Answer:
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
