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Lesson 13
Managerial Accounting
Managers must understand the cost of operating a business:
Two categories of costs:

Lesson 13
Cost Volume Profit Analysis

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The Behavior of Costs with Changes in Volume
Volume: The number of units of goods purchased or produced and how many units are sold. Simplifying Assumption: The amount of or number of units we produce or purchase will be the same as the number we sell.

The Behavior of Costs with Changes in Volume
Variable Costs Fixed Costs
Understanding how your costs behave with changes in volume allows management to understand the effect on profits given changes in volume.

Cost-Volume-Profit Analysis

CVP Analysis

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Variable Cost: A cost that varies in total with changes in volume.

Total Direct Material Costs

Total Variable Costs
\$ 80,000 \$ 60,000 \$ 40,000 \$ 20,000 \$0 0 1,000 2,000 3,000 Volume (# Units Sold)
Slope = VC per Unit Slope = rise/run

20,000 1,000 4,000 20 1

Direct Material Costs Per Unit

Variable Cost Per Unit
\$ 40 \$ 30 \$ 20 \$ 10 \$0 0 1,000 2,000 3,000 Volume (# Units Sold) 4,000

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Fixed Costs
Total Rental Costs/month

Variable costs vary in total but are fixed per unit with changes in volume.

\$ 80,000 \$ 60,000 \$ 40,000 \$ 20,000 \$0

0

1,000

2,000 3,000 4,000 Volume (# Units Sold)

5,000

6,000

Fixed Costs Per Unit
\$8 \$7 \$6 \$5 \$4 \$3 \$2 \$1 \$0 Rental costs per unit

0 500 1,000

2,000

3,000

4,000

5,000

6,000

Volume (# Units Sold)

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Real World Fixed Costs Fixed Costs are fixed in total
Total Rental Costs/month

\$30,000 \$20,000 \$10,000

Relevant Range

0

400,000

600,000

infinity

Volume (# units produced/sold per month)

Within the Relevant Range, a fixed cost is assumed to be fixed throughout that range of volume.

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Stepped Costs
Total Supervisor Salaries/year \$200,000 \$160,000 \$120,000 \$80,000 \$40,000 \$0 0 10,000 20,000 30,000 40,000 50,000 Total Rental Costs/Month \$6,000 \$5,000 \$4,000 \$3,000 \$2,000 \$1,000 \$0 \$0

Mixed Costs:
(Costs which have a fixed and variable portion)

Intersection = Total Fixed Cost Portion \$10,000 \$20,000 \$30,000 \$40,000 \$50,000

Volume (# units sold) per year

Volume in sales revenues (\$) per month

Slope = VC/Unit 1,000 = 0.10 = 10% 10,000

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Analysis of Mixed Costs
What portion is fixed and what portion is variable?
1. Scattergraph or Visual-Fit Method 2. High-Low Method 3. Least Square Method

Example: Management believes its utility costs are mixed in their behavior with changes in volume. Given the data below for the last six months of operations, determine if utility costs are indeed mixed, and, if so, calculate the variable and fixed cost components using first the scattergraph method and then the high-low method.

Month Jan. Feb. Mar. Apr. May June

# Units Produced 10,000 7,000 15,000 8,000 13,000 12,000

Utility Costs \$17,000 \$14,000 \$24,000 \$15,000 \$20,000 \$18,000

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Total Utility Cost

Month Jan. Feb. Mar. Apr. May June

# Units Produced 10,000 7,000 15,000 8,000 13,000 12,000

Utility Costs \$17,000 \$14,000 \$24,000 \$15,000 \$20,000 \$18,000

Scattergraph Method
\$ 25,000 \$ 20,000 \$ 15,000 \$ 10,000 \$ 5,000 \$ 3,000 \$0
(Mar. 24,000/15,000) (June 18,000/12,000) (Apr. 15,000/8,000) (May 20,000/13,000) (Jan. 17,000/10,000) (Feb. 14,000/7,000)

Slope = Rise/Run =

Fixed Cost Component

7,000 = 1.40 5,000 VC/Unit

Scattergraph Method
\$ 25,000 \$ 20,000 \$ 15,000 \$ 10,000 \$ 5,000 \$ 3,000 \$0 Total Utility Cost
(Apr. 15,000/8,000)

(Mar. 24,000/15,000)

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Volume in thousands (# of units produced)

(June 18,000/12,000) (May 20,000/13,000) (Jan. 17,000/10,000) (Feb. 14,000/7,000)

Total Utility Costs = Variable Costs + Fixed Costs 24,000 = (1.40 x 15,000) + x 24,000 = 21,000 + 3,000

Fixed Cost Component

7,000 Slope = Rise/Run = = 1.40 5,000 VC/Unit

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Volume in thousands (# of units produced)

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High-Low Method
\$25,000 \$20,000 \$15,000 \$10,000 \$5,000 \$0 0
Total Utility Cost
(June 18,000/12,000)

High-Low Method
Total Utility Cost
(Mar. 24,000/15,000) (May 20,000/13,000) (Jan. 17,000/10,000)

Fixed Cost Component

(Apr. 15,000/8,000)

(Feb. 14,000/7,000)

slope = VC per unit = 1.25 per unit

\$25,000 \$20,000 \$15,000 \$10,000 \$5,000 \$0 0

(Mar. 24,000/15,000) (June 18,000/12,000) (Apr. 15,000/8,000) (May 20,000/13,000) (Jan. 17,000/10,000) (Feb. 14,000/7,000)

Fixed Cost = 5,250 Component

slope = VC per unit = 1.25 per unit

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Volume in thousands (# of units produced)

Volume in thousands (# of units produced)

Total Cost = Variable Cost + Fixed Cost VC per unit = Slope = = 10,000 8,000 1.25 per unit At High Point: 24,000 = (1.25 x 15,000) + FC + FC 24,000 = 18,750 24,000 - 18,750 = FC 5,250 = FC

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Total Costs & Total Revenues Per Month

High-Low Method
\$25,000 \$20,000 \$15,000 \$10,000 \$5,000 \$ 3,000 \$0 0
Total Utility Cost
(Mar. 24,000/15,000) (June 18,000/12,000) (Apr. 15,000/8,000) (May 20,000/13,000) (Jan. 17,000/10,000) (Feb. 14,000/7,000)

CVP or Breakeven Analysis
\$480,000 \$440,000 \$400,000 \$360,000 \$320,000 \$280,000 \$240,000 \$200,000 \$160,000 \$120,000 \$80,000 \$40,000 \$0

Sales Revenues Slope = Sales Price per unit 160,000 80 2,000 = 1 Total Cost slope = Variable Cost = \$20 per unit

Fixed Cost = 5,250 Component

Scattergraph Line slope = 1.40

slope = VC per unit = 1.25 per unit

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Volume in thousands (# of units produced)

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Total Cost = Variable Cost + Fixed Cost At Low Point: 14,000 = (1.25 x 7,000) + FC + FC 14,000 = 8,750 14,000 - 8,750 = FC 5,250 = FC

Volume in thousands (# of units produced)

Breakeven Point: Sales Revenues - Variable Costs - Fixed Costs = 0 \$160,000 \$40,000 (\$80 x 2,000) - (\$20 x 2,000) \$120,000 = 0 \$120,000 = 0

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Total Costs & Total Revenues Per Month

Calculating Profit/Loss Graphically
\$480,000 \$440,000 \$400,000 \$360,000 \$320,000 \$280,000 \$240,000 \$200,000 \$160,000 \$120,000 \$80,000 \$40,000 \$0

Problem #53 Sales Revenues Slope = 80/1 Sales Price = \$80 per unit

Which of the following are true statements?
a. b. Fixed costs per unit decrease with increases in volume. Variable costs per unit are assumed to be fixed within the relevant range. Direct labor costs are typically a variable cost. Mixed costs are costs that have both a fixed and variable component. CVP Analysis requires all costs (product and period) to be distinguished as perfectly variable or perfectly fixed within the relevant range.

\$140,000

Loss = \$60,000

Total Cost Slope = 20/1 Variable Cost = \$20 per unit 4 5 6

c. d.

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Volume in thousands (# of units produced)

Calculating profit at 1,000 units of volume: Sales Revenues - Variable Costs - Fixed Costs = Net Income (\$80 x 1,000) - (\$20 x 1,000) \$80,000 \$20,000 \$120,000 = ? \$120,000 = (\$60,000)

e.

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Problem #54

March Cash Collections:
From January Sales: 25,000 x \$10 x 70% x 10% = From February Sales: 30,000 x \$10 x 70% x 35% = From March Sales: Cash Sales35,000 x \$10 x 30% \$17,500 \$73,500

If over the last year, the two months of highest and lowest production volume were April and August, respectively, and the manufacturing supplies in those two months were as follows: Volume/Units April August a. 26,000 14,000 Manufacturing Supplies \$12,000 \$9,000

Calculate the fixed cost and variable cost per unit portion of the supplies cost if it is in fact a mixed cost. What would be the anticipated manufacturing supplies cost in a month where a volume of 20,000 units was projected? Describe the scattergraph approach to determine the fixed and variable cost per unit components of a mixed cost and explain why it is probably preferable to the method used above.

= \$105,000

b. c.

Credit Sales35,000 x \$10 x 70% x 50% = \$122,500 Total Cash Collections \$318,500

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a. Calculate the fixed cost and variable cost per unit portion of the supplies cost if it is in fact a mixed cost.
Mixed Cost Calculations for Manufacturing Supplies Variable Cost Per Unit Slope of Line " " two points " " Cost " " Volume = = =

At High Point in Volume: \$ 9,000 = (.25 x 14,000) + FC \$ 9,000 = 3,500 + FC \$ 5,500 = FC At Low Point in Volume: \$ 12,000 = (.25 x 26,000) + FC + FC \$ 12,000 = 5,500 \$ 5,500 = FC

=

\$3,000 12,000

= \$ .25 per unit

Total Costs = Variable Costs + Fixed Costs

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b. What would be the anticipated manufacturing supplies cost in a month where a volume of 20,000 units was projected?
TC TC \$ 10,000 = = = VC (.25 x 20,000) 5,000 + + + FC 5,500 5,000

c. The scattergraph method identifies each monthly amount of production volume and related cost on a graph. A line is drawn to best fit the resulting relationship between cost and volume. The slope of this line is then calculated and represents the variable cost per unit. The intersection of the line with the vertical (cost) axis of the graph is the fixed cost portion. The scattergraph may prove a better approximation of the amount of fixed and variable cost per unit components of a mixed cost because more than just two months of data is considered in the approach.

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Problem #55

Problem #55

Given the graph presented below provide responses to the following:
Total Sales Revenues & Total Costs \$200,000 \$180,000 \$160,000 \$140,000 \$120,000 \$100,000 \$80,000 \$60,000 \$40,000 \$20,000 \$0

Given the graph presented below provide responses to the following:
Total Sales Revenues & Total Costs \$200,000 \$180,000 \$160,000 \$140,000 \$120,000 \$100,000 \$80,000 \$60,000 \$40,000 \$20,000 \$0

A B

A B

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Volume in Thousands (# Units Sold)

Volume in Thousands (# Units Sold)

a. What does line A represent? b. Calculate the sales price per unit. c. What does line B represent? d. Determine the amount of total fixed costs.

e. Calculate the variable cost per unit. f. Determine the breakeven point in sales dollars and number of units. g. Determine the total variable costs at a volume of 5,000 units. h. Determine the net income (loss) at a volume of 2,000 units.

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a. What does line A represent? Line A represents Sales Revenues. b. Calculate the sales price per unit. Sales Price per unit equals the slope of line A. 80,000 2,000 = 40 1 = \$40

e. Calculate the variable cost per unit. Variable cost per unit equals the slope of line B. 120,000 - 80,000 3,000 - 0 = 40,000 3,000 = 13.33

f. Determine the breakeven point in sales dollars and number of units. 3,000 units or \$120,000 of Sales Revenues. g. Determine the total variable costs at a volume of 5,000 units. VC per unit = 13.33 13.33 x 5,000 units = \$66,667 h. Determine the net income (loss) at a volume of 2,000 units. SR VC (40 x 2,000) - (13.33 x 2,000) 80,000 26,667 FC 80,000 80,000 = = = NI NI (\$26,667)

c. What does line B represent? Line B represents Total Costs. d. Determine the amount of total fixed costs. Fixed costs equal \$80,000, the point of intersection of the Total Cost line with the vertical axis.

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GAAP Income Statement Format
Sales Revenues Less: Cost of Goods Sold Gross Margin Less: Selling & Administrative Expenses Operating Income \$1,000,000 600,000 400,000 \$ 350,000 50,000

CVP Analysis
CVP analysis can be used with historical information or prospective budgeted information to respond to the following kinds of questions:

Contribution Margin Format Income Statement
Sales Revenues Less: Total Variable Costs Contribution Margin Less: Total Fixed Costs Operating Income \$1,000,000 700,000 300,000 250,000 \$ 50,000

. . .

How many units did we need to sell last year or do we need to sell next year in order to simply breakeven? How many units did we need to sell last year or do we need to sell next year to generate a certain target net income? What effect would changes in sales price, costs, or volume have on net income?

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An Equational Approach to CVP Analysis
Basic Equation: SR \$100,000 VC \$60,000 FC \$25,000 \$25,000 \$25,000 = NI

Example: Given the following information, determine the sales price per unit required at an anticipated sales volume of 10,000 units to achieve net income of \$100,000: Fixed Costs VC Ratio
SR
(10,000 X) 3,000 X

= \$15,000 = \$15,000

\$25,000 70%
VC -

(SP/Unit x # Units) - (VC/Unit x # Units) ( \$10 x 10,000 ) - ( \$6 x 10,000 ) (VC Ratio x SR) ( 60% x \$100,000 ) CM \$40,000 ( CM/Unit x # Units ) ( \$4 x 10,000 ) ( CM Ratio x SR ) ( 40% x \$100,000 )

-

FC

=

NI

(SP/Unit x #Units Sold) - (70% x SP/Unit x #Units Sold) (.70 . 10,000 X) 7,000 X 10,000 X

25,000 = 100,000 25,000 = 100,000 25,000 = 100,000 25,000 = 100,000 3,000 X = 125,000 3,000 3,000 X = \$41.67 Per unit

FC - \$25,000

= NI = \$15,000

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Example: Calculate the amount of sales revenues at breakeven given
the following information for last year: Sales Revenues Net Income CM Ratio SR CM VC -

Example: Calculate the amount of sales revenues at breakeven given
the following information for last year: Sales Revenues Net Income CM Ratio SR CM VC -

\$350,000 \$50,000 25% FC FC
FC FC

\$350,000 \$50,000 25% FC FC = = NI NI
0 0

= =
= =

NI NI
0 0

(CM Ratio x SR) .25 X

(CM Ratio x SR) .25 X

FC = 37,000 =

Calculate FC at a different level of volume:
(.25 . 350,000) 87,500 87,500 CM FC FC FC 50,000 = = = = NI 50,000 50,000 FC FC .25 X = 37,500 .25 .25 X = \$150,000

37,500 =

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Problem #56

Solve the following problems using the equational approach to CVP analysis:
a. Calculate the breakeven volume in number of units given the following information: Fixed costs \$39,000 Variable cost ratio 70% Sales price per unit \$10 b. Calculate the contribution margin per unit given the following information: Breakeven volume 25,000 units Fixed costs \$50,000 Variable cost per unit \$7 c. How many units must be sold at \$20/unit to generate net income of \$100,000 given the following: Fixed costs \$40,000 Contribution margin ratio 60%

a.

Calculate the breakeven volume in number of units given the following information: Fixed costs Variable cost ratio Sales price per unit SR 10x VC 7x \$39,000 70% \$10 FC = NI 0

39,000 = 3x 3 x =

39,000 3 = 13,000 units

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b.

Calculate the contribution margin per unit given the following information: Breakeven volume Fixed costs Variable cost per unit SR VC 25,000x 175,000 25,000 units \$50,000 \$7 FC = NI 50,000 = 0 25,000x 225,000 = 25,000 25,000 x = \$9 per unit sales price

b.

Calculate the contribution margin per unit given the following information: Breakeven volume Fixed costs Variable cost per unit VC CM CM/unit x #units sold 25,000x SR 25,000 units \$50,000 \$7 FC FC FC 50,000 25,000x 25,000 x NI NI 0 0 50,000 = 25,000 = \$2 contribution margin per unit = = = =

Contribution Margin per Unit: Sales price/unit - Variable cost/unit \$9 \$7 = \$2

OR...

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Problem #57

c.

How many units must be sold at \$20/unit to generate net income of \$100,000 given the following: Fixed costs Contribution margin ratio \$40,000 60% FC FC FC 40,000 12x 12 x = = = = = = NI NI 100,000 100,000 140,000

A.

Given the following: Sales Revenues (\$100/unit) # of Units Sold Fixed Costs Net Income

\$100,000 1,000 units \$20,000 \$30,000

VC CM \$20 (.60 x SP/unit x #units sold) 12x -

SR

i. Calculate the breakeven point in # of units. ii. Calculate the breakeven point in sales revenues. B. Given the following: Variable Cost Ratio Fixed Costs

12 11,667 units rounded

65% \$14,700

Calculate the breakeven Sales Revenue.

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Problem #57

C.

Given the following: Breakeven Sales Revenues Contribution Margin Ratio Sales Price pre Unit Contribution Margin per Unit Variable Cost per Unit Variable Cost Ratio

A. \$500,000 40% \$100 \$40 \$60 60%

Given the following: Sales Revenues (\$100/unit) # of Units Sold Fixed Costs Net Income

\$100,000 1,000 units \$20,000 \$30,000 NI 0 20,000 50 400

Calculate the # of units which must be sold to produce net income of \$20,000.

i. Calculate the breakeven point in # of units. SR VC FC = ( 100 * X ) - ( 50 * X ) = 20,000 50 X = 50 X = ii. Calculate the breakeven point in sales revenues. Sales Revenues (SP/unit * sold) 100 * 400 = \$40,000

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B.

Given the following: Variable Cost Ratio Fixed Costs

C. 65% \$14,700

Calculate the breakeven Sales Revenue. SR X VC 0.65x FC 14,700 .35 X .35 X = = = = NI 0 14,700 .35 \$42,000

Given the following: Breakeven Sales Revenues Contribution Margin Ratio Sales Price pre Unit Contribution Margin per Unit Variable Cost per Unit Variable Cost Ratio

\$500,000 40% \$100 \$40 \$60 60%

Calculate the # of units which must be sold to produce net income of \$20,000. First, you must determine the amount of fixed costs at breakeven: SR 500,000 500,000 VC - (60% x 500,000) 300,000 FC FC FC 200,000 = = = = NI 0 0 FC

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Problem #58

Then solve the problem: Calculate the # of units which must be sold to produce net income of \$20,000. SR 100X 40X VC 60X FC 200,000 40X 40 X = = = = NI 20,000 220,000 40 5,500 units

Business Feasibility Study for HEAVENLY MOLDS, INC.
Heber Smith, a college student in Utah, is investigating what he believes is a promising business opportunity. His idea is to manufacture and sell plastic jello molds in the form of the Salt Lake Temple. Heber has a tentative purchase commitment from a book and gift retail chain for 4,000 units over the first three months of initial operations. Based on his personal research and preliminary marketing efforts, he believes that the following is a reasonable estimate of total sales volume at a price of \$ 2.50 per unit for the first quarter of operations beginning September 1, 20X1: Sept. Projected sales in # of units 2,000 Oct. 3,000 Nov. 4,000

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Problem #58

Problem #58

Heber currently plans to manufacture the jello molds rather than contract out their production. The raw materials required for production of a single jello mold, regardless of design, is 1 lb. of polypropylene which can be purchased from a local supplier for \$ .30 per lb. Direct manufacturing labor costs are projected on a piece rate basis at \$.20 per unit produced. Employer payroll taxes are estimated at 10% of the direct labor cost. Heber can lease a used injection molding machine for \$2,000 per month plus \$.08 per unit of production on a three year lease. Other manufacturing overhead costs expected on a monthly basis include the following: Indirect materials (equipment maintenance supplies and other) Indirect labor (equipment and mfg. building maintenance) \$ 300 per month plus \$.03 per unit \$ 250 per month

Workman’s compensation insurance Utilities (80% of total fixed utility costs are manufacturing related and 20% due to selling and administrative office space)

10% of direct labor costs before payroll taxes \$200 per month plus \$.05 per unit produced

Building rent (2,000 total sq. ft. of which \$.70 per sq. ft. per month 80% of the building space will be for manufacturing and 20% for selling and administrative purposes)

In order to produce any plastic product through an injection molding process (i.e., plastic cups, kitchen utensils or even a plastic jello mold) a metal production mold created from a prototype of the given product must first be manufactured. Assume the cost of creating one production mold of the Salt Lake Temple is \$20,000 and such a mold would be capable of producing a maximum of approximately 200,000 jello molds with no salvage value. Depreciation of the \$20,000 production mold development costs are to be calculated based on the units of production method. At this time Heber plans to produce only temple jello molds.

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Problem #58

Problem #58

Selling and administrative costs are projected as follows: Building Rent (see above) Utilities (see above) Telephones, fax Copy machine rent, paper and other Other office supplies Sales commissions to manufacturer’s sales representative General liability insurance Accounting services \$300 per month \$250 per month \$150 per month \$.10 per unit sold \$50 per month \$500 per month

PART 1: CVP ANALYSIS
Required: 1. Show the detail and totals of the following anticipated costs: A. Manufacturing (Product) Costs 1. Variable cost per unit (including direct materials, labor and mfg. overhead) 2. Fixed costs per month B. Selling and Administrative (Period) Costs 1. Variable costs per unit 2. Fixed costs per month 2. Determine the # of jello molds that would have to be sold in any month to simply breakeven. 3. Determine the # of jello molds that would have to be sold in any month in order to provide Heber with a profit of \$2,000 for the month. 4. Calculate the sales price per unit that must be charged if Heber wishes to generate a monthly profit of at least \$3,000 at a sales volume of 4,000 units per month.

Heber plans to administer and manage the business and does not plan to pay himself a salary until the business can afford it.

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1A.1 Manufacturing (Product) Costs: Variable Costs Per Unit: Direct Materials Direct Labor Mfg. Overhead: Employer Payroll Tax Machine Lease Indirect Materials Workman's Comp. Utilities Mold Depreciation TOTAL \$ .30 .20 .02 .08 .03 .02 .05 .10 \$ .80

1A.2 Manufacturing (Product) Costs: Fixed Costs Per Unit: Mfg. Overhead: Machine Lease Indirect Materials Indirect Labor Utilities (80% of fixed utility costs of \$200) Building Rent (80% of fixed rent costs of \$1,400) \$2,000 300 250 160 1,120

TOTAL

\$3,830

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1B.1 Selling and Administrative Costs: Variable Costs Per Unit: Sales Commissions 1B.2 Selling and Administrative Costs: Fixed Costs Per Unit: Building Rent (20% of fixed rent costs of \$1,400) Utilities (20% of fixed utility costs of \$200) Telephones, Fax etc. Copy Machine, Paper Other Office Supplies General Liability Ins. Accounting Service TOTAL

2. Determine the # of jello molds that would have to be sold in nay month to simply breakeven. \$0.10 SR 2.50 X VC 0.90 X 1.60 X \$280 40 300 250 150 50 500 \$1,570 FC 5,400 5,400 1.60 X 1.60 X = = = = = NI 0 0 5,400 1.60 3,375 units

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3. Determine the # of jello molds that would have to be sold in any month in order to provide Heber with a profit of \$2,000 for the month. SR 2.50 X VC 0.90 X 1.60 X FC 5,400 5,400 1.60 X 1.60 X = = = = = NI 2,000 2,000 7,400 1.60 4,625 units

4. Calculate the sales price per unit that must be charged if Heber wishes to generate a monthly profit of at least \$3,000 at a sales volume of 4,000 units per month. SR 4,000 X VC 3,600 4,000 X FC 5,400 9,000 4,000 X 4,000 X = = = NI 3,000

3,000 12,000 = 4,000 = \$3.0 per unit

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