To find the dollar sales volume a company must generate for a given target of operating income, we could first compute the required sales volume in units and then multiply our answer by the average selling price per unit. Thus ProGlide would have to generate approximately $72,000 in revenue (800 pairs of skates x $90) to earn a monthly operating income of $5,400.

Taking a more direct approach to compute the required sales volume, we can simply substitute the contribution margin ratio for the contribution margin per unit in our CVP formula, as follows

To illustrate, let us again compute the sales volume required for ProGhde to earn a monthly operating income of $5,400

**What Is Our Margin of Safety**

The dollar amount by which actual sales volume exceeds the break-even sales volume is called the margin of safety. It also represents the dollar amount by which sales can decline before an operating loss is incurred. In today’s volatile economy, it is important for managers to understand the extent to which rheir companies can endure a downturn in sales. ProGlide’s monthly sales volume required to break even is:

Thus, if monthly sales total $73,000, the margin of safety for that month is $/0,000 ($73.000 – $63,(00).

The margin of safety can provide a quick means of estimating operating income at any projected sales level. This relationship is summarizedas follows:

**Operating Income = Margin of Safety x Contribution Margin Ratio**

To illustrate, let us assume that we estimate ProGlide’s sales to be $72,000 next month. Given that its break-even sales volume is $63,000, its estimated margin of safety is $9,000. Thus the projected operating income is $5,400 ($9,000 X 60%).

**What Change in Operating Income Do We Anticipate?**

As stated. the contribution margin ratio ‘in our example is 60%. Thus, once break-even is reached, every additional dollar of sales increases ProGlide’s operating income by 60 cents. Conversely, a $1 sales decline lowers profitability by 60 cents. This relationship may be summarized as follows:

**Change in Change in Contribution**

** – *
OPerating Income Sales Volume Margin Ratio**

Therefore, if ProGlide estimates a $5,{)()()increase in monthly sales, it would anticipate a corresponding increase in operating income of $3,000 ($5,000 X 60%).

**Vice PreSident of Sales**

The vice president of sales isn’t convinced that an increase in the monthly advertising budget of $1.500 wi II yield sales of 500 units per month in the East Coast region. Her estimate is more conservative, at 350 units per month (for total monthly sales of 1.250 1111 its). Assume that the monthly advertising budget is increased by $1.500. and that direct lahar costs actually do increase by $).80 per unit because of the overtime premium required to meet increased production-demands.

If the vice president of saks is correct regarding her 1,250 unit projection s . she wants to know the extent to which the company would have to raise its selling prices (above the current price of $90 per unit) to achieve’ a target monthly income . figure of $36,300.

**Analysis**

If 1.250 units arc sold each month instead of J,4oo units, the contribution margin per unit must increase in order for the company to achieve the same target income (taking the increases in advertising and direct labor costs into consideration). Once again. we use the following formula:

Recall that the unit contribution margin is computed as follows

**Unit Contribution Margin = Unit Selling- Price – Unit Variabl-: Cost**

Faced with an extremely competitive wholesale sporting goods market. the vice president of sales is worried that a 9.2% price increase (from $90.00 per unit to $98.28 per unit) is likely to have an adverse effect on the company’s total sales. Therefore, she recomn ends that the price remain at $90 per unit and that the company’s target monthly income figure be lowered accordingly

**Additional Considerations in CVP**

In practice, the application of cost-volume-profit analysis is often complicated by various operating factors, including (I) different products with different contribution margins, (2) dete mining semi variable cost elements, and (3) complying with the assurnplions of cost-volume-profit analysis. Let us address such considerations.

**Improving the “Quality” of the Sales Mix**

Notice that helmets have, a higher contribution margin ratio than skates. A business can improve its average contribution ratio, and its overall profitability, by shifting its sales mix to include more products with high contribution margin ratios

Sales of products with the high contribution margins often are described as quality sales’ because they contribute so greatly to the company’s profitability. At ProGlide, management should be thinking of ways to sell more helmets. Almost every business encourages its salespeople to aggressively market the high-margin products.

**Determining Semi variable Cost Elements The High-low Method**

As previously discussed, semi variable costs have both a ‘fixed Portion and a variable portion. Throughout this chapter We have simplified the handling of serrti variable costs by providing the fixed and variable components for you. In practice, one must estimate the fixed and variable elements of semi variable costs. Several mathematical techniques may be used to accomplish this task. We will focus on one approach called the l}ig~low method.”

To illustrate the high-low method, assume that’ some portion of ProGlide’s total administrative cost is fixed and that some portion varies with the level of production. Information pertaining to production and administrative costs for the first six months of the year is shown below:

To find the variable portion’ of total ‘administrative costs, we relate the change in cost to the change in the activity base between the highest and the lowest months of production activity

Notice that a 100-unit increase in production results in a $240 increase in administrative costs. Therefore, the vat iable element of this cost may be estimated at $240 per 100 units, or $2.40 per unit.

To determine the fixed portion of the monthly administrative cost. we take the total monthly cost at either the high point <‘JI- the low point, and deduct the variable administrative cost from that amount. The following computation uses the highest level of activity to determine the fixed cost portion:

**Fixed Cost = Total Cost – Variable Cost**

** = $25,280 – ($2.40 per unit x 950 units)**

** = $25,280 – $2,280**

** = $23,000 per month**

Note that the variable and fixed administrative costs correspond ,to those reported in ProGlide’s monthly summary of average operating statistics on page 833.

We have now developed a cost formula for monthly administrative costs: $23.000 + $2.40 per unit. In addition to helping the company evaluate the reasonableness of administrative costs incurred in a given month. this formula is also valuable in forecasting administrative costs Iikcly to be incurred in the future. For example,

what amount of administrative cost should ProGlide expect in a month in which it has scheduled 930 units of production? The answer is approximately $25.232. determined as follows: