Question

1. Mastery Problem: Cost-Volume-Profit Analysis

   Cost Behavior

   Cover-to-Cover Company is a manufacturer of shelving for books. The company has compiled the following cost data, and wants your help in determining the cost behavior. After reviewing the data, complete requirements (1) and (2) that follow.

   Units Produced	Total Lumber Cost	Total Utilities Cost	Total Machine Depreciation Cost
   15,000 shelves	$165,000	$19,250	$140,000
   30,000 shelves	330,000	36,500	140,000
   60,000 shelves	660,000	71,000	140,000
   75,000 shelves	825,000	88,250	140,000

   1. Determine whether the costs in the table are variable, fixed, mixed, or none of these.

   Lumber	Variable Cost
   Utilities	Mixed Cost
   Depreciation	Fixed Cost

   2. For each cost, determine the fixed portion of the cost, and the per-unit variable cost. If there is no amount or an amount is zero, enter "0". Recall that, for N = Number of Units Produced, Total Costs = (Variable Cost Per Unit x N) + Fixed Cost. Complete the following table with your answers. Round variable portion of cost (per unit) answers to two decimal places.

   Cost	Fixed Portion of Cost	Variable Portion of Cost (per Unit)
   Lumber	$	$
   Utilities
   Depreciation

   Feedback

   Review the definitions for fixed, variable, and mixed costs, and the relationships between units produced and total cost for each type of cost. Recall that the high-low method may be used to separate a cost into its fixed and variable components.

   High-Low

   Biblio Files Company is the chief competitor of Cover-to-Cover Company in the bookshelf business. Biblio Files is analyzing its manufacturing costs, and has compiled the following data for the first six months of the year. After reviewing the data, answer questions (1) through (3) that follow.

   	Units Produced		Total Cost
   January	4,360	units	$65,600
   February	300		6,250
   March	1,000		15,000
   April	5,800		88,750
   May	1,750		32,500
   June	3,015		48,000

   1. From the data previously provided, help Biblio Files Company estimate the fixed and variable portions of its total costs using the high-low method. Recall that Total Costs = (Variable Cost Per Unit x Number of Units Produced) + Fixed Cost. Complete the following table.

   Total Fixed Cost	Variable Cost per Unit
   $	$

   2. With your Total Fixed Cost and Variable Cost per Unit from the high-low method, compute the total cost for the following values of N (Number of Units Produced).

   Number of Units Produced	Total Cost
   3,500	$
   4,360
   5,800

   3. Why does the total cost computed for 4,360 units not match the data for January?

   a. The high-low method is accurate only for months in which production is at full capacity.

   b. The high-low method only gives accurate data when fixed costs are zero.

   c. The high-low method gives a formula for the estimated total cost and may not match levels of production other than the highest and lowest.

   d. The high-low method gives accurate data only for levels of production outside the relevant range.

   c

   Feedback

   Review the high-low method, and use the smallest and largest levels of production in your computation.

   Contribution Margin

   Review the contribution margin income statements for Cover-to-Cover Company and Biblio Files Company on their respective Income Statements. Complete the following table from the data provided on the income statements. Each company sold 79,800 units during the year.

   	Cover-to-Cover Company	Biblio Files Company
   Contribution margin ratio (percent)	%	%
   Unit contribution margin	$	$
   Break-even sales (units)
   Break-even sales (dollars)	$	$

   Feedback

   Review the definitions of contribution margin ratio and unit contribution margin. Also review the formulas for break-even in terms of units sold and sales dollars.

   Income Statement - Cover-to-Cover

   Cover-to-Cover Company Contribution Margin Income Statement For the Year Ended December 31, 20Y8
   Sales		$399,000
   Variable costs:
   Manufacturing expense	$239,400
   Selling expense	19,950
   Administrative expense	59,850	(319,200)
   Contribution margin		$79,800
   Fixed costs:
   Manufacturing expense	$5,000
   Selling expense	4,000
   Administrative expense	10,950	(19,950)
   Operating income		$59,850

   Income Statement - Biblio Files

   Biblio Files Company Contribution Margin Income Statement For the Year Ended December 31, 20Y8
   Sales		$399,000
   Variable costs:
   Manufacturing expense	$159,600
   Selling expense	15,960
   Administrative expense	63,840	(239,400)
   Contribution margin		$159,600
   Fixed costs:
   Manufacturing expense	$81,750
   Selling expense	8,000
   Administrative expense	10,000	(99,750)
   Operating income		$59,850

   Sales Mix

   Biblio Files Company is making plans for its next fiscal year, and decides to sell two new types of bookshelves, Basic and Deluxe. The company has compiled the following estimates for the new product offerings.

   Type of Bookshelf	Sales Price per Unit	Variable Cost per Unit
   Basic	$5.00	$1.75
   Deluxe	9.00	8.10

   The company is interested in determining how many of each type of bookshelf would have to be sold in order to break even. If we think of the Basic and Deluxe products as components of one overall enterprise product called “Combined,” the unit contribution margin for the Combined product would be $2.31. Fixed costs for the upcoming year are estimated at $332,640. Recall that the totals of all the sales mix percents must be 100%. Determine the amounts to complete the following table.

   Type of Bookshelf	Percent of Sales Mix	Break-Even Sales in Units	Break-Even Sales in Dollars
   Basic	%		$
   Deluxe	%		$

   Feedback

   Review the definition of break-even point.

   Recall that the Combined unit contribution margin is given by [(Basic unit contribution margin) x (Basic percent of sales mix)] + [(Deluxe unit contribution margin) x (Deluxe percent of sales mix)]. Since these percents must add up to 100%, we have the following:

   (Basic percent of sales mix) + (Deluxe percent of sales mix) = 100%, so that

   (Deluxe percent of sales mix) = 100% - (Basic percent of sales mix)

   Target Profit

   Refer again to the income statements for Cover-to-Cover Company and Biblio Files Company on their respective Income Statement. Note that both companies have the same sales and net income. Answer questions (1) - (3) that follow, assuming that all data for the coming year is the same as the current year, except for the amount of sales.

   1. If Cover-to-Cover Company wants to increase its profit by $20,000 in the coming year, what must their amount of sales be?
   $

   2. If Biblio Files Company wants to increase its profit by $20,000 in the coming year, what must their amount of sales be?
   $

   3. What would explain the difference between your answers for (1) and (2)?

   a. Biblio Files Company has a higher contribution margin ratio, and so more of each sales dollar is available to cover fixed costs and provide operating income.

   b. Cover-to-Cover Company’s contribution margin ratio is lower, meaning that it’s more efficient in its operations.

   c. The companies have goals that are not in the relevant range.

   d. The answers are not different; each company has the same required sales amount for the coming year to achieve the desired target profit.

   a

Answer 1

Variable cost varies with per unit of output while fixed cost remains constant.
Lumber is variable cost
Utilities is mixed cost
Depreciation is a fixed cost
Using high low method, variable cost per unit = (Cost at highest level - Cost at lowest level)/Difference in units
	Fixed Portion	Variable cost per unit
Lumber	0	11
Utilities	2,000	1.15
Depreciation	140,000	0
Biblio Files
1.Variable cost per unit = (88,750-6250)/(5800-300) = $15 per unit
Total Fixed cost = Total cost - Variable costs
=6250 - 300*15 = $1,750
2
Number of units	Total cost
3500	54,250
4360	67,150
5800	88,750
c. The high-low method gives a formula for the estimated total cost and may not match levels of production other than the highest and lowest.
	Cover-to-Cover	Biblio Files
	Company	Company
Contribution margin ratio (percent) = Contribution Margin/Sales	20%	40%
Unit contribution margin	1	2
Break-even sales (units) = Fixed costs/Unit CM	19,950	49,875
Break-even sales (dollars) = Fixed costs/CM ratio	99,750	249,375

Weighted average contribution Margin = Contribution Margin from product 1*Weight of Product 1 + Contribution Margin from Product 2*Weight of Product 2
Let the weight of Basic be x
2.31 = 3.25*x + 0.9*(1-x)
2.31 = 3.25x + 0.9 - 0.9x
x = 0.6 i.e. 60%
Hence, weight of basic = 60%, Deluxe = 40%
Overall Break even sales In units = Fixed costs/Weighted average CM per unit
=332,640/2.31 = 144,000 units
Type of Bookshelf	Percent of Sales Mix	Break-Even Sales in Units	Break-Even Sales in Dollars
Basic	60%	86,400	432,000
Deluxe	40%	57,600	518,400
Cover to Cover
Contribution Margin ratio = 74800/374000	20%
Desired Sales = (Desired Profit + Fixed costs)/CM ratio	499,000
2.Biblio
Contribution Margin ratio	40%
Desired Sales = (Desired Profit + Fixed costs)/CM ratio	449,000
a. Biblio Files Company has a higher contribution margin ratio, and so more of each sales dollar is available to cover fixed costs and provide operating income.