decisions.

ABC and long-term decisions

ABC is particularly suited for long-term and strategic decisions (such as long-run pricing, capacity management and product mix decisions) for a number of reasons.
1. It assumes all costs are variable in relation to product choice or production-level decisions.
2. It has strategic relevance because it allows for a full understanding of activities and their resource consumption.
3. Short-run changes in consumption do not translate into changes in spending (as real cash savings or expenditure are not made/incurred in the short run).
Activity based management (ABM)

The cost management version of ABC.

Definition – ‘System of management which uses activity-based cost information for a variety of purposes including cost reduction, cost modelling and customer profitability analysis.’

ABM is simply using the information derived from an ABC analysis for cost management. ABM seeks to classify each activity within a process as a value-added or non-value-added activity.

Non-value-added activities are unnecessary and represent waste. The aim should be to eliminate them.

Two questions can be used to assess whether an activity adds value.
1. Would an external customer encourage the organisation to do more of the activity?
2. Would the organisation be more likely to achieve its goals by performing the activity?
If both answers are yes, the activity adds value.

ABM acts as an ‘umbrella’ for a number of techniques – such as customer profitability analysis (CPA). It uses the information generated by ABC to control or reduce cost drivers and also to reduce overheads.

ABM focuses on activities within a process, decision making and planning relative to those activities and the need for continuous improvement of all organisational activity. Management and staff must determine which activities are critical to success and decide how these are to be clearly defined across all functions.

Everyone must co-operate in defining:
- cost pools;
- cost drivers;
- key performance indicators.
Outputs from the ABM information system

Organisations that are designing and implementing ABM will find there are five basic information outputs:
1. The cost of activities and business processes – the basic output of the ABM system must be to provide relevant cost information about what a business does. Instead of reporting what money is spent for and by whom, costs are assigned to activities.
2. The cost of non-value-added activities – Identification of these wasteful activities is invaluable to management as it provides a crucial focal point for management.
3. Activity based performance measures – Knowing the total cost of an activity is insufficient to measure activity performance. Activity measures of quality, cycle time, productivity and customer service may also be required to judge performance. Measuring the performance of activities provides a scorecard to report how well improvement efforts are working and is an integral part of continuous improvement.
4. Accurate product/service cost – costs must be accurately determined.
5. Cost drivers – With this information it is possible to understand and manage these activity levels
ABM can be used in assessing strategic decisions such as:
1. whether to continue with a particular activity;
2. how cost structures measure up to those of competitors;
3. how changes in activities and components affect the suppliers and value chain.
ABM and employee empowerment take a critical step forward beyond ABC by recognising the contribution that people make as the key resource in any organisation’s success:
- It nurtures good communication and team work.
- It develops quality decision making.
- It leads to quality control and continuous improvement.
*ABM will not reduce costs; it will only help the manager understand costs better.

Implementing ABM
1. Get the support of senior management.
2. Know what ABM can achieve and what information you want from the system.
3. Involve people in the field.
4. Do not underestimate the need to manage the change process.
Distribution Channel Profitability

This looks at distribution channel profitability and why it is so important to manage these channels. It is linked to ABC and ABM. Distribution channel are in simple terms the means of transacting customers. Companies may transact with their customers through direct channel e.g. sales team, telephone, shops, internet or through indirect channels e.g. retailers, wholesalers, resellers and agents.

The channel a company selects is therefore a critical driver to business profitability. Regardless of whether a company’s channels are direct or indirect they should always consider the ultimate needs of the customer and therefore use the channel to ensure that those needs are satisfied.

Key aspects that the company need to consider in relation to their distribution channels include:
- access to the customer base
- brand awareness
- competitiveness, achieving sales and market targets
- speed of payment, customer retention rates and most importantly of all profitability
In companies it is just as important to cost channels as it is to cost products and customers. Different channels will differ in profitability.

Approaches to determining distribution channel profitability

Traditional approach

Product costs are allocated to distribution channels based on standard costs and the product mix sold through the channel, whereas, Sales, general and administrative costs are typically allocated to distribution channels on the basis of sales volume or net revenue for each channel.

*The approach also obviously has all the disadvantages associated with the traditional approach to product costing.

The ABC approach

Material costs and activity costs are allocated direct to products to produce product-related costs, which are then allocated to distribution channels on the basis of the mix of products sold in each channel.

This approach, which carries with it all the advantages of ABC, should result in more accurate information.

The main disadvantage to this approach is that the allocation is based on the assumption that all costs are driven by the production of particular products and hence must be allocated to products. For most organisations, however, the products they produce is just one of a range of cost drivers.

A refined ABC approach

This approach is based on the assumption that costs are driven not only by products produced, but by the customers served and the channels through which the products are offered.

*In conclusion, Distribution Channel Profitability used to determine the relative profitability of different distribution channels.

Activity based profitability analysis

Activity based profitability analysis can be linked to ABC techniques. By comparing the costs of products, customers and distribution channels with revenues, a tier of contribution levels can be established by applying the concept of the activity-based cost hierarchy.

The activity based analysis therefore assigns the costs to the appropriate level in the hierarchy (depending on whether a cost is incurred in relation to an activity that supports a product, product line/customer/distribution channel) and then aggregates the costs down the hierarchy to determine contribution margins by product, product line, customer and distribution channel.

Direct Product Profitability (DPP)

As traditional absorption costing, which normally uses labour hours as a basis for absorption, is rarely suitable for service and retail organisations other methods had to be devised. One relatively new way of spreading overheads in retail organisations, which is used in the grocery trade in particular, is direct product profitability (DPP).

Directly-attributable costs are grouped and are deducted from the gross margin to determine the product’s Direct product profit (DPP).

The benefits of DPP may be summarised as:
1. Better cost analysis;
2. Better pricing decisions;
3. Better management of store and warehouse space;
4. The rationalisation of product ranges;
5. Better merchandising decisions.
Pareto Analysis

Pareto analysis simply aims to identify the most significant areas within one aspect of the business, thus allowing management to focus on and control these most important areas.

The 80/20 rule as it is known is often illustrated by drawing a component percentage bar chart. The 80/20 rule states that for example, the majority of a firm’s profit or revenue may be generated by a small percentage of total number of customers/product lines/divisions.

Procedure
1. The first step is to rearrange the products in descending order of contribution
2. Calculate the cumulative contribution.
3. Turn this into a cumulative percentage.
4. Draw a diagram to illustrate the principle
The term ‘Pareto diagram’ usually refers to a histogram or frequency chart on product quality.

The position of the products with most contributions needs protecting, perhaps through careful attention to branding and promotion. The other products require investigation to see whether their contribution can be improved through increased prices, reduced costs or increased volumes.

Customer Profitability Analysis (CPA)

Customers use some activities but not all, and different groups of customers have different activity profiles. Different customers or groups of customers differ in their profitability. This is a relatively new technique that ABC makes possible because it creates cost pools for activities.

Service organisations such as a bank or a hotel in particular need to cost customers. A bank’s activities for a customer will include the following types of activities:
- Withdrawal of cash;
- Unauthorised overdraft;
- Request for a statement;
- Stopping a cheque;
- Returning a cheque because of insufficient funds.
Different customers or categories of customers will each use different amounts of these activities and so customer profitability profiles can be built up, and customers can be charged according to the cost to serve them.

Example

Cruise Ltd sells a single product, the TopG. The selling price to its four main customers is different because of trade discounts offered.

The data below concerns individual customer requirements:

Solution
February 12, 2022
Learning curve | Life cycle costing
Learning curve

The learning curve is ‘The mathematical expression of the commonly observed effect that, as complex and labour-intensive procedures are repeated, unit labour times tend to decrease. These learning curve notes are prepared by mindmaplab team and covering the learning curve meaning, factors affecting learning curve, learning rate curve with examples. These learning curve in management accounting notes also covers skill curve and learning curve questions with answers and solutions. These summary notes also covers the life cycle costing process, calculating life cycle cost, life cycle costing questions and answers pdf. We have also prepared the learning curve pdf version download.

The learning curve

The learning curve theory

The learning curve is ‘The mathematical expression of the commonly observed effect that, as complex and labour-intensive procedures are repeated, unit labour times tend to decrease. The learning curve models mathematically this reduction in unit production time.’

The learning curve theory states that the cumulative average time per unit produced is assumed to decrease by a constant (fixed) percentage every time total output of the product doubles.

The doubling of output is an important feature of the learning curve measurement.

The learning curve improves performance, which in turn reduces the time taken per unit and increases the productivity.

The effect that learning casts on employees, can be represented by a line called a learning curve. It displays the relationship between the production time per unit and the cumulative number of units produced. Learning curve has a direct impact on direct labor wages.

Eventually when the worker has had enough experience and nothing more is left for him to learn, then the learning process stops i.e. the learning would stop after a certain time limit and beyond specific number of units produced.

Improvements in the learning effect will not continue indefinitely. There will come a time when no further improvements can be made (known as a steady state).

For Example:

If the first unit of output requires 100 hours and a 70% learning effect occurs, then determine the production times for:
- Total production
- Incremental total hours
- Incremental hours per unit
Formula for the learning curve

The formula for the learning curve is

Y_x = aX^b

Where

Y = cumulative average time per unit to produce X units

a = the time required to produce the first unit of output

X = the cumulative number of units

b = the learning coefficient or the index of learning/learning index

By calculating the value of b, using logarithms or a calculator, expected labour times can be calculated for certain work.

Example:

Find the value of b when a 90% learning curve effect takes place.

b = log 0.9/log 2

= -0.0458/0.3010

= -0.152

Derivation of the learning rate

The approach to derive the learning rate very much depends on the information given in the question. If you are provided with details about cumulative production levels of 1, 2, 4, 8 or 16 (etc) units, the following approach should be used:

Example:

BL is planning to produce product A. Development tests suggest that 60% of the variable manufacturing cost of product A will be affected by a learning and experience curve. This learning effect will apply to each unit produced and continue at a constant rate of learning until cumulative production reaches 4,000 units, when learning will stop. The unit variable manufacturing cost of the first unit is estimated to be $1,200 (of which 60% will be subject to the effect of learning), while the average unit variable manufacturing cost of four units will be $405.

Calculation of the percentage learning effect

If other than details about cumulative production levels of 1, 2, 4, 8 or 16 (etc.) units given, use the following approach, which involves the use of logarithms.

Example:

XX is aware that there is a learning effect for the production of one of its new products, but is unsure about the degree of learning. The following data relate to this product.

Time taken to produce the first unit                                         28 direct labour hours

Production to date                                                                          15 units

Cumulative time taken to date                                                   104 direct labour hours

Calculation of percentage learning effect using logs

What costs are affected by the learning curve?
1. Direct labour time and costs
2. Variable overhead costs, if they vary with direct labour hours worked
3. Materials costs are usually unaffected by learning among the workforce, although it is conceivable that materials handling might improve, and so wastage costs be reduced.
4. Fixed overhead expenditure should be unaffected by the learning curve (although in an organisation that uses absorption costing, if fewer hours are worked in producing a unit of output, and the factory operates at full capacity, the fixed overheads recovered or absorbed per unit in the cost of the output will decline as more and more units are made).
Experience curves

The learning curve effect can be applied more broadly than just to labour. There are also efficiency gains in other areas;
1. As methods are standardised material wastage and spoilage will decrease
2. Machine costs may decrease as better use is made of the equipment
3. Process redesign may take place. As understanding of the process increases, improvements and short-cuts may be developed.
4. Learning curve labour efficiency will have a knock-on effect on the fixed cost per unit.
Comprehensive Examples

Life cycle costing

Life cycle costing is another technique used in cost planning.

Product life cycle costs are incurred from the design stage through development to market launch, production and sales, and their eventual withdrawal from the market.

Component elements of a product’s cost over its life cycle:
1. Research & development (R&D) costs – design, testing, production process and equipment
2. Technical data cost – cost of purchasing any technical data required
3. Training costs – including initial operator training and skills updating
4. Production costs
5. Distribution costs – transportation and handling costs
6. Marketing costs – customer service, field maintenance, brand promotion
7. Inventory costs – holding spare parts, warehousing and so on
8. Retirement and disposal costs – costs occurring at the end of the product’s life
Life cycle costs can apply to:
- Services;
- physical products
- customers
- projects
Life cycle costing, on the other hand, tracks and accumulates actual costs and revenues attributable to each product over the entire product life cycle.

Life cycle cost of Product A = Total costs of Product A over its entire lifecycle

Total number of units of A

Then, the total profitability of any given product can be determined.

The application of life cycle costing requires the establishment of a life cycle cost budget for a given product which in turn necessitates identification of costs with particular products. Actual costs incurred in respect of the product are then monitored against life cycle budget costs.

The product life cycle

It is important to know where a product is in its life cycle as this will affect expectations regarding sales volume and types of costs incurred. The stages include:
1. Development
2. Introduction
3. Growth
4. Maturity
5. Decline
Where the product is in its life cycle will also affect the returns that are expected.

If a product is in the introductory or growth stages, it cannot be expected to be a net generator of cash, as all the cash it generates will be used in expansion through increased sales and so on. As the product moves from maturity towards decline, it is of prime importance that the product still generates a profit and cash and that its return on capital is acceptable.

Maximising the return over the product life cycle

There are a number of factors that need to be managed in order to maximise a product’s return over its lifecycle:
- Careful design of the product and manufacturing and other processes will keep cost to a minimum over the life cycle.
- If an organisation is launching a new product, it is vital to get it to the market place as soon as possible. This will give the product as long a period as possible without a rival in the market place and should mean increased market share in the long run.
- A short breakeven time (BET) is very important in keeping an organisation liquid. The sooner the product is launched, the quicker the R&D costs will be repaid.
- Product life cycles are not predetermined; they are set by the actions of management and competitors. Generally, the longer the life cycle, the greater the profit that will be generated, assuming that production ceases once the product goes into decline and becomes unprofitable. One way to maximise the life cycle is to get the product to market as quickly as possible because this should maximise the time in which the product generates a profit. Only on knowing the lifecycle costs of a product can a business decide appropriately on its price.
Service and project life cycles

A service organisation will have services that have life cycles. For example, a company leasing heavy machinery to clients could use LCC to predict the total costs, resources, utilisation and productivity for an asset over its entire life cycle: thus, LCC is an excellent tool for assessing alternatives, which has made it very common in the procurement of large assets.

Products that take years to produce or come to fruition are usually called projects, and discounted cash flow calculations are invariably used to cost them over their life cycle in advance. The projects need to be monitored very carefully over their life to make sure that they remain on schedule and that cost overruns are not being incurred.

Customer life cycles

Not all investment decisions involve large initial capital outflows or the purchase of physical assets. The decision to serve and retain customers can also be a capital budgeting decision even though the initial outlay may be small. Customers also have life cycles, and an organisation will wish to maximise the return from a customer over their life cycle. The aim is to extend the life cycle of a particular customer.

Target costing

Definition: Target costing is an activity which is aimed at reducing the life-cycle costs of new products, while ensuring quality, reliability, and other consumer requirements, by examining all possible ideas for cost reduction at the product planning, research and development, and the prototyping phases of production.

Target costing works in the opposite way to normal methods of pricing, by setting a selling price and then working backwards to find the target cost.

The planning, design and development stages of a product’s cycle are therefore critical to an organisation’s cost management process.

*The traditional approach is to develop a product, determine the expected standard production cost of that product and then set a selling price.

* The target costing approach is to develop a product concept and the primary specifications for performance and design and then to determine the price customers would be willing to pay for that concept. The desired profit margin is deducted from the price, leaving a figure that represents total cost. This is the target cost and the product must be capable of being produced for this amount, otherwise the product will not be manufactured.

Target Cost

Target Cost is a pro-active cost control system. The target cost is calculated by deducting the target profit from a predetermined selling price based on customers’ views. (Target cost = Selling price – Target profit margin)

Cost Gap

A cost gap is to be calculated by comparing current cost (estimated cost) and the target cost. This cost gap is to be close/reduced over time by applying effective cost reduction techniques, improving technologies and processes such as value engineering, Functional analysis, value analysis, which looks at every aspect of the value chain business function.

Target cost gap = Estimated product cost – Target cost

Questions that a manufacturer may ask in order to close the gap include:
1. Can any materials be eliminated, e.g. cut down on packing materials?
2. Can a cheaper material be substituted without affecting quality?
3. Can labour savings be made without compromising quality, for example, by using lower skilled workers?
4. Can productivity be improved, for example, by improving motivation?
5. Can production volume be increased to achieve economies of scale?
6. Could cost savings be made by reviewing the supply chain?
7. Can part-assembled components be bought in to save on assembly time?
8. Can the incidence of the cost drivers be reduced?
9. Is there some degree of overlap between the product-related fixed costs that could be eliminated by combining service departments or resources?
A key aspect of this is to understand which features of the product are essential to customer perceived quality and which are not. This process is known as ‘value analysis’. Attention should be focused more on reducing the costs of features perceived by the customer not to add value.

*Closing the cost gap by increasing the selling price is not a viable option as the price is determined by market forces rather than the company.

Target costing in service organisations

Target costing is as relevant to the service sector as the manufacturing sector. Key issues are similar in both: the needs of the market need to be identified and understood as well as its customers and users; and financial performance at a given cost or price (which does not exceed the target cost when resources are limited) needs to be ensured.

Problems with target costing in service industries

Unlike manufacturing, service industries have the following characteristics which could make target costing more difficult:
1. The intangibility of what is provided means that it is difficult to define the ‘service’ and attribute costs.
2. Heterogeneity – The quality and consistency varies, because of an absence of standards or benchmarks to assess services against.
3. Perishability – the unused service capacity from one time period cannot be stored for future use. Service providers and marketers cannot handle supply-demand problems through production scheduling and inventory techniques.
4. No transfer of ownership – Services do not result in the transfer of property. The purchase of a service only confers on the customer access to or a right to use a facility.
Value analysis

Value analysis is ‘A systematic inter-disciplinary examination of factors affecting the cost of a product or service, in order to devise means of achieving the specified purpose most economically at the required standard of quality and reliability’.

It looks at trying to reduce costs without reducing the value to the customer. The value of the product must therefore be kept the same or else improved, at a reduced cost.

Value Engineering – is ‘Redesign of an activity, product or service so that value to the customer is enhanced while costs are reduced (or at least increase by less than the resulting price increase)’.

*Value engineering is cost avoidance or cost prevention before production, whereas value analysis is cost reduction during production.

There are two features of value analysis that distinguish it from other approaches to cost reduction.
1. It encourages innovation and a more radical outlook for ways of reducing costs because ideas for cost reduction are not constrained by the existing product design.
2. It recognises the various types of value which a product or service provides, analyses this value, and then seeks ways of improving or maintaining aspects of this value, but at a lower cost.
Any commercial organisation should be continually seeking lower costs, better products and higher profits. These can be achieved in any of the following ways:
1. Cost elimination or cost prevention
2. Cost reduction
3. Improving product quality and so selling greater quantities at the same price as before
4. Improving product quality and so being able to increase the sales price Value analysis can achieve all four of these objectives.
Four aspects of value should be considered in value analysis are:
1. cost value
2. exchange value
3. use value
4. esteem value
Functional analysis

Functional analysis is ‘An analysis of the relationships between product functions, their perceived value to the customer and their cost of provision’.

Functional analysis is a cost management technique which has similarities with value analysis.

Advantages
1. Competitive advantage resulting from improved, cost-effective design or redesign of products.
2. Information about product functions and about the views of customers is integrated into the formal reporting system.
3. Probably of most benefit during the planning and design stages of new products.
Comparison of value and functional analysis

Value analysis focuses on cost reduction through a review of the processes required to produce a product or service. Functional analysis focuses on the value to the customer of each function of the product or service and then makes a decision as to whether cost reduction is necessary.
February 12, 2022
Transfer pricing
Transfer Pricing

A transfer price is the ‘Price at which goods or services are transferred between different units of the same company’. These transfer pricing notes are prepared by mindmaplab team and covering introduction to transfer pricing, transfer costs, international transfer pricing, market-based transfer pricing, cost-based transfer pricing, the minimum transfer pricing and methods of transfer pricing management. transfer pricing short note are also available in pdf version too download.

The basic principles of transfer pricing

A transfer price is the ‘Price at which goods or services are transferred between different units of the same company’.

When a company has a divisionalised structure, some of the divisions might supply goods or services to other divisions in the same company.
- One division sells the goods or services. This will be referred to as the ‘selling division’.
- Another division buys the goods or services. This will be referred to as the ‘buying division’.
For accounting purposes, these internal transfers of goods or services are given a value. Transfers could be recorded at cost. However, when the selling division is a profit centre or investment centre, it will expect to make some profit on the sale.

Therefore, there will be two sources of revenue.
1. External sales revenue from sales made to other organisations
2. Internal sales revenue from sales made to other responsibility centres within the same organisation, valued at the transfer price
Internal sales are referred to as transfers, so the internal selling and buying price is the transfer price. A decision has to be made about what the transfer price should be. A transfer price may be:
- the cost of the item (to the selling division), or
- a price that is higher than the cost to the selling division, which may be cost plus a profit margin or related to the external market price of the item transferred.
Transfer prices should be set at a level which ensures that profits for the organisation as a whole are maximised.

Main uses/objectives of transfer prices

Goal congruence

The decisions made by each profit centre manager should be consistent with the objectives of the organisation as a whole, i.e. the transfer price should assist in maximising overall company profits.

Performance measurement

The buying and selling divisions will be treated as profit centres. The transfer price should allow the performance of each division to be assessed fairly. Divisional managers will be demotivated if this is not achieved.

Autonomy

Transfer prices are particularly appropriate for profit centres because if one profit centre does work for another, the size of the transfer price will affect the costs of one profit centre and the revenues of another. The system used to set transfer prices should seek to maintain the autonomy of profit centre managers. If autonomy is maintained, managers tend to be more highly motivated but sub-optimal decisions may be made.

Recording the movement of goods and services

In practice, an extremely important function of the transfer pricing system is simply to assist in recording the movement of goods and services.

The ideal solution

Ideally a transfer price should be set at a level that overcomes these problems:
1. The transfer price should provide an ‘artificial’ selling price that enables the transferring division to earn a return for its efforts, and the receiving division to incur a cost for benefits received.
2. The transfer price should be set at a level that enables profit centre performance to be measured ‘commercially’. This means that the transfer price should be a fair commercial price.
3. The transfer price, if possible, should encourage profit centre managers to agree on the amount of goods and services to be transferred, which will also be at a level that is consistent with the aims of the organisation as a whole, such as maximising company profits.
General rules

The general rules highlight the boundaries within which transfer prices should fall to make them acceptable to both the supplying and receiving divisions. The limits within which transfer prices should fall are as follows:
- The Minimum Price:
The sum of the supplying division’s marginal cost and opportunity cost of the item transferred.

The minimum results from the fact that the supplying division will not agree to transfer if the transfer price is less than the marginal cost + opportunity cost of the item transferred (because if it were, the division would incur a loss).
- The Maximum Price:
The lowest market price at which the receiving division could purchase the goods or services externally, less any internal cost savings in packaging and delivery.

The maximum results from the fact that the receiving division will buy the item at the cheapest price possible.

Opportunity cost

The opportunity cost included in determining the lower limit will be one of the following:
1. The maximum contribution forgone by the supplying division in transferring internally rather than selling goods externally.
2. The contribution forgone by not using the same facilities in the producing division for their next best alternative use.
If there is no external market for the item being transferred, and no alternative uses for the division’s facilities, the transfer price = standard variable cost of production.

If there is an external market for the item being transferred and no alternative, more profitable use for the facilities in that division, the transfer price = the market price.

Setting the transfer price

In broad terms, there are three bases for setting a transfer price:
1. Market based prices
2. Cost based prices
3. Negotiated prices
I. The use of Market Price as a basis for transfer prices

It is more realistic to set the transfer price at or close to a market price for the item transferred, but this is only possible if an external market exists for the item. If an external market exists for the product being transferred (and there is unsatisfied demand externally), the ideal transfer price will be the market price.

*If variable costs and market prices are constant, regardless of the volume of output, a market-based transfer price is the ideal transfer price.

*If a perfect external market exists, market price is the ideal transfer price.

The external market is also sometimes known as the intermediate market.

Adjusted market price

Internal transfers are often cheaper than external sales, with savings in selling and administration costs, bad debt risks and possibly transport/delivery costs. It would therefore seem reasonable for the buying division to expect a discount on the external market price.

Advantages of this method:
1. The transfer price should be deemed to be fair by the managers of the buying and selling divisions. The selling division will receive the same amount for any internal or external sales. The buying division will pay the same for goods if they buy them internally or externally.
2. The company’s performance will not be impacted negatively by the transfer price because the transfer price is the same as the external market price.
Disadvantages of this method:
1. There may not be an external market price.
2. The external market price may not be stable. For example, discounts may be offered to certain customers or for bulk orders.
3. Savings may be made from transferring the goods internally. For example, delivery costs will be saved. These savings should ideally be deducted from the external market price before a transfer price is set, giving an “adjusted market price”.
II. Transfer prices based on Full cost

A cost-based transfer price could be:
- the marginal cost to the selling division of making the product or providing the service
- the selling division’s marginal cost plus a mark-up for profit
- the full cost to the selling division of making the product, or
- the selling division’s full cost plus a markup for profit.
Under this approach, unsurprisingly, the full cost (including fixed production overheads absorbed) that has been incurred by the supplying division in making the intermediate product is charged to the receiving division. If a full cost-plus approach is used, a profit margin is also included in this transfer price.

The transfer price fails on all three criteria (divisional autonomy, performance measurement and corporate profit measurement) for judgement.

Transfer prices based on Variable or marginal cost

A variable or marginal cost approach entails charging the variable cost that has been incurred by the supplying division to the receiving division.

Dual pricing

One of the problems with a variable cost approach to transfer pricing is that the selling division will not cover its fixed costs. Dual pricing, results in different prices being used by the selling and buying divisions.

The selling division will use a price that will allow it to report a reasonable profit (usually the external market price if there is one). The buying division will be charged with the variable cost.

The difference between the two prices will be debited to a group account which will then be cancelled out when divisional results are consolidated to arrive at the group profit.

If transfer prices are set at variable cost with an imperfect external market, the supplying division does not cover its fixed costs. Dual pricing or a two-part tariff system can be used in an attempt to overcome this problem.

Two-part tariff system

A two-part tariff system can be used to ensure that the selling division’s fixed costs are covered. Transfer prices are set at variable cost and once a year there is a transfer of a fixed fee as a lump sum payment to the supplying division, representing an allowance for its fixed costs.

This method risks sending the message to the supplying division that it need not control its fixed costs, however, because the company will subsidise any inefficiencies.

III. Negotiating a transfer price

Negotiation might be a method of identifying the ideal transfer price in situations where an external intermediate market does not exist. A negotiated transfer price is a price that is negotiated between the managers of the profit centres.

A transfer price based on opportunity cost is often difficult to identify, for lack of suitable information about costs and revenues in individual divisions.

In this case it is likely that transfer prices will be set by means of negotiation. If divisional managers are allowed to negotiate transfer prices with each other, the agreed price may be finalised from a mixture of accounting arithmetic, negotiation and compromise.
1. A negotiated price might be based on market value, but with some reductions to allow for the internal nature of the transaction, which saves external selling and distribution costs.
2. Where one division receives near-finished goods from another, a negotiated price might be based on the market value of the end product, minus an amount for the finishing work in the receiving division.
Disadvantages of negotiation are as follows:
1. The divisional managers might be unable to reach agreement. When this happens, management from head office will have to act as judge or arbitrator in the case.
2. The transfer prices that are negotiated might not be fair, but a reflection of the bargaining strength or bargaining skills of each divisional manager.
Transfer pricing when there is no external market for the transferred item

There may be instances when there is no external market for the item being transferred. The question arises as how to set an appropriate transfer price in such circumstances.

When there is no external market for the item being transferred, the transfer price should be greater than or equal to the variable cost in the supplying division, but less than or equal to the selling price minus variable costs (net marginal revenue) in the receiving division.

If there is no similar item sold on an external market, and if the transferred item is a major product of the transferring division, there is a strong argument that profit centre accounting is a waste of time. It would be more appropriate, perhaps, to treat the transferring division as a cost centre, and to judge performance on the basis of cost variances.

If profit centres are established, in the absence of a market price, the optimum transfer price is likely to be one based on standard cost plus, but only provided that the variable cost per unit and selling price per unit are unchanged at all levels of output. A standard cost plus price would motivate divisional managers to increase output and to reduce expenditure levels.

Transfer pricing and changing costs/prices

No external market for the transferred item

When there is no external market for the transferred item and changing costs/prices for the final output, the transfer price should be greater than or equal to the marginal cost in the supplying division, but less than or equal to the net marginal revenue in the receiving division.

If cost behaviour patterns change and the selling price to the external market (for the receiving division’s product) is reduced at higher levels of output, there will be a profit-maximising level of output: to produce more than an ‘optimum’ amount would cause reductions in profitability.

Under such circumstances, the ideal transfer price is one which would motivate profit centre managers to produce at the optimum level of output, and neither below nor above this level.

With an external market for the transferred item

Where there is an imperfect external market for the transferred item and changing costs/prices for the final output, the transfer price should again fall between marginal cost in the supplying division and net marginal revenue in the receiving division.

The approach is essentially the same as ‘No external market for the transferred item’, except that the supplying division may also have income, and so its marginal revenue needs to be taken into account.

Maximising profits when the transferred item is in short supply

Where there is a capacity constraint resulting in short supplies of the product, a transfer price based on matching marginal cost and marginal revenue will not encourage corporate profit maximisation.

Profit maximisation with a perfect external market

When there is a perfect external market for the transferred item and changing costs/prices for the final output, profits are maximised when market price is used on the transfer price.

Identifying the optimal transfer price

How to determine ideal transfer price?

There are various rules involved in the determination of the optimal transfer price:
1. The ideal transfer price should reflect the opportunity cost of sale to the supply division and the opportunity cost to the buying division.
2. Where a perfect external market price exists and unit variable costs and unit selling prices are constant, the opportunity cost of transfer will be external market price or external market price less savings in selling costs.
3. In the absence of a perfect external market price for the transferred item, but when unit variable costs are constant, and the sales price per unit of the end product is constant, the ideal transfer price should reflect the opportunity cost of the resources consumed by the supply division to make and supply the item and so should be at standard variable cost + opportunity cost of making the transfer.
4. When unit variable costs and/or unit selling prices are not constant, there will be a profit- maximising level of output and the ideal transfer price will only be found by sensible negotiation and careful analysis.
There may be a range of prices within which both profit centres can agree on the output level that would maximise their individual profits and the profits of the company as a whole. Any price within the range would then be ‘ideal’.

International Transfer Pricing

Transfers within an international group will often be cross-border, between divisions in different countries. With international transfers and international transfer pricing, certain factors need to be considered.

Different tax rates

A multinational company will seek to minimise the group’s total tax liability. One way of doing this might be to use transfer pricing to:
- reduce the profitability of its subsidiaries in high-tax countries, and
- increase the profitability of its subsidiaries in low-tax countries.
Changes in the transfer price can redistribute the pre-tax profit between subsidiaries, but the total pre-tax profit will be the same. However, if more pre-tax profit is earned in low-tax countries and less profit is earned in high-tax countries, the total tax bill will be reduced.

Groups of corporations around the world park their profit in subsidiaries which operate in jurisdictions with low tax rates and park their losses jurisdictions with high tax rates in order to increase net benefits.

Governments around the world try to address this issue with special rules for pricing of cross border sales of goods.

It is also possible, that some countries wishing to attract business might have tax laws that are very favourable to business. A country with the status of a ‘tax haven’ might offer:
1. a low rate of tax on profits
2. a low withholding tax on dividends paid to foreign holding companies
3. tax treaties with other countries
4. no exchange controls
5. a stable economy
6. good communications with the rest of the world
7. a well-developed legal framework, within which company rights are protected.
Multinationals might set up subsidiary companies in tax havens, trade through these companies, and hope to reduce their total tax liabilities.

Transfer Pricing to manage cash flow

Some governments might place legal restrictions on dividend payments by companies to foreign parent companies.

In this situation, it would be tempting for a multinational to sell goods or services to a subsidiary in the country concerned from other divisions in other countries, and charge very high transfer prices as a means of getting cash out of the country.

International Transfer pricing and currency management

When inter-divisional transfers are between subsidiaries in different countries or currency zones, a decision has to be made about the currency to select for transfer pricing.

Exchange rates, even for strong currencies, can be very volatile and subsidiaries could make unexpected profits or losses from movements in an exchange rate.
February 12, 2022