# Calculating The Break-Even Point. Cost-Volume-Profit Analysis. Sales Revenue = Px Total Costs = Vx + F When Firm Breaks Even (BE):

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1 Cost-Volume-Profit Analysis Calculating The Break-Even Point P = Selling Price Per Unit Units Produced and Sold V = Variable Cost Per Unit F = Total Fixed Costs OP = Operating Profits-Before Tax t = Tax rate Sales Revenue = Px Total Costs = Vx + F When Firm Breaks Even (BE): Sales Revenue Total Costs = 0 Sales Revenue = Total Costs Revenue = Total Costs P Vx + F Px - V F x(p - V) = F F (P -V) (FORMULA "A") Denominator also called CMU (Contribution Margin Per Unit) F (FORMULA "A") CMU 1

2 E.g., Assume Firm has following costs, revenues and tax rates: P = \$200 V = \$120 F = \$2,000 Formula A: F/(P-V) 2,000 ( ) 2, units This is common sense Firm makes \$80 every time it sells a unit. 2, = 25 units x _F = (P-V) (Formula A ) P _FP_ (P-V) ` P F (FORMULA "B") (P-V)/P F P (P-V)/P (Formula B ) Denominator also called CMR (Contribution Margin Ratio) P F (FORMULA "B") CMR Formula B: P PX = F/((P-V)/P) 2,000 ( ) /200 P 2, P \$5,000 2

3 Why do we need Formula B? 25 units x \$200 = \$5,000 E.g., What is BE Point for Co.? Revenue: \$100K (Px) Less VCs: -30K (Vx) CM: \$ 70K (Px Vx) Less FCs: -50K (F) OP: \$ 20K (Px - Vx F) What is BE? We do not know the # of units sold We do not know P or V We cannot use Formula A _\$50K_ (P-V) We can calculate the CMR So we can use Formula B We know CM/Rev, which is the CMR CM Sales Revenue = Px - Vx Px The CMR is.70 (70,000/100,000) The BE Point in Sales Revenue is: P F/CMR = 50,000/.70 = \$71, = (P-V) (P-V) = CMR Px P Revenue - Costs = OP Targeted Operating Profits Px - Vx F = OP Px - V F + OP x(p - V) = F + OP (F + OP) Modified (P - V) Formula A (F + OP) CMU 3

4 (F + OP) Modified (P - V) Formula A P (F + OP)P (P - V) P _(F + OP)_ Modified (P - V)/ P Formula B P (F + OP) CMR Same E.g. Assume Co wants Target OP of \$40K (\$2,000 + \$40,000) (\$200 - \$120) \$42,000 \$ units OP do not include tax expense OP Tax Expense = Net Income What if given Targeted NI? Convert your Net Income figure into the Operating Profits that will result in the Net Income that you desire E.g., Given target NI (after-tax) of \$50K & tax rate of 40% Convert \$50K NI into OP: OP - Taxes = NI OP -.4 (OP) = 50,000.6 (OP) = 50,000 OP = 50,000/.6 OP = 83,334 You can check this: OP: \$83,334 Taxes (40%): -33,334 NI: \$50,000 What if Target OP is given as % of Revenue? E.g., OP = 10% of Px P (F+OP) / (P-V)/P P (2, Px) [( )/200] P (2,000+.1Px) /.40.4 P 2, Px.4Px -.1 P 2, Px.3 P 2,000 P 2,000/.3 P \$6,667 4

5 Multiple Products If using CMR (Formula B) Firm has >1 product Same analysis but use composite: CMU (Formula A) or CMR (Formula B) The easiest way to calculate BE is to calculate CMR for entire Company Remember: (Px Vx)/P (P-V)/P CMR = CM/Sales We did this earlier Revenue: \$100K (Px) Less VCs: -30K (Vx) CM: \$ 70K (Px Vx) Less FCs: -50K (F) OP: \$ 20K (Px - Vx F) If using CMU (Formula A) Calculate composite CMU Basket (Package) Method Weighted Average CM Method CMR = 70K/100K =.7 E.g., Co sells 3 Bananas for each Orange that it sells (75% vs. 25%) Bananas Oranges Price: \$2 \$4 VC per -\$1 -\$2 Unit: CMU: \$1 \$2 Common Fixed Costs: \$2,000 Basket Method: (75%:25%) Basket 3 Bs & 1 Or: CM B = 3 CM ban + 1CM or CM B = 3 (1) + 1 (2) CM B = 5 5

6 Now, plug CM B into BE formula Gives you BE Point in Baskets: Bananas: 3 x 400 Baskets = 1200 Oranges: 1 x 400 Baskets = 400 Baskets = F/CM B Baskets = 2,000/ 5 Baskets = 400 Baskets Weighted Average Method CM WA =.75 CM ban +.25 CM or CM WA =.75 (1) +.25 (2) CM WA = = \$1.25 The BE Point in units is: F/CM WA 2,000/ units Margin of Safety Bananas:.75 (1600) = 1200 Oranges:.25 (1600) = 400 Margin Of Safety Amount that actual sales (dollars or units) exceed BE Point If Co actually sells 40 units (\$8,000) & its BE Point is 25 units (or \$5,000) Margin Of Safety is 15 units (or \$3,000) 6

7 Operating Leverage If we increase our CM by a given percentage, what will be our new OP? OL gives you the answer quickly Current Rev: \$ 8,000 (200 x 40 units) VCs: -\$4,800 (120 x 40 units) CM: \$ 3,200 (80 x 40 units) FCs: -\$2,000 OP: \$1,200 Projected Rev: \$12,000 (200 x 60 units) VCs: -\$7,200 (120 x 60 units) CM: \$4,800 (80 x 60 units) FCs: -\$2,000 OP: \$2,800 Operating Leverage (OL) Divide CM by OP OL x (% increase in Co s CM) Gives you % increase in Co s OP There is a 50% increase in: Units Revenue CM Operating Leverage: Current CM = \$3,200 = 2.67 OP \$1,200 Remember that CM increases by 50% OL x CM % = OP % 2.67 x 50% = 133% OP of \$1,200 will increase by \$1,600 (1.33 x \$1,200) New OP \$ \$1600 = \$2,800 7

8 Formula B P (F/CMR) The CMR is for all of your products The easiest way to do this is to prepare an income statement for the whole business and then divide the CM by the Sales BUT, some people try to figure it out using the weighted-average method. Apples Pears Price: \$2 \$4 VC per Unit: -\$1 -\$3 CMU: \$1 \$1 CMR [(p-v)/p]: 1/2 1/4 Sales (Units) Common Fixed Costs: \$2,000 The Sales Revenue is: 60x(P A ) + 40x(P P ) 60x(2) + 40x(4) = = 280 The Variable Costs are: 60x(V A ) + 40x(V P ) 60x(1) + 40x(3) = = 180 Income Statement Sales \$280K Less: Variable Costs: -180K Contribution Margin: \$100K Less: Fixed Costs -2K Operating Profits \$98K CMR= CM/Sales CMR= \$100K/\$280K CMR= 35.71% BUT, If you are going to calculate the weighted average CMR using a formula, then remember, the product mix is in Sales dollars: Formula A: Calculates needed UNITS CMU Weights based on UNITS Formula B: Calculates need DOLLARS CMR Weights based on DOLLARS What is the Relative Sales in DOLLARS? Revenue From Each Product: Apples: 60 x \$2 = \$120 Pears: 40 x \$4 = \$160 Total Revenue = \$120 + \$160 = \$280 Relative Revenue From Each Product: Apples \$120/\$280 = 42.86% Pears \$160/\$280 = 57.14% You must use these percentages not the relative unit percentages (60% Apples & 40% Pears) 8

9 Weighted Average Method CMR WA =.4286 CMR a CMR p CMR WA =.4286 (.5) (.25) CMR WA = = Please note that this is the same weighted average CMR that we got from the income statement Using Formula B The BE Point in Sales Dollars is: P F/CMR WA P 2,000/ P \$5600 Apples:.4286 (\$5600) = \$2400 Pears:.5714 (\$5600) = \$3200 Apples: \$2400/\$2 = 1200 apples Pears: \$3200/\$4 = 800 pears Let s Check To See if Correct Answer: Sales (1200 x 2) + (800 x 4) \$5,600 VC (1200 x 1) + (800 x 3) -3,600 Contribution Margin \$2,000 Fixed Costs -2,000 Operating Profits 0 THE END Dr. Michael Constas

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