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BEA2010 Managerial Accounting

BEA2010 Managerial Accounting. Lecture 2: Short-run decision making – Cost Volume Profit Analysis. Use of C-V P Analysis in short-run decision-making. Setting prices Whether to make-in or buy from outside a product or component Retain existing equipment or replace decisions

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BEA2010 Managerial Accounting

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  1. BEA2010 Managerial Accounting Lecture 2: Short-run decision making – Cost Volume Profit Analysis

  2. Use of C-V P Analysis in short-run decision-making Setting prices Whether to make-in or buy from outside a product or component Retain existing equipment or replace decisions Advisability of a marketing campaign What will happen to our profitability if we expand capacity? What is the appropriate sales mix that will maximize the contribution margin per unit of the scarce resource?

  3. Economists’ versus Accountants’

  4. Cost Volume Profit Assumptions Relevant range • Price does not vary with quantity • Variable cost per unit does not vary with quantity • Fixed costs, variable costs and selling price/s are known with certainty For simplicity • The analysis is limited to a single product or a constant sales mix in the multiple product situation • All output is sold • Tax rates are constant for profits or losses • Does not consider risk • Does not consider the time value of money as it is applied to short run decisions

  5. Dealing with Semi-variable Costs Total semi-variable costs = Fixed cost + Total variable cost - [FC + (VC x Q) where Q is output as we assume a linear relationship Y = a + bx There are two methods for separating mixed costs into fixed and variable components: • High-Low Method • Method of Least Squares

  6. The High-Low Method A method of determining the equation of a straight line by pre-selecting two points (the high and low points) and using them to compute the intercept and slope parameters. The High Point is defined as the point with the highest output activity level. The Low Point is defined as the point with the lowest output or activity level. The equations for determining the variable costs and fixed costs are: • Variable cost = Change in Cost/Change in Output = (High Cost – Low Cost)/(High Output – Low Output) • Fixed Cost =Total Cost for High Point – (Variable Rate x High Output); or Fixed Cost =Total Cost for Low Point – (Variable Rate x Low Output)

  7. Example – processing student applications for University degree courses

  8. EXAMPLE 1 High-Low method Variable Rate =Change in Cost/Change in Output = (High Cost – Low Cost))/(High Output – Low Output)) Variable cost per unit = (78,000-50,000)/(24,000-10,000)= £2 per unit Fixed Cost =Total Cost for High Point – ((Variable Rate x High Output) or Fixed Cost =Total Cost for Low Point – ((Variable Rate x Low Output) Fixed cost =78,000 – (2 x 24,000) = £30,000 or Fixed cost = 50,000 – (2 x 10,000) = £30,000

  9. Algebraic approach You could do his algebraically by letting a = fixed cost and b – variable cost. We know that TC = a + (b x output) and therefore we have: • (1) 78,000 = a + (24,000 x b) and • (2) 50,000 = a + (10,000 x b) and by subtraction of (2) from (1) • 28,000 = 14,000 x b and so b (variable cost) equals £2.

  10. Limitations However the equation derived [Total cost =30,000 + (2 x No of applications)] does not work exactly. Look at 18,000 applications as it is only an approximation • Total cost = 30,000 + (2 x 18,000) = £66,000 hence more accurate methods are needed

  11. Break-even analysis - Graphical Method B-E CHART A Break-even chart is drawn as follows: • The sales revenue line would start at the origin and slope upward at a rate equal to the selling price per unit. • The total cost line would start at the amount of fixed costs, and slope upward at a rate equal to the variable cost per unit. • The break-even point is that volume where the revenue and cost lines intersect

  12. Break-even Point (BEP) Techniques Graphical Method

  13. Graphical Method – PROFIT VOLUME CHART A Profit volume chart is drawn as follows: • The fixed cost will be the maximum loss. • Calculate the profit/loss at a chosen output and plot the point. • Draw a line from the maximum loss and the profit/loss point that you calculate • The break-even point is that volume where the line intersects the x axis

  14. Profit volume graph

  15. Break-even Point (BEP) Techniques Contribution Margin Technique Contribution per unit equals selling price per unit (P) minus variable cost per unit (VC): • C = (P – VC). Total cost at a given volume (Q) is fixed cost (FC) plus variable cost (VC): • TC = FC + (VC) x Q And total revenue (TR) at a given volume is selling price per unit (P) times the number of units (Q) • TR = P x Q

  16. Breakeven At break-even, total cost (TC) equals total revenue (TR) and net income equals zero. TR =TC or (P x Q ) = FC + (VC x Q ) This can be rewritten as: [(P - VC) x Q ] =FC QBE = [FC/(P –VC)] Therefore QBE = (FC/C) Thus at break-even, the total contribution (QBE x C) equals fixed costs (FC).

  17. Contribution Margin % or Profit Volume Ratio CM% or PV ratio = (contribution per unit/selling price per unit) x 100 in essence it is saying what proportion of each £1 of sales is contribution. Break-even revenues = FC/CM% (as a decimal)

  18. The rule The question asks for: The number of units - Contribution margin per unit The revenues (sales in £s) - Contribution margin % (a.k.a PV Ratio)

  19. Example Admiral Ltd manufactures chess sets in a local factory. The following information is available on the revenues and costs involved for April 2005. £ per Unit Selling price 60.00 Variable cost of each item 30.00 Total fixed expenses per month £ 24,000 What is the break-even Sales Volume in Total Units and Revenue?

  20. Workings The contribution per unit = P - VC = (60-30) = £30 per unit At break-even total contribution equals fixed cost so 30 x QBEBE = 24,000 QBE = 800 units (or £48,000 in sales - £60 x 800)

  21. Contribution Margin % CM% or PV ratio = (contribution per unit/selling price per unit) x 100 This would be (30/60) x 100 = 50% and it can be used to find the break-even point or target profits. Break-even revenues = FC/CM% = (24,000/ 0.5) = £48,000 which at £60 each is 800 units

  22. Costs and Revenues TR TC £48,000 24,000 FCC Units Breakeven analysis

  23. Profit 6,000 1,000 0 Units 800 Loss 24,000 Profit volume chart

  24. Deriving Target Profit Total Revenue -Total Costs = TP QTP =(TP + FC )/Contribution per unit RTP = (TP + FC )/CM% expressed as a decimal

  25. Target profit of £6,000 and previous example P - VC = (60-30) = £30 per unit QTP = (FC + TP)/Contribution per unit QTP = (24,000 + 6,000)/30 = 1,000 units or RTP = (FC + TP)/CM % RTP = (24,000 + 6,000)/0.5 = £60,000 (or 1,000 units @ £60)

  26. Margin of Safety Margin of Safety % = Expected sales - Break-even sales x 100 Expected sales Suppose sales of chess sets are estimated at 900 units, what is the Margin of Safety? Break even is at 800 units. Therefore the Margin of Safety (%) = [(900 – 800)/900] x 100 = 11.11%

  27. Example Galaxy Ltd sells two types of products: Sweet and Sour. The following table summarises prices and variable costs for the two products. Fixed costs amounted to £800,000. £ £ Sweet Sour • Price per unit 120 90 • Variable cost per unit 60 70 • Contribution per unit 60 20 For every unit of Sweet sells, two units of Sour are sold. What volume of sales is needed to breakeven?

  28. Example The contribution margin per 'bundle' of two Sour and one Sweet is [(2 x 20) + 60] = £100 Break-even number of 'bundles' = Fixed Costs/100 = 800,000/100 =8,000 Sour 2 x 8,000 16,000 Sweet 8,000

  29. Example proved £s £s : Sweet Sour £s Revenue 960,000 1,440,000 2,400,000 Variable Cost 480,000 1,120,000 1,600,000 Contribution 800,000 Fixed cost (800,000) Break-even 0

  30. Operating leverage Operating leverage is the proportion of total costs that are fixed and is often expressed in terms of a percentage: Operating leverage (%) = Contribution margin/Profit

  31. Consequences of high operating leverage Firms with high operating leverage have: rapid increases in profits when sales expand rapid increases in losses when sales fall greater variability in cash flow greater risk

  32. Leverage example

  33. Sensitivity Analysis If the only change is in the selling price - the contribution margin also changes in the same direction by the same amount. If the only change is in the variable cost - the contribution margin changes in the opposite direction by the same amount. If the only change is in the fixed cost, there is no change in the contribution margin. If there are changes in both the fixed cost and the variable cost, there will be a change in the contribution margin – direction dependent on facts

  34. What if analysis - Example Fragments Limited manufactures a range of 1,000 piece wooden jigsaw puzzles themed on the Harry Potter books through a range of outlets. The selling price is £10 per puzzle and variable material and labour costs are £5 per jigsaw plus there is a £1 per jigsaw royalty for use of the Harry Potter name. Total fixed costs amount to £84,000 per annum.

  35. Would the company show an operating profit or loss, if 25,000 puzzles are sold in a year? Contribution per unit is (10 – 5 - 1) £4 and 25,000 units x £4 is £100,000 contribution which exceeds fixed costs by £16,000, or Profit/Loss = Sales -VC -FC £250,000 – 125,000 – 25,000 - 84,000 = £16,000

  36. What is the Contribution Margin %? Use it to find the total contribution and the when revenues from puzzles are sold are £300,000. The Contribution Margin % (PV ratio) is (4/10) x 100 = 40% and 300,000 x 0.4 = 120,000. Revenues of £300,000 imply 30,000 puzzles sold (£10 each) and at a contribution of £4 each this is £120,000.

  37. If Fragments Limited has a target operating income of £50,000, how many puzzles must be sold and what is the total revenue? Quantity for target profit = (FC + Target profit)/Contribution per unit (£84,000 +£50,000) ÷ £4 =33,500 units Or using CM% - (FC+ Target Profit/Contribution Margin %)=(£84,000 +£50,000)÷ 40%=£335,000 (or 33,500 puzzles x £10)

  38. Given the following scenarios should Fragments Limited advertise or not? Suppose the management of Fragments anticipates selling only 30,000 puzzles unless it supports an advertising campaign by the shops that stock its products. This would be paid for by a reduction in the price charged to the shops by £0.50 to £9.50 and £10,000 payment to cover the extra costs incurred by stores. The advertising campaign is expected to raise sales to 35,000 puzzles.

  39. Example cont. 30,000 puzzles sold with no advertising: £ Contribution margin (30,000*£4) 120,000 Fixed costs 84,000 Operating income 36,000 35,000 puzzles sold with advertising: £ Contribution margin (35,000*£3.50) 122,500 Fixed costs (£84000 +£10000) 94,000 Operating income 28,500

  40. Why? The additional contribution of 5,000 x £3.50 = £17,500 is offset by the £10,000 increase in fixed costs and the £0.50 loss of contribution on the 30,000 puzzles resulting from the price reduction, which totals £15,000 so we are £7,500 worse off (36,000 down to £28,500).

  41. What volume of sales is necessary for the advertising scheme to perform as well as the existing state does at 30,000 units (i.e. £36,000 operating income)? Quantity = (Target profit + FC)/Contribution per unit Revenue = (Target profit + FC)/Contribution Margin % Quantity = (36,000 + 84,000 + 10,000)/3.50 = 37,143 units Revenue = (36,000 + 84,000 + 10,000)/0.368421 = £352,858 (£9.50 x 37,143) Net income is £352,858-£222,858 (6 x 37,143) – FC £94,000 = £36,000 net income

  42. Make in or buy - Example The cost of a producing a Murgatroid is: £ Variable costs 10 Share of fixed ohds 5 (based on a normal weekly output of 10,000 units) Cost 15 A MURGATROID sells for £20. A supplier has offered to provide Murgatroids at £12 each, should the firm buy them?

  43. Example cont. £ Contribution per unit - Made in 10 (20 – 10) Bought out 8 (20 –12) Therefore make in to maximise contribution.

  44. If the spare capacity released enabled the firm to produce 5,000 Murgads with a contribution of £5 per unit; Contribution lost (10-8) x 10,000 (20,000) Contribution from Murgads 25,000 Therefore buy in as £5000 extra contribution from use of spare capacity created

  45. If 60% of the fixed costs would be eliminated if Murgatroids were bought in. Contribution lost (20,000) Saving in fixed overheads (.6 x 50,000) 30,000 Therefore buy in as £10,000 extra contribution

  46. Discontinuation – Surf Shack

  47. Suppose £40,000 of the fixed costs of the Boscombe shop represent a lease that cannot be sold or an alternative use found on closure (other fixed costs are eliminated). By closing Boscombe you save £35,000 of fixed costs but lose contribution of £60,000 and are therefore worse off by £25,000

  48. Suppose the Boscombe shop lease can be sublet for £30,000. The residual fixed costs of £40,000 from the lease are offset by the subletting income of £30,000 and so the loss is reduced from £15,000 to £10,000 thus improving group performance to £30,000.

  49. Limiting Factor Analysis When seeking to maximising profits, the rule is to: Maximise the CONTRIBUTION PER UNIT OF LIMITING FACTOR

  50. Cobbler Limited Cobbler Ltd manufactures shoes. The management accountant has analysed the performance of the three lines offered as follows: A B C Contribution per pair of shoes 2.00 2.52 3.75 The firm has just scrapped three of its machines, which are irreplaceable, and therefore can no longer produce the same number of shoes that it has in the past. The management accountant notes the machine hours per pair of shoes are as follows: A B C Machine hours per pair (a) 0.50 0.60 1.00 Likely demand for a period when there are 600 machine hours available is A 300, B 600 and C 700 What should the output be?

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