Silver River Company sells Products S and T and has made the following estimates

Question

Silver River Company sells Products S and T and has made the following estimates for the coming year: Product Unit Selling Price Unit Variable Cost Sales Mix S $30 $24 60% T 70 56 40 Fixed costs are estimated at $202,400. Determine (a) the estimated sales in units of the overall product necessary to reach the break-even point for the coming year, (b) the estimated number of units of each product necessary to be sold to reach the break-even point for the coming year, and (c) the estimated sales in units of the overall product necessary to realize an operating income of $119,600 for the coming year.

Explanation / Answer

Step 1: Calculate the contribution margin per unit for each product: Cont pu of S = SP pu - VC pu = 30-24 = $6 pu Cont pu of T = 70-56= 14 pu Step 2: Calculate the weighted-average contribution margin per unit for the sales mix using the following formula: S CM per Unit × S Sales Mix Percentage + T CM per Unit ×T Sales Mix Percentage = Weighted Average Unit Contribution Margin Product S T Sales Price per Unit $30 $70 - Variable Cost per Unit $24 $56 Contribution Margin per Unit $6 $14 × Sales Mix Percentage 60% 40% $3.60 $5.60 Sum: Weighted Average CM per Unit $9.20 Step 3: Calculate total units of sales mix required to break-even using the formula: Break-even Point in Units of Sales Mix = Total Fixed Cost /Weighted Average CM per Unit Total Fixed Cost $202,400 / Weighted Average CM per Unit $9.20 Break-even Point in Units of Sales Mix = 22,000 ..............Ans (a) Step 4: Calculate number units of product S & T at break-even point: Product King Queen Sales Mix Percentage 60% 40% × Total Break-even Units 22,000 ----------------------------------------------- Product Units at Break-even Point 13,200 8,800 ............Ans (b) We have Total COnt = FC + Net Income = 202,400+ 119,600 = $322,000 So the estimated sales in units of the overall product = Total COnt/Mix Cont pu = 322,000/9.20 = 35000 units .............Ans (c)

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