Head$-$First Company plans to sell $5,000$ bicycle helmets at $$70$ each in the coming year. Unit variable

cost is $$49($includes direct materials, direct labour, variable overhead, and variable selling expense$).$

Total fixed cost equals $$29,400($includes fixed factory overhead and fixed selling and administrative

expense$).$

Requirements:

$1.$ Calculate the number of helmets Head$-$First must sell to earn operating income of $$81,900$ before

income taxes $($ie$,$ ignore income taxes$).$

$2.$ Calculate the sales revenue that Head$-$First must make to earn operating income of $$81,900$

before income taxes $($ie$,$ ignore income taxes$).$

$3.($a$)$ Calculate the margin of safety in terms of the number of units at $5,000$ units sold.

$($b$)$ Calculate the margin of safety in terms of sales revenue at $5,000$ units sold.

$4.$ For Head$-$First Company, operating income at $5,000$ units sold is $$75,600.$ Calculate the degree of

operating leverage at this level of sales. $($Round your answer to the nearest tenth.$)$

$5.$ Now assume that Head$-$First expects to increase sales by $15\%$ next year. Calculate the percent

change in operating income expected, and calculate the operating income expected next year

using the percent change in operating income calculated in Requirement $1.$

$6.$ For this requirement, ignore the above facts and assume instead that assume that Head$-$First

Company now sells both bicycle helmets and motorcycle helmets. The bicycle helmets are priced

at $$70$ and have variable costs of $$49$ each. The motorcycle helmets are priced at $$220$ and have

variable costs of $$143$ each. Total fixed costs for Head$-$First as a whole equal $$54,600($includes all

fixed factory overhead and fixed selling and administrative expense$).$ Next year, Head$-$First expects

to sell $5,000$ bicycle helmets and $1,000$ motorcycle helmets.

$($a$)$ Create a package $($or bundled product$)$ of bicycle and motorcycle helmets based on the desired

sales mix, and calculate the package contribution margin. Calculate the break$-$even point in units

for bicycle helmets and units for motorcycle helmets.

$($b$)$ Check your answer by preparing a contribution margin income statement