CostVolumeProfit Relationships Learning Objectives Explain the purpose of

Cost-Volume-Profit Relationships

Learning Objectives • Explain the purpose of cost-volume-profit (CVP) analysis • Explain the contribution margin (CM) concept • Compute the break-even (BE) point by using graph, equation, and contribution margin methods • Compute profit (income) at a given level of sales and also target sales by using the methods above • Calculate the effect on profit of changes in variable costs, fixed costs, selling price, and volume • Perform CVP analysis for a multi-product company • Compute the margin of safety and operating leverage and explain their significance

Cost-Volume-Profit (CVP) Analysis • CVP analysis is an analysis of the relationships among activity level, revenue, costs and profit. • Classification of cost items into fixed and variable is paramount in CVP analysis. • Contribution margin (CM) concept facilitates CVP analysis.

The CM Concept • Assume the following budgeted (expected) annual data for ABC, a single-product company. Total Per Unit Percent Sales (500 units) $10, 000 20 100% -Variable costs 6, 000 12 60% Contribution margin $ 4, 000 8 40% -Fixed costs 3, 000 Net income $ 1, 000

The CM Concept • Assume the following budgeted (expected) annual data for ABC, a single-product company. Total Per Unit Percent Sales (500 units) $10, 000 20 100% -Variable costs 6, 000 12 60% Contribution margin $ 4, 000 8 40% -Fixed costs 3, 000(CM) is the amount Contribution Margin Net income from sales $ 1, 000 remaining revenue after variable costs have been deducted.

The CM Concept • Assume the following budgeted (expected) annual data for ABC, a single-product company. Total Per Unit Percent Sales (500 units) $10, 000 20 100% -Variable costs 6, 000 12 60% Contribution margin $ 4, 000 8 40% -Fixed costs 3, 000 Net income $ 1, 000 fixed costs. CM goes to cover

The CM Concept • Assume the following budgeted (expected) annual data for ABC, a single-product company. Total Per Unit Percent Sales (500 units) $10, 000 20 100% -Variable costs 6, 000 12 60% Contribution margin $ 4, 000 8 40% -Fixed costs 3, 000 Net income $ 1, 000 After covering fixed costs, any remaining CM contributes to profit.

The CM Concept • Assume the following budgeted (expected) annual data for ABC, a single-product company. Total Per Unit Percent Sales (500 units) $10, 000 20 100% -Variable costs 6, 000 12 60% Contribution margin $ 4, 000 8 40% -Fixed costs 3, 000 CM per unit is the amount that each unit contributes to fixed$costs and profit. Net income 1, 000 CM Per unit therefore measures the change in profit as a result of a one unit change in sales.

The CM Concept • Assume the following budgeted (expected) annual data for ABC, a single-product company. Total Per Unit Percent Sales (500 units) $10, 000 20 100% -Variable costs 6, 000 12 60% Contribution margin $ 4, 000 8 40% -Fixed costs 3, 000 that each dollar of sales CM percentage is the amount contributes to$fixed Net income 1, 000 costs and profit. CM percentage therefore measures the change in profit as a result of a one dollar change in sales.

Quick Test Carver Company produces a product which sells for $30. Variable manufacturing costs are $15 per unit. Fixed manufacturing costs are $5 per unit based on the current level of activity, and fixed selling and administrative costs are $4 per unit. A sales commission of 10% of the selling price is paid on each unit sold. The contribution margin per unit is: a. $ 3 b. $15 c. $ 8 d. $12

Applications of CVP Analysis • • • Break-even analysis (calculation) Profit at a given level of sales Target sales The effect on profit of changes in cost structure The effect on profit of changes in selling price The effect on profit of changes in costs and selling price • The effect on profit of changes in sales mix (for a multi-product company)

Break-even (BE) Analysis • The objective of BE analysis is to determine the quantity or dollar amount of sales that generates zero profit. • There are basically three methods for BE analysis: – Graph – Equation – Contribution margin

BE Analysis – Graphic Method $, Y C F = t s l co ota T FC V l a ot 12 ( C C V VC/unit + ) X * VC/unit Total FC ($3, 000) T 0 # of units produced and sold, X

) BE Analysis – Graphic Method en ue (20 *X $, Y BE in $ (7, 500) To tal rev C F = st C V + o c l a t To FC 0 BE in units (375) # of units produced and sold, X

BE Analysis – Equation Method Revenue = (Unit SP) * Volume Total cost = (Unit VC) * Volume + Total FC Profit = Revenue - Total cost = (Unit SP) * Volume - (Unit VC) * Volume Total FC = (Unit SP - Unit VC) * Volume - Total FC At break-even, profit is zero. Thus: Volumebe = (Total FC) / (Unit SP - Unit VC) Dollarbe = Volumebe * Unit SP

BE Analysis – CM Method • CM per unit (CM ratio) is the amount that each unit (dollar of sales) contributes toward recovering fixed costs and then toward earning a profit for the period. • The volume and dollar sales at break-even then are: Volumebe = (Total FC) / (Unit CM) = $3, 000 / $ 8 Dollarbe = (Total FC) / (CM ratio) = $3, 000 /. 40 • CM formulas can be derived from the equation method.

Profit at a Given Level of Sales • The same three methods as in BE analysis can be used. See next slide for graphic solution. • Using equation method, Profit = Revenue - Total cost = (Unit SP) * Volume - (Unit VC) * Volume Total FC = (Unit SP - Unit VC) * Volume - Total FC • Using CM method, Profit = (CM/unit) * Volume - Total FC or, (CM ratio) * Revenue - Total FC

Profit Calculation – Graphic Method To tal rev en ue $, Y l a t o t s o c C F = C V + Pretax profit=Total revenue minus Total cost T FC 0 -FC CM/unit # of units produced and sold, X

Target Sales • The objective here is to determine the level of sales that has to be achieved to make a given amount of profit. • The same three methods as in BE analysis can be used. Using contribution margin method: Volumets = (Fixed cost + Profit) / (Unit CM) Dollarts = (Fixed cost + Profit) / (CM ratio) Assuming ABC desires a profit of $1, 000, then Volumets = ($3, 000 + $1, 000) / $8 = 500 units

The Effect of Changes in Parameters • Selling price and costs in the computations above are estimates and thus may not materialize. • It may also be possible to change the proportions of fixed and variable costs, e. g. , through automation or use of higher quality material. • Thus, managers often perform an (a sensitivity) analysis to determine the impact of changes in estimates or cost components on BE point and profit.

The Effect of Change in Cost Elements • For example, NBC produces a surge protector. • SP = $30; VC = $18; total FC = $15, 000; and sales volume = 2, 000. • A proposed automation decreases VC by $3 per unit, but increases FC by $5, 000. • What is the impact on profit? Increase in CM ($3 * 2, 000) $ 6, 000 Increase in FC (5, 000) Net effect on profit $ 1, 000

The Effect of Change in Selling Price • For example, XYZ produces a spray paint. • SP = $20; VC = $8; total FC = $10, 000; and sales volume = 1, 000. • Sales people insist that reducing the selling price by $4 per unit increases sales volume by 20%. • What is the impact on profit? Proposed CM (8 * 1, 200) $ 9, 600 Current CM (12 * 1, 000) 12, 000 Net effect on profit $(2, 400)

The Effect of Change in Sales Volume and Costs • For example, XYZ produces a spray paint. • SP = $20; VC = $8; total FC = $10, 000; and sales volume = 1, 000. • An advertising campaign costing $3, 000 increases sales volume by 20%. • What is the impact on income? Increase in CM (12 * 200) $ 2, 400 Increase in FC (3, 000) Net change in profit $ (600)

Multi-Product Case • A multi-product case can be converted into a single-product case by use of the weighted-average CM per unit or a composite unit. • Example: Sam Corp. sells two products with the following SP and VC: A B SP/unit $ 12 $ 20 VC/unit 5 8 • Sam has been selling two units of A for every three units of B. • Total FC is $ 20, 000. • What is the BE point?

Multi-Product – WA Approach • W. A. CM/unit = 2/5 * $7 + 3/5 * $12 = $ 10 • Now we can assume that we have one product with a CM of $ 10 per unit. • BE in units = total FC / CM per unit = $20, 000 / $10 = 2, 000 units • Units of A to be sold = 2/5 * 2, 000 = 800 • Units of B to be sold = 3/5 * 2, 000 = 1, 200

Multi-Product – Composite Unit • We introduce a composite unit, Z, consisting of 2 units of A and 3 units of B. • CM per unit of Z = 2 * $7 + 3 * $12 = $ 50 • Now we can assume that we have one product (Z) with CM of $ 50 per unit. • BE in units = total FC / CM per unit = $20, 000 / $50 = 400 units of Z • Units of A to be sold = 2 * 400 = 800 • Units of B to be sold = 3 * 400 = 1, 200

Assumptions in CVP Analysis • Linearity of revenues and costs, i. e. , efficiency, productivity, and selling price do not change • Accurate classification of costs into variable and fixed (i. e. , only one cost driver, unit) • Constancy of sales and production mix • Constancy of the inventory level, i. e. , sales = production • Equality of revenues and expenses with cash flows • Ignoring time value of money and non-quantitative information

Margin of Safety • Margin of safety is the excess of budgeted sales over the break-even sales. It is the amount by which sales can drop before losses are incurred. Margin of safety = Budgeted sales - Break-even sales Let’s calculate the margin of safety for ABC.

Margin of Safety • ABC has a break-even sales of $7, 500; budgeted sales are $10, 000. The margin of safety is $2, 500. Sales -Variable costs Contribution margin -Fixed costs Net income Budgeted $10, 000 6, 000 $ 4, 000 3, 000 $ 1, 000 BE Sales $7, 500 4, 500 $3, 000 $ 0

Margin of Safety • The margin of safety can be expressed as 25 percent of sales. ($2, 500 ÷ $10, 000) Budgeted BE Sales $10, 000 $7, 500 -Variable costs 6, 000 4, 500 Contribution margin $ 4, 000 $3, 000 -Fixed costs 3, 000 Net income $ 1, 000 $ 0

Operating Leverage • Operating leverage measures the percentage change in current profit as a result of a given percentage change in sales. • It is a measure of how sensitive net income is to change in sales. Degree of operating leverage = Contribution margin Net income

Operating Leverage Budgeted Sales -Variable costs Contribution margin -Fixed costs Net income $4, 000 $10, 000 6, 000 $ 4, 000 3, 000 $ 1, 000 = 4

Operating Leverage • With an operating leverage of 4, if ABC increases its sales by 10%, net income would increase by 40%.

Mixed Costs – Definition • Mixed costs are costs that contain both variable and fixed components, e. g. , utilities. – Costs aggregated in various ways are also mixed, e. g. , overhead or machining. • The fixed component represents the minimum cost of having a service available for use; the variable component represents the cost of actual consumption. • Graphically, a mixed cost is represented by a straight line that intersects the vertical (Y) axis.

Mixed Costs lm a t o T i t s o c xed Variable Utility charge Fixed Utility charge

Analysis of Mixed Costs (Cost Estimation) • Involves estimating the fixed and the variable components of a mixed (or total) cost, i. e. , generally estimating a linear cost formula Y= a + b. X that can be used to estimate cost at various levels of activity. • Y is the total mixed cost (the dependent variable – it is affected by the level of activity). • a is the total fixed cost (the constant). • b is the variable cost per unit (the multiplier for X). • X is the level of activity (the independent variable).

Methods of Cost Estimation • Engineering Method – It is based on a study of input-output relationship. – The cost of all inputs are added to estimate the cost of the output. – This method is used only when input-output relationship remains stable over-time and indirect costs are a small portion of total cost; it is also used when there is no past data to analyze. • Analysis of Past Data

Analysis of Past Data • Analysis of Past Data – High-low Method – Scatter-graph – Simple Ordinary Least-Square (OLS) Regression • Note: all of these methods assume linearity and one independent variable (one cost driver).

Cost Estimation Example • Wise Co. recorded the following machine hours and Overhead cost for the last six months. Machine Hours Overhead Cost 10 23 15 37 8 19 20 48 22 49 18 40

High-low Method • Graphically, a line that connects the observations with the highest and lowest value for the dependent variable.

High-low Method • Mathematically, choose the observations with the highest and lowest value for the dependent variable to estimate a and b in the cost formula Y = a + b. X • b = rise/run = change in cost / change in activity = (49 - 19) / (22 - 8) = 2. 14 • Go to the high or low observation only: • Y = a + b. X a = Y - b. X • a = 49 - 2. 14 * 22 a = 1. 92 • Cost formula: Y = 1. 92 + 2. 14 X

Notes on High-low Method • The 1. 92 is not the estimated fixed overhead at zero level of activity. It is the estimated fixed overhead within the relevant range. Similarly, 2. 14 is the estimated variable overhead per machine hour within the relevant range. • The method ignores all but two extreme observations. Thus, the accuracy of cost estimates depends on how representative the two points are of the entire set of observations.

Scatter-graph • Plot the data points on a graph and draw a line through those points that best fits the data.

Scatter-graph • To estimate a and b in the cost formula: – Read the intercept and the slope from the graph. – Alternatively, use the coordinates of any two points on the line and the formulas as in the high-low method. • The method uses all the observations, but it is subjective (thus the reason for low usage and the quick-and-dirty label).

Simple Ordinary Least-Squares Regression • Estimate a and b in the cost formula in such a way that the sum of the squared errors (vertical distances between observations and regression line) is minimized. • Regression analysis is more appealing because we can measure the goodness of fit of the regression equation, and more importantly, because we can make probability statements about the estimated coefficient (b) and the estimated costs (Y).

Simple Ordinary Least-Squares Regression • Many computer programs provide estimates of a and b in the cost formula and regression related statistics; one only needs to understand the output. • Alternatively, for a simple regression, you can solve the following system of equations: Y = na + b X XY = a X + b X 2 where, n is the number of observations

Measures of Goodness of Fit for OLS • R 2 , the % of variation in Y that is explained by X. R 2 is between 0 and 1. • Standard error of regression (standard error of Y estimate), S(e), is an estimate of the standard deviation of the error term. – Note that the regression equation is Y = a + b. X + e (e is the random variation, error term), and the estimated regression equation is: Y = a + b. X

Measures of Goodness of Fit for OLS • Standard error of b, S(b), is an estimate of the standard deviation of b. • t = b/S(b) – As a rule of thumb, if t > 2, the estimated coefficient (b) is significantly different from zero, i. e. , X explains a significant portion of the variation in Y. – Computer programs report the p-value, i. e. , the significance level, for each variable.

Cost Estimation Example – Summary Fixed Cost Variable Cost period (a) per unit (b) High-Low 1. 92 2. 14 Scatter-graph 2. 00 2. 12 Regression 1. 41 2. 23 Estimated cost for the next month at 17 MH: High-Low = $1. 92 + $2. 14 * 17 = $38. 30 Scatter-graph = $2. 00 + $2. 12 * 17 = $38. 04 Regression = $1. 41 + $2. 23 * 17 = $39. 32

Data Analysis Steps • Before using any of the three methods above, a few data analysis steps should be taken. – Review alternative activity bases • activity base chosen should be closely related to cost item (Y) – Plot the data • catch outliers and omit them – Examine data correspondence and period of accumulation – Examine the constancy of production process