BUSINESS MATHEMATICS Breakeven Analysis Breakeven Analysis Defined o

BUSINESS MATHEMATICS Breakeven Analysis

Breakeven Analysis Defined o o o Breakeven can be defined as the minimum level of sales revenue or units of goods that an organisation must meet or produce to cover all costs. To determine these level, costs must be determined appropriately and accurately. To determine cost accurately, the cost of every factor of production (land, labour, capital, and entrepreneur must be accounted for.

Break-Even Analysis q The Objective of breakeven analysis is to find the level of output at which cost equals revenue q Requires estimation of fixed costs, variable costs, and revenue

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

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

Decision making and Breakeven Analysis q o o How many units must be sold to breakeven? How many units must be sold to achieve a target profit? How will profits and or breakeven volume be affected if fixed cost, variable cost, and or total revenue increased or reduced?

Key Terminology: Breakeven Analysis o o Break even point-the point at which a company makes neither a profit or a loss (i. e. total revenue is equal to total cost – TR = TC) Contribution per unit-the sales price minus the variable cost per unit. It measures the contribution made by each item of output to the fixed costs and profit of the organisation. (i. e. price per unit – variable cost per unit)

Key Terminology ctd. Margin of safety-a measure in which the budgeted volume of sales is compared with the volume of sales required to break even. (i. e. Budgeted volume of sales – Breakeven volume) Example: If a firm budgets to sell 2000 units and it requires 1600 units to breakeven, then the margin of safety is: 2000 – 1600 = 400. (We could also use the value of these goods in cedis to determine the margin of safety) o o Marginal Cost – cost of producing one extra unit of output

Breakeven Formula o Breakeven volume can be determined mathematically or graphically. Fixed Cost Price per unit – Variable cost per unit Selling Price per unit – Variable Cost per unit = Contribution per unit NB: This formula is used to determine the breakeven for single items only. To determine breakeven for multiple items, the multiple case formula is used.

Break-Even Analysis BEPq = Break-even point in units P= Price per unit (after all discounts) q = Number of units produced TR F Vq TC = = Total revenue = P x q Fixed costs Variable costs per unit Total costs = F + Vx Break-even occurs when TR = TC or Pq = F + Vq F BEPq = P-V

Example o o Ante Araba sells biscuits in a shop around the corner. If her monthly fixed cost is Ȼ 1, 800 and her variable cost per unit is Ȼ 6. 75, determine the number of biscuits Ante Araba must sell to breakeven if a biscuit sells at Ȼ 9. 25. Solution BEPq = f = 1800 =Ȼ 654. 5 p–v 9. 25 – 6. 75

Example Determine the breakeven volume if Fixed costs = Ȼ 10, 000 Material = Ȼ 0. 75/unit Direct labor = Ȼ 1. 50/unit Selling price = Ȼ 4. 00 per unit BEPq = F p-v = $10, 000 [400 – (1. 50 + 0. 75)] Note that variable cost was given here as cost of labour and material.

Break-Even in Monetary Terms BEPq BEPȻ P = = = Break-even point in units Break-even point in dollars Price per unit (after all discounts) BEP$ = BEPq × P F = P P-V F = (P - V)/P F = 1 - V/P q = Number of units produced TR F V TC = = Total revenue = PQ Fixed costs Variable costs Total costs = F + Vq Profit = TR - TC = Pq - (F + Vq) = Pq - F - Vq = (P - V)q - F

Example Determine the value of sales at breakeven if: Fixed costs = Ȼ 10, 000 Material = Ȼ 0. 75/unit Direct labor = Ȼ 1. 50/unit Selling price = Ȼ 4. 00 per unit BEPȻ = F 1 - (V/P) = Ȼ 10, 000 1 - [(1. 50 +. 75)/(4. 00)] Ȼ 10, 000 =. 4375 = Ȼ 22, 857. 14 F BEPq = P-V Ȼ 10, 000 = 4. 00 - (1. 50 +. 75) = 5, 714 units

Graphical Representation of Example in Previous Slide 50, 000 – Total Revenue Cedis 40, 000 – Break-even point 30, 000 – Total costs 20, 000 – Fixed costs 10, 000 – –| 0 | | | 2, 000 4, 000 6, 000 8, 000 10, 000 Units

Graphical Breakeven Analysis – Total revenue line 900 – r Cost/Revenue in cedis 800 – do rri Break-even point Total cost = Total revenue 700 – Total cost line o it c of Pr 600 – 500 – Variable cost 400 – 300 – 200 – 100 – – 0 | ss r Lo rido r co | | Fixed cost | | | | | 100 200 300 400 500 600 700 800 900 1000 1100 Volume (units period)

Multiproduct Breakeven Analysis o o o What we have discussed so far applies to single products or items only. Where the firm deal with multiple products, the multiple product formula is used. The breakeven under the multiple product is determine in monetary terms only. That means that if the firm wants to know how much of each item to sell to breakeven, they have to use the single case approach

Multiple Product Formula Multiproduct Case F BEPȻ = ∑ 1 where V P F W i Vi Pi x (Wi) = variable cost per unit = price per unit = fixed costs = percent each product is of total dollar sales = each product

Multiproduct Example Fixed costs = Ȼ 3, 500 per month Item Sardine Soft drink Biscuit Pencil Milk Price Ȼ 2. 95. 80 1. 55. 75 2. 85 Cost Ȼ 1. 25. 30. 47. 25 1. 00 Annual Forecasted Sales Units 7, 000 5, 000 3, 000

Multiproduct Example Fixed costs = $3, 500 per month Item Sandwich Soft drink Baked potato Tea Salad bar Price $2. 95. 80 1. 55. 75 2. 85 Cost $1. 25. 30. 47. 25 1. 00 Annual Forecasted Sales Units 7, 000 5, 000 3, 000

Multiproduct Example Fixed costs = $3, 500 per month and so to get annual, we multiply by 12 BEPȻ = = F ∑ 1 - Vi Pi Ȼ 3, 500 x 12. 625 = Ȼ 67, 200 x(Wi)

Margin of Safety o o o The difference between budgeted or actual sales and the breakeven point The margin of safety may be expressed in units or revenue terms Shows the amount by which sales can drop before a loss will be incurred

Example 1 Using the following data, calculate the breakeven point, contribution per unit and margin of safety in units: q Selling Price = Ȼ 50 o Variable Cost = Ȼ 40 o Fixed Cost = Ȼ 70, 000 o Budgeted Sales = 7, 500 units

Example 1: Solution o o Contribution = Ȼ 50 - Ȼ 40 = Ȼ 10 per unit Breakeven point = Ȼ 70, 000/Ȼ 10 = 7, 000 units Margin of safety = 7500 – 7000 = 500 units To determine the margin of safety in monetary terms, we multiple 500 by 50 to get Ȼ 25, 000

Target Profits o o o Sometime, firms do not just want to breakeven. They may want a target profit In that case, contribution per unit will need to cover profit as well as fixed costs Required profit is accordingly treated as an addition to Fixed Costs

Example 2 Using the following data, calculate the level of sales required to generate a profit of Ȼ 10, 000: o Selling Price = Ȼ 35 o Variable Cost = Ȼ 20 o Fixed Costs = Ȼ 50, 000

Example 2: Solution o o q Contribution = Ȼ 35 – Ȼ 20 = Ȼ 15 Level of sales required to generate profit of Ȼ 10, 000: Ȼ 50, 000 + Ȼ 10, 000 Ȼ 15 = 4000 units The firm will need to sell 4000 units to not only breakeven, but make a target profit of Ȼ 10, 000