Chapter 3, Problem 69P

Extensions of the CVP Model—Multiple Products and Taxes

Assume that Painless Dental Clinics, Inc., offers three basic dental services. Here are its prices and costs:

Variable costs include the labor costs of the dental hygienists and dentists. Fixed costs of $400,000 per year include building and equipment costs, marketing costs, and the costs of administration. Painless Dental Clinics is subject to a 30 percent tax rate on income. A cleaning “unit” is a routine teeth cleaning that takes about 45 minutes. A filling “unit” is the work done to fill one or more cavities in one session. A capping “unit” is the work done to put a crown on one tooth. If more than one tooth is crowned in a session, then the clinic counts one unit per tooth (e.g., putting crowns on two teeth counts as two units).

Required

1. a.      Given the above information, how much will Painless Dental Clinics, Inc., earn each year after taxes?
2. b.      Assuming the above sales mix is the same at the break-even point, at what sales revenue does Painless Dental Clinics, Inc., break even?
3. c.       Assuming the above sales mix, at what sales revenue will the company earn $140,000 per year after taxes?
4. d.      Painless Dental Clinics, Inc., is considering becoming more specialized in cleanings and fillings. What would be the company’s revenues per year if the number of cleanings increased to 12,000 per year, the number of fillings increased to 1,000 per year, while the number of cappings dropped to zero? With this change in product mix, the company would increase its fixed costs to $450,000 per year. What would be the effect of this change in product mix on the clinic’s earnings after taxes per year? If the clinic’s managers seek to maximize the clinic’s after-tax earnings, would this change be a good idea?

To determine

Calculate the profit after tax for Company P.

Answer to Problem 69P

Company P earns $84,000 of profit after tax.

Explanation of Solution

Operating profit: The operating profit is the excess of total revenues over total expenses after adjusting for depreciation and taxes.

Contribution margin:

Particulars	Cleaning	Filling	Capping
Sales price (unit)	$120	$400	$1,200
Less: variable cost (unit)	$80	$300	$500
Contribution margin (unit)	$40	$100	$700
Units sold per year	9,000	900	100
Fixed cost	$400,000
Tax rate	30%

Table: (1)

Compute the profit after tax of Company P:

Particulars	Amount
Sales revenue $\left(\text{Sales unit}\times \text{Sales price}\right)$:
Cleaning $\left(9,000\times \$120\right)$	$1,080,000
Filling $\left(900\times \$400\right)$	$360,000
Capping $\left(100\times \$1,200\right)$	$120,000
Total sales revenue (a)	$1,560,000
Less:
Variable cost $\text{[sales unit}\times \text{variable cost }\left(\text{unit}\right)]$
Cleaning $\left(9,000\times \$80\right)$	$720,000
Filling $\left(900\times \$300\right)$	$270,000
Capping $\left(100\times \$500\right)$	$50,000
Total variable cost (b)	$1,040,000
Contribution:$c=\left(a-b\right)$	$520,000
Less:
Fixed cost (d)	$400,000
Profit before tax:$e=\left(c-d\right)$	$120,000
Tax rate	30%
Tax (f)	$36,000
Profit after tax: $g=\left(e-f\right)$	$84,000

Table: (2)

Thus, Company P earns $84,000 of profit after tax.

To determine

Calculate the sales revenue for cleaning, filling and capping at the break-even point.

Answer to Problem 69P

The sales revenue for cleaning, filling, and capping is $830,760, $276,800 and $91,200 respectively.

Explanation of Solution

Breakeven point (BEP): The breakeven point or BEP is that level of output at which the total revenue is equal to the total cost. The BEP means there are no operating income and no operating losses. The management keeps an eye on the breakeven point in order to avoid the operating losses in order to avoid losses.

Compute the total sales revenue of each product:

Particulars	Sales mix	Break-even point $\text{a}=(7,692\left(1\right)\times salesmix)$	Sales Price (b)	Total sales revenue $\text{c}=\left(a\times b\right)$
Cleaning	90%	6,923	$120	$830,760
Filling	9%	692	$400	$276,800
Capping	1%	76	$1,200	$91,200

Table: (3)

Thus, the sales revenue for cleaning, filling, and capping is $830,760, $276,800 and $91,200 respectively.

Working note 1:

Compute the break-even point:

$\begin{array}{c}\text{Break-even point = }\frac{\text{Fixed cost}}{\text{Combined weighted average contribution margin (2)}}\\ =\frac{\$400,000}{\$52}\\ =\text{ 7,692 units}\end{array}$

Working note 2:

Compute the total weighted average contribution margin:

Particulars	Sales price (a)	Variable cost (b)	Contribution margin $c=\left(a\times b\right)$	Sales mix (d)	Weighted average contribution margin $e=\left(c\times d\right)$
Cleaning	$120	$80	$40			90%	$36
Filling	$400	$300	$100	9%	$9
Capping	$1,200	$500	$700	1%	$7
Total weighted average contribution margin					$52

Table: (4)

To determine

Calculate the dollar sales required to earn the profit after tax of $140,000.

Answer to Problem 69P

To earn the profit after tax of $140,000, Company P must make the sales revenue of $1,246,104, $415,200 and $138,000 for cleaning, filling and capping for respectively.

Explanation of Solution

Breakeven point (BEP): The breakeven point or BEP is that level of output at which the total revenue is equal to the total cost. The BEP means there are no operating income and no operating losses. The management keeps an eye on the breakeven point in order to avoid the operating losses in order to avoid losses.

Compute the dollar sales required to earn the profit after tax of $140,000:

The total target volume is 11,538, so it will be distributed among the products in their sales mix ratio.

Particulars	Sales mix	Sales units $(11,538\left(3\right)\times salesmix)$	Sales price	Sales revenue
Cleaning	90%	10,384	$120	$1,246,104
Filling	9%	1,038	$400	$415,200
Capping	1%	115	$1,200	$138,000
Total sales revenue				$1,799,304

Table: (5)

Thus, to earn the profit after tax of $140,000, Company P must make the sales revenue of $1,246,104, $415,200 and $138,000 for cleaning, filling and capping respectively.

Working note 3:

Compute the volume of sales required to earn the profit after tax of $140,000:

$\begin{array}{c}\text{Target}\text{volume}\text{=}\text{Fixed}\text{cost}\text{+}\text{}\frac{\text{Target}\text{operating}\text{profit }}{\text{(1 - t)}}\\ =\text{\$400,000}\text{+}\text{}\frac{\text{\$140,000 }}{\text{(1 - 0}\text{.3)}}\\ ==\text{\$400,000}\text{+}\text{}\$200,000\\ =\$600,000\end{array}$

$\begin{array}{c}\text{Target}\text{volume}\text{=}\frac{600,000}{\text{Contribution}\text{margin}\text{(2)}}\\ =\frac{\$600,000}{\$52}\\ =11,538\text{units}\end{array}$

To determine

1. I.                    Calculate the revenue of Company P if the number of cleanings increased to 12,000 per year, the number of fillings increased to 1,000 per year, while the number of capping dropped to zero.
2. II.                 Calculate the effect on the profit after tax if the company increases its fixed cost to $450,000 with the given product mix.
3. III.              Suggest that the given change is a good idea or not.

Answer to Problem 69P

1. I.                    The revenue of Company P would be $1,840,000 if the number of cleanings increased to 12,000 per year, the number of fillings increased to 1,000 per year, while the number of capping dropped to zero.
2. II.                 The profit after tax increases by $7,000 if the company increases its fixed cost to $450,000 with the given product mix.
3. III.              Yes, the change of sales mix and an increase in fixed cost is a good idea for Company P.

Explanation of Solution

I.

Compute the revenue of Company P if the number of cleanings increased to 12,000 per year, the number of fillings increased to 1,000 per year, while the number of capping dropped to zero:

Particulars	Amount
Sales revenue $\left(\text{Sales unit}\times \text{Sales price}\right)$:
Cleaning $\left(12,000\times \$120\right)$	$1,440,000
Filling $\left(1,000\times \$400\right)$	$400,000
Capping $\left(0\times \$1,200\right)$	$0
Total sales revenue (a)	$1,840,000

Table: (6)

Thus, the revenue of Company P is $1,840,000 if the number of cleanings increased to 12,000 per year, the number of fillings increased to 1,000 per year, while the number of capping dropped to zero.

II.

Compute the effect on the profit after tax if the company increases its fixed cost to $450,000 with the given product mix:

$\begin{array}{c}\text{Increase}\text{in}\text{profit}\text{=}\text{Current}\text{profit}\text{(4)}-\text{Original}\text{profit}\\ \text{=}\$91,000-\text{\$84,000}\\ =\$7,000\end{array}$

Thus, the profit after tax increases by $7,000 if the company increases fixed cost to $450,000 with the given product mix.

Working note 4:

Compute the profit after tax of Company P:

Particulars	Amount
Sales revenue $\left(\text{Sales unit}\times \text{Sales price}\right)$:
Cleaning $\left(12,000\times \$120\right)$	$1,440,000
Filling $\left(1,000\times \$400\right)$	$400,000
Capping $\left(0\times \$1,200\right)$	$0
Total sales revenue (a)	$1,840,000
Less:
Variable cost $\text{[sales unit}\times \text{variable cost }\left(\text{unit}\right)]$
Cleaning $\left(12,000\times \$80\right)$	$960,000
Filling $\left(1,000\times \$300\right)$	$300,000
Capping $\left(0\times \$500\right)$	$0
Total variable cost (b)	$1,260,000
Contribution: $c=\left(a-b\right)$	$580,000
Less:
Fixed cost (d)	$450,000
Profit before tax:$e=\left(c-d\right)$	$130,000
Tax rate	30%
Tax (f)	$39,000
Profit after tax: $g=\left(e-f\right)$	$91,000

Table: (7)

III.

If the clinic’s managers seek to maximize the clinic’s after-tax earnings, this is a good idea as the profit has increased by 7,000 with the change in sales mix and an increase in fixed cost.

Thus, the change in sales mix and an increase in fixed cost is a good idea for Company P.