Problem $4-25$ Sales Mix; Multi$-$Product Break$-$Even Analysis; Target Profit; Margin of Safety $[$LO$6,$ LO$7,$ LO$9]$

Warm Hands, a small company based in Prince Edward Island, manufactures and sells two types of lightweight gloves for runners$$Warm and Cozy. Current revenue, cost, and unit sales data for the two products appear below:

Warm Cozy

Selling price per pair $ $5\mathrm{.}00$ $ $7\mathrm{.}50$

Variable expenses per pair $ $1\mathrm{.}25$ $ $3\mathrm{.}75$

Number of pairs sold monthly $2,700$ units $900$ units

Fixed expenses are $$3,240$ per month.

Required:

$1.$ Assuming the sales mix above, do the following:

a$.$ Prepare a contribution format income statement showing both dollars and percentage columns for each product and for the company as a whole. $($Round percentage answers to $2$ decimal places.$)$

b$.$ Compute the break$-$even point in sales dollars for the company as a whole and the margin of safety in both dollars and percentage of sales. $($Do not round your intermediate calculations. Round percentage answer to $2$ decimal places.$)$

c$.$ Compute the break$-$even point in units for the company as a whole and the margin of safety in both units $($pairs of gloves$)$ and percentage of sales. $($Round percentage answer to $2$ decimal places.$)$

d$.$ Compute how many pairs of gloves must be sold overall if the company wants to make an after$-$tax target profit of $$5,250$ and the tax rate is $30\%.$ Assume that the sales mix remains the same as shown above.

$2.$ The company has developed another type of gloves that provide better protection in extreme cold, Toasty, which the company plans to sell for $$15\mathrm{.}50$ per pair. At this price, the company expects to sell $900$ pairs per month of the product. The variable expense would be $$12\mathrm{.}40$ per pair. The company$$s fixed expenses would not change.

a$.$ Prepare another contribution format income statement, including sales of Toasty $($sales of the other two products would not change$).($Round percentage answers to $2$ decimal places.$)$

b$.$ Compute the company$$s new break$-$even point in sales dollars for the company as a whole and the new margin of safety in both dollars and percentage of sales. $($Round your break$-$even sales to the nearest whole dollar amount and percentage answer to $2$ decimal places.$)$