Carrot Jewelry is considering two mutually exclusive product lines, based on either an emerald ring or a ruby bracelet, to introduce next year. The board of directors of the company has established a target net income of $30,000 for the new product line but wishes to maximize profit in any case. For the emerald ring line, Carrot expects to sell 200 rings during the year at a selling price per ring of $1,500. Estimated variable costs are $800 per ring, and fixed costs will amount to $90,000 for the year. For the ruby bracelet line, the company anticipates sales of 500 units at a selling price of $1,100 per bracelet. Fixed costs will come to $110,000 for the year, and the variable costs will also be $800 each. Carrot Jewelry will have a tax rate of 30% next year. How much more or less will Carrot have to spend in fixed costs on the proposed bracelet line in order for it to have the same net income as the ring product line?

Question

Quizplus · Accepted Answer

If Carrot produces and sells rings, the contribution margin per ring sold will be $1,500 F1F1F1S1?F1F1F10 $800 = $700. With 200 rings sold, this will produce a contribution margin of $700 F1F1F1S1?F1F1F10 200 = $140,000. If fixed costs are $90,000, then total pretax income will be $140,000 F1F1F1S1?F1F1F10 $90,000 = $50,000. At a 30% tax rate, tax will be 30% F1F1F1S1?F1F1F10 $50,000 = $15,000, resulting in net income of $50,000 F1F1F1S1?F1F1F10 $15,000 = $35,000. If Carrot produces and sells bracelets, the contribution margin per bracelet sold will be $1,100 F1F1F1S1?F1F1F10 $800 = $300. With 500 bracelets sold, this will produce a contribution margin of $300 F1F1F1S1?F1F1F10 500 = $150,000. In order to match the income generated by the ring product line, fixed costs will have to be reduced to $100,000 so that total pretax income will be $150,000 F1F1F1S1?F1F1F10 $100,000 = $50,000. Then, as with the ring line, tax will be 30% F1F1F1S1?F1F1F10 $50,000 = $15,000, resulting in net income of $50,000 F1F1F1S1?F1F1F10 $15,000 = $35,000. Therefore, fixed costs must be reduced on the bracelet line from $110,000 to $100,000, or by $10,000, in order for the bracelet line to generate the same net income as the ring product line.

Carrot Jewelry Is Considering Two Mutually Exclusive Product Lines, Based