A mixed cost function includes both fixed and variable costs. If there are fixed costs in the cost function, then total costs will increase at a smaller rate than the increase in total sales volume. If there are variable costs in the cost function, then total costs will increase with total sales volume. When there is a combination of fixed and variable costs, a volume increase will increase total costs by less than 10% because only the increase in variable cost is reapportionment to volume; the fixed cost does not change with volume. 3. 2 Outweighed average contribution margin per unit is calculated only when performing C.V. analysis for multiple products.

There are two ways to calculate it: (1) Calculate the total contribution of all products by subtracting total variable costs from total revenues. Then calculate the weighted average contribution margin per unit by dividing the total contribution margin by the total number of units (the sum of units for all products). (2) Calculate the sales mix for each product by dividing the number of units old for that product by the total number of units sold for all products. Calculate the contribution margin per unit for each product by subtracting that product’s variable cost from its revenues and dividing the result by that product’s number of units sold.

Then calculate the weighted average contribution margin per unit by summing the following computation for all products: Each products sales mix percentage times its contribution margin per unit. 3. 3 The firm has only variable costs and no fixed costs. If there were fixed costs, income would increase by more than 20% when sales increase by 20%. 3. 4 None. The firm does not pay income taxes at the breakable point. 3. 5 Assumptions:Fixed costs remain fixed, variable costs per unit or as a percentage of revenue remain constant, selling prices per unit remain constant, the sales mix remains constant, and operations are within a relevant range where all of these assumptions are met. These are very strong assumptions. There is always some variation in fixed costs because they include costs such as electricity that varies with weather.

In addition, organizations often get or give volume discounts, so variable costs and prices per unit may change at high volumes. However, results using these assumptions are accurate enough for general planning and decision making purposes. 3. 6 The margin of safety percentage and degree of operating leverage are related as follows. Margin of Safety Percentage = Degree of Operating Leverage Degree of Operating Leverage = 0 201 2 John Wiley and Sons Canada, Ltd. Margin of Safety Percentage Chapter 3: Cost-volume-profit Analysis 97 As the degree of operating leverage gets larger (a higher proportion of fixed costs), the margin of safety percentage gets smaller, and vice versa. 3. 7 The cost function is assumed to be linear over a relevant range.

If there are illume discounts, the cost function becomes piece-wise linear and the range of operations within which the organization is performing must be taken into account in C.V. analysis. The level of operations must be matched with the appropriate part of the function. Each piece can be considered as a separate relevant range, and the estimated level of activity needs to be matched with the appropriate relevant range. Otherwise, the analysis will either understate or overstate variable costs. 3. 8 Sales mix is the specific proportion of total sales of each type of good or service that is sold. A simple example was presented in the chapter for an ice ream store.

Usually about of revenue was from beverages and the rest from ice cream products. As the proportion of specific products sold changes, the contribution margin ratio changes because the contribution per unit is different for the different products in the sales mix. 3. 9 C.V. refers to changes in income over the relevant range of activity; as such, it includes the notion Of breakable. Breakable is more narrowly constructed; it focuses on only one outcome-?the single point at which total revenue equals total cost. 3. 10 By definition, the margin of safety is the difference between expected unit ales and breakable unit sales. If expected unit sales are below breakable unit sales, the margin of safety will be negative.

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