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STRATHMORE UNIVERSITY
SCHOOL OF ACCOUNTANCY
PERFORMANCE MANAGEMENT (PM)
TOPICS: CVP ANALYSIS; RISK & UNCERTAINTY; PRICING DECISIONS
COST VOLUME PROFIT (CVP) ANALYSIS
SINGLE PRODUCT
Contribution per unit = Selling price per unit – Variable cost per unit Breakeven units = Fixed Costs ÷ Contribution per unit Breakeven revenue = Breakeven units x Selling price per unit Breakeven revenue = Fixed costs ÷ C/S ratio Contribution to sales ratio [C/S ratio] = Contribution per unit ÷ Sales per unit Contribution to sales ratio [C/S ratio] = Total Contribution ÷ Total Sales Revenue Margin of safety (in units) = Budgeted sales volume – Breakeven sales volume Margin of safety (as a %) = [Margin of safety units ÷ Budgeted sales volume] x 100 Sales volume required to achieve the target profit level = [Fixed costs + Required profit] ÷ Unit contribution Sales revenue required to achieve the target profit level = [Fixed costs + Required profit] ÷ C/S ratio Question 1 A company makes one product, the gamma. The selling price per unit is $100. The variable cost per unit is $20. Fixed costs per year are $1,000,000. The company expects to sell 20,000 units of the gamma per year. Calculate: (a) The C/S ratio. (b) The breakeven units and breakeven revenue. (c) The margin of safety in units and percentage. (d) The sales volume and sales revenue required to make a profit of $100,000. Question 2 A company manufactures a single product with the following cost structure based on a production budget of 10,000 units. $ $ Materials Labour Variable overheads Variable distribution
Fixed overheads Fixed selling and distribution Administration
Total variable cost 89 Selling price 129 Calculate: (a) Breakeven units and Breakeven revenue. (b) Target revenue for a net profit of $40,000. Question 3 H Co uses a marginal cost plus pricing system to determine the selling price for one of its products, Product X. Product X has the following costs: $ Direct materials Direct labour Variable overheads Fixed overheads
Fixed overheads are $20,000 for the year. Budgeted output and sales for the year are 500 units and this should be sufficient for Product X to breakeven. What profit mark-up would H Co need to add to the marginal cost to allow H Co to breakeven?
Question 4 The standard costs and revenues of Log Co’s only product are as follows: $ per unit Sales price 60 Direct materials Direct labour Variable production overhead Fixed production overhead
Profit 15 Fixed overheads are absorbed on budgeted production and sales of 10,000 units per year. Sales staff receive a sales commission of 5% of sales revenue. What is Log Co’s margin of safety (to the nearest whole %)? Question 5 A company has fixed costs of $1.3 million. Variable costs are 55% of sales up to a sales level of $1.5 million, but at higher volumes of production and sales, the variable cost for incremental production units falls to 52% of sales. What is the breakeven point in sales revenue, to the nearest $1,000? MULTIPLE PRODUCTS Sales revenue per mix (average selling price per unit) = Total sales revenue ÷ Total units Sales revenue per mix (average selling price per unit) = ∑ [Product sales mix x Selling price per unit] Contribution per mix (average contribution per unit) = Total contribution ÷ Total units Contribution per mix (average contribution per unit)= ∑ [Product sales mix x Contribution per unit] Breakeven units = Fixed Costs ÷ Contribution per mix Breakeven revenue =Break even units x Sales revenue per mix Breakeven revenue = Fixed costs ÷ Weighted average C/S ratio Weighted average contribution to sales (C/S) ratio = Contribution per mix ÷ Sales revenue per mix Weighted average contribution to sales (C/S) ratio = Total contribution ÷ Total sales revenue Margin of safety units = Budgeted sales in standard mix – Breakeven sales in standard mix Margin of safety (as a %) = [Margin of safety units ÷ Budgeted sales volume] x 100 Sales volume required to achieve the target profit level = [Fixed costs + Required profit] ÷ Contribution per mix Sales revenue required to achieve the target profit level = BEP (Units) x Sales revenue per mix Sales revenue required to achieve the target profit level = [Fixed costs + Required profit] ÷ Weighted average C/S ratio Question 6 Product A B Budgeted sales units 1,200 600 Unit contribution $300 $ Selling price $1,000 $ Budgeted fixed costs = $245, Calculate: (a) Weighted average C/S ratio. (b) Breakeven units and Breakeven revenue. (c) Breakeven units and Breakeven revenue for products A and B. (d) Margin of safety units and as a % (e) Target sales volume and Target sales revenue for Target profit of $45,000. Question 7 M N Budgeted sales units 300 600
Required: a) What is the budgeted breakeven point in units for Period 1? b) How many units need to be produced and sold to achieve a profit of $6,600 for Period 2 [to the nearest whole unit]? c) What is the breakeven sales revenue for Period 4 to the nearest $’000? d) Based on the Period 5 PV chart, are the following statements true or false? (1) Point X is the breakeven point. TRUE FALSE (2) Product D is the most profitable product in terms of C/S ratio. TRUE FALSE (3) Point Y is the fixed cost amount. TRUE FALSE e) What does the solid line of the Period 5 PV chart indicate? A The cumulative sales as each product’s sales are in turn added to the sales mix. B The cumulative profit/loss as each product’s contribution are in turn added to the sales mix. C The average variable costs which will be incurred in the production and sale of the three products in this mix. D The average profit which will be earned from the sales of the three products in this mix. RISK AND UNCERTAINTY Question 1 A medium-sized company manufactures product ‘Ndovu’. The current variable production cost per unit of product ‘Ndovu’ is $8 while the selling price is $11.50 per unit. However, the demand for product ‘Ndovu’ is uncertain and has the following probability distribution: Number of units of product ‘Ndovu’ demanded Probability 10 0. 20 0. 30 0. a) Prepare the payoff table. b) Advise the company on the optimal number of units of product ‘Ndovu’ to produce using: (i) Maximin (ii) Maximax (iii) Minimax regret (iv) Expected values c) Calculate the value of perfect information about demand. Question 2 A baker must decide whether to bake brown bread or white bread for a new market. Demand at the market can either be small or large with probability estimated to be 0.3 and 0.7 for brown bread and white bread respectively. Additional information:
1. If brown bread is baked and demand proves to be high, the baker may choose not to expand (payoff = $35,000) or to expand (payoff = $42,000). 2. If brown bread is baked and demand is low, there is no reason to expand and the payoff is $31,000. 3. If white bread is baked and demand proves to be low, the choice is to do nothing ($9,000) or to stimulate demand through local advertising. The response to advertising may be either modest or sizeable, with their probabilities estimated to be 0.4 and 0.6 respectively. If it is modest, the payoff is estimated to be $5,000; the payoff grows to $34,000 if the response is sizeable. 4. If white bread is baked and the demand turns out to be high, the payoff is $140,000. Required: (i) A decision tree showing the payoff and expected monetary value of each alternative decision. (ii) Advise the management of the bakery on the best product to introduce into the market.
Question 3 A decision tree is a way of representing decision choices in the form of a diagram. It is usual for decision trees to include probabilities of different outcomes. The following statements have been made about decision trees. (1) Each possible outcome from a decision is given an expected value. (2) Each possible outcome is shown as a branch on a decision tree. Which of the above statements is/are true? A 1 only B 2 only C Neither 1 nor 2 D Both 1 and 2 Question 4 Analysing the range of different possible outcomes from a particular situation, with a computer model that uses random numbers, is known as which of the following? A Probability analysis B Sensitivity analysis C Simulation modelling D Stress testing Question 5 A company wishes to go ahead with one of three mutually exclusive projects, but the profit outcome from each project will depend on the strength of sales demand, as follows. Strong demand profit, $ Moderate demand profit, $ Weak demand profit, $ Project 1 70,000 10,000 (7,000) Project 2 25,000 12,000 5, Project 3 50,000 20,000 (6,000) Probability of demand
What is the value to the company of obtaining this perfect market research information, ignoring the cost of obtaining the information? A $3, B $5, C $6, D $7, PRICING DECISIONS Question 1 Suppose a rise in the price of peaches from $5.50 to $6.50 per bushel decreases the quantity demanded from 12,500 to 11,500 bushels. What is the price elasticity of demand? A 0. B 1000. C 2. D 1. Question 2 New Possum (NP) is a profit seeking company that operates in one country. NP was founded 20 years ago and NP has now established itself as a small but profitable player in its chosen market. The emphasis of the company has always been on product innovation backed up by a small but dynamic sales team. One of the products that NP sells is product X. Last quarter the company sold each X for $15 and sold 50, units. This quarter the company raised the price to $20 and 45,000 units were sold.
Number of batches imported and sold Average cost per unit including import taxes, $ Total fixed costs per month, $ Expected selling price per unit, $ 1 10·00 10,000 20 2 8·80 10,000 18 3 7·80 12,000 16 4 6·40 12,000 13 5 6·40 14,000 12 Required: (a) Calculate how many batches Jewel Co should import and sell. (6 marks) (b) Explain why Jewel Co could not use the algebraic method to establish the optimum price for its product. (4 marks) The algebraic model requires several assumptions to be true. First, there must be a consistent relationship between price (P) and demand (Q), so that a demand equation can be established, usually in the form P = a – bQ. Here, although there is a clear relationship between the two, it is not a perfectly linear relationship and so more complicated techniques are required to calculate the demand equation. It also cannot be assumed that a linear relationship will hold for all values of P and Q other than the five given. Similarly, there must be a clear relationship between demand and marginal cost, usually satisfied by constant variable cost per unit and constant fixed costs. The changing variable costs per unit again complicate the issue, but it is the changes in fixed costs which make the algebraic method less useful in Jewel’s case. The algebraic model is only suitable for companies operating in a monopoly and it is not clear here whether this is the case, but it seems unlikely, so any ‘optimum’ price might become irrelevant if Jewel’s competitors charge significantly lower prices. Other more general factors not considered by the algebraic model are political factors which might affect imports, social factors which may affect customer tastes and economic factors which may affect exchange rates or customer spending power. The reliability of the estimates themselves – for sales prices, variable costs and fixed costs – could also be called into question. Question 7 TR Co is a pharmaceutical company which researches, develops and manufactures a wide range of drugs. One of these drugs, ‘Parapain’, is a pain relief drug used for the treatment of headaches and until last month TR Co had a patent on Parapain which prevented other companies from manufacturing it. The patent has now expired and several competitors have already entered the market with similar versions of Parapain, which are made using the same active ingredients. TR Co is reviewing its pricing policy in light of the changing market. It has carried out some market research in an attempt to establish an optimum price for Parapain. The research has established that for every $2 decrease in price, demand would be expected to increase by 5,000 batches, with maximum demand for Parapain being one million batches. Each batch of Parapain is currently made using the following materials: Material Z: 500 grams at $0·10 per gram Material Y: 300 grams at $0·50 per gram Each batch of Parapain requires 20 minutes of machine time to make and the variable running costs for machine time are $6 per hour. The fixed production overhead cost is expected to be $2 per batch for the period, based on a budgeted production level of 250,000 batches. The skilled workers who have been working on Parapain until now are being moved onto the production of TR Co’s new and unique anti-malaria drug which cost millions of dollars to develop. TR Co has obtained a patent for this revolutionary drug and it is expected to save millions of lives. No other similar drug exists and, whilst demand levels are unknown, the launch of the drug is eagerly anticipated all over the world. Agency staff, who are completely new to the production of Parapain and cost $18 per hour, will be brought in to produce Parapain for the foreseeable future. Experience has shown there will be a significant learning curve involved in making Parapain as it is extremely difficult to handle. The first batch of Parapain made using one of the agency workers took 5 hours to make. However, it is believed that an 80% learning curve exists, in
relation to production of the drug, and this will continue until the first 1,000 batches have been completed. TR Co’s management has said that any pricing decisions about Parapain should be based on the time it takes to make the 1,000th batch of the drug. Note: The learning co-efficient, b = – 0 · Required: (a) Calculate the optimum (profit-maximising) selling price for Parapain and the resulting annual profit which TR Co will make from charging this price. Note: If P = a – bQ, then MR = a – 2 bQ (12 marks) (b) Discuss and recommend whether market penetration or market skimming would be the most suitable pricing strategy for TR Co when launching the new anti-malaria drug. (8 marks) Market penetration pricing With penetration pricing, a low price would initially be charged for the anti-malaria drug. The ideology behind this is that the price will make the product accessible to a larger number of buyers and therefore the high sales will compensate for the lower prices being charged. The anti-malaria drug would rapidly become accepted as the only drug worth buying, i.e. it would gain rapid acceptance in the marketplace. The circumstances which would favour a penetration pricing policy are:
- Highly elastic demand for the anti-malaria drug, i.e. the lower the price, the higher the demand. There is no evidence that this is the case.
- If significant economies of scale could be achieved by TR Co so that higher sales volumes would result in sizeable reductions in costs. It cannot be determined if this is the case here.
- If TR Co was actively trying to discourage new entrants into the market, however in this case, new entrants cannot enter the market anyway due to the patent.
- If TR Co wished to shorten the initial period of the drug’s life-cycle so as to enter the growth and maturity stages quickly but there is no evidence the company wish to do this. Market skimming pricing With market skimming, high charges would initially be charged for the anti-malaria drug rather than low prices. This would enable TR Co to take advantage of the unique nature of the product. The most suitable conditions for this strategy are:
- The product has a short life cycle and high development costs which need to be recovered. There is no information about the drug’s life cycle but development costs have been high.
- Since high prices attract competitors, there needs to be barriers to entry if competitors are to be deterred. In TR Co’s case it has a patent for the drug and also the high development costs could act as a barrier.
- Where high prices in the early stages of a product’s life cycle are expected to generate high initial cash flows, this will help TR Co recover the high development costs it has incurred. Recommendation Given the unique nature of the drug and the barriers to entry, a market skimming pricing strategy would appear to be the far more suitable pricing strategy. Also, whilst there is demand curve data, it is unknown how reliable this data is, in which case a skimming strategy may be the safer option.
