Breakeven Analysis Individual Assignment Due April 12, 2023 Breakeven analysis is performed to determine the value of a variable of a project that makes two elements equal, e.g. sales volume that will equate revenues and costs. Single Project The analysis is based on the relationship: Profit = revenue - total cost =RTC At breakeven, there is no profit or loss, hence, revenue=totalcost or, R=TC Note: It is to be noted that +ve sign is used for both the revenue and the costs. If we are to use -ve sign for costs and +ve sign for revenue, then the above relationships become: Profit =R+TC and R+TC=0 at breakeven. With revenue and costs given in terms of a decision variable, the solution yields the breakeven quantity for the decision variable. Costs, which may be linear or non-linear, usually include two components: Fixed costs (FC) - includes costs such as buildings, insurance, fixed overhead, equipment capital recovery, etc. These costs are essentially constant for all values of the decision variable. Variable costs (VC) - Includes costs such as direct labour, materials, contractors, marketing. advertisement, etc. These costs change linearly or non-linearly with the decision variable, eg. production level, workforce size, etc. For the analysis to be followed here, the variation will generally be assumed to be linear. Then, total cost, TC=FC+VC Revenue also changes with the decision variable. Again, for the analysis, the variation will generally be assumed to be linear. The following diagram illustrates the basics of the breakeven analysis. Revenue, R Revenue Total Cost, TC or Cost VC FC QBE, Breakeven quantity Production, Q units/year It can be seen that we have profit if the production level is above the breakeven quantity and loss if it is below. Now Answer the following two questions: 1. The fixed costs at Company X are $1 million annually. The main product has revenue of $8.90 per unit and $4.50 variable cost. (a) Determine the breakeven quantity per year, and (b) Annual profit if 200000 units are sold. 2. A product currently sells for $12 per unit. The variable costs are $4 per unit, and 10,000 units are sold annually and a profit of $30,000 is realized per year. A new design will increase the variable costs by %20 and Faxed Costs by %10 but sales will increase to 12,000 units per year. (a) At what selling price do we break even, and (b) If the selling price is to be kept same (\$12/unit) what will the annual profit be