Problem 1: Head-First Company plans to sell 5,100 bicycle helmets at $78 each in the coming year. Product costs include:
Direct materials per helmet $32
Direct labor per helmet 5.50
Variable factory overhead per helmet 5.25
Total fixed factory overhead 21,000
Variable selling expense is a commission of $3.40 per helmet; fixed selling and administrative expense totals $29,800.
Required:
Q1. Calculate the total variable cost per unit.
Q2. Calculate the total fixed expense for the year.
Q3. Prepare a contribution margin income statement for Head-First Company for the coming year.
Problem 2: Head-First Company plans to sell 4,400 bicycle helmets at $84 each in the coming year. Unit variable cost is $45 (includes direct materials, direct labor, variable factory overhead, and variable selling expense). Total fixed cost equals $60,450 (includes fixed factory overhead and fixed selling and administrative expense).
Required:
Q1. Calculate the break-even number of helmets.
Q2. Check your answer by preparing a contribution margin income statement based on the break-even units.
Problem 3: Head-First Company plans to sell 4,400 bicycle helmets at $84 each in the coming year. Unit variable cost is $50.40 (includes direct materials, direct labor, variable factory overhead, and variable selling expense). Fixed factory overhead is $19,000 and fixed selling and administrative expense is $30,300.
Required:
Q1. Calculate the variable cost ratio.
Q2. Calculate the contribution margin ratio.
Q3. Prepare a contribution margin income statement based on the budgeted figures for next year. In a column next to the income statement, show the percentages based on sales for sales, total variable cost, and total contribution margin.
Problem 4: Head-First Company plans to sell 4,200 bicycle helmets at $67 each in the coming year. Variable cost is 66% of the sales price; contribution margin is 34% of the sales price. Total fixed cost equals $42,585 (includes fixed factory overhead and fixed selling and administrative expense).
Required:
Q1. Calculate the sales revenue that Head-First must make to break even by using the break-even point in sales equation.
Q2. Check your answer by preparing a contribution margin income statement based on the break-even point in sales dollars.
Problem 5: Head-First Company plans to sell 4,200 bicycle helmets at $71 each in the coming year. Unit variable cost is $44 (includes direct materials, direct labor, variable factory overhead, and variable selling expense). Total fixed cost equals $50,000 (includes fixed factory overhead and fixed selling and administrative expense).
Required:
Q1. Calculate the number of helmets Head-First must sell to earn operating income of $67,990.
Q2. Check your answer by preparing a contribution margin income statement based on the number of units calculated.
Problem 6: Head-First Company plans to sell 4,400 bicycle helmets at $78 each in the coming year. Variable cost is 60% of the sales price; contribution margin is 40% of the sales price. Total fixed cost equals $50,300 (includes fixed factory overhead and fixed selling and administrative expense).
Required:
1. Calculate the sales revenue that Head-First must make to earn operating income of $93,220 by using the point in sales equation.
2. Check your answer by preparing a contribution margin income statement based on the sales dollars calculated in Requirement 1.
Problem 7: Suppose that Head-First Company now sells both bicycle helmets and motorcycle helmets. The bicycle helmets are priced at $77 and have variable costs of $45 each. The motorcycle helmets are priced at $230 and have variable costs of $135 each. Total fixed cost for Head-First as a whole equals $66,500 (includes all fixed factory overhead and fixed selling and administrative expense). Next year, Head-First expects to sell 5,200 bicycle helmets and 2,080 motorcycle helmets.
Required:
Q1. Form a package of bicycle and motorcycle helmets based on the sales mix expected for the coming year.
Q2. Calculate the break-even point in units for bicycle helmets and for motorcycle helmets.
Q3. Check your answer by preparing a contribution margin income statement.
Problem 8: Head-First Company now sells both bicycle helmets and motorcycle helmets. Next year, Head- First expects to produce total revenue of $585,000 and incur total variable cost of $372,000. Total fixed cost is expected to be $60,000.
Required:
Q1. Calculate the break-even point in sales dollars for Head-First. Round the contribution margin ratio to four decimal places and sales to the nearest dollar.
Q2. Check your answer by preparing a contribution margin income statement.
Problem 9: Margin of Safety: Head-First Company plans to sell 5,240 bicycle helmets at $70 each in the coming year. Unit variable cost is $45 (includes direct materials, direct labor, variable factory overhead, and variable selling expense). Total fixed cost equals $49,500 (includes fixed factory overhead and fixed selling and administrative expense). Break-even units equal 1,980.
Required:
Q1. Calculate the margin of safety in terms of the number of units.
Q2. Calculate the margin of safety in terms of sales revenue.
Problem 10: Head-First Company plans to sell 5,000 bicycle helmets at $75 each in the coming year. Unit variable cost is $50 (includes direct materials, direct labor, variable factory overhead, and variable selling expense). Total fixed cost equals $49,500 (includes fixed factory overhead and fixed selling and administrative expense). Operating income at 5,000 units sold is $75,500.
Required: Calculate the degree of operating leverage.
Problem 11: Head-First Company had planned to sell 5,000 bicycle helmets at $74 each in the coming year. Unit variable cost is $50 (includes direct materials, direct labor, variable factory overhead, and variable selling expense). Total fixed cost equals $49,500 (includes fixed factory overhead and fixed selling and administrative expense). Operating income at 5,000 units sold is $70,500. The degree of operating leverage is 1.7. Now Head-First expects to increase sales by 10% next year.
Required:
Q1. Calculate the percent change in operating income expected.
Q2. Calculate the operating income expected next year using the percent change in operating income calculated in Requirement 1.
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