Question

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

	Price per Unit			Variable Cost per Unit			Units Sold per Year
Cleaning	$	140		$	90		8,000
Filling		420			400		1,700
Capping		1,225			530		300

Variable costs include the labor costs of the dental hygienists and dentists. Fixed costs of $410,000 per year include building and equipment costs, marketing costs, and the costs of administration. Painless Dental Clinics is subject to a 20 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:

a. How much will Painless Dental Clinics, Inc., earn each year after taxes?

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? (Do not round intermediate calculations. Round your final answer up to the nearest whole unit.)

c. Assuming the above sales mix, at what sales revenue will the company earn $142,000 per year after taxes? (Do not round intermediate calculations.)

d-1. Painless Dental Clinics, Inc., is considering becoming more specialized in cleanings and fillings. Assume the number of cleanings increased to 11,000 per year, the number of fillings increased to 1,800 per year, while the number of cappings dropped to zero? With this change in product mix, the company would increase its fixed costs to $460,000 per year. What would be the effect of this change in product mix on the clinic’s earnings after taxes per year?

d-2. If the clinic's managers seek to maximize the clinic's after-tax earnings, would this change be a good idea?

	No
	Yes

Answer 1

Requirement 1:
Given the above information, how much will Painless Dental Clinics, Inc., earn each year after taxes? (Omit the "$" sign in your response.)
Painless Dental Clinics, Inc.
Income statement
	Cleaning	Filling	Caping	Total
Sales	$1,120,000	$714,000	$367,500	$2,201,500
Less: Variable cost	$720,000	$680,000	$159,000	$1,559,000
Contribution Margin	$400,000	$34,000	$208,500	$642,500
Less: Fixed Cost				($410,000)
Profit before taxes				$232,500
Less Taxes @20%				$46,500
Profit				$186,000
b) Assuming the above sales mix is the same at the break­even point, at what sales revenue does Painless Dental Clinics, Inc., break even? (Do not round your intermediate calculation.)
Weighted-average contribution margin percentages for each product.	A	B	C	D	E = B x C	F = B x D	G= E-F
Services	Units sold per year	Weights	Price Per unit	Variable cost per unit	weighted price per unit	weighted variable cost per unit	weighted contribution margin
Cleaning	8000	80.00%	$140	$90	$112	$72.00	$40.00
Filling	1700	17.00%	$420	$400	$71.40	$68.00	$3.40
Caping	300	3.00%	$1,225	$530	$36.75	$15.90	$20.85
Total	10000	100.00%			$220.15	$155.90	$64.25
Contribution Margin % = $64.25/220.15	29.18%
Break Even = Fixed cost ÷ Weighted­ average CM%
Break Even = $410000/29%	$1,404,848
c)
Before Tax Profit = After Tax Profit/(1- Tax )
Before Tax Profit = $142000/(1-20%)	$177,500
Required revenue: (Fixed cost + Required profit) ÷ Weighted­ average CM%
Required revenue: ($410000+177500)/29.18%	$2,013,365
d)
Services	Price Per unit	Variable cost per unit	Units sold per year
Cleaning	$140	$90	11000
Filling	$420	$400	1800
Caping	$1,225	$530	0
Painless Dental Clinics, Inc.
Income statement
	Cleaning	Filling	Caping	Total
Sales	$1,540,000	$756,000	$0	$2,296,000
Less: Variable cost	$990,000	$720,000	$0	$1,710,000
Contribution Margin	$550,000	$36,000	$0	$586,000
Less: Fixed Cost				($460,000)
Profit before taxes				$126,000
Less Taxes @20%				$25,200
Profit				$100,800
d(/2)
No, Based on after­ tax profit, Painless Dental Clinics should not change the product mix.