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 $ 260 $ 150 7,500 Filling 540 520 2,000 Capping 1,375 710 500 Variable costs include the labor costs of the dental hygienists and dentists. Fixed costs of $470,000 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: (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 your intermediate calculation.) (c) Assuming the above sales mix, at what sales revenue will the company earn $154,000 per year after taxes? (Do not round your intermediate calculation.) (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 10,500 per year, the number of fillings increased to 2,100 per year, while the number of cappings dropped to zero? With this change in product mix, the company would increase its fixed costs to $520,000 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? Yes No

Answer 1

a). For Revenue we calculate the total revenue for product mix and accordingly calculate total variable cost (VC) and after deducting fixed costs and taxes we get after tax earnings for firm to be $509250.

b). For breakeven since the product mix is same we sum the prices and VC for all the services provided. Thus we get the price for a single unit to be $ 2175 and VC for single unit to be $ 1380. Thus margin = 2175-1380 = $795. Thus for breakeven we have equation -> Q*(795) = 470000, thus we get breakeven quantity Q to be 591.195. Thus total revenue at breakeven will be $1285849.

c). For earnings to be $ 154000 and same tax rate we get PBT to be 220000 and with the same fixed costs we get operating profit to be 690,000. Thus for this operating profit we get the total quantity sold to be 690000/795 = 867.92. For this we get the revenue to be $ 1887736.

d-1). For the new product mix we get the revenue to be $ 3864000, so the level of revenue has increased drastically. But the profit after tax has reduced to $ 473900.

d-2). Management should not go for this is they want to maximize profit. Because in this units for cleaning are increased and also cost for it is high as labor requirement would be higher because it has to be done every 45 minutes for every new patient. Margins are not very high but here we can say sales revenue increased because this is more of volume based top line while costs are also high in this case. Also in capping margins are quite higher. So instead of increasing filling where margins are very low if firm specializes in capping business and maintains and optimum mix for cleaning and capping this would give rather a boost to profits. Also costs need to be considered.

I am attaching excel for reference: