Cost-Volume-Profit Relationships November 17, 2015 Cost-Volume-Profit Relationships Chapter 6: Cost-Volume-Profit Relationships Cost-volume-profit (CVP) analysis helps managers understand the interrelationships among cost, volume, and profit by focusing their attention on the interactions among the prices of products, volume of activity, per unit variable costs, total fixed costs, and mix of products sold. It is a vital tool used in many business decisions such as deciding what products to manufacture or sell, what pricing policy to follow, what marketing strategy to employ, and what type of productive facilities to acquire.

Agenda A deeper look at Contribution Analysis Break even Cost-Volume-Profit Variable Costing and Decision Making

Basics of Cost-Volume-Profit Analysis The contribution income statement is helpful to managers in judging the impact on profits of changes in selling price, cost, or volume. The emphasis is on cost behavior. The contribution income statement is helpful to managers in judging the impact on profits of changes in selling price, cost, or volume. For example, let's look at a hypothetical contribution income statement for Racing Bicycle Company (RBC). Notice the emphasis on cost behavior. Variable costs are separate from fixed costs. The contribution margin is defined as the amount remaining from sales revenue after variable expenses have been deducted. Contribution Margin (CM) is the amount remaining from sales revenue after variable expenses have been deducted.

Basics of Cost-Volume-Profit Analysis Contribution margin is used first to cover fixed expenses. Any remaining contribution margin contributes to net operating income. CM is used first to cover fixed expenses. Any remaining CM contributes to net operating income.

The Contribution Approach If RBC sells 400 units in a month, it will be operating at the break-even point. If Racing sells 400 units a month, it will be operating at the break-even point. Total sales will be 400 units times $500 each or $200,000, and total variable expenses will be 400 units times $300 each for $120,000. Contribution margin is exactly equal to total fixed expenses. Let’s see what happens if Racing sells one more bike or a total of 401 bikes.

CVP Relationships in Equation Form This equation can be used to show the profit RBC earns if it sells 401. Notice, the answer of $200 mirrors our earlier solution. Profit = (Sales – Variable expenses) – Fixed expenses 401 units × $500 401 units × $300 $80,000 We begin by calculating sales. Sales are equal to $200,500, that is, 401 units sold at $500 per unit. Variable expenses are $120,300, 401 units sold at $300 per unit. With fixed expenses of $80,000, we can see that profit or net operating income is equal to $200, exactly the same answer we got using the contribution income statement approach. Profit = ($200,500 – $120,300) – $80,000 $200 = ($200,500 – $120,300) – $80,000

Preparing the CVP Graph Break-even point (400 units or $200,000 in sales) Profit Area Dollars The break-even point is where the total revenue and total expenses lines intersect. In the case of Racing Bicycle, break-even is 400 bikes sold, or sales revenue of $200,000. The profit or loss at any given sales level is measured by the vertical distance between the total revenue and the total expenses lines. Loss Area Units

Contribution Margin Ratio (CM Ratio) The CM ratio is calculated by dividing the total contribution margin by total sales. The contribution margin ratio is calculated by dividing the total contribution margin by total sales. In the case of Racing Bicycle, the ratio is 40%. Thus, each $1.00 increase in sales results in a total contribution margin increase of 40¢. $100,000 ÷ $250,000 = 40%

Contribution Margin Ratio (CM Ratio) If Racing Bicycle increases sales from 400 to 500 bikes ($50,000), contribution margin will increase by $20,000 ($50,000 × 40%). Here is the proof: A $50,000 increase in sales revenue results in a $20,000 increase in CM ($50,000 × 40% = $20,000). Let’s see how we can use the contribution margin ratio to look at the contribution margin income statement of Racing Bicycle in a little different way. If RBC is able to increase its sales from 400 to 500 bikes, the increase in contribution margin by $20,000, that is, $50,000 (100 bikes times $500 per bike) times 40%.

Break-Even in Unit Sales: Equation Method Profits = Unit CM × Q – Fixed expenses Suppose RBC wants to know how many bikes must be sold to break-even (earn a target profit of $0). To find the break-even point, we set profits equal to zero, and solve for the unknown quantity, Q. Suppose RBC wants to know how many bikes must be sold to break-even (earn a target profit of $0). Racing Bicycle has a unit contribution margin of $200, and total fixed expenses of $80,000. Take a second and solve this equation. $0 = $200 × Q + $80,000 Profits are zero at the break-even point.

Break-Even in Unit Sales: Formula Method Let’s apply the formula method to solve for the break-even point. Fixed expenses CM per unit = Unit sales to break even A quicker way to solve this problem is to add the desired profits to the fixed cost and divide the total by the contribution margin per unit. Notice we get the same result of 400 bikes. $80,000 $200 Unit sales = Unit sales = 400

Contribution Analysis Below is a Contribution Income Statement for the Go Fast Car Company The Contribution Margin is $52 million, $4,727 per unit, or 39% With this analysis in place, we can test different volume scenarios

Calculating Break Even Under a Contribution Analysis framework, calculating break-even becomes very straight forward Break Even Volume = Fixed Costs / Unit Contribution Margin Break Even Sales = Break Even Volume * Unit Sales Price At sales volume of $96.5 million, Go Fast Car Co will make $0 For every additional sale, the company will add $4.7k to its operating income

Target Profit: Formula Method The formula uses the following equation. Target profit + Fixed expenses CM per unit = Unit sales to attain the target profit Target profit is expressed in units sold. For this equation we divide the sum of the desired target profit plus total fixed expenses by the contribution margin per unit.

Target Profit Analysis in Terms of Unit Sales Suppose Racing Bicycle Company wants to know how many bikes must be sold to earn a profit of $100,000. Target profit + Fixed expenses CM per unit = Unit sales to attain the target profit Suppose Racing Bicycle Company wants to earn net operating income of $100,000. How many bikes must the company sell to achieve this profit level? Let’s use the formula method. Unit sales to attain the target profit level is equal to the sum of $100,000 (the target profit) plus $80,000 (total fixed expenses) divided by the unit contribution margin of $200. We arrive at 900 units sold to earn net operating income of $100,000. $100,000 + $80,000 $200 Unit sales = Unit sales = 900

Contribution Margin Ratio The Contribution margin ration is: For Go Fast Car Co 52,000,000 / 132,000,000 = 39% For every additional $1 sold, the company will see 39 cents go to Operating Income Total CM Total sales CM Ratio =

Contribution Margin Ratio (CM Ratio) The relationship between profit and the CM ratio can be expressed using the following equation: Profit = (CM ratio × Sales) – Fixed expenses If Racing Bicycle increased its sales volume to 500 bikes, what would management expect profit or net operating income to be? The relationship between profit and the CM ratio can be expressed using the following equation: Profit equals CM ratio times Sales less Fixed expenses. If Racing Bicycle reported sales of $250,000, what would management expect net operating profits to be? As you can see, the expected net operating profit is $20,000. Profit = (40% × $250,000) – $80,000 Profit = $100,000 – $80,000 Profit = $20,000

Cost Structure and Profit Stability There are advantages and disadvantages to high fixed cost (or low variable cost) and low fixed cost (or high variable cost) structures. An advantage of a high fixed cost structure is that income will be higher in good years compared to companies with lower proportion of fixed costs. A disadvantage of a high fixed cost structure is that income will be lower in bad years compared to companies with lower proportion of fixed costs. Generally, companies with a high fixed cost structure will show higher net income in good years than companies with lower fixed cost structures. Just the opposite is true in bad years. Companies with low fixed cost structures enjoy greater stability in income across good and bad years. Companies with low fixed cost structures enjoy greater stability in income across good and bad years.

Operating Leverage Operating leverage is a measure of how sensitive net operating income is to percentage changes in sales. It is a measure, at any given level of sales, of how a percentage change in sales volume will affect profits. Contribution margin Net operating income Degree of operating leverage = Operating leverage is a measure of how sensitive net operating income is to percentage changes in sales. The degree of operating leverage is a measure, at any given level of sales, of how a percentage change in sales volume will affect profits. It is computed by dividing contribution margin by net operating income. Let’s look at Racing Bicycle.

Degree of Operating Leverage To illustrate, let’s look at the contribution income statement for RBC. Recall that Racing is currently selling 500 bikes and producing net income of $20,000. Contribution margin is $100,000. Operating leverage is 5, which is determined by dividing the $100,000 contribution margin by the net income of $20,000. Now that we have calculated the degree of operating leverage for RBC, let’s see exactly what this means to management. $100,000 $20,000 = 5 Degree of Operating Leverage =

Here’s the verification! Operating Leverage With an operating leverage of 5, if RBC increases its sales by 10%, net operating income would increase by 50%. If Racing is able to increase sales by 10%, net income will increase by 50%. We multiply the percentage increase in sales by the degree of operating leverage. Let’s verify the 50% increase in profit. Here’s the verification!

10% increase in sales from . . . results in a 50% increase in Operating Leverage A 10% increase in sales would increase bike sales from the current level of 500 to 550. Look at the contribution margin income statement and notice that income increased from $20,000 to $30,000. That $10,000 increase in net income is a 50% increase. So it is true that a 10% increase in sales results in a 50% in net income. This is powerful information for a manager to have. 10% increase in sales from $250,000 to $275,000 . . . . . . results in a 50% increase in income from $20,000 to $30,000.

Multiple Volume Scenarios & Cost Volume Profit The Variable Cost Model allows us to easily test a multitude of volume scenarios and assess the impact on income What would Operating Income be at unit sales of 20,000? Graph the company’s CVP (X axis -$s; Y axis – units)

Assumptions and Shortcomings The Contribution Model can be very helpful, but it does make a number of simplifying assumptions Selling price is constant Costs are linear Sales/product mix is constant Inventories do not change (production = sales) Ultimately, reliable models will be much more detailed Nonetheless, and certainly within certain bounds, these concepts are most helpful

Decision Making The VP Sales wants to undertake a $3 million promotional campaign How many more cars would Go Fast have to sell to justify that level of expenditure?

Decision Making How many more cars would Go Fast have to sell to justify that level of expenditure? COST OF CAMPAIGN / UNIT CONTRIBUTION ($) = INCREMENTAL # OF UNITS REQUIRED

Decision Making Analysis of how many cars would need to be sold to justify a $3 million promotional expenditure In this case, if the VP Sales signed up to selling more than 635 incremental cars, the company should proceed The VP Sales compensation should be driven by the success of this Of course, the company would only do this for substantially more than break even

Decision Making An economist reported that demand for Go Fast’s cars is highly elastic A decrease in price of 2% would increase unit sales volume by 10% Would Go Fast Car Co be better off by doing this?

Decision Making Analysis of a 2% decrease in price resulting in 10% increase in unit sales Results in a decrease in Contribution per car, but an increase in operating income

Multi-Product Companies and Sales Mix Analysis of a multi-product company What is break-even? Which product would the company rather sell and why?

Multi-Product Companies and Sales Mix Break even sales = Fixed Costs/Contribution Margin $53 million / .36 = $147 million The company would rather sell a car as they contribute more in absolute dollars and profitability

Multi-Product Companies and Sales Mix Break even sales = Fixed Costs/Contribution Margin

Structuring Sales Commissions Companies generally compensate salespeople by paying them either a commission based on sales or a salary plus a sales commission. Commissions based on sales dollars can lead to lower profits in a company. Let’s look at an example. You have probably heard that salespersons can be compensated on a commission basis. The commission is usually based on sales revenue generated. Some salespersons work on a salary plus commission. When salespersons are paid a commission based on sales dollars generated, the income statement impact may not be fully understood. Let’s look at an example.

Structuring Sales Commissions Pipeline Unlimited produces two types of surfboards, the XR7 and the Turbo. The XR7 sells for $100 and generates a contribution margin per unit of $25. The Turbo sells for $150 and earns a contribution margin per unit of $18. Pipeline Unlimited produces two surfboards. The XR7 model sells for $100 dollars and has a contribution margin per unit of $25. The second surfboard, the Turbo model, sells for $150 and has a contribution margin of $18 per unit sold. The sales force at Pipeline is paid on sales commissions. The sales force at Pipeline Unlimited is compensated based on sales commissions. Which product would you prefer to sell if you were a salesperson?

Structuring Sales Commissions If you were on the sales force at Pipeline, you would push hard to sell the Turbo even though the XR7 earns a higher contribution margin per unit. To eliminate this type of conflict, commissions can be based on contribution margin rather than on selling price alone. If you were on the sales force, you would try to sell all the Turbo models you could because it has a higher selling price per unit. The problem is that the XR7 model produces a higher contribution margin to the company. It might be a good idea for Pipeline to base its sales commissions on contribution margin rather than selling price alone.

Review A deeper look at Contribution Analysis Break even Cost-Volume-Profit Variable Costing and Decision Making

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