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Answer :
Cove's Cakes requires selling 358 units to reach break-even in units, with $5,015.58 in sales dollars. The business has a margin of safety of $1,008.72 based on current monthly sales, and must sell 543 cakes to achieve a $2,000 profit.
To determine Cove's Cakes break-even point in units and sales dollars, we apply the formula for break-even units: Break-Even Units = Fixed Costs / (Price per Unit - Variable Cost per Unit). Here, the variable cost per cake equals the sum of the ingredients, direct labor, and overhead, or $2.26 + $1.16 + $0.23 = $3.65. Therefore, the break-even units would be $3,626.00 / ($14.01 - $3.65) = 357.12 units, which we'd round up to 358 units because you can't sell a fraction of a unit. To find the break-even sales dollars, simply multiply the break-even units by the price per cake, resulting in 358 units * $14.01 = $5,015.58.
For the margin of safety, we subtract the break-even sales dollars from the current sales dollars (430 cakes * $14.01 per cake). The margin of safety in sales dollars is thus $6,024.30 ($14.01 * 430) - $5,015.58 = $1,008.72.
To achieve a profit of $2,000, we need to account for the fixed costs and additional profit desired. The total revenue required is fixed costs plus profit, which is $3,626.00 + $2,000.00 = $5,626.00. Dividing this by the price per cake minus variable cost per cake ($14.01 - $3.65) gives us the number of cakes Cove must sell to generate $2,000 in profit, which results in $5,626.00 / $10.36 = 542.86, rounded up to 543 cakes.
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