Question

Cleaning Price per Unit $ 360 640 1,500 Variable Cost per Unit $200 620 860 Units Sold per Year 9,000 900 100 Filling Capping Variable costs include the labor costs of the dental hygienists and dentists. Fixed costs of $520,000 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 $164,000 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 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 $570,000 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

1. Income before tax = (Cleaning Income - Variable expenses) + (Filling revenue - Variable expenses )  + ( Capping revenue - Variable ) - Fixed costs

Cleaning Profit = Units sold (price - variable cost) = 9000 (360 - 200) = 9000 * 160 = 1440000

Filling Profit = 900 (640-620) = 900 *20 = 18000

Capping profit = 100 (1500 - 860) = 64000

Income before tax = 1440000+18000+64000 - 520,000 = 1,002,000

Income after taxed = 1002000 * 0.80 = $801,600

2. Assume sales of capping = x

given sales mix Filling = 9x

Cleaning = 90x

Income before tax = 90x(360-200) + 9x(640-620) + x (1500-860) - 520,000

Given IBT = 0

0 = 14400x + 180x + 640x - 520000

520000= 15220x

X = 34.16

Round off to 34

Then

capping = 34

given sales mix Filling = 9*34 = 306

Cleaning = 90*34 = 3060

3. Income after tax = Income before tax * 0.80

Income after tax =  (90x(360-200) + 9x(640-620) + x (1500-860) - 520,000) 0.80

164000= (90x(360-200) + 9x(640-620) + x (1500-860) - 520,000) 0.80

205,000 = 90x(360-200) + 9x(640-620) + x (1500-860) - 520,000

725000 = 14400x + 180x + 640x
725000/15220 = x

X = 47

capping = 47

given sales mix Filling = 9*47 = 423

Cleaning = 90*47 = 4230

D1. New income = 1200*160 + 1000*20 - 570,000 = 1920000+20000-570000 = 1370000

Income after tax = 137000 * 0.8 = 1096000

D2. No this is not the best idea, as Capping has a higher marginal profit rate than filling, and for profit maximisation the dental clinic should not forego this service.