1. Management Decision Making Management Decision Making Supplement – Break Even Analysis

2. Break-Even Analysis  Technique for evaluating process and equipment alternatives  Objective is to find the point in dollars and units at which cost equals revenue  Requires estimation of fixed costs, variable costs, and revenue

3. Break-Even Analysis  Fixed costs are costs that continue even if no units are produced  Depreciation, taxes, debt, mortgage payments  Variable costs are costs that vary with the volume of units produced  Labor, materials, portion of utilities  Contribution is the difference between selling price and variable cost

4. Break-Even Analysis  Costs and revenue are linear functions  Generally not the case in the real world  We actually know these costs  Very difficult to accomplish  There is no time value of money Assumptions

5. Profit corridor Loss corridor Break-Even Analysis Total revenue line Total cost line Variable cost Fixed cost Break-even point Total cost = Total revenue – 900 900 – 800 800 – 700 700 – 600 600 – 500 500 – 400 400 – 300 300 – 200 200 – 100 100 – – |||||||||||| 010020030040050060070080090010001100 Cost in dollars Volume (units per period) Figure S7.6

6. Break-Even Analysis BEP x =break-even point in units BEP $ =break-even point in dollars P=price per unit (after all discounts) x=number of units produced TR=total revenue = Px F=fixed costs V=variable cost per unit TC=total costs = F + Vx TR = TC or Px = F + Vx Break-even point occurs when BEP x = F P - V

7. Break-Even Analysis BEP x =break-even point in units BEP $ =break-even point in dollars P=price per unit (after all discounts) x=number of units produced TR=total revenue = Px F=fixed costs V=variable cost per unit TC=total costs = F + Vx BEP $ = BEP x P = P ==F (P - V)/P F P - V F 1 - V/P Profit= TR - TC = Px - (F + Vx) = Px - F - Vx = (P - V)x - F

8. Break-Even Example Fixed costs = $10,000 Material = $.75/unit Direct labor = $1.50/unit Selling price = $4.00 per unit BEP $ = = F 1 - (V/P) $10,000 1 - [(1.50 +.75)/(4.00)]

9. Break-Even Example Fixed costs = $10,000 Material = $.75/unit Direct labor = $1.50/unit Selling price = $4.00 per unit BEP $ = = F 1 - (V/P) $10,000 1 - [(1.50 +.75)/(4.00)] = = $22,857.14 $10,000.4375 BEP x = = = 5,714 F P - V $10,000 4.00 - (1.50 +.75)

10. Break-Even Example 50,000 50,000 – 40,000 40,000 – 30,000 30,000 – 20,000 20,000 – 10,000 10,000 – – |||||| 02,0004,0006,0008,00010,000 Dollars Units Fixed costs Total costs Revenue Break-even point

11. Break-Even Example BEP $ = F ∑ 1 - x (W i ) ViViPiPiViViPiPi Multiproduct Case whereV= variable cost per unit P= price per unit F= fixed costs W= percent each product is of total dollar sales i= each product

12. Multiproduct Example Annual Forecasted ItemPriceCostSales Units Sandwich$2.95$1.257,000 Soft drink.80.307,000 Baked potato1.55.475,000 Tea.75.255,000 Salad bar2.851.003,000 Fixed costs = $3,500 per month

13. Multiproduct Example Annual Forecasted ItemPriceCostSales Units Sandwich$2.95$1.257,000 Soft drink.80.307,000 Baked potato1.55.475,000 Tea.75.255,000 Salad bar2.851.003,000 Sandwich$2.95$1.25.42.58$20,650.446.259 Soft drink.80.30.38.625,600.121.075 Baked 1.55.47.30.707,750.167.117 potato Tea.75.25.33.673,750.081.054 Salad bar2.851.00.35.658,550.185.120 $46,3001.000.625 AnnualWeighted SellingVariableForecasted% ofContribution Item (i)Price (P)Cost (V)(V/P)1 - (V/P)Sales $Sales(col 5 x col 7) Fixed costs = $3,500 per month

14. Multiproduct Example Annual Forecasted ItemPriceCostSales Units Sandwich$2.95$1.257,000 Soft drink.80.307,000 Baked potato1.55.475,000 Tea.75.255,000 Salad bar2.851.003,000 Fixed costs = $3,500 per month Sandwich$2.95$1.25.42.58$20,650.446.259 Soft drink.80.30.38.625,600.121.075 Baked 1.55.47.30.707,750.167.117 potato Tea.75.25.33.673,750.081.054 Salad bar2.851.00.35.658,550.185.120 $46,3001.000.625 AnnualWeighted SellingVariableForecasted% ofContribution Item (i)Price (P)Cost (V)(V/P)1 - (V/P)Sales $Sales(col 5 x col 7) BEP $ = F ∑ 1 - x (W i ) ViPiViPi = = $67,200 $3,500 x 12.625 Daily sales = = $215.38 $67,200 312 days.446 x $215.38 $2.95 = 32.6  33 sandwiches per day