Chapter 3 Cost-Volume-Profit Analysis Breakeven point…. Dr.Mohamed Mousa

Effects of Sales Mix on CVP : Sales Mix is the quantity or proportion of various products or services that constitute a company’s total unit sales. It is often the case that the various products or services have different contribution margins. Up to this point, we’ve assumed a single product; more realistically, we’ll have multiple products with different costs and different margins. So far, we’ve been contemplating a business with one product and, therefore, one contribution margin. More usually, a company has multiple products with varying contribution margins. We can still use the tools of CVP analysis but instead of using the contribution margin for the one product, we will use an average contribution margin. The average CM is calculated based on a defined product mix. In other words, the CM is determined based on a specific relationship of sales of product 1 to total sales, sales of product 2 to total sales, etc. If that relationship of sales changes, so will our average CM. Dr . Mohamed Mousa

Effects of Sales Mix on CVP : We can use the same formula in our CVP calculations but must use an average contribution margin for the products. This technique assumes a constant mix at different levels of total unit sales. So far, we’ve been contemplating a business with one product and, therefore, one contribution margin. More usually, a company has multiple products with varying contribution margins. We can still use the tools of CVP analysis but instead of using the contribution margin for the one product, we will use an average contribution margin. The average CM is calculated based on a defined product mix. In other words, the CM is determined based on a specific relationship of sales of product 1 to total sales, sales of product 2 to total sales, etc. If that relationship of sales changes, so will our average CM. Dr . Mohamed Mousa

Example no 1: Magi Industrial Company produces the products( x & y & z )and you have the following data: z y x Description 40000 100000 60000 Sales revenue 16 20 30 Unit Sale Price 11,2 15 24 Variable Cost / u 20% 50% 30% Sales mix ratio So far, we’ve been contemplating a business with one product and, therefore, one contribution margin. More usually, a company has multiple products with varying contribution margins. We can still use the tools of CVP analysis but instead of using the contribution margin for the one product, we will use an average contribution margin. The average CM is calculated based on a defined product mix. In other words, the CM is determined based on a specific relationship of sales of product 1 to total sales, sales of product 2 to total sales, etc. If that relationship of sales changes, so will our average CM. Dr . Mohamed Mousa

Example no 1: If you know that the fixed costs of the company is 19600 $. Required : 1. Determine the quantity and value of the B.E.P of each product. 2 - What is the sales number required to achieve a target profit capacity of 49000 $? So far, we’ve been contemplating a business with one product and, therefore, one contribution margin. More usually, a company has multiple products with varying contribution margins. We can still use the tools of CVP analysis but instead of using the contribution margin for the one product, we will use an average contribution margin. The average CM is calculated based on a defined product mix. In other words, the CM is determined based on a specific relationship of sales of product 1 to total sales, sales of product 2 to total sales, etc. If that relationship of sales changes, so will our average CM. Dr . Mohamed Mousa

Solution 1.Determine the weighted average return on contribution of the unit: Average Contribution S.M.R C.M.R C.M.U V.C.U S.P Product 0,060 30% 20% 6 24 30 x 0,125 50% 25% 5 15 20 y 4,8 11,2 16 z 0,245 100% - Total So far, we’ve been contemplating a business with one product and, therefore, one contribution margin. More usually, a company has multiple products with varying contribution margins. We can still use the tools of CVP analysis but instead of using the contribution margin for the one product, we will use an average contribution margin. The average CM is calculated based on a defined product mix. In other words, the CM is determined based on a specific relationship of sales of product 1 to total sales, sales of product 2 to total sales, etc. If that relationship of sales changes, so will our average CM. Dr . Mohamed Mousa

Solution 2 - The Value of B.E.P To the company as a whole: B.E.PR = F. C / Total Average Contribution = 19600 / 0,245 = 80000 $ the value of B.E.P per product: = The value of B.E.P To the company as a whole × sales mix ratio. So far, we’ve been contemplating a business with one product and, therefore, one contribution margin. More usually, a company has multiple products with varying contribution margins. We can still use the tools of CVP analysis but instead of using the contribution margin for the one product, we will use an average contribution margin. The average CM is calculated based on a defined product mix. In other words, the CM is determined based on a specific relationship of sales of product 1 to total sales, sales of product 2 to total sales, etc. If that relationship of sales changes, so will our average CM. Dr . Mohamed Mousa

Solution B.E.P R To Product x = 80000 x 30% = 24000 $. B.E.P u To Product x = 24000 $ / 30 (s.p) = 800 Unit. B.E.P R To Product y = 80000 x 50% = 40000 $. B.E.P u To Product y = 40000 $ / 20 (s.p) = 2000 Unit. B.E.P R To Product z = 80000 x 20% = 16000 $. B.E.P u To Product z = 16000$ / 16(s.p) = 1000Unit. So far, we’ve been contemplating a business with one product and, therefore, one contribution margin. More usually, a company has multiple products with varying contribution margins. We can still use the tools of CVP analysis but instead of using the contribution margin for the one product, we will use an average contribution margin. The average CM is calculated based on a defined product mix. In other words, the CM is determined based on a specific relationship of sales of product 1 to total sales, sales of product 2 to total sales, etc. If that relationship of sales changes, so will our average CM. Dr . Mohamed Mousa

Solution 3 – The B.E.P R that earn a profit of 49000 $ : = ( F. C + O.I ) / Total Average Contribution = (19600 + 49000 ) / 0,245 = 280000 $ the value of sales that earn a profit per product: = The B.E.P R that earn a profit To the company as a whole × sales mix ratio. So far, we’ve been contemplating a business with one product and, therefore, one contribution margin. More usually, a company has multiple products with varying contribution margins. We can still use the tools of CVP analysis but instead of using the contribution margin for the one product, we will use an average contribution margin. The average CM is calculated based on a defined product mix. In other words, the CM is determined based on a specific relationship of sales of product 1 to total sales, sales of product 2 to total sales, etc. If that relationship of sales changes, so will our average CM. Dr . Mohamed Mousa

Solution V.S.P To Product x = 280000 x 30% = 84000 $. N.S.P To Product x = 84000 $ / 30 (s.p) = 2800 Unit. V.S.P To Product y = 280000 x 50% = 140000 $. N.S.P To Product y = 140000 $ / 20 (s.p) = 7000 Unit. V.S.P To Product z = 280000 x 20% = 56000$. N.S.P To Product z = 56000$ / 16(s.p) = 3500Unit. So far, we’ve been contemplating a business with one product and, therefore, one contribution margin. More usually, a company has multiple products with varying contribution margins. We can still use the tools of CVP analysis but instead of using the contribution margin for the one product, we will use an average contribution margin. The average CM is calculated based on a defined product mix. In other words, the CM is determined based on a specific relationship of sales of product 1 to total sales, sales of product 2 to total sales, etc. If that relationship of sales changes, so will our average CM. Dr . Mohamed Mousa

Exercises:( Case Study ) ZAAT Industrial Company produces the products( K & L & M )and you have the following data: M L K Description 90 25 50 Unit Sale Price 72 19 30 Variable Cost / u 10000 4000 6000 Number of units sold So far, we’ve been contemplating a business with one product and, therefore, one contribution margin. More usually, a company has multiple products with varying contribution margins. We can still use the tools of CVP analysis but instead of using the contribution margin for the one product, we will use an average contribution margin. The average CM is calculated based on a defined product mix. In other words, the CM is determined based on a specific relationship of sales of product 1 to total sales, sales of product 2 to total sales, etc. If that relationship of sales changes, so will our average CM. Dr . Mohamed Mousa

Exercises : If you know that the fixed costs of the company is 166800 $. Required : 1. Determine the quantity and value of the B.E.P of each product. 2 - What is the sales number required to achieve a target profit capacity of 133200 $? So far, we’ve been contemplating a business with one product and, therefore, one contribution margin. More usually, a company has multiple products with varying contribution margins. We can still use the tools of CVP analysis but instead of using the contribution margin for the one product, we will use an average contribution margin. The average CM is calculated based on a defined product mix. In other words, the CM is determined based on a specific relationship of sales of product 1 to total sales, sales of product 2 to total sales, etc. If that relationship of sales changes, so will our average CM. Dr . Mohamed Mousa

CVP for Service and Not-For-Profit Organizations : CVP isn’t just for merchandising and manufacturing companies. Service and Not-For-Profit businesses need to focus on measuring their output which is different from the units sold that we’ve been dealing with. For example, a service agency might measure how many persons they assist or an airline might measure how many passenger miles they fly. What measure might a hotel use? A restaurant? CVP, though more prevalent for manufacturing and merchandising companies, is certainly useful for service and not-for-profits as well. The challenge is to focus on a measure of output which is generally going to be different from the measure of “units sold” that we’ve been dealing with so far.

Contribution Margin versus Gross Margin : Recall from Chapter 2 that Gross Margin = Revenue – Cost of Goods Sold. In Chapter 3, we learned about Contribution Margin which is Revenue – All Variable Costs. Gross Margin measures how much a company charges for its products over and above the cost of acquiring or producing them. Contribution Margin indicates how much of a company’s revenue is available to cover fixed costs. This is especially significant in the manufacturing sector where businesses carry inventory. The gross margin is obtained by subtracting all manufacturing costs from revenues. Those manufacturing costs include fixed as well as variable components. Contribution margin is obtained by subtracting all variable costs, both manufacturing and non-manufacturing, from revenues. In a period where there is no change in inventory, the operating income will not differ between the two calculations. However, as inventory increases, the fixed manufacturing costs will be absorbed into inventory causing a higher operating income. Both formats are important for their particular purposes and one shouldn’t be dismissed in favor of the other. Each should be used for the particular purpose.

Responsibility accounting “ The Next Lecture Chapter 6 “ The Master Budget and Responsibility accounting “ Dr . Mohamed Mousa