1 Cost-Volume-Profit Analysis Page 1 2. Cost-Volume-Profit Analysis Now that we have discussed a company s cost function, learned how to identify its fixed and variable costs. We will now discuss a manner in which a company can use that information in order to make strategic decisions. Breaking Even? Understanding the relationship between a firm s costs, profits and its volume levels is very important for strategic planning. When you are considering undertaking a new project, you will probably ask yourself, How many units do I have to produce and sell in order to Break Even? The feasibility of obtaining the level of production and sales indicated by that answer is very important in deciding whether or not to move forward on the project in question. Similarly, before undertaking a new project, you have to assure yourself that you can generate sufficient profits in order to meet the profit targets set by your firm. Thus, you might ask yourself, How many units do I have to sell in order to produce a target income? You could also ask, If I increase my sales volume by 50%, what will be the impact on my profits? This area is called Cost-Volume-Profit (CVP) Analysis. In this discussion we will assume that the following variables have the meanings given below: Break-Even Point P = Selling Price Per Unit Units Produced and Sold V = Variable Cost Per Unit F = Total Fixed Costs Op = Operating Profits (Before Tax Profits) t = Tax rate Your Sales Revenue is equal to the number of units sold times the price you get for each unit sold: Sales Revenue = Px Assume that you have a linear cost function, and your total costs equal the sum of your Variable Costs and Fixed Costs: Total Costs = Vx + F When you Break Even, your Sales Revenue minus your Total Costs are zero: Sales Revenue Total Costs = 0
2 Cost-Volume-Profit Analysis Page 2 This is the Operating Income Approach described in your book. If you move your Total Costs to the other side of the equation, you see that your Sales Revenue equals your Total Costs when you Break Even: Sales Revenue = Total Costs Now, solve for the number of units produced and sold (x) that satisfies this relationship: Revenue = Total Costs P Vx + F Px - V F x(p - V) = F F (P -V) (FORMULA "A") Formula "A" is the Contribution Margin Approach that is described in your book. You can see that both approaches are related and produce the same result. Break-Even Example Assume Bullock Net Co. is an Internet Service Provider. Bullock offers its customers various products and services related to the Internet. Bullock is considering selling router packages for its DSL customers. For this project, Bullock would have the following costs, revenues and tax rates: P = $200 V = $120 F = $2,000 Tax Rate (t) = 40% Using Formula A, we can compute the Break-Even Point in units: 2,000 ( ) 2, units Sometimes, you see the (P-V) replaced by the term "Contribution Margin Per Unit" (CMU): F CMU (FORMULA "A")
3 Cost-Volume-Profit Analysis Page 3 This is way that your textbook presents Formula A. This makes sense if you think about it. Every time that you sell a unit, you earn the Contribution Margin per unit. The Contribution Margin per unit is the portion of the Sales Price that is left after paying the Variable Cost per unit. It is available to pay the Fixed Costs. If every time you sell a unit you earn $80 to help pay your Fixed Costs of $2,000, how many units do you need to sell in order to pay off the $2,000 completely? 2, = 25 Break-Even Point In Sales Dollars Taking Formula "A," you can multiply both sides of the equation by P: P _F_ (P-V) F x P (P-V) Recall what you do when you have a fraction in the denominator of a fraction: _a_ b/c = (a)x(c) b This works backwards as well: (a)x(c) b = _a_ b/c We can rewrite this equation: P F (P-V) P (FORMULA "B")
4 Cost-Volume-Profit Analysis Page 4 Formula B gives you the Sales Revenue that you need in order to Break Even. The Denominator [(P-V)/P] is referred to as the Contribution Margin Ratio. It tells you, what percentage of every dollar of Sales Revenue goes to help pay off the Fixed Costs. You can see this if you break up the Contribution Margin Ratio: (P-V)/P P/P - V/P 1 - V/P V/P gives you the percentage of the Sales Price that goes to pay off the Variable Costs (the Variable Cost Ratio or Variable Margin). Thus, one minus the Variable Cost Ratio gives you the percentage of the Sales Price that is available to help pay the Fixed Costs. Sometimes Formula B is rewritten by replacing [(P-V)/P] with the Contribution Margin Ratio (CMR): P F CMR (FORMULA "B") This is the way Formula B is presented in your book Break-Even Point In Sales Dollars Examples Let us continue using the Bullock example. Using Formula B, we can compute the Break-Even Point in Sales Revenue: P 2,000 ( ) 200 P 2, P $5,000 So, what is the big deal? We already knew that Bullock needed to sell 25 units to Break Even by using Formula A. We also know that each unit sells for $200. We therefore know that selling the 25 units will produce Sales Revenue of $5,000. Why do we need a separate formula? We have the two formulas because sometimes you might not have enough information to use Formula A, but you will have enough information to use Formula B.
5 Cost-Volume-Profit Analysis Page 5 For example, Cuba Radio Co produces portable sports radios. It has released the following Variable Costing Income Statement. This is the only financial information that we have regarding the Cuba s operations: Sales Revenue: $100,000 (Px) Less Variable Costs: -30,000 (Vx) Contribution Margin: $ 70,000 (Px Vx) Less Fixed Costs: -50,000 (F) Operating Profit: $ 20,000 (Px - Vx F) What is the Break-Even point for Cuba? We do not know the number of units that Cuba sells in a year. We do not know the Price or the Variable Cost per unit. For all we know, Cuba sells one radio for $100,000 each (or 100,000 radios for $1 each). So, we cannot use Formula A. Although you do not know the price or the Variable Cost per unit, you are still able to calculate the Contribution Margin Ratio. Contribution Margin Px - V = (P-V) (P-V) Sales Revenue Px Px P Thus, we can use Formula B. The Contribution Margin Ratio is.70 (70,000/100,000), and the Break-Even Point in Sales Revenue is: P F/CMR = 50,000/.70 = $71, Keep in mind that the reason that Cuba s Sales Revenue is lower than it was before is because Cuba sold fewer units. Cuba s price and Variable Cost per unit remained unchanged. Let's check if Cuba Breaks Even at this Sales Revenue figure: Sales Revenue: $ 71, P[ (old unit volume)] Less Variable Costs (30%): -21, V[ (old unit volume)] Contribution Margin: $50, (old Contribution Margin) Less Fixed Costs: -$50,000 Operating Profit: $ 0
6 Cost-Volume-Profit Analysis Page 6 Profit Targets You can use this same analysis to figure out how many units you need to sell in order to generate a target before-tax profit (Operating Profits). Operating Profits are determined as follows: Operating Profits = Revenue - Costs Op = Px - Vx - F If you move the costs to the other side of the equation, you end up with: P Vx + F + Op If you solve for x, you will see how many units you need to produce and sell in order to generate your target Operating Profits: P Vx + F + Op Px - V F + Op x(p - V) = F + Op (F + Op) (P - V) Or (F + Op) CMU Modified Formula A As was true with Formula B, we can multiply both sides of Modified Formula A by price to produce the formula that gives the Sales Revenue that is necessary to produce the target Operating Profits: P P (F + Op) (P - V) (F + Op)P (P - V) _(F + Op)_ (P - V) P Or P (F + Op) CMR Modified Formula B
7 Cost-Volume-Profit Analysis Page 7 Profit Target Example Assume that Bullock Net Co. has established a target Operating Profits figure of $40,000. Using Modified Formula A, you can determine the number of units that Bullock will need to sell in order to generate this target: 525 units (2, ,000) ( ) 42, If you think about it, it makes sense to add the Fixed Costs and the Target Operating Profits together and then divide by the Contribution Margin. If you make $80 every time you sell a unit, then you have to sell 25 units to Break Even (2,000/80). After you Break Even, you make $80 of profits every time that you sell a unit, and you have to sell 500 units in order to generate Operating Profits of $40,000 (40,000/80). Using Modified Formula B, you can determine the Sales Revenue that Bullock will need in order to generate Operating Profits of $40,000: After-Tax Profit Targets $105,000 (2, ,000) ( ) ,000.4 The Operating Profits to which we have been referring do not include tax expense. Once you subtract your tax expense from your Operating Profits, you have your Net Income. If you want to know how many units that you need to produce and sell in order to generate a target Net Income (or after-tax profit), just convert the after-tax number into a before-tax number. You can then substitute the before-tax profit figure in the above formulas.
8 Cost-Volume-Profit Analysis Page 8 For example, if you are told that you want to generate a Net Income (after-tax) of $50,000 and your tax rate is 40%, then you can convert the $50,000 after-tax, Net Income into the before-tax, Operating Profits that you need in order to produce Net Income of $50,000: You can check this: Operating Profits - Taxes = Net Income Op -.4 (Op) = 50,000.6 (Op) = 50,000 Op = 50,000/.6 Op = 83,334 Operating Profits: $83,334 Taxes (40%): -33,334 Net Income: $50,000 Targeted Income As A Percent Of Sales Revenue What if you are given a before tax target income, which is equal to a percentage of Sales Revenue? Just plug a formula for the target (e.g.,.1px for 10% of Sales Revenue) into the formula in place of "Op" (instead of a dollar figure). For example, assume that Bullock Net Co. desires a target Operating Profits that are equal to 10% of its Sales Revenue: Multiple-Product Analysis P (2, Px) / [( )/200] P 2, Px /.40.4 P 2, Px.3 P 2,000 P 2,000/.3 P $6,667 What if you are interested in performing a CVP analysis, but you have more than one product? You can perform this analysis in the same manner as we described above if you assume that your sales mix is fixed. You use the same formulas that are described above, but you substitute a composite Contribution Margin (for the entire product line) in place of the Contribution Margin for one product that we used above. When using a version of Formula B, you need to calculate the Contribution Margin Ratio for all of your products. Assume that you have a Company that sells two models, Good and Better::
9 Cost-Volume-Profit Analysis Page 9 Total fixed expenses are $39,600 Good Better Price: $60 $80 Variable Costs: Units Sold: Construct an income statement for the company: Sales: (1800 x60=108k)+(600x80=48k) $156,000 Variable Costs: (1800 x44=79.2k)+(600x56=33.6k) -112,800 Contribution Margin: 43,200 Fixed Costs: -39,600 Operating Profits: -$8,400 The Contribution Margin Ratio for the Company is % (43,200/156,000) You can also get the Contribution Margin Ratio for the Company by calculating the individual Contribution Margin Ratios for each product: Colonial Early American Price: $60 $80 Variable Costs: Contribution Margin: $16 $24 Contribution Margin Ratio: 26.67% 30% What you have to remember, however, is that the product mix (when calculating Contribution Margin Ratios) is based on relative sales revenue of the product (not the relative units sold): Colonial Early American Product Sales Revenue: $108K $48K Total Sales Revenue: 156K 156K Product Mix: 69.23% 30.77% Weighted Average Contribution Margin Ratio:.6923(.2667) (.30)= = The difference between the two Contribution Margin Ratios for the Company is due to rounding. Using Formula B, you get the Break Even point in Dollars PX = F/CMR = $39,600/ = $143,000
10 Cost-Volume-Profit Analysis Page 10 If you use a version of Formula A, you have to come up with composite Contribution Margin per Unit that represents the entire product line. In constructing the composite Contribution Margin Per Unit, the sales mix is based on the relative number of UNITS sold of each product (not the relative dollar sales revenue). There are two methods that are commonly used to develop the needed composite variables: (i) Basket (Package) Method, and (ii) Weighted Average Contribution Margin Method. A major competitor of Carmen s Banana Business, Inc. is Woody s Bananas, Ltd. Competition between Woody and Carmen has become so fierce on the Banana front that Woody has been suspected of engaging in guerilla tactics. (This suspicion could just be based on the CEO s strange fashion statements.) Unlike Carmen, who specializes in various banana products, Woody only sells raw fruit. Woody s main emphasis is Bananas, but it also sells Oranges. Woody sells 3 Bananas for each Orange that it sells (The sales mix is 75% Bananas and. 25% Oranges). Bananas Oranges Price: $2 $4 Variable Cost per Unit: $1 $2 Contribution Margin per Unit: $1 $2 Common Fixed Costs: $2,000 With the Basket Method, you create a Basket that reflects Woody s sales mix (75%:25%). Assume that each basket contains 3 Bananas and 1 Orange. What is the Contribution Margin of that Basket? CM basket = 3 CM banana + 1CM orange CM basket = 3 (1) + 1 (2) CM basket = CM basket = 5
11 Cost-Volume-Profit Analysis Page 11 Now, you plug the Contribution Margin for the Basket into the Formula that you wish to use. The Break-Even point in Baskets is: Baskets = F/CM basket Baskets = 2,000/ 5 Baskets = 400 Baskets You now describe the units of fruit contained in the Baskets: Bananas: Oranges: There are 3 Bananas in every Basket, so we need to sell 3 x 400 Baskets = 1200 Bananas in order to Break-Even. There is one Orange in every Basket, so we need to sell 400 Oranges in order to Break-Even. With the Weighted Average Contribution Margin Method, we calculate the Weighted Average Contribution Margin for one unit of fruit, using the given sales mix. The Break-Even Point in units is: CM wa =.75 CM banana +.25 CM orange CM wa =.75 (1) +.25 (2) CM wa = = $1.25 F/CM wa 2,000/ units Since we know that the total units of fruit sold should be 1600, and we know the sales mix is 75%:25%: Bananas: Oranges:.75 (1600) = 1200 Bananas.25 (1600) = 400 Oranges Margin of Safety The "Margin Of Safety" is the amount of sales (in dollars or units) by which the actual sales of the company exceeds the Break-Even Point. We know that Bullock s Break- Even Point is 25 units or $5,000. If Bullock really sells 40 units (Sales Revenue of $8,000), then its Margin Of Safety is 15 units (40-25) or $3,000 ($8,000 - $5,000). Operating Leverage If you take the total Contribution Margin and divide it by the Operating Profits, this gives you the Operating Leverage (or degree of Operating Leverage).
12 Cost-Volume-Profit Analysis Page 12 For example, if Bullock Net Co had actual sales of 40 units, its Operating Profits would be calculated as follows: Revenue: $ 8,000 (200x40) Variable Costs: -$4,800 (120x40) Contribution Margin: $ 3,200 Fixed Costs: -$2,000 Operating Profits: $1,200 The Operating Leverage is calculated as follows: Contribution Margin $3,200 = Operating Profits $1,200 = 2.67 The Operating Leverage of 2.67 indicates that if Bullock can increase its sales by 50%, then its Operating Profits will increase by 2.67 x 50% or 133%. Thus, the Operating Profits of $1,200 will increase by $1,600 (1.33 x $1,200) to $2,800. This calculation assumes that the Price, Variable Cost per Unit, and the Fixed Costs do not change. You are assuming that the increase in sales is caused by a 50% increase in the number of units sold (x): OLD NEW Revenue: $ 8,000 (200x40) $12,000 (200 x 60) Variable Costs: -$4,800 (120x40) -$7,200 (120 x 60) Contribution Margin: $ 3,200 $4,800 (80 x 60) Fixed Costs: -$2,000 -$2,000 Operating Profit: $1,200 $2,800 Questions E-1. Rider Company sells a single product. The product has a selling price of $40 per unit and variable expenses of $15 per unit. The company's fixed expenses total $30,000 per year. The company's break-even point in terms of total dollar sales is: A) $100,000. B) $80,000. C) $60,000. D) $48,000.
13 Cost-Volume-Profit Analysis Page 13 Use the following to answer questions E-2 and E-3: Weiss Corporation produces two models of wood chairs, Colonial and Early American. The Colonial sells for $60 per chair and the Early American sells for $80 per chair. Variable expenses for each model are as follows: Early Colonial American Variable production cost per unit... $35 $48 Variable selling expense per unit Total fixed expenses are $39,600 per month. Expected monthly sales are: Colonial, 1,800 units; Early American, 600 units. E-2. The contribution margin per chair for the Colonial model is: A) $51. B) $16. C) $35. D) $25. E-3. If the sales mix and sales units are as expected, the break-even in sales dollars is closest to: A) $132,000. B) $148,500. C) $143,000. D) $139,764. Use the following to answer questions E-4 and E-5: Southwest Industries produces a sports glove that sells for $15 per pair. Variable expenses are $8 per pair and fixed expenses are $35,000 annually. E-4. The break-even point for Southwest industries is: A) 8,000 pairs. B) 5,000 pairs. C) 4,375 pairs. D) pairs.
14 Cost-Volume-Profit Analysis Page 14 E-5. The contribution margin ratio is closest to: A) 46.7%. B) 53.3%. C) 33.3%. D) 42.9%. The answer is a. CMR = (P-V)/P = ($15 - $8)/$15 = % Use the following to answer questions E-6 through E-8: Budget data for the Bidwell Company are as follows: Fixed Variable Sales (100,000 units)... $1,000,000 Expenses: Raw materials... $300,000 Direct labor ,000 Overhead... $100, ,000 Selling and administrative ,000 50,000 Total expenses... $210,000 $700, ,000 Net operating income... $ 90,000 E-6. Bidwell's break-even sales in units is: A) 30,000 units. B) 91,000 units. C) 60,000 units. D) 70,000 units. E-7. The number of units Bidwell would have to sell to earn a net operating income of $150,000 is: A) 100,000 units. B) 120,000 units. C) 112,000 units. D) 145,000 units. E-8. If fixed expenses increased $31,500, the break-even sales in units would be: A) 34,500 units. B) 80,500 units. C) 69,000 units. D) 94,500 units.
15 Cost-Volume-Profit Analysis Page 15 Use the following to answer questions E-9 and E-10: Henning Corporation produces and sells two models of hair dryers, Standard and Deluxe. The company has provided the following data relating to these two products: Standard Deluxe Selling price... $40 $55 Variable production cost... $10 $16 Variable selling and administrative expense... $15 $12 Expected monthly sales in units ,200 The company's total monthly fixed expense is $13,800. E-9. The break-even in sales dollars for the expected sales mix is (rounded): A) $36,800. B) $30,000. C) $28,105. D) $31,222. Standard Deluxe Price: $40 $55 Variable Production Cost: Variable Selling Expense: Contribution Margin: $15 $27 Contribution Margin Ratio: 37.5% 49.09% Sales Mix 33% 67% E-10. If the expected monthly sales in units were divided equally between the two models (900 Standard and 900 Deluxe), the break-even level of sales would be: A) lower than with the expected sales mix. B) higher than with the expected sales mix. C) the same as with the expected sales mix. D) cannot be determined with the available data. P-1 The controller of Miller Company is preparing data for a conference concerning certain independent aspects of its operations. Prepare answers to the following questions for the controller: 1. Total Fixed Costs are $1,440,000 and a unit of product is sold for $12 in excess of its unit Variable Cost. What is break-even unit sales volume? 2. The company will sell 60,000 units of product each having a unit Variable Cost of $22 at a price that will enable the product to absorb $600,000 of Fixed Cost. What minimum unit sales price must be charged to break even?
16 Cost-Volume-Profit Analysis Page An Operating Profit of $320,000 is desired after covering $1,200,000 of Fixed Cost. What minimum Contribution Margin Ratio must be maintained if total Sales Revenue is to be $3,800,000? 4. Operating Profit is 10% of Sales Revenue, the Contribution Margin Ratio is 30%, and the break-even dollar sales volume is $640,000. What is the amount of total Sales Revenue? 5. Total Fixed Costs are $1,000,000, Variable Cost per unit is $30, and unit sales price is $80. What dollar sales volume will generate a net income of $84,000 when the income tax rate is 40%? P-2. Jensen Company has recently leased facilities for the manufacture of a new product. Based on studies made by its accounting personnel, the following data are available: Estimated annual sales: 40,000 units Estimated Costs Amount Unit Cost Direct Materials $696,000 $17.40 Direct Labor 584, Manufacturing Overhead 376, Administrative Expenses 187, Selling expenses are expected to be 10% of Sales Revenues, and the selling price is $64 per unit. Ignore income taxes in this problem. 1. Compute a break-even point in units. Assume that Manufacturing Overhead and Administrative Expenses are fixed but that other costs are variable. 2. How many units must be sold to earn an Operating Profit of 10% of sales? P-3. Kenton Company manufactures and sells the three products below: Economy Standard Deluxe Unit Sales 10,000 6,000 4,000 Unit Sales Price $48 $56 $68 Unit Variable Cost $30 $32 $36 Assume that total fixed costs are $339,000. Compute the number of each kind of unit necessary to sell in order to break even, assuming that the sales mix is fixed.
17 Cost-Volume-Profit Analysis Page 17 P-4. The following information relates to financial projections of Big Co. 2003: Project Sales $60,000 Projected Variable Costs $2.00 per unit Projected Fixed Costs $50,000 per year Projected Unit Sales Price $7.00 Big Co s tax rate is 20%. a. How many units would Big Co. need to sell in 2003 to earn a profit before taxes of $10,000? b. How many units must it sell to earn a net income of $12,500? P-5. P-6. Signal Co. manufactures a single product. For 2002, the company had sales of $90,000, variable costs of $50,000, and fixed costs of $30,000. Signal expects its cost structure and sales price per unit to remain the same in 2003, however total sales are expected to jump by 20%. If the 2003 projections are realized, operating profits in 2003 should exceed operating profits in 2002 by what percentage? Diversified Corp. manufactures and sells two products: X and Y. Fixed Costs are $9,000. The operating results of the company for 2002 follow: Product X Product Y Sales in units 2,000 3,000 Sales price per unit $10 $5 Variable Costs per unit $7 $3 Assume that the product mix remains the same. a. How many total units would the company have needed to sell to breakeven in 2002? b. If the company would have sold a total of 6,000 units in 2002, consistent with CVP assumptions how many of those units would you expect to be Product Y?
18 Cost-Volume-Profit Analysis Page 18 E-1. The answer is d. Solutions CMR = (P-V)/P = ($40 - $15)/$40 = 62.5% P F/ (CMR) P $30,000/.625 = $48,000 E-2. The answer is b. CM = P-V = $60 - $35 - $9 = $16. E-3. The answer is c. Construct an income statement for the company: Sales (1800 x60=108k)+(600x80=48k) $156,000 VC (1800 x44=79.2k)+(600x56=33.6k) -112,800 CM 43,200 Fixed Costs: -39,600 Oper. Profits: -$8,400 The Contribution Margin Ratio for the Company is % You can also get the Contribution Margin Ratio for the Company by calculating the individual Contribution Margin Ratios for each product: Colonial Early American Price: $60 $80 Variable Costs: Contribution Margin: $16 $24 Contribution Margin Ratio: 26.67% 30% What you have to remember, however, is that the product mix (when calculating Contribution Margin Ratios) is based on relative sales revenue of the product (not the relative units sold): Colonial Early American Product Sales Revenue: $108K $48K Total Sales Revenue: 156K 156K Product Mix: 69.23% 30.77% Weighted Average Contribution Margin Ratio:
19 Cost-Volume-Profit Analysis Page (.2667) (.30)= = The difference between the two Contribution Margin Ratios for the Company is due to rounding. Using Formula B, you get the Break Even point in Dollars PX = F/CMR = $39,600/ = $143,000 In this question, you had enough information to use Formula A. For example, using the Weighted Average Method: Weighted Average Contribution Margin:.75(16) +.25(24) = 12+6 = $18 X = F/CMU = $39,600/$18 = 2,200 units Colonial Sales Revenue:.75(2,200) = 1,650 x $60 = $99,000 Early American Revenue:.25(2,200) = 550 x $80 = 44,000 $143,000 E-4. The answer is b. X = F/(P-V) = $35,000/($15-$8) = 5,000 E-5. The answer is a. CMR = (P-V)/P = ($15 - $8)/$15 = % E-6. The answer is d. Contribution Margin For Company: Sales Revenue Variable Costs $1,000,000 - $700,000 = $300,000 Contribution Margin Per Unit = $300,000/100,000 = $3 X = F/CMU = $210,000 / 3 = 70,000 units E-7. The answer is b. X = F + Operating Profit/ CMU = $210,000 +$150,000 / 3 = 120,000 units E-8. The answer is b. X = F/CMU = ($210,000 + $31,500) / 3 = 80,500 units E-9. The answer is b. Weighted Average Contribution Margin Ratio: Sales: $90,000 ($40x600)+(55x1200)
20 Cost-Volume-Profit Analysis Page 20 VarCosts: $48,600 (25x600)+(28x1200) Contrib.Marg. $41,400 CMR: 46% ($41.500/$90,000) P F/CMR = $13,800/.46 = $30,000. Weighted Average Contribution Margin:.33(15) +.67(27) = 5+18 = $23 X = F/CMU = $13,800/23 = 600 Standard:.33(600) = 200 x $40 = $8,000 Deluxe:.67(600) = 400 x $55 = 22,000 $30,000 E-10. The answer is b. If the sales mix was 50%-50%, the weighted average contribution margin would be smaller, and dividing a smaller number into the same fixed cost would produce a higher break even point. Weighted Average Contribution Margin:.5(15) +.5(27) = = $21 X = F/CMU = $13,800/21 = 657 units P F = $1,440,000 = 120,000 units (P-V) 12 60,000 = P - 22 = F + Op (P-V) $600,000 P -22 $600,000 60,000 P - 22 = 10 P = P $3,800,000 = F + Op (P-V)_ P 1,200, ,000 CMR CMR = 1,200,000 +
21 Cost-Volume-Profit Analysis Page ,000 $3,800,000 CMR =.4 4. You have two unknowns, Sales Revenue and Fixed Costs. So you just can't plug in the known variables. You are given the Sales Revenue to break-even (here we want income as well). If we use the break even formula, then there is only one unknown (the Fixed Costs). P $640,000 = F (P-V) P _F_.3 640,000 x.3 = F $192,000 = F Now that you know the fixed costs, you can plug it into the formula to find the sales revenue you need in order to generate the target income. P P F + Op (P-V)_ P 192, Px.3.3 P 192, Px.2 P 192,000 P 192,000.2 P $960,000
22 Cost-Volume-Profit Analysis Page Net Income is an after-tax term. First convert the after-tax, Net Income into a before tax, Operating Profit: I - t (Op) = Net Income (Op) = $84,000.6 (Op) = $84,000 Op = $84,000.6 Op = $140,000 Plug the Operating Profit into the formula. P F+Op (P-V) P P 1,000, , P $1,824,000 P-2 1. Fixed Costs: $376,000 + $187,200 = $563,200 Variable costs include the selling expenses. On one unit, the sales expenses would be $6.40 (.1 x $64). Variable Costs: $ $14,60 + $6.40 = F + Op (P-V) _563,200_ ,000 units 2. F +.1Px (P-V) 563, (64)x , x ,200
23 Cost-Volume-Profit Analysis Page 23 P-3 Basket Method: 29,333 units A basket contains 5 Economies, 3 Standards, and 2 Deluxes. Econom y Standar d Delux e Price Variable Costs Contributi on Margin: The Contribution Margin of a Basket is 5(18) + 3(24) + 2 (32) =$226 F (P-V) Weighted-Average Method: $339, Baskets Economy = 1500 (5) = 7,500 Standard = 1500 (3) = 4,500 Deluxe = 1500 (2) = 3,000 15,000 The Weighted-Average Contribution Margin is :.5 (18) +.3 (24) +.2 (32) = 22.6 F (P-V) $339, ,000 Units Economy = 15,000 (.5) = 7,500 Standard = 15,000 (.3) = 4,500 Deluxe = 15,000 (.2) = 3,000 15,000
24 Cost-Volume-Profit Analysis Page 24
25 Cost-Volume-Profit Analysis Page 25 P-4 (a) Revenue = Costs + Profit P Vx + F + Op Px V F+ Op (P-V) F + Op (F + Op)/(P-V) ($50,000 + $10,000)/($7 - $2) ($60,000)/($5) 12,000 (b) Before Tax Income Taxes = After Tax Income Op -.2Op = $12,500.8Op = $12,500 Op = ($12,500)/.8 Op = $15,625 Revenue = Costs + Profit P Vx + F + Op Px V F+ Op (P-V) F + Op (F + Op)/(P-V) ($50,000 + $15,625)/($7 - $2) ($65,625)/($5) 13,125
26 Cost-Volume-Profit Analysis Page 26 P-5 Old Numbers 20% Increase in Sales Sales (Px) $90,000 $108,000 P*(x *1.2) V Costs (Vx) -50,000-60,000 V* (x*1.2) Contribution Margin $40,000 $48,000 (P-V)(x*1.2) F Costs (F) -30,000-30,000 F Oper. Profits $10,000 $18,000 This is an 80% increase. Operating Leverage: Contribution Margin / Operating Profit $40,000/$10,000 = 4 CM increase(20%) x Operating Leverage (4) = Op Increase (80%) Old Numbers 20% Increase in Sales Sales (Px) $90,000 $108,000 P*(x *1.2) V Costs (Vx) -50,000-60,000 V* (x*1.2) CM 40,000 48,000 CMU (x 1.2) F Costs (F) -30,000-30,000 F Oper. Profits $10,000 $18,000 P-6 Sales Mix Product X = 2,000 units / 5,000 total units = 40% of sales Product Y = 3,000 units / 5,000 total units = 60% of sales Contribution Margin CM = P - V CM Product X = $10 - $7 = $3 CM Product Y = $5 - $3 = $2 Blended Contribution Margin CM average =.4($3) +.6($2) = $1.2 + $1.2 = $2.4 CM basket = 2($3) + 3($2) = $6 + $6 = $12
27 Cost-Volume-Profit Analysis Page 27 (a) Weighted Average Method Revenue = Costs P Vx + F Px V F (P-V) F (F)/(P-V) ($9,000)/($2.4) 3,750 total units Basket Method Revenue = Costs P Vx + F Px V F (P-V) F (F)/(P-V) ($9,000)/($12) 750 baskets Each of these basket has five units. Total Units = 750 x 5 = 3750 (b) Product Y is 60% of Sales Product Y Units = 6,000 x.6 = 3600 units
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