Topic 3 CA (2015)

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 Universidad Universidad Pompeu Fabra (UPF) Grado International Business Economics - 3º curso Asignatura Cost Accounting I Año del apunte 2015 Páginas 8 Fecha de subida 21/01/2016 Descargas 19 Puntuación media Subido por ssegues

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Cost Accounting - ssegues TOPIC 3: BREAKEVEN POINT. COST VOLUME – PROFIT ANALYSIS OUTLINE - - Cost-Volume-Profit (CVP) Analysis – Definition CVP – Terminology and Assumptions Breakeven Point: o Equation method o Contribution margin method o Graph method Sensitivity Analysis – Margin of Safety Sales mix and the CVP analysis COST – VOLUME – PROFIT ANALYSIS ! DEFINITION CVP analysis provides information of the possible consequences that a change in one of the variables that sets the selling price would have on a company’s costs and results. These variables are: • • • • The output level The selling price The variable costs, or The fixed costs CVP – TERMINOLOGY AND ASSUMPTIONS CVP terminology: - Total costs = VC + FC Operating profit = total revenues – total costs Net profit = Operating profit – Income taxes USp = unit selling price UVC = unit variable costs UCM = unit contribution margin (USp – UVC) - CM % = contribution margin percentage ! - FC = fixed costs Q = output level !"# !"# Major CVP assumptions: - Total costs can be divided into fixed part and variable part depending on the level of output Cost Accounting - ssegues - Total revenues and total costs are linear in relation to output units within relevant range (out of that range the formula is not going to work ! things will become a mess) - Unit selling price, unit variable cost and fixed costs are known Analysis for a single product or a constant sales-mix Number of output units is the only revenue and cost driver. THE BREAKEVEN POINT Definition: quantity of output where total revenues and total costs are equal; that is, where operating profit is zero (OP = 0) Calculation: • • • Equating method Contribution margin method Graph method Equation Method: - - Numerical definition (at breakeven point the Op. profit = 0) 𝑂𝑝. 𝑝𝑟𝑜𝑓𝑖𝑡 = 𝑈𝑆𝑝 𝑥 𝑄 − (𝐹𝐶 + 𝑈𝑉𝐶 𝑥 𝑄 ) Play with the equation to perform sensitivity analysis. For example, to check for the quantity amount at the breakeven (Op. profit = 0) 𝑄 ∗ 𝑈𝑆𝑝 − 𝑈𝑉𝐶 = 𝐹𝐶 𝑄= 𝐹𝐶 → 𝑈𝑆𝑝 − 𝑈𝑉𝐶 = 𝑈𝐶𝑀 (𝑈𝑆𝑝 − 𝑈𝑉𝐶) Cost Accounting - ssegues - Breakeven in revenue € (exception; FC=0 no computation): 𝑄 ∗ 𝑈𝑆𝑝 = 𝐹𝐶 ∗ 𝑈𝑆𝑝 𝐹𝐶 𝐹𝐶 𝐹𝐶 = = = 𝑈𝑉𝐶 𝑉𝐶 𝑈𝑆𝑝 − 𝑈𝑉𝐶 𝑈𝑆𝑝 − 𝑈𝑉𝐶 1− 1− 𝑈𝑆𝑝 𝑠𝑎𝑙𝑒𝑠 𝑈𝑆𝑝 (* exercise 1.3.1 Automobile Auxiliary) Contribution Margin Method: Revenues – Variable costs – Fixed costs = Operating Profit 𝑂𝑝. 𝑝𝑟𝑜𝑓𝑖𝑡 = 𝑈𝑆𝑝 𝑥 𝑄 − (𝐹𝐶 + 𝑈𝑉𝐶 𝑥 𝑄 ) Breakeven number of units (Op. Profit = 0) 𝑄 ∗ 𝑈𝑆𝑝 − 𝑈𝑉𝐶 = 𝐹𝐶 ; 𝑄 ∗ 𝑈𝐶𝑀 = 𝐹𝐶 𝑄= 𝐹𝐶 𝑈𝐶𝑀 Breakeven in revenue € 𝑄 ∗ 𝑈𝑆𝑝 = 𝐹𝐶 ∗ 𝑈𝑆𝑝 𝐹𝐶 𝐹𝐶 = = 𝑈𝐶𝑀 𝐶𝑀% 𝑈𝐶𝑀 𝑈𝑆𝑝 → 𝐶𝑀% 𝑖𝑠 𝑡ℎ𝑒 𝑐𝑜𝑛𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 𝑚𝑎𝑟𝑔𝑖𝑛 𝑟𝑎𝑡𝑖𝑜 Cost Accounting - ssegues Sales 100 - VC -50 =CM 50 CM% = 50% = !" !"" Changes in VC Changes in FC and VC SENSITIVITY ANALYSIS – MARGIN OF SAFETY - - Sensitivity analysis: A “what if” technique examining how a result will change if the original predicted data are not achieved or if an assumption changes. o Example: what will operating profit be if unit variable cost increase by 5%? Margin of Safety: Indicates by how much sales may decrease before resulting in a loss. o Calculation: " Absolut: Expected sales – breakeven sales " In %: (!"#\$%&\$' !"#\$!!!"#\$%#&#' !"#\$!) !"#!\$%!& !"#\$! Cost Accounting - ssegues THE BREAKEVEN POINT OF A CONSTATN SALES MIX - Up until now, we have been considering one possible rate or amount for Variable costs. What if there are different products? ! VC will diverge There is no unique breakeven number of units for a multiple-product situation. The breakeven quantity depends on the sales mix. To compute it: o Equation method o Contribution margin method A SIMPLE EXAMPLE - FC = 35.000€ For each box with markers, we sell 2 with pens and 3 with pencils Breakeven point (BP)? Method I – Equation method (MIX UNIT) - We define a fictitious mix unit through the combination of sales ! 2 / 1 / 3 (pen / market / pencil) CM (mix) = (2x6) + (1x5) + (3x3) = 26€ / mix units BP = FC / CM mix unit = 35.000 /26 = 1.347 mix units o 𝑄∗ = !" !"#!!"# = !" !"# This means that we must sell: - Pens: 1.347 x 2 = 2.694 boxes Markers: 1.347 x 1 = 1.347 boxes Pencils: 1.347 x 3 = 4.041 boxes PEN MARKER PENCIL Total Revenue 17*2.694 =45.798 17*1.347 22.899 = 8*4.041 32.328 = 101.025 VC (11)*2.694 29.634 = (5)*4.041 20.205 = (66.003) CM 16.164 6.735 12.123 ≈ 35.000 FC (35.000) Op. Profit 0 = (12)*1.347 16.164 TOTAL Cost Accounting - ssegues In this scenario we were asked an operating profit = 0. What happens now if we want an operating profit =30.000? 𝑄∗ = 𝐹𝐶 + 𝑂𝑝. 𝑃𝑟𝑜𝑓𝑖𝑡 𝐶𝑀𝑚𝑖𝑥 → 𝑤𝑒 𝑗𝑢𝑠𝑡 𝑝𝑙𝑢𝑔 𝑖𝑛 𝑡ℎ𝑒 𝑛𝑒𝑤 𝑜𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔 𝑝𝑟𝑜𝑓𝑖𝑡 To reach a targeted operating profit, say 30.000€, we must sell the following quantity (Q): • Q = (FC + OP)/ CM (mix) = (35.000 + 30.000) / 26 = 2.500 mix units This means that we must sell: - Pens: 2.500 x 2 =5.000 boxes Markers: 2.500 x 1 = 2.000 boxes Pencils: 2.500 x 3 =7.500 boxes Method II – Contribution Margin Method - calculate the weighted-average contribution margin per unit for all products (A, B, ..) together: Weighted average contribution margin per unit: 𝑈𝐶𝑀 ∗ 𝑛º 𝑜𝑓 𝑢𝑛𝑖𝑡𝑠 𝑠𝑜𝑙𝑑 + 𝑈𝐶𝑀 ∗ 𝑛º 𝑢𝑛𝑖𝑡𝑠 𝑠𝑜𝑙𝑑 + ⋯ 𝑛º 𝑢𝑛𝑖𝑡𝑠 𝑠𝑜𝑙𝑑 + 𝑛º 𝑢𝑛𝑖𝑡𝑠 𝑠𝑜𝑙𝑑 + ⋯ - Breakeven point for each product: 𝐹𝐶 𝑊𝑒𝑖𝑔ℎ𝑡𝑒𝑑 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝐶𝑀 For the previous example: - CM Weighted = (6x 2/6) + (5 x 1/6) + (3 x 3/6) = 4.33€/unit BP = 35.000/4,33 = 8.083 units (total boxes to sell) This means that we must sell: o Pens : 8.083 x 2/6 = 3.694 boxes o Markers: 8.083 x 1/6 =1.347 boxes o Pencils: 8.083 x 3/6 = 4.041 boxes Cost Accounting - ssegues 2013 EXAM PROBLEM PRODUCT UVC USp % SALES A 11 16 60% B 10 13 40% FC = 168.000 1) Assuming the given sales mix, units of B to breakeven? a. 12.000 b. 16.000 c. 18.000 d. 40.000 Ratio = A : B = 6 : 4 (proportions)!!! CMmix = (5 x6) + (3x4) =42€ 𝑄∗ = 168.000 = 4.000 𝑚𝑖𝑥 𝑢𝑛𝑖𝑡𝑠 42 Product A ! 4.000 x 6 = 24.000 products Product B ! 4.000 x 4 =16.000 products 2) Draw a graphical illustration of the situation above Cost Accounting - ssegues OPERATING LEVERAGE - Useful to express relationships between VC and FC OL = CM /OP - OL (F1) = 5.000 /2.000 =2,5 OL (F2) = 7.000 /2.000 = 3,5 o If sales increase by 10%: " Profit F1 increases by: 10% x 2,5 =25% " Profit F2 increases by: 10% x 3,5 =35% Profit F1 increases by: 10% x 25 =25% 2.000 x 1,25 =2.500 (VC also increase!!!!!) ...