Northwood Company manufactures basketballs. The company has a ball that sells for $$25.$ At present, the ball is manufactured in a small plant that relies heavily on direct labor workers. Thus, variable expenses are high, totaling $$15\mathrm{.}00$ per ball, of which $60\%$ is direct labor cost.

Last year, the company sold $32,750$ of these balls, with the following results:

Sales $(32,750$ balls$)$ $ $818,750$

Variable expenses $491,250$

Contribution margin $327,500$

Fixed expenses $225,400$

Net operating income $ $102,100$

Required:

$1.$ Compute $($a$)$ last year's CM ratio and the break$-$even point in balls, and $($b$)$ the degree of operating leverage at last year$$s sales level.

$2.$ Due to an increase in labor rates, the company estimates that next year's variable expenses will increase by $$3\mathrm{.}00$ per ball. If this change takes place and the selling price per ball remains constant at $$25\mathrm{.}00,$ what will be next year's CM ratio and the break$-$even point in balls?

$3.$ Refer to the data in requirement $2.$ If the expected change in variable expenses takes place, how many balls will have to be sold next year to earn the same net operating income, $$102,100,$ as last year?

$4.$ Refer again to the data in requirement $2.$ The president feels that the company must raise the selling price of its basketballs. If Northwood Company wants to maintain the same CM ratio as last year $($as computed in requirement $1$a$),$ what selling price per ball must it charge next year to cover the increased labor costs?

$5.$ Refer to the original data. The company is discussing the construction of a new, automated manufacturing plant. The new plant would slash variable expenses per ball by $40\mathrm{.}00\%,$ but it would cause fixed expenses per year to double. If the new plant is built, what would be the company$$s new CM ratio and new break$-$even point in balls?

$6.$ Refer to the data in requirement $5.$

a$.$ If the new plant is built, how many balls will have to be sold next year to earn the same net operating income, $$102,100,$ as last year?

b$.$ Assume the new plant is built and that next year the company manufactures and sells $32,750$ balls $($the same number as sold last year$).$ Prepare a contribution format income statement and compute the degree of operating leverage.