Concept explainers
More-Power Company has projected sales of 75,000 regular sanders and 30,000 mini-sanders for next year. The
Required:
- 1. Set up the given income statement on a spreadsheet (e.g., ExcelTM). Then, substitute the following sales mixes, and calculate operating income. Be sure to print the results for each sales mix (a through d).
- 2. Calculate the break-even units for each product for each of the preceding sales mixes.
1.
Show the income statement on the spreadsheet, for the given sales mixes and compute the operating income.
Explanation of Solution
Sales mix: Sales mix refers to relative distribution of the total sales amongst the total number of units sold by a company. It is also expressed as a percentage of units sold for each product produced with respect to the total units sold for all the products produced.
Compute the operating income for the given sales mixes:
Particulars | RegularSander | Mini-Sander | Amount ($) |
Sales Mix of 2:1 | |||
Sales | $3,000,000 | $2,250,000 | $5,250,000 |
Less: Variable expenses | $1,800,000 | $1,125,000 | $2,925,000 |
Contribution margin | $1,200,000 | $1,125,000 | $2,325,000 |
Less: Direct Fixed Expenses | $250,000 | $450,000 | $700,000 |
Product Margin | $950,000 | $675,000 | $1,625,000 |
Less: Common fixed expenses | $600,000 | ||
Operating income | $1,025,000 | ||
Sales Mix of 1:1 | |||
Sales | $2,400,000 | $3,600,000 | $6,000,000 |
Less: Variable expenses | $1,440,000 | $1,800,000 | $3,240,000 |
Contribution margin | $960,000 | $1,800,000 | $2,760,000 |
Less: Direct Fixed Expenses | $250,000 | $450,000 | $700,000 |
Product Margin | $710,000 | $1,350,000 | $2,060,000 |
Less: Common fixed expenses | $600,000 | ||
Operating income | $1,460,000 | ||
Sales Mix of 1:3 | |||
Sales | $1,200,000 | $5,400,000 | $6,600,000 |
Less: Variable expenses | $720,000 | $2,700,000 | $3,420,000 |
Contribution margin | $480,000 | $2,700,000 | $3,180,000 |
Less: Direct Fixed Expenses | $250,000 | $450,000 | $700,000 |
Product Margin | $230,000 | $2,250,000 | $2,480,000 |
Less: Common fixed expenses | $600,000 | ||
Operating income | $1,880,000 | ||
Sales Mix of 1:2 | |||
Sales | $1,200,000 | $3,600,000 | $4,800,000 |
Less: Variable expenses | $720,000 | $1,800,000 | $2,520,000 |
Contribution margin | $480,000 | $1,800,000 | $2,280,000 |
Less: Direct Fixed Expenses | $250,000 | $450,000 | $700,000 |
Product Margin | $230,000 | $1,350,000 | $1,580,000 |
Less: Common fixed expenses | $600,000 | ||
Operating income | $980,000 |
Table (1)
Working notes:
Compute the sales mix ratio for given sales mixes.
Particulars | RegularSander | Mini-Sander | Sales Mix Ratio |
Number of actual units | 75000 | 30000 | 5:2 |
Sales mix a | 75000 | 37500 | 2:1 |
Sales mix b | 60000 | 60000 | 1:1 |
Sales mix c | 30000 | 90000 | 1:3 |
Sales mix d | 30000 | 60000 | 1:2 |
Table (2)
Compute the sales amount and variable expenses for the given sales.
Particulars | Cost per unit ($) | Number of units | Amount ($) |
Sales Mix of 2:1 | |||
Sales of Regular Sander | $40 | 75000 | $3,000,000 |
Sales of Mini Sander | $60 | 37500 | $2,250,000 |
Variable Cost of Regular Sander | $24 | 75000 | $1,800,000 |
Variable Cost of Mini Sander | $30 | 37500 | $1,125,000 |
Sales Mix of 1:1 | |||
Sales of Regular Sander | $40 | 60000 | $2,400,000 |
Sales of Mini Sander | $60 | 60000 | $3,600,000 |
Variable Cost of Regular Sander | $24 | 60000 | $1,440,000 |
Variable Cost of Mini Sander | $30 | 60000 | $1,800,000 |
Sales Mix of 1:3 | |||
Sales of Regular Sander | $40 | 30000 | $1,200,000 |
Sales of Mini Sander | $60 | 90000 | $5,400,000 |
Variable Cost of Regular Sander | $24 | 30000 | $720,000 |
Variable Cost of Mini Sander | $30 | 90000 | $2,700,000 |
Sales Mix of 1:2 | |||
Sales of Regular Sander | $40 | 30000 | $1,200,000 |
Sales of Mini Sander | $60 | 60000 | $3,600,000 |
Variable Cost of Regular Sander | $24 | 30000 | $720,000 |
Variable Cost of Mini Sander | $30 | 60000 | $1,800,000 |
Table (3)
2.
Compute for each sales mix the break-even point.
Explanation of Solution
Sales mix a:
Compute the package contribution margin units:
Input | Price (A) | Unit Variable cost (B) | Unit Contribution margin | Sales Mix (D) |
Package Unit Contribution margin |
Regular Sander | $40 | $24 | $16 | 2 | $32 |
Mini Sander | $60 | $30 | $30 | 1 | $30 |
Package Total | $62 |
Table (4)
Compute the break-even packages:
The number of break-even packages is 20,967.74.
Compute the break-even for Regular Sander:
The number of break-even for Regular Sander is 41,935.
Compute the break-even for Mini Sander:
The number of break-even for Mini Sander is 20,968.
Sales mix b:
Compute the package contribution margin units:
Input | Price (A) | Unit Variable cost (B) | Unit Contribution margin | Sales Mix (D) |
Package Unit Contribution margin |
Regular Sander | $40 | $24 | $16 | 1 | $16 |
Mini Sander | $60 | $30 | $30 | 1 | $30 |
Package Total | $46 |
Table (5)
Compute the break-even packages:
The number of break-even packages is 28,260.87.
Compute the break-even for Regular Sander:
The number of break-even for Regular Sander is 28,261.
Compute the break-even for Mini Sander:
The number of break-even for Mini Sander is 28,261.
Sales mix c:
Compute the package contribution margin units:
Input | Price (A) | Unit Variable cost (B) | Unit Contribution margin | Sales Mix (D) |
Package Unit Contribution margin |
Regular Sander | $40 | $24 | $16 | 1 | $16 |
Mini Sander | $60 | $30 | $30 | 3 | $90 |
Package Total | $106 |
Table (6)
Compute the break-even packages:
The number of break-even packages is 12,264.15.
Compute the break-even for Regular Sander:
The number of break-even for Regular Sander is 12,264.
Compute the break-even for Mini Sander:
The number of break-even for Mini Sander is 36,792.
Sales mix d:
Compute the package contribution margin units:
Input | Price (A) | Unit Variable cost (B) | Unit Contribution margin | Sales Mix (D) |
Package Unit Contribution margin |
Regular Sander | $40 | $24 | $16 | 1 | $16 |
Mini Sander | $60 | $30 | $30 | 2 | $60 |
Package Total | $76 |
Table (7)
Compute the break-even packages:
The number of break-even packages is 17,105.26.
Compute the break-even for Regular Sander:
The number of break-even for Regular Sander is 17,105.
Compute the break-even for Mini Sander:
The number of break-even for Mini Sander is 34,211.
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Chapter 16 Solutions
EBK CORNERSTONES OF COST MANAGEMENT
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