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# break-even quantities and operating leverages

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Based on the attached spreadsheets, how would the attached questions 1- 6 be answered?

1. Describe how the break-even quantities and operating leverages are affected by the relationships between fixed and variable costs.

2. Explain what will happen to company profits if sales in the software and keyboard divisions increase at the same rate, and identify which division will have the fastest growth in profits.
3. Describe how expanding the division with the highest operating leverage would affect the company's risk position.
4. For the sound-card division, calculate the profits associated with each production technology at the possible quantities. Identify the break-even quantities associated with each production technology.
5. Provide a recommendation for whether the company should begin producing the new sound card. If you believe the company should begin production, in which production technology should the company invest? In each case, state why or why not and support your claim.
6. Describe how the break-even calculations affect your analysis, and use the notion of operating leverage to assess the risks and rewards associated with each production option.
Scenario Background:
We've reviewed the marketing report and are convinced that the company would be well served by expanding the Electric 88 keyboard division instead of the software division.
Using our current sales and cost data, and assuming that we keep our costs at their current levels, we have calculated the break-even quantities for our division using the marketing division's list of possible prices.
Our current fixed costs are \$470,000 per year. Our current variable costs are about \$285 per keyboard?and I think we can hold that steady. So if, as the marketing department says is possible, keyboard prices fall to \$290 each, then our variable margin will be \$5 per keyboard, and we will need to sell 94,000 keyboards per year to break even. We're not likely to be able to do that. But suppose keyboard prices remain at their current \$305. Then our variable margin is \$20, and we only need to sell 23,500 keyboards to break even?we're doing better than that now. If prices rise, then our break-even quantities fall. I've prepared the following table, which reports our break-even quantities for various prices
Table. Break-Even Quantities
Keyboard Price Variable Margin Break-Even Quantity
\$290 \$5 94,000
\$305 \$20 23,500
\$320 \$35 13,429
\$335 \$50 9,400
\$350 \$65 7,231
Of course, if the price falls below our variable cost of \$285 per keyboard, then we won't break even?no matter how many keyboards we sell. But because our fixed costs are the lowest of any of our divisions, our break-even quantities are low for any reasonable prices.
Factoring in our fixed costs, our current average cost is about \$295.44. That means that at our current prices, our degree of operating leverage is 2.09?this is the ratio of our contribution margin of \$20 to our unit profit of about \$9.56. So if our quantity sold increases by 5 percent, then our division's profits increase by more than 10 percent. Our division is primed to expand.
We anticipate that the price of DigiMuse's software might decline over the next two years. We think the likelihood of this is rather small, and if it occurs the decline will be minimal, to about \$120 per unit. (There is a very small chance of a larger drop, to \$114 or \$108 per unit).
Of course, the price could increase by \$6 or up to \$132 per unit. We think a price increase is just as likely as a price decrease.
During the market life of the new sound card, the marketing department will incur additional expenses. We will need to hire three additional salespersons at salaries of \$35,000/year each, plus a \$1.50 commission per sound card with quantities in the thousands. Administrative, travel, and other expenses for the new salespersons will be \$25,000/year each. Direct-marketing expenses will be \$125,000/year.
We expect that the market price of the new sound card will be stable at \$105. However, because of uncertainty over macroeconomic and market conditions, we have some concern about the quantity DigiMuse will be able to sell.
The best-case scenario involves very high demand for the new sound card. With the additional advertising and new salespeople, we expect to be able to sell about 250,000 of the new sound cards per year. There is about a 15 percent chance that demand will be lower, and we will sell around 120,000 sound cards per year, and there is an even slighter chance, around 5 percent, that demand will be very low, and sales will only be around 40,000 units per year.