Dana’s ribbon world makes award rosettes. following is information about the company: variable cost per rosette $ 1.20 sales price per rosette 4.00 total fixed costs per month 2800.00 required: 1. suppose dana’s would like to generate a profit of $880. determine how many rosettes it must sell to achieve this target profit. 2. if dana’s sells 1,200 rosettes, compute its margin of safety in units, in sales dollars, and as a percentage of sales. 3. calculate dana’s degree of operating leverage if it sells 1,200 rosettes. 4a. using the degree of operating leverage, calculate the change in dana’s profit if unit sales drop to 1,080 units. 4b. prepare a new contribution margin income statement to verify change in dana's profit.

1. Dana needs to sell 1,315 rosettes to achieve this target profit

2. Margin of safety in units=200 rosettes

Margin of safety in sales dollars=$800

Percentage margin of safety=1.67%

3. Dana's degree of operating leverage=6

4. a) An increase in the degree of operating leverage implies a reduction

       in the profits by 750%

   b) Contribution margin=$3,024

Explanation:

1. Calculate number of units he needs to sell to make a profit of $880

We can derive the expression below;

Profit=Revenue from sales-cost of goods sold

where;

Profit=$880

Revenue from sales=sale price per unit×number of units

sale price per unit=$4.00

number of units=n

Revenue from sales=(4×n)=4 n

Cost of goods sold=Fixed cost+(variable cost per unit×number of units sold)

Fixed cost=2,800

variable cost per unit=$ 1.20

number of units sold=n

Cost of goods sold=2,800+1.2 n

replacing in the original expression;

880=(4 n)-(1.2 n+2,800)

880=4 n-1.2 n-2,800

4 n-1.2 n=2,800+880

2.8 n=3,680

n=3,680/2.8

n=1,314.29 round up to 1,315

Dana needs to sell 1,315 rosettes to achieve this target profit

2. Margin of safety=Current sales-break-even point sales

break-even point sales, sales when revenue from sales=cost of goods sold

Using the expressions above;

4 n=1.2 n+2,800

4 n-1.2 n=2,800

2.8 n=2,800

n=2,800/2.8

n=1,000

The break-even point sales=1,000 rosettes

Current sales level=1,200 rosettes

Margin of safety in units=(1,200-1,000)=200 rosettes

Margin of safety in sales dollars=(200×4)=$800

Percentage margin of safety=(200/1,200)×100=1.67%

3. Operating leverage={Quantity×(price-variable cost per unit)}/{quantity×(price-variable cost per unit)}-fixed cost

where;

Quantity=1,200

Price=$4

variable cost per unit=$1.20

fixed cost=$2,800

Operating leverage={1,200×(4-1.2)}/{1,200×(4-1.2)}-2,800

Operating leverage=3,360/560=6

Dana's degree of operating leverage=6

4.a Degree of operating leverage can also be written as;

Degree of operating leverage=(sales-variable costs)/profits

{1080×(4-1.2)}/{1080×(4-1.2)}-2,800

3,024/224=13.5

An increase in the degree of operating leverage implies a reduction in the profits by (13.5-6)=(7.5×100)=750%

4.b

Contribution margin=sales-variable expenses

where;

sales=(1,080×4)=4,320

variable expenses=(1.2×1,080)=1,296

replacing;

Contribution margin=(4,320-1,296)=3,024

Contribution margin=$3,024

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