Chapter 21, Problem 15E

To determine

Concept Introduction:

Variable cost and fixed costs:

Variable costs: The variable costs can be defined as the cost that change directly with the change in the level of output. They are directly related with the level of output. These costs are termed relevant costs as well.

Fixed costs: The fixed costs can be defined as the cost that do not change directly with the change in the level of output. They are not related with the level of output. These costs are termed irrelevant costs generally.

To compute:

The expected −

1. Variable cost
2. Fixed cost

For the expected units to be sold next year

Answer to Problem 15E

Solution:

The expected −

1. Variable cost for the expected units to be sold next year = $ 12,000,000
2. Fixed cost for the expected units to be sold next year = $ 3,750,000

Explanation of Solution

The expected variable costs and fixed costs are calculated as under −

1. Variable cost for the expected units to be sold next year -

Given,

• The expected total sales revenue = $ 17,000,000
• Expected units to be sold = 200,000 units
• Contribution margin per unit = $ 25 per unit
• Expected Pre-tax income for the next year = $ 1,250,000

The sales price per unit will be calculated as under −

  $\begin{array}{l}Salespriceperunit=\frac{Expectedsalesrevenue}{Expectedunitstobesold}\\ Salespriceperunit=\frac{\$17,000,000}{\text{200,000 }units}\\ Salespriceperunit=\$85perunit\end{array}$

The expected sales price per unit = $ 85.
Now, variable cost per unit will be calculated as under −

  $\begin{array}{l}Variablecostperunit=Salespriceperunit–Contributionmarginperunit\hfill \\ Variablecostperunit=\$85-\$25\hfill \\ Variablecostperunit=\$60perunit\hfill \end{array}$

The total expected variable costs are calculated as under −

  $\begin{array}{l}Totalvariablecost=VariablecostperunitXExpectedunitstobesold\hfill \\ Totalvariablecost=\$60perunitX200,000units\hfill \\ Totalvariablecost=\$12,000,000\hfill \end{array}$

The total expected variable costs = $ 12,000,000.
 2 Fixed cost for the expected units to be sold next year −

The total expected fixed costs will be calculated as under −
Given,

• Expected units to be sold = 200,000 units
• Contribution margin per unit = $ 25 per unit
• Expected Pre-tax income for the next year = $ 1,250,000
• Total expected variable costs = $ 12,000,000

First, total contribution margin will be calculated as −
  $\begin{array}{l}Totalcontributionmargin=ContributionmarginperunitXExpectedunitstobesold\hfill \\ Totalcontributionmargin=\$25perunitX200,000units\hfill \\ Totalcontributionmargin=\$5,000,000\hfill \end{array}$

Now, fixed costs will be calculated as −
  $\begin{array}{l}Fixedcosts=Totalcontributionmargin-ExpectedPre-taxincomeforthenextyear\hfill \\ Fixedcosts=\$5,000,000-\$1,250,000\hfill \\ Fixedcosts=\$\text{ 3},750,000\hfill \end{array}$

The expected fixed costs for the next year = $ 3,750,000

Conclusion

Thus, the expected fixed costs and expected variable costs have been calculated for the next year.