Wayward Enterprises manufactures and sells three distinct styles of bicycles: the Youth model sells for $300 and has a unit contribution margin of $105; the Adult model sells for $850 and has a unit contribution margin of $450; and the Recreational model sells for $1,000 and has a unit contribution margin of $500. The company's sales mix includes: 5 Youth models; 9 Adult models; and 6 Recreational models. If the firm's annual fixed costs total $6,500,000, calculate the firm's break-even point in sales dollars.

Question

Quizplus · Accepted Answer

To calculate the break-even point in sales dollars, we first need to find the weighted average contribution margin ratio. 1. Calculate the contribution margin ratio for each model:   - Youth: $105 / $300 = 0.35   - Adult: $450 / $850 = 0.5294   - Recreational: $500 / $1,000 = 0.52. Calculate the sales mix ratio:   - Total units in the mix = 5 Youth + 9 Adult + 6 Recreational = 20 units   - Youth ratio = 5/20 = 0.25   - Adult ratio = 9/20 = 0.45   - Recreational ratio = 6/20 = 0.33. Calculate the weighted average contribution margin ratio:   - Weighted average = (0.35 * 0.25) + (0.5294 * 0.45) + (0.5 * 0.3) = 0.0875 + 0.23823 + 0.15 = 0.475734. Calculate the break-even point in sales dollars:   - Break-even point = Fixed Costs / Weighted average contribution margin ratio   - Break-even point = $6,500,000 / 0.47573 = $13,660,000 approximatelyHowever, since the exact option is not listed, we need to reevaluate our calculation, particularly focusing on the correct method to calculate the weighted average contribution margin in dollars, not the ratio, and then apply the sales mix properly.Correct Calculation:1. Find the total contribution margin for one cycle of the sales mix:   - (5 Youth * $105) + (9 Adult * $450) + (6 Recreational * $500) = $525 + $4050 + $3000 = $75752. Find the total sales value for one cycle of the sales mix:   - (5 Youth * $300) + (9 Adult * $850) + (6 Recreational * $1000) = $1500 + $7650 + $6000 = $151503. Calculate the weighted average contribution margin ratio for the sales mix:   - $7575 / $15150 = 0.54. Calculate the break-even point in sales dollars using the correct weighted average contribution margin ratio:   - Break-even point = $6,500,000 / 0.5 = $13,000,000The correct calculation involves understanding the sales mix and contribution margins properly, leading to the realization that the break-even point in sales dollars is $13,000,000.

Wayward Enterprises Manufactures and Sells Three Distinct Styles of Bicycles