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Cost-Volume-Profit Relationships & Cost Estimation

Learn about the basics of cost-volume-profit analysis and the process of cost estimation. Explore the relationship between costs, volume, and profit and understand how to calculate the average cost per pool table and estimate fixed costs per month.

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Cost-Volume-Profit Relationships & Cost Estimation

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  1. Cost-Volume-Profit Relationships Chapter Six

  2. 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

  3. 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.

  4. 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) + (3.192 x £598.6) = £2275 + £1911

  5. 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.

  6. COST VOLUME PROFIT ANALYSIS • HELPFUL TO UNDERSTAND THE RELATIONSHIP AMONG VARIABLE COSTS, FIXED COSTS AND PROFIT • BASIC ASSUMPTIONS: • SELLING PRICE IS CONSTANT • COSTS ARE LINEAR AND CAN BE DIVIDED INTO FIXED AND VARIABLE • FIXED ELEMENT CONSTANT OVER THE RELEVANT RANGE • UNIT VARIABLE COST CONSTANT OVER RELEVANT RANGE • SALES MIX IS CONSTANT • INVENTORIES STAY AT THE SAME LEVEL

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

  8. 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.

  9. The Contribution Approach Each month Racing must generate at least $80,000 in total CM to break even.

  10. The Contribution Approach If Racing sells 400 unitsin a month, it will be operating at the break-even point.

  11. The Contribution Approach If Racing sells one more bike (401 bikes), net operating income will increase by $200.

  12. 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.

  13. 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.

  14. 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

  15. Fixed Expenses CVP Graph Dollars Units

  16. Total Expenses Fixed Expenses CVP Graph Dollars Units

  17. Total Sales Total Expenses Fixed Expenses CVP Graph Dollars Units

  18. Break-even point(400 units or $200,000 in sales) CVP Graph Profit Area Dollars Loss Area Units

  19. 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¢.

  20. 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:

  21. A $50,000 increase in sales revenue results in a $20,000 increase in CM. ($50,000 × 40% = $20,000) Contribution Margin Ratio

  22. 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?

  23. 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

  24. 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

  25. 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?

  26. $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.

  27. Changes in Fixed Costs and Sales Volume The Shortcut Solution

  28. 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?

  29. 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.

  30. 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?

  31. 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.

  32. 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?

  33. 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.

  34. 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?

  35. Change in Regular Sales Price

  36. Break-Even Analysis Break-even analysis can be approached in two ways: • Equation method • Contribution margin method

  37. At the break-even point profits equal zero Equation Method Profits = (Sales – Variable expenses) – Fixed expenses OR Sales = Variable expenses + Fixed expenses + Profits

  38. Break-Even Analysis Here is the information from Racing Bicycle Company:

  39. 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

  40. 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

  41. 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

  42. 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

  43. 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.

  44. $80,000 40% Break-even point in total sales dollars = $200,000 break-even sales Fixed expenses CM ratio = Contribution Margin Method Let’s use the contribution margin method to calculate the break-even point in total sales dollars at Racing.

  45. 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 break-even sales in units? 872 cups b. 3,611 cups c. 1,200 cups d. 1,150 cups Quick Check 

  46. Fixed expenses Unit CM Break-even = $1,300 $1.49/cup - $0.36/cup = $1,300 $1.13/cup = = 1,150 cups 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 break-even sales in units? a. 872 cups b. 3,611 cups c. 1,200 cups d. 1,150 cups

  47. 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 break-even sales in dollars? a. $1,300 b. $1,715 c. $1,788 d. $3,129 Quick Check 

  48. Fixed expenses CM Ratio Break-evensales = $1,300 0.758 = = $1,715 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 break-even sales in dollars? a. $1,300 b. $1,715 c. $1,788 d. $3,129

  49. DERIVATION OF EQUATIONS SALES= VARIABLE COSTS+FIXED COSTS + PROFIT p*q= vcu *q + FC + ¶ AT BREAKEVEN PROFIT = 0 p*q=vcu *q +FC q * (p-vcu) = FC q= FC / (p - vcu) OR q=FC/ cmu CM= SALES - TOTAL VC VC= SALES - CM= INCLUDE VARIABLE PRODUCTION AND SELLING EXPENSES cmu=CONTRIBUTION MARGIN PER UNIT= p - vcu=CM/q vcu= VARIABLE COST PER UNIT= VC/ q q number of units

  50. PROFIT ANALYSIS • AT BREAKEVEN PROFIT = 0 • BEFORE BREAKEVEN LOSS; AFTER BREAKEVEN PROFIT • CM COVERS FIXED COST UPTO BREAKEVEN POINT • AFTER BREAKEVEN POINT INCREASE IN CM WILL INCREASE NET INCOME • CM = FC + INCOME BEFORE TAX

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