Appendix D:  Cost-Volume-Profit Analysis – Sample Case Study

Note:  The following case study may be adapted for classroom use.  If desired, teachers may present cost-volume-profit analysis closely following the developmental progression in this case study.

Wonderful Wally's Widget Wholesale (WWWW)

Wally Walker recently began a business which he calls Wonderful Wally's Widget Wholesale (WWWW).  Wally has asked for advice regarding the relationships between the cost of his product (a widget), other expenses, the volume of sales, and his profit levels.

Wally's business is a simple one.  He purchases a partially complete widget (called a pre-widget) from a local manufacturer for $5.00 each.  This price includes the cost of the widget and delivery to Wally's warehouse.  Wally then hires local students to make some minor modifications to the pre-widget using simple tools like pliers and screwdrivers.  The students receive $2.00 for each widget that they complete.  The students are too young to pay Canada Pension Plan (CPP), and do not work enough to pay Unemployment Insurance (UI), and receive no other benefits from WWWW so the $2.00 is the entire labour cost of the modifications.  The modifications also require some parts.  These additional parts cost $1.00 per widget.

Wally has only two other expenses:  Rent is $6,000 per year ($500 per month) and interest expenses are $4,000 per year.

Wally can sell all the widgets he can modify as soon as they are complete so there is never any inventory of finished widgets on hand.  Customers purchase the finished widgets at the warehouse so there are no delivery expenses.  The suppliers of the pre-widgets will also deliver at any time.  WWWW does not need to keep a supply of pre-widgets or materials on hand.

1.       What is the variable cost of one widget?

2.       What is the contribution margin per unit?

3.       What is WWWW total fixed cost for a year?

Break-even Analysis

How many widgets must WWWW modify and sell to break even?

Let x  = the number of widgets WWWW must modify and sell to break even.

WWWW must modify and sell 2,500 widgets per year to break even.

4.       Target Net Income

How many widgets must WWWW modify and sell to earn an annual profit of:

a)  $20,000.00?

Let x  = number of widgets WWWW must modify and sell to earn a profit of $20,000

WWWW would need to modify and sell 7,500 widgets per year to make an annual profit of $20,000.

b) Let x  = number of widgets WWWW must modify and sell to earn a profit of $50,000

WWWW would need to modify and sell 15,000 widgets per year to make an annual profit of $50,000.

c) Let x  = number of widgets WWWW must modify and sell to earn a profit of $100,000

WWWW would need to modify and sell 27,500 widgets per year to make an annual profit of $100,000.

5.       Change in Variable Costs

Suppose Wally found some students that were willing to modify the pre-widgets for $1 per widget.  All other costs and the selling price are expected to remain the same as given in the original data.

How many widgets must WWWW modify and sell to:

a)   break even for the year?
b)   earn an annual profit of $20,000?
c)   earn an annual profit of $50,000?
d)   earn an annual profit of $100,000?

Solutions:

a)   Let x = number of widgets WWWW must modify and sell to break even.

WWWW would need to modify and sell 2 000 units to break even.

b) Let x = number of widgets WWWW must modify and sell to earn an annual profit of $20,000

WWWW would need to modify and sell 6,000 widgets to earn an annual profit of $20,000.

c) Let x = number of widgets WWWW must modify and sell to earn an annual profit of $50,000

WWWW would need to modify and sell 12,000 widgets to earn an annual profit of $50,000.

d) Let x = number of widgets WWWW must modify and sell to earn an annual profit of $100,000

WWWW would need to modify and sell 22,000 widgets to earn an annual profit of $100,000.

6.       Compare your answers in 6 a-d with those of 4 and 5 a-c.  What can you conclude about the effect of a decrease in variable cost on profits?

      Solution:  A decrease in variable costs per unit will increase profits if the volume of activity remains constant.  6 a) to d) demonstrates that a decrease in variable cost per unit will mean that less units must be sold to earn a target net income.

7.       Change in Fixed Cost

Refer to the original data for WWWW.  Suppose that Wally finds a new warehouse that he can rent for $4,200 per year ($350 per month).  All other cost and the selling price are expected to remain the same as those in the original data.

      How many widgets must WWWW modify and sell to:

a)         break even for the year?
b)         earn an annual profit of $20,000?
c)         earn an annual profit of $50,000?
d)         earn an annual profit of $100,000?

Solutions:

a)   Let x = number of widgets WWWW must modify and sell to break even.

WWWW would need to modify and sell 2,050 widgets to break even.

      b) Let x = number of widgets WWWW must modify and sell to earn an annual profit of $20,000

WWWW would need to modify and sell 7,050 widgets to earn a profit of

                        $20,000.

      c) Let x = number of widgets WWWW must modify and sell to earn an annual profit of $50,000

WWWW would need to modify and sell 14,550 widgets to earn a profit of $50,000.

      d) Let x = number of widgets WWWW must modify and sell to earn an annual profit of $100,000

WWWW would need to modify and sell 27,050 widgets to earn a profit of $100,000.

8.       Compare your answers in 8 a) to d) with those of 4 and 5 a) to c).  What can you conclude about the effect of a decrease in fixed cost on profits with all other factors remaining constant?

Solution:  A decrease in total fixed costs will increase profit if the volume of activity remains constant.  8 a) to d) demonstrates that a decrease in total fixed cost will mean less units must be sold to earn a target net income.

9.       Change in Selling Price

Refer to the original data for WWWW.  Suppose that Wally has found a new market for the widgets which will pay $13 for each.  All costs remain the same as given in the original data.

How many widgets must WWWW modify and sell to:

a)  break even for the year?
b)  earn an annual profit of $20,000?
c)  earn an annual profit of $50,000?
d)  earn an annual profit of $100,000?

a)        Let x = number of widgets WWWW must modify and sell to break even.

      WWWW would need to modify and sell 2,000 widgets to break even.

      b) Let x = number of widgets WWWW must modify and sell to earn an annual profit of $20,000

WWWW would need to modify and sell 6,000 widgets to earn an income of $20,000 per year.

      c) Let x = number of widgets WWWW must modify and sell to earn an annual profit of $50,000

WWWW would need to modify and sell 12,000 widgets to earn an income of $50,000 per year.

      d) Let x = number of widgets WWWW must modify and sell to earn an annual profit of $100,000

WWWW would need to modify and sell 22,000 widgets to earn an income of $100,000 per year.

10.   Compare your answers in 10 a) to d) with those of 4 and 5 a) to c).  What can you conclude about the effect of an increase in the selling price on profits (all other factors remain the same)?

Solution:  An increase in selling price will increase profits if the volume of activity remains constant.  Question 8 a) to d) demonstrate that an increase in selling price will mean less units must be sold to earn a target net income.

11.   Missing Selling Price Given Costs, Volume and Desired Profit

Refer to the original data for WWWW.  Suppose that Wally plans to modify and sell 20,000 widgets per year.  What price must Wally charge for the widget in order to earn an annual profit of $50,000 if all costs remain the same as that in the original data?

Let x = selling price required.

      WWWW must sell the widgets for $11 each.

12.   Missing Variable Cost Given Selling Price, Other Costs, Volume and Desired Profit

Refer to the original data.  Suppose that Wally plans to modify and sell 20,000 widgets per year.  What is the maximum price that Wally can pay the students to modify each widget in order that WWWW will earn an annual profit of $50,000 if all other cost and prices remain the same?

Let x = maximum labour cost for 1 widget

The maximum that WWWW can pay for labour is $3 per widget.

13.   Calculate Contribution Margin (CM) Ratio

Refer to the original data and calculate the contribution margin ratio:

14.   Calculate Dollar Sales to Break Even

Refer to the original data.  How many dollars of sales must WWWW have to break

even?

Let x = dollars sales of widgets to break even.

WWWW must modify and sell $30,000 of widgets to break even.

Another method

From question 4 we know WWWW must sell 2,500 units to break even.

2,500 widgets @ $12/widget = $30,000

Therefore, there are essentially two ways in which one may determine the volume necessary to achieve a target profit -- by units or by dollar sales.

15.   Refer to the original data.  How many dollars of widgets must WWWW modify and sell to earn an annual profit of:

a)  $20,000?
b)  $50,000?
c)  $100,000?

a)  Let x = dollars sales of widgets required to earn a profit of $20,000

WWWW would need to modify and sell $90,000 of widgets to earn an annual income of $20,000.

Other method

From 5a) we know that WWWW must sell 7,500 widgets to make an annual profit of $20,000.

7,500 widgets @ $12/widget = $90,000

b) Let x = number of widgets WWWW must modify and sell to earn an annual profit of $50,000

WWWW would need to modify and sell $180,000 of widgets to make an annual profit of $50,000.

Other method

From 5b) we know that WWWW must sell 15,000 widgets to make an annual profit of $50,000.

15,000 widgets @ $12 = $180,000

c) Let x = number of widgets WWWW must modify and sell to earn an annual profit of $100,000

WWWW would need to modify and sell $330,000 of widgets to earn an annual income of $100,000.

Other method:

From 5c) we know that WWWW must sell 27,500 widgets to make an annual profit of $100,000.

27,500 widgets @ $12/widget = $330,000

Summary