Question

You are currently trying to decide between two cost structures for your business: one that has a greater proportion of short-term fixed costs and another that is more heavily weighted to variable costs. Estimated revenue and cost data for each alternative are as follows:

Cost Structure

Alternative #1 Alternative #2

Selling price per unit $ 50 $ 50

Variable cost per unit 20 15

Short-term fixed costs/year 85,000 90,000

Required:

1. What sales volume, in units, is needed for the total costs in each cost-structure alternative to be the same?

2. Suppose your profit goal for the coming year is 10% of sales (i.e., operating profit ÷ sales = 10%). What sales level in units is needed under each alternative to achieve this goal?

3. Suppose again that your profit goal for the coming year is 10% of sales. What sales volume in dollars is needed under each alternative to achieve this goal?

Answer 1

1) Sales volume at which total costs in each cost-structure alternative to be the same is calculated as follows:-

Let sales volume required to be sold = X

Total cost in Alternative 1 = (Variable cost per unit*Units sold)+Short term Fixed cost

= ($20*X)+$85,000 = 20X+85,000

Total cost in Alternative 2 = (Variable cost per unit*Units sold)+Short term Fixed cost

= ($15*X)+$90,000 = 15X+90,000

Total cost in Alternative 1 = Total cost in Alternative 2

20X+85,000 = 15X+90,000

20X - 15X = 90,000 - 85,000

5X = 5,000

X = 5,000/5 = 1,000

Therefore at the sales volume of 1,000 units total costs in each cost-structure alternative will be same.

2) Alternative 1 :

Contribution per unit = Selling price per unit - Variable cost per unit

= $50 - $20 = $30 per unit

Required Profit per unit = Sale price*10% = $50*10% = $5 per unit

Total contribution = Fixed cost+Operating profit

(Contribution per unit*units sold) = Short term fixed cost+(Profit per unit*units sold)

($30*Units sold) = $85,000+($5*Units sold)

($30*Units sold) - ($5*Units sold) = $85,000

($30-$5)*Units sold = $85,000

Units sold = $85,000/$25 = 3,400 units

Alternative 2 :

Contribution per unit = Selling price per unit - Variable cost per unit

= $50 - $15 = $35 per unit

Required Profit per unit = Sale price*10% = $50*10% = $5 per unit

Total contribution = Fixed cost+Operating profit

(Contribution per unit*units sold) = Short term fixed cost+(Profit per unit*units sold)

($35*Units sold) = $90,000+($5*Units sold)

($35*Units sold) - ($5*Units sold) = $90,000

($35-$5)*Units sold = $90,000

Units sold = $90,000/$30 = 3,000 units

3) Sales volume in dollars for Alternative 1 = Sales units*Selling price per unit

= 3,400 units*$50 per unit = $170,000

Sales volume in dollars for Alternative 2 = Sales units*Selling price per unit

= 3,000 units*$50 per unit = $150,000