EMBA 5403 Fall 2010 Cost-Volume-Profit Relationships
Cost Estimation 1 Constant 250 Std Err of Y Est 299.304749934466 R squared 0.944300518134715 No. of Observations 5 Degrees of Freedom 3 X Coefficient(s) 6.75 Std Err of Coef. 0.9464847243
Estimation (continued) The results gives rise to the following equation: Utility Costs = £250 + (£6.75 x # of units produced) R2 = .944, or 94.4 percent of the variation in setup costs is explained by the number of setup hours variable.
Estimation (continued) Given: *T-value for sample size of 5 at 95% confidence level is 3.182 (two-tale test and 3 degrees of freedom) *Standard error of estimate for this sample at the 95% confidence level is 598.6 The confidence interval for 300 units is: TC = £250 + 6.75 (300) + (3.182 x £598.6) = £2275 + £1911
Cost Estimation Example 2 • In each month, Exclusive Billiards produces between 4 to 10 pool tables. The plant operates on 40-hr shift to produce up to seven tables. Producing more than seven tables requires the craftsmen to work overtime. Overtime work is paid at a higher hourly wage. The plant can add overtime hours and produce up to 10 tables per month. The following table contains the total cost of producing between 4 and 10 pool tables. Required: a. compute average cost per pool table for 4 to 10 tables • Estimate fixed costs per month.
Cost-Volume-Profit Analysis • Examines the behavior of total revenues, total costs, and operating income as changes occur in the output level, selling price, variable costs or fixed costs • helpful to understand the relationship among variable costs, fixed costs and profit Assumptions of CVP Analysis • revenues change in relation to production and sales • costs can be divided in variable and fixed categories and fixed element constant over the relevant range • revenues and costs behave in a linear fashion • costs and prices are known • if more than one product exists, the sales mix is constant • inventories stay at the same level • we can ignore the time value of money Page 67
Contribution Margin • Contribution margin is equal to the difference between total revenue and total variable costs Contribution margin per unit = Selling price - Variable cost per unit Contribution margin percentage = Contribution margin per unit / selling price per unit Total for Per Unit 2 units % Revenue $200 $400 100% Variable costs 12024060% Contribution margin $80 $160 40% Pages 68 - 69
Contribution Margin Income Statement • Income statement that groups line items by cost behaviour to highlight the contribution margin Packages Sold 0 1 2 25 40 Revenue $0 $200 $400 $5,000 $8,000 Variable costs 0 120 240 3,000 4,800 Contribution margin 0 80 160 2,000 3,200 Fixed costs 2,000 2,000 2,000 2,000 2,000 Operating income $(2,000) $(1,920) $(1,840) $0 $1,200 Page 69
Breakeven Point • Quantity of output where total revenues equal total costs • Point where operating income equals zero Breakeven point in units = Fixed costs / Contribution margin per unit = $2,000 / $80 = 25 units Breakeven point in dollars = Fixed costs / contribution margin % = $2,000 / 40% = $5,000 Page 71
Cost-Volume-Profit Graph Total revenues line Breakeven Point 25 units $10,000 $8,000 $6,000 $4,000 $2,000 $0 Total costs line Operating income Operating loss 0 10 20 30 40 50 Units Sold Page 72
Target Operating Income • For most firms in the private sector, the main objective is not to breakeven • Convert after-tax desired net income to its before-tax equivalent operating income Target operating income = Target net income / (1 - tax rate) Target Unit Sales = (Fixed costs + Target operating income) / Contribution margin per unit Target Dollar Sales = (Fixed costs + Target operating income) / Contribution margin % Pages 73 - 75
Sensitivity Analysis • sensitivity analysis is a “what-if” technique that examines how a result will change if the original predicted data are not achieved or if an underlying assumption changes • What will happen to operating income if volume declines by 5%? • What will happen to operating income if variable costs increase by 10% per unit? • sensitivity analysis broadens management’s perspectives about possible outcomes Pages 76 - 77
Option 2 $1,400 Fixed Fee + 5% Commission Option 1 $2,000 Fixed Fee Option 3 20% Commission Rev Rev Rev $ $ $ Cost Cost Cost Units Units Units Breakeven = 25 units Breakeven = 20 units Breakeven = 0 units Alternative Cost Structures • CVP helps managers assess the risks and potential benefits of adopting alternative cost structures Example: Alternative rental arrangements Pages 77 - 78
Basics of Cost-Volume-Profit Analysis CM is used first to cover fixed expenses. Any remaining CM contributes to net operating income.
The Contribution Approach Sales, variable expenses, and contribution margin can also be expressed on a per unit basis. If Racing sells an additional bicycle, $200 additional CM will be generated to cover fixed expenses and profit.
The Contribution Approach Each month Racing must generate at least $80,000 in total CM to break even.
The Contribution Approach If Racing sells 400 unitsin a month, it will be operating at the break-even point.
The Contribution Approach If Racing sells one more bike (401 bikes), net operating income will increase by $200.
The Contribution Approach We do not need to prepare an income statement to estimate profits at a particular sales volume. Simply multiply the number of units sold above break-even by the contribution margin per unit. If Racing sells 430 bikes, its net income will be $6,000.
CVP Relationships in Graphic Form The relationship among revenue, cost, profit and volume can be expressed graphically by preparing a CVP graph. Racing developed contribution margin income statements at 300, 400, and 500 units sold. We will use this information to prepare the CVP graph.
CVP Graph Dollars In a CVP graph, unit volume is usually represented on the horizontal (X) axis and dollars on the vertical (Y) axis. Units
Fixed Expenses CVP Graph Dollars Units
Total Expenses Fixed Expenses CVP Graph Dollars Units
Total Sales Total Expenses Fixed Expenses CVP Graph Dollars Units
Break-even point(400 units or $200,000 in sales) CVP Graph Profit Area Dollars Loss Area Units
Total CM Total sales CM Ratio = $80,000 $200,000 = 40% Contribution Margin Ratio The contribution margin ratio is:For Racing Bicycle Company the ratio is: Each $1.00 increase in sales results in a total contribution margin increase of 40¢.
Unit CM Unit selling price CM Ratio = $200 $500 = 40% Contribution Margin Ratio Or, in terms of units, the contribution margin ratiois:For Racing Bicycle Company the ratio is:
A $50,000 increase in sales revenue results in a $20,000 increase in CM. ($50,000 × 40% = $20,000) Contribution Margin Ratio
CONTRIBUTION MARGIN RATIO CMR= CONTRIBUTION MARGIN RATIO = CM / SALES OR cmu/p VCR = VARIABLE COST RATIO = VC/SALES OR vcu/p CMR +VCR= 1 EFFECT OF CHANGE IN FIXED COSTS? EFFECT OF CHANGE IN VARIABLE COSTS? EFFECT OF CHANGE IN SELLING PRICE?
Quick Check Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the CM Ratio for Coffee Klatch? a. 1.319 b. 0.758 c. 0.242 d. 4.139
Unit contribution margin Unit selling price CM Ratio = ($1.49-$0.36) $1.49 = $1.13 $1.49 = = 0.758 Quick Check Coffee Klatch is an espresso stand in a downtown office building. The average selling price of a cup of coffee is $1.49 and the average variable expense per cup is $0.36. The average fixed expense per month is $1,300. 2,100 cups are sold each month on average. What is the CM Ratio for Coffee Klatch? a. 1.319 b. 0.758 c. 0.242 d. 4.139
Changes in Fixed Costs and Sales Volume What is the profit impact if Racing can increase unit sales from 500 to 540 by increasing the monthly advertising budget by $10,000?
$80,000 + $10,000 advertising = $90,000 Changes in Fixed Costs and Sales Volume Sales increased by $20,000, but net operating income decreased by $2,000.
Changes in Fixed Costs and Sales Volume The Shortcut Solution
Change in Variable Costs and Sales Volume What is the profit impact if Racing can use higher quality raw materials, thus increasing variable costs per unit by $10, to generate an increase in unit sales from 500 to 580?
580 units × $310 variable cost/unit = $179,800 Change in Variable Costs and Sales Volume Sales increase by $40,000, and net operating income increases by $10,200.
Change in Fixed Cost, Sales Price and Volume What is the profit impact if Racing (1) cuts its selling price $20 per unit, (2) increases its advertising budget by $15,000 per month, and (3) increases unit sales from 500 to 650 units per month?
Change in Fixed Cost, Sales Price and Volume Sales increase by $62,000, fixed costs increase by $15,000, and net operating income increases by $2,000.
Change in Variable Cost, Fixed Cost and Sales Volume What is the profit impact if Racing (1) pays a $15 sales commission per bike sold instead of paying salespersons flat salaries that currently total $6,000 per month, and (2) increases unit sales from 500 to 575 bikes?
Change in Variable Cost, Fixed Cost and Sales Volume Sales increase by $37,500, variable costs increase by $31,125, but fixed expenses decrease by $6,000.
Change in Regular Sales Price If Racing has an opportunity to sell 150 bikes to a wholesaler without disturbing sales to other customers or fixed expenses, what price would it quote to the wholesaler if it wants to increase monthly profits by $3,000?
Break-Even Analysis Break-even analysis can be approached in two ways: • Equation method • Contribution margin method
At the break-even point profits equal zero Equation Method Profits = (Sales – Variable expenses) – Fixed expenses OR Sales = Variable expenses + Fixed expenses + Profits
Break-Even Analysis Here is the information from Racing Bicycle Company:
Equation Method • We calculate the break-even point as follows: Sales = Variable expenses + Fixed expenses + Profits $500Q = $300Q + $80,000 +$0 Where: Q = Number of bikes sold $500 = Unit selling price $300 = Unit variable expense $80,000 = Total fixed expense
Equation Method • We calculate the break-even point as follows: Sales = Variable expenses + Fixed expenses + Profits $500Q = $300Q + $80,000 + $0 $200Q = $80,000 Q = $80,000 ÷ $200 per bike Q = 400 bikes
Equation Method • The equation can be modified to calculate the break-even point in sales dollars. Sales = Variable expenses + Fixed expenses + Profits X = 0.60X + $80,000 +$0 Where: X = Total sales dollars 0.60 = Variable expenses as a % of sales $80,000 = Total fixed expenses
Equation Method • The equation can be modified to calculate the break-even point in sales dollars. Sales = Variable expenses + Fixed expenses + Profits X = 0.60X + $80,000 + $0 0.40X = $80,000 X = $80,000 ÷ 0.40 X = $200,000
Break-even point in units sold Fixed expenses Unit contribution margin = Break-even point in total sales dollars Fixed expenses CM ratio = Contribution Margin Method The contribution margin method has two key equations.