Austin Co. sells three products and incurs $18,000 per period in fixed costs. The three products have the following characteristics: $\begin{array}{rllr}\text { Product} & \text { Price } & \text { Variable Cost } & \text { Sales Mix }\\hline
P & \$ 40 & \$ 20 & 3 \text { units } \
Q & 20 & 10 & 9 \text { units } \
R & 49 & 24 & 12 \text { units }
\end{array}$ How many units of Product P will be sold at the breakeven point?

Question

Quizplus · Accepted Answer

To find the breakeven point in units for Product P, we first need to calculate the weighted average contribution margin per unit. The sales mix ratio is 3:9:12 for P:Q:R. 1. Calculate the contribution margin per unit for each product:- P: $40 - $20 = $20- Q: $20 - $10 = $10- R: $49 - $24 = $252. Calculate the total units in one cycle of the sales mix:- Total units = 3P + 9Q + 12R = 24 units3. Calculate the total contribution margin for one cycle of the sales mix:- Total contribution = (3 units * $20) + (9 units * $10) + (12 units * $25) = $60 + $90 + $300 = $4504. Calculate the weighted average contribution margin per unit:- Weighted average = Total contribution / Total units = $450 / 24 = $18.755. Calculate the total units needed to break even:- Total units to break even = Fixed costs / Weighted average contribution margin per unit = $18,000 / $18.75 = 960 units (total units of the mix to break even)6. Calculate the number of cycles needed to break even:- Number of cycles = Total units to break even / Total units in one cycle = 960 / 24 = 40 cycles7. Calculate the number of units of Product P needed to break even:- Units of P to break even = Number of cycles * Units of P per cycle = 40 * 3 = 120 unitsTherefore, 120 units of Product P will be sold at the breakeven point.

Austin Co Sells Three Products and Incurs $18,000 Per Period in in Fixed