1 BREAKEVEN ANALYSIS Introduction Introduction What is Break-even Analysis? What is Break-even Analysis? Break-even in comparing alternative propositions Break-even in comparing alternative propositions Break-even in single project analysis Break-even in single project analysis Break-even in decision making Break-even in decision making Optimisation Optimisation

2 INTRODUCTION Break-even analysis – a powerful management tool Break-even analysis – a powerful management tool A tool for cost comparison A tool for cost comparison Example: How can we choose between two different options for a required piece of equipment? Example: How can we choose between two different options for a required piece of equipment? A tool for single project analysis A tool for single project analysis Example: How many units are required to be sold before the project yields a positive profit? Example: How many units are required to be sold before the project yields a positive profit? A tool for decision making A tool for decision making Example: is an investment in a marketing initiative that is believed to have a certain benefit worth undertaking? Example: is an investment in a marketing initiative that is believed to have a certain benefit worth undertaking?

3 COMPARING ALTERNATIVES In situations where the alternatives are affected in some way by a common variable In situations where the alternatives are affected in some way by a common variable Total cost of Option 1 = TC 1 Total cost of Option 1 = TC 1 Total cost of Option 2 = TC 2 Total cost of Option 2 = TC 2 There exists a common, independent decision variable affecting both Options – ‘x’ There exists a common, independent decision variable affecting both Options – ‘x’

4 EQUIPMENT SELECTION EXAMPLE 2 pump options 2 pump options Electric: Capital cost + Annual maintenance + Energy cost Electric: Capital cost + Annual maintenance + Energy cost Diesel: Capital cost + Hourly maintenance + Hourly operator cost + Energy cost Diesel: Capital cost + Hourly maintenance + Hourly operator cost + Energy cost 4 year project life 4 year project life 12% interest rate 12% interest rate Which is the lowest cost option? Which is the lowest cost option?

5 PROBLEM SOLVING PROCESS Identify the common, independent decision variable Identify the common, independent decision variable Translate the cost information for each option into cost function form Translate the cost information for each option into cost function form Do the number crunching Do the number crunching Solve analytically or graph both cost functions Solve analytically or graph both cost functions Locate the break-even value (the intersection of the two cost functions) Locate the break-even value (the intersection of the two cost functions)

6 SOLUTION 1 Common, independent decision variable Common, independent decision variable ‘h’, pump operational hours per year ‘h’, pump operational hours per year Cost function for Pump 1 Cost function for Pump 1 Initial cost  Annual Equivalent Initial cost  Annual Equivalent Annual maintenance cost  Annual amount Annual maintenance cost  Annual amount Energy cost  Hourly rate Energy cost  Hourly rate Cost function for Pump 2 Cost function for Pump 2 Initial cost  Annual Equivalent Initial cost  Annual Equivalent Maintenance cost  Hourly rate Maintenance cost  Hourly rate Energy cost  Hourly rate Energy cost  Hourly rate Operator cost  Hourly rate Operator cost  Hourly rate

7 SOLUTION 2 Common cost function: Common cost function: Total Annual Equivalent Cost = Annual Cost + Hourly Rate * h Equation of a straight line Equation of a straight line y (TAEC) = m (Hourly rate). x (h) + c (Annual cost) Result is two straight lines, one for each option Result is two straight lines, one for each option

8 SOLUTION 3 – NUMBER CRUNCHING Pump 1 Pump 1 Initial Capital cost = 1,800 m.u. Annual Equivalent = Initial Cost * A/P(12,4) = 1,800 * = m.u. Annual maintenance cost= m.u. Total Annual cost= m.u. Hourly rate= 1.10 m.u. / hour Total Annual Equivalent cost= *h ………(1)

9 SOLUTION 4 – NUMBER CRUNCHING Pump 2 Pump 2 Initial Capital cost = 550 m.u. Annual Equivalent = Initial Cost * A/P(12,4) = 550 * Total Annual cost= 181 m.u. Hourly rate= m.u. / hour = 2.35 m.u. / hour Total Annual Equivalent cost= *h ………(2)

10 SOLUTION 5 – SOLVE Analytical Analytical Total Annual Equivalent cost= *h ………(1) Total Annual Equivalent cost= *h ………(1) Total Annual Equivalent cost= *h ………(2) Total Annual Equivalent cost= *h ………(2) Break-even is when these are equal, i.e. Break-even is when these are equal, i.e *h = *h = 1.25*h h =

11 MULTIPLE – ALTERNATIVE PROBLEMS The same solution approach applies The same solution approach applies Reduce all problems to common cost function Reduce all problems to common cost function Graphical solution is best way of visualising the solution Graphical solution is best way of visualising the solution V < 50 Blue 50 < V < 150Green 150 < V Red

12 BREAK-EVEN IN A SINGLE PROJECT Definition of Costs Definition of Costs Fixed: “A cost is said to be fixed if it does not change in response to changes in the level of activity” Fixed: “A cost is said to be fixed if it does not change in response to changes in the level of activity” Variable: “The cost that is directly associated with the production of one unit” Variable: “The cost that is directly associated with the production of one unit” Cv Cf Total Cost (Ct) Volume (v) Total Cost

13 COST – VOLUME – PROFIT EXAMPLE Telephone:Annual line rental charge25.00 m.u. Telephone:Annual line rental charge25.00 m.u. Cost per call0.10 m.u. Cost for 100 callsLine rental + call cost35.00 m.u. [0.35] Cost for 100 callsLine rental + call cost35.00 m.u. [0.35] Cost for 500 calls Line rental + call cost75.00 m.u. [0.25] Cost for 500 calls Line rental + call cost75.00 m.u. [0.25] 25 Total Cost (Ct) Volume (v) Average Cost “Average cost is the total cost of providing a product or service, divided by the number that are provided.”

14 LINEARITY OF VARIABLE COSTS Variable costs = f (volume), but the relationship is not linear Variable costs = f (volume), but the relationship is not linear Limitations on linearity Limitations on linearity Bulk purchase price break point Bulk purchase price break point Demand fluctuations Demand fluctuations Economic climate Economic climate Production capability Production capability Efficiency & Productivity changes Efficiency & Productivity changes Technology changes Technology changes

15 REALISTIC COST FUNCTIONS Fixed Cost Volume Variable Cost Volume Total Cost Volume + = Relevant Range

16 CVP ANALYSIS Profit (P) = Sales Revenue (SR) – Total Costs (C t ) Profit (P) = Sales Revenue (SR) – Total Costs (C t ) SR = Selling Price (S p ) * Volume (V) SR = Selling Price (S p ) * Volume (V) C t = Fixed Costs (C f ) + Variable Costs (CV) C t = Fixed Costs (C f ) + Variable Costs (CV) Marginal cost: “The cost of providing one additional unit/item Marginal cost: “The cost of providing one additional unit/item C v = Marginal Cost (C v ) * Volume C v = Marginal Cost (C v ) * Volume Break-even when P=0 Break-even when P=0

17 BREAK-EVEN ANALYSIS CfCf Gradient = (S p - C v ) Break-Even Volume Profit Volume At Breakeven P = 0

18 SINGLE PRODUCT DECISIONS You buy and sell a product which sells for m.u. each. The cost for you to purchase the product is 3.00 m.u. In order for you to trade you require premises and equipment which, in total, represent a fixed cost to you of 25,000 m.u. Your total planned volume for the year of the product is 4,000 units. You buy and sell a product which sells for m.u. each. The cost for you to purchase the product is 3.00 m.u. In order for you to trade you require premises and equipment which, in total, represent a fixed cost to you of 25,000 m.u. Your total planned volume for the year of the product is 4,000 units. 1) How many units do you need to sell to break-even? 2) How many units do you need to sell to make 1,000 m.u. profit? 3) Would it be worth the introduction of advertising at a cost of 6,000 m.u. to increase sales to 4,450? 4) What impact would a 10% drop in selling price have on the break-even volume?

19 SOLUTION - 1 Problem 1) How many units to breakeven? P = (S p - C v ) * V - C f Definition of Break-Even : P = 0 Profit £25k Break-Even Volume = Break-Even Volume = 2084

20 SOLUTION - 2 Problem 2) How many units to make £1000 profit? P = (S p - C v ) * V - C f Volume for Profit = £1000 Profit £26k Volume = Volume = 2167

21 SOLUTION - 3 Problem 3) Would it be worth the introduction of advertising at a cost of £6,000 to increase sales to 4450? P = (S p - C v ) * V - C f Profit for V = 4000 is £23,000 Profit for V = 4450 is £28,400 Gain in Profit = £5,400 Cost to Achieve Gain = £6,000 Hence Not Worth Pursuing!

22 SOLUTION - 4 Problem 4) What impact would a 10% drop in selling price have on the break even volume. ? P = (S p - C v ) * V - C f Profit £25k Break-Even Volume = 2381 Increase = 298 units or 14.3%

23 CONTRIBUTION Problem 3) Would it be worth the introduction of advertising at a cost of £6,000 to increase sales to 4450? P = (S p - C v ) * V - C f Profit for V = 4000 is £23,000 Profit for V = 4450 is £28,400 Gain in Profit = £5,400 Cost to Achieve Gain = £6,000 There is an alternative way of solving this.

24 CONTRIBUTION Problem 3) Would it be worth the introduction of advertising at a cost of £6,000 to increase sales to 4450? P = (S p - C v ) * V - C f Per unit Profit = (S p - C v ) = £12 Increase in Volume with Advertising : 450 units Increase in Profit = £12 * 450 = £5,400 Cost to Achieve Gain = £6,000 “£12 is the contribution or profit margin per unit”

25 CONTRIBUTION Marginal Contribution = Selling Price - Variable Cost Revenue / Cost Cf Volume Sales Revenue Variable Costs Contribution Total Contribution = (Selling Price - Variable Cost) * Volume

26 OPTIMISATION ANALYSIS Some cost components vary directly with a common decision variable while others vary inversely with the decision variable Some cost components vary directly with a common decision variable while others vary inversely with the decision variable In such cases an optimum (lowest cost) exists In such cases an optimum (lowest cost) exists The general form of such a cost function is: The general form of such a cost function is: Where: Where: x = common decision variable x = common decision variable TC = Total cost TC = Total cost A, B, C = constants A, B, C = constants

27 OPTIMISATION ANALYSIS The general form can be solved analytically and/or graphically The general form can be solved analytically and/or graphically

28 ALTERNATIVE OPTIONS - 1 Single cross-over Single cross-over Lowest cost option changes once Lowest cost option changes once

29 ALTERNATIVE OPTIONS - 2 Double cross-over Double cross-over Lowest cost option changes twice Lowest cost option changes twice

30 ALTERNATIVE OPTIONS - 3 No cross-overs No cross-overs Lowest cost option never changes Lowest cost option never changes

31 OPTIMISATION CASE STUDY Sometown Compressors