Problem $20\mathrm{.}1$A $($Static$)$ Setting Sales Price and Computing the Break$-$Even Point $($LO$20-4,$ LO$20-5,$ LO$20-6,$ LO$20-7)$

Ionic Charge is a newly organized manufacturing business that plans to manufacture and sell $50,000$ units per year of a new product. The following estimates have been made of the company$$s costs and expenses $($other than income taxes$)$:

FixedVariable per UnitManufacturing costs: Direct materials $ $40$Direct labor $21$Manufacturing overhead$ $900,00016$Period costs: Selling expenses $3$Administrative expenses$600,000$ Totals$ $1,500,000$$ $80$

Required:

What should the company establish as the sales price per unit if it sets a target operating income of $$500,000$ by producing and selling $50,000$ units during the first year of operations? $($Hint: First compute the required contribution margin per unit.$)$

At the unit sales price computed in part a$,$ how many units must the company produce and sell to break even? $($Assume all units produced are sold.$)$

What will be the margin of safety $($in dollars$)$ if the company produces and sells $50,000$ units at the sales price computed in part a$?$

Assume that the marketing manager thinks that the price of this product must be no higher than $$100$ to ensure market penetration. Will setting the sales price at $$100$ enable Ionic Charge to break even, given the plans to manufacture and sell $50,000$ units?