Hilary\'s Jewels sells cubic zirconium (fake diamond) rings for $80 each. The pr

Question

Hilary's Jewels sells cubic zirconium (fake diamond) rings for $80 each. The projected income statement for 2016 follows: Sales Variable costs S4,000,000- (2.200.000 1,800,000. (1.600.000 S 200.000 Contribution Margin Fixed costs Pre-tax profit Required: aCompute the contribution margin per ring and the number of rings that b. Compute the contribution margin ratio and the breakeven point in total c. Suppose the total revenues were $200,000 greater than expected. What is d. What is the margin of safety in number of rings? must be sold to break even. revenue. the total pre-tax profit?- e. o. How many rings must be sold to earn an after-tax profit of $300,000?

Explanation / Answer

Ans a) Calculation of Contribution Margin per ring Total No of ring sold as per present sales = Total Sales/Sale Price per ring = $4,000,000/$80 = 50,000 rings Contribution Margin = $1,800,000 Therefore, Contribution Margin per ring = Total Contribution Margin/No of rings sold = $1,800,000/$50,000 = $36 (Ans) Therefore, No of rings must be sold to break even = Fixed Cost/Contribution per ring = $1,600,000/$36 = 44,444.44 rings. Or 44,445 rings (Ans) (approx) Ans b) Contribution Margin Ratio = Total contribution Margin/Total Sales = $1,800,000/$4,000,000 = 45% (Ans) Break Even Point Sales = 44,445 rings * $80 = $3,555,600 Break Even Point in Total Revenue = Break Even Sales/Total Revenue = $3,555,600/$4,000,000 = 88.89% (Ans) Ans c) If Total Revenue were $2,00,000 greater than expected, then:- New Sales $4,200,000 Less: Variable Cost ($2,310,000) ($44 per ring*52,500 rings sold) (Working Note 1 & 2)           Contribution Margin 1,890,000 Less: Fixed Cost 1,600,000 Pre Tax Profit 290,000 (Ans) Ans d) Margin of Safety = (Total Sales minus Break Even Sales)/Total Sales = ($4,200,000 minus $3,555,600)/$4,200,000 = 15.342857% (Ans) Ans e) Given, Tax Rate = 25%, After Tax Profit = $300,000. Therefore, Pre tax profit = $300,000*100/75 = $400,000 Let x be the no of ring sold to earn after tax profit of $300,000. We know that, Sales- Variable Cost- Fixed Cost = Pre Tax Profit or, 80x-44x-1,600,000 = 400,000 or, 36x = 1,600,000+400,000 or, 36x = 2,000,000 or, x = 55,555.5555 rings or 55,556 rings (Ans) Working Note: 1. Variable Cost per ring = Total Variable Cost/Total No of ring sold = $2,200,000/50,000 rings = $44 per ring 2. Total No of ring sold as per new sales = Total Sales (New)/Sale Price per ring = $4,200,000/$80 = 52,500 rings 3. Break even sales = $3,555,600 (calculated above)

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