Question

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

	Price per Unit			Variable Cost per Unit			Units Sold per Year
Cleaning	$	380		$	210		8,000
Filling		660			640		1,700
Capping		1,525			890		300

Variable costs include the labor costs of the dental hygienists and dentists. Fixed costs of $530,000 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. Given this information, how much will Painless Dental Clinics, Inc., earn each year after taxes?

b. Assuming the given sales mix is the same at the break-even point, at what sales revenue does Painless Dental Clinics, Inc., break even?

c. Assuming the given sales mix, at what sales revenue will the company earn $166,000 per year after taxes?

d-1. 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 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 $580,000 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?

Answer 1

a.

	Cleaning	Filling	Capping	Total
Price per unit	$                     380	$                   660	$            1,525
Variable Cost per unit	$                     210	$                   640	$               890
Contribution Margin per unit	$                     170	$                     20	$               635
Units	8000	1700	300
Contribution Margin	$          1,360,000	$             34,000	$       190,500	$      1,584,500
Fixed Costs				$         530,000
Net Operating Income				$      1,054,500
Income tax expense				$         210,900
Net Income				$         843,600

b.
Total Sales Revenue = 8000 x $380 + 1700 x $660 + 300 x $1525 = $4619500
Contribution Margin Ratio = $1584500 / 4619500 = 34.30%

Break Even Point = Fixed costs / Contribution Margin Ratio
= $530000 / 34.30% = $1545190

c.
Required Earnings before taxes = $166000 / 0.8 = $207500
Required Sales Revenue = ($530000+207500) / 34.30% = $2150146

d-1

	Cleaning	Filling	Capping	Total
Price per unit	$                     380	$                   660	$            1,525
Variable Cost per unit	$                     210	$                   640	$               890
Contribution Margin per unit	$                     170	$                     20	$               635
Units	11000	1800	0
Contribution Margin	$          1,870,000	$             36,000	$                  -	$      1,906,000
Fixed Costs				$         580,000
Net Operating Income				$      1,326,000
Income tax expense				$         265,200
Net Income				$      1,060,800

Increase in Earnings after taxes = $1060800 - 843600 = $217200

d-2
It is a good idea, since earnings after taxes increases