Assumption 5: Product-mix assumption. With many products, CVP analysis assumes a
known and constant product mix. However, in most instance, the product-mix itself has
to be decided. Changing the product-mix may be best the way to react to changes in
demand for the different products in the mix.
Exercises
1. Ajay Singh plans to offer gift-wrapping services at the local mall during the month of December. Ajay will wrap each package, regardless of size, in the customer’s choice of wrapping paper and bow for a price of $3. Ajay estimates that his variable costs will total $1 per package wrapped and that his fixed costs will total $600 for the month.
Required:
a. Express Ajay’s profit before taxes in terms of the number of packages sold.
b. How many packages does Ajay need to wrap to break even?
c. How many packages must Ajay wrap to earn a profit of $1,400?
2. Gina Matheson owns and operates a successful florist shop in Bloomington, Indiana. Gina estimates that her variable costs are $0.25 per sales dollar (i.e., variable costs represent 25% of revenue) and that her fixed costs amount to $6,000 per month.
Required:
a. How much revenue does Gina need to generate to earn a profit of $3,600 per month?
b. Suppose Gina estimates that she will be able to generate revenue of $15,000 in a month.
Assume also that she wishes to earn $4,000 in profit each month. What is the maximum amount that she can spend on fixed costs?
c. Suppose Gina’s variable costs were to increase by 50%. What is Gina’s breakeven revenue per month?
3. Zap, Inc., manufactures an organic insecticide that is marketed and sold via television infomercials.
Each “ZAP” kit sells for $22, which includes a base price of $20 per “ZAP” kit plus $2 in shipping and handling fees. Zap’s contribution margin ratio is 60%. In addition, Zap expects to break even if it sells 17,500 “ZAP” kits per month.
Required:
a. What is the unit variable cost of a “ZAP” kit?
b. What are Zap’s monthly fixed costs?
c. Suppose Zap introduces an offer for “free” shipping and handling. How many additional
“ZAP” kits must be sold each month to break even?
4. The Cottage Bakery sells a variety of gourmet breads, cakes, pies, and pastries. Although its wares are considerably more expensive than those available at supermarkets and other bakeries, the Cottage Bakery has a loyal clientele willing to pay a premium price for premium quality. In a typical month, the Cottage Bakery generates revenue of $150,000 and earns a profit of $7,500. The Cottage Bakery’s contribution margin ratio is 40%.
Required:
a. What is the Cottage Bakery’s margin of safety at its current sales level?
b. What is the Cottage Bakery’s operating leverage?
c. What is the revenue required for Cottage Bakery to break even on a cash basis? Assume that 30% of the Cottage Bakery’s fixed costs represent noncash items (e.g., depreciation expense on the ovens, furniture, and fixtures). All other expenses are paid in cash and all revenues are received in cash.
5. Tom and Lynda operate Hercules Gym. The club currently has 900 individual members and 300 family memberships. The fee for individual memberships is $100 per month, and families pay $150 per month. Variable costs are $35 per month for individual and $60 per month for a family. Monthly fixed costs amount to $42,750.
Required:
a. Calculate Hercules’ weighted contribution margin. Use this answer to calculate the number of individual and family memberships at breakeven volume.
b. Calculate Hercules’ weighted contribution margin ratio. Use this answer to calculate the total revenue to achieve breakeven.
Solutions to Exercises 1. (LO1 and LO2)
a. Recall that:
Profit before taxes = (unit contribution margin sales volume in units) – fixed costs.
Additionally,
Unit contribution margin = Unit selling price – Unit variable cost.
= $3.00 – $1.00 = $2.00 per package.
The problem also informs us that Ajay’s fixed costs for the month = $600.
Thus, Ajay’s profit is:
Profit before taxes = ($2.00 number of packages sold) – $600.
b. Breaking even implies a profit of zero. Thus, we have:
$0 = ($2.00 Breakeven volume) – $600, Or, breakeven volume in packages =
00
c. Substituting Ajay’s target profit of $1,400 into the expression for profit we developed in part [a], we have:
$1,400 = $2.00 Required number of packages – $600.
OR, Required sales =
a. Substituting a target profit of $3,600 into the monthly profit equation, we have:
$3,600 = (0.75 Required revenue) – $6,000.
OR, Required revenue =
( $6,000 0.75 $3,600 )
= $12,800 per month.b. Substituting the data into Gina’s profit equation, we have:
$4,000 = (0.75 $15,000) – Fixed costs.
Maximum expenditure on fixed costs = $11,250 – $4,000 = $7,250.
c. Gina’s new variable cost is $0.25 (1 + 0.5) = $0.375 per $1.00 of sales.
Thus, Gina’s new contribution margin ratio is:
( $1.00 $1.00 - $.375 )
= 0.625.Substituting this information into the profit calculation and setting profit equal to $0, we have:
$0 = (0.625 Breakeven revenue)– $6,000. Breakeven revenue = $9,600.
3. (LO2 and LO3)
a. The contribution margin ratio =
( )
Price
With Zap’s information, we have the contribution margin ratio
=
Contribution margin ratio = 1 – Variable cost ratio.
0.60 = 1 – Variable cost ratio, or Variable cost ratio = 40% of sales price That is, unit variable cost = 0.40 × $22 = $8.80 per unit.
b. Let us use the profit expression:
Profit before taxes = (Contribution margin ratio Revenue) – Fixed costs.
We know that Zap expects to break even at 17,500 “ZAP” kits – thus, revenue = 17,500 × $22.00
= $385,000. We know that profit = $0 at the breakeven point. Thus, we have:
$0 = (0.60 $385,000) – Fixed costs.
Solving, we find that fixed costs = $231,000.
Or
$0 = (Unit contribution margin Breakeven volume) – Fixed costs.
From part [a], we know that the unit variable cost = $8.80. Because the selling price = $22.00, we know that the unit contribution margin = $22.00 – $8.80 = $13.20. Thus, we have:
$0 = ($13.20 17,500) – Fixed costs.
Again, we find that fixed costs = $231,000.
c. The free shipping and handling offer reduces Zap’s revenue per “ZAP” kit to $20.00. With the knowledge acquired in parts [a] and [b] (i.e., the variable cost per “ZAP” kit and Zap’s monthly fixed costs, respectively), we can calculate Zap’s breakeven volume as:
$0 = (Unit contribution margin Breakeven volume) – Fixed costs.
or, $0 = [($20.00 – $8.80) Breakeven volume] – $231,000 Breakeven number of kits ( Breakeven volume ) = 20,625.
Consequently, Zap must sell an additional 20,625 – 17,500 = 3,125 kits to break even if the company decides to offer “free” shipping.