Case $4-54$ Cost$-$Volume$-$Profit with Multiple Products, Sales Mix Changes,

Changes in Fixed and Variable Costs

Artistic Woodcrafting Inc. began several years ago as a one$-$person, cabinet$-$making operation.

Employees were added as the business expanded. Last year, sales volume totaled $$850,000.$

Volume for the first five months of the current year totaled $$600,000,$ and sales were expected

to be $$1\mathrm{.}6$ million for the entire year. Unfortunately, the cabinet business in the region where

Artistic is located is highly competitive. More than $200$ cabinet shops are all competing for the

same business.

Artistic currently offers two different quality grades of cabinets: Grade I and Grade II$,$ with

Grade I being the higher quality. The average unit selling prices, unit variable costs, and direct

fixed costs are as follows:

Unit Price Unit Variable Cost Direct Fixed Cost

Grade I $$3,400$ $$2,686$ $$95,000$

Grade II $1,6001,32895,000$

Common fixed costs $($fixed costs not traceable to either cabinet$)$ are $$35,000.$ Currently, for

every three Grade I cabinets sold, seven Grade II cabinets are sold.

Required:

$1.$ Calculate the number of Grade I and Grade II cabinets that are expected to be sold during

the current year.

$2.$ Calculate the number of Grade I and Grade II cabinets that must be sold for Artistic to break

even.

$3.$ Artistic can buy computer$-$controlled machines that will make doors, drawers, and frames.

If the machines are purchased, the variable costs for each type of cabinet will decrease by

$9$ percent, but common fixed cost will increase by $$44,000.$ Compute the effect on operating income, and also calculate the new break$-$even point. Assume the machines are purchased

at the beginning of the sixth month. Fixed costs for the company are incurred uniformly

throughout the year.

$4.$ Refer to the original data. Artistic is considering adding a retail outlet. This will increase

common fixed cost by $$70,000$ per year. As a result of adding the retail outlet, the additional

publicity and emphasis on quality will allow the firm to change the sales mix to $1$:$1.$

The retail outlet is also expected to increase sales by $30$ percent. Assume that the outlet is

opened at the beginning of the sixth month. Calculate the effect on the company$$s expected

profits for the current year, and calculate the new break$-$even point. Assume that fixed costs

are incurred uniformly throughout the year.