$$

Problem $2-20(75$ minutes$)$

$1.$

a$.$

Selling price......................

$$25$

$100\%$

$$

$$

Variable expenses.............

$$

$\%$

$$

$$

Contribution margin..........

$$$

$\%$

$$

$$

Profit

$=$ Unit CM $$ Q $$ Fixed expenses

$$

$

$=$ $ $$ Q $$ $

$$

$$ Alternative solution:

$$

Unit sales to break even $=$ Fixed Expenses $/$ Unit Contribution Margin

$$

$$

$$

$$

$$ b$.$ The degree of operating leverage is:

$$

Degree of operating leverage $=$ Contribution Margin $/$ Net Operating Income

$$

$2.$ The new CM ratio will be:

$$

Selling price.....................

$$ $$$

$\%$

Variable expenses............

$18$

$72\%$

Contribution margin.........

$$$

$\%$

$$

$$ The new break$-$even point will be:

$$

$$

Profit

$=$ Unit CM $$ Q $$ Fixed expenses

$$

$$0$

$=$ $$7$ Q $$ $

$$

$$

$$

$$

$$

$$

Alternative solution:

$$

$$

Unit sales to break even $=$ Fixed Expenses $/$ Unit Contribution Margin

$$

$$

$$

$3.$

Profit

$=$ Unit CM $$ Q $$ Fixed expenses

$$

$$

$$

$$

$$

$$

$$

$$

$$

$$

$$

$$

$$

$$

Alternative solution:

$$

Unit Sales to attain target profit $=$

$$

$($Target profit $+$ Fixed Expenses$)/$ Unit Contribution Margin

$$

$$

$$

$$ Thus, sales will have to increase by $.....$

$$

$$

Present

Expected

Break$-$even point $($in balls$)...................................$

$21,000$

$30,000$

Sales $($in balls$)$ needed to earn a $$90,000$ profit...

$30,000$

$??,???$

$$

$$ Note that if variable costs do increase next year, then the company will just break even if it sells the same number of balls $(30,000)$ as it did last year.

Problem $2-20($continued$)$

$4.$ The contribution margin ratio last year was $40\%.$ If we let P equal the new selling price, then:

$$

P $=$

$$+0\mathrm{.}40$P

$0\mathrm{.}60$P $=$

$

P $=$

$$0\mathrm{.}60$

P $=$

$

$$

$$ To verify:

$$

Selling price.....................

$$$

$100\%$

$$

Variable expenses............

$18$

$60\%$

$$

Contribution margin.........

$

$40\%$

$$

$$ Therefore, to maintain a $40\%$ CM ratio, a $$?$ increase in variable costs would require a $$?$ increase in the selling price.

$$

$5.$ The new CM ratio would be:

Selling price..........................

$$25$

$100\%$

Variable expenses.................

$\_\_*$

$\_\_\%$

Contribution margin..............

$$\_\_$

$\_\_\%$

$$

$*$$$($$$40\%)=$ $

$$

$$ The new break$-$even point would be:

$$

$$

Profit

$=$ Unit CM $$ Q $$ Fixed expenses

$$

$$

$$

$$

$$

$$

$$

$$

$$

$$

$$

$$

$$

$$ Alternative solution:

$$

Unit sales to break even $=$ Fixed Expenses $/$ Unit Contribution Margin

Problem $2-20($continued$)$

$6.$

a$.$

Profit

$=$ Unit CM $$ Q $$ Fixed expenses

$$

$$

$$90,000$

$=$ $$$ Q $$ $

$$

$$

$$

$$

$$

$$

$$

$$

$$

$$

$$

$$

$$

$$ Alternative solution:

$$

Unit Sales to attain target profit $=$

$$

$($Target profit $+$ Fixed Expenses$)/$ Unit Contribution Margin

$$

$$

$$ b$.$ The contribution income statement would be:

$$

Sales $(30,000$ balls $$ $$25$ per ball$)......................$

$$750,000$

Variable expenses $(30,000$ balls $$ $$9$ per ball$)....$

$270,000$

Contribution margin............................................

$$

Fixed expenses....................................................

$\_\_\_\_\_\_\_$

Net operating income..........................................

$$\_\_\_\_\_\_$

$$

$$

$$

Degree of operating leverage $=$ Contribution margin $/$ Net operating income

$$

$$ c$.$

$$