Chapter 16, Problem 32P

More-Power Company has projected sales of 75,000 regular sanders and 30,000 mini-sanders for next year. The projected income statement is as follows:

Required:

1. 1. Set up the given income statement on a spreadsheet (e.g., Excel^TM). Then, substitute the following sales mixes, and calculate operating income. Be sure to print the results for each sales mix (a through d).

1. 2. Calculate the break-even units for each product for each of the preceding sales mixes.

To determine

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)

To determine

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 $\left(\text{C = A}-\text{B}\right)$	Sales Mix (D)	Package Unit Contribution margin $\left(\text{E = C × D}\right)$
Regular Sander	$40	$24	$16	2	$32
Mini Sander	$60	$30	$30	1	$30
Package Total					$62

Table (4)

Compute the break-even packages:

$\begin{array}{c}\text{Break-even packages }=\frac{\text{Total fixed cost}}{\text{Package Contribution margin}}\\ =\frac{\$1,300,000}{\$62}\\ =20,967.74\end{array}$

The number of break-even packages is 20,967.74.

Compute the break-even for Regular Sander:

$\begin{array}{c}\text{Break-even for regular sander }=\text{Sales mix }\times \text{Break-even packages}\\ =2\times 20,967.74\\ =41,935\left(\text{rounded}\right)\end{array}$

The number of break-even for Regular Sander is 41,935.

Compute the break-even for Mini Sander:

$\begin{array}{c}\text{Break-even for mini sander }=\text{Sales mix }\times \text{Break-even packages}\\ =1\times 20,967.74\\ =20,968\left(\text{rounded}\right)\end{array}$

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 $\left(\text{C = A}-\text{B}\right)$	Sales Mix (D)	Package Unit Contribution margin $\left(\text{E = C × D}\right)$
Regular Sander	$40	$24	$16	1	$16
Mini Sander	$60	$30	$30	1	$30
Package Total					$46

Table (5)

Compute the break-even packages:

$\begin{array}{c}\text{Break-even packages }=\frac{\text{Total fixed cost}}{\text{Package Contribution margin}}\\ =\frac{\$1,300,000}{\$46}\\ =\text{28,260}\text{.87}\end{array}$

The number of break-even packages is 28,260.87.

Compute the break-even for Regular Sander:

$\begin{array}{c}\text{Break-even for regular sander }=\text{Sales mix }\times \text{Break-even packages}\\ =1\times \text{ 28,260}\text{.87}\\ =\text{28,261 }\left(\text{rounded}\right)\end{array}$

The number of break-even for Regular Sander is 28,261.

Compute the break-even for Mini Sander:

$\begin{array}{c}\text{Break-even for mini sander }=\text{Sales mix }\times \text{Break-even packages}\\ =1\times \text{ 28,260}\text{.87}\\ =\text{28,261}\left(\text{rounded}\right)\end{array}$

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 $\left(\text{C = A}-\text{B}\right)$	Sales Mix (D)	Package Unit Contribution margin $\left(\text{E = C × D}\right)$
Regular Sander	$40	$24	$16	1	$16
Mini Sander	$60	$30	$30	3	$90
Package Total					$106

Table (6)

Compute the break-even packages:

$\begin{array}{c}\text{Break-even packages }=\frac{\text{Total fixed cost}}{\text{Package Contribution margin}}\\ =\frac{\$1,300,000}{\$106}\\ =\text{12,264}\text{.15}\end{array}$

The number of break-even packages is 12,264.15.

Compute the break-even for Regular Sander:

$\begin{array}{c}\text{Break-even for regular sander }=\text{Sales mix }\times \text{Break-even packages}\\ =1\times \text{ 12,264}\text{.15}\\ =\text{12,264 }\left(\text{rounded}\right)\end{array}$

The number of break-even for Regular Sander is 12,264.

Compute the break-even for Mini Sander:

$\begin{array}{c}\text{Break-even for mini sander }=\text{Sales mix }\times \text{Break-even packages}\\ =3\times \text{ 12,264}\text{.15}\\ =36,792\left(\text{rounded}\right)\end{array}$

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 $\left(\text{C = A}-\text{B}\right)$	Sales Mix (D)	Package Unit Contribution margin $\left(\text{E = C × D}\right)$
Regular Sander	$40	$24	$16	1	$16
Mini Sander	$60	$30	$30	2	$60
Package Total					$76

Table (7)

Compute the break-even packages:

$\begin{array}{c}\text{Break-even packages }=\frac{\text{Total fixed cost}}{\text{Package Contribution margin}}\\ =\frac{\$1,300,000}{\$76}\\ =\text{17,105}\text{.26}\end{array}$

The number of break-even packages is 17,105.26.

Compute the break-even for Regular Sander:

$\begin{array}{c}\text{Break-even for regular sander }=\text{Sales mix }\times \text{Break-even packages}\\ =1\times \text{ 17,105}\text{.26}\\ =\text{17,105 }\left(\text{rounded}\right)\end{array}$

The number of break-even for Regular Sander is 17,105.

Compute the break-even for Mini Sander:

$\begin{array}{c}\text{Break-even for mini sander }=\text{Sales mix }\times \text{Break-even packages}\\ =2\times \text{ 17,105}\text{.26}\\ =34,211\left(\text{rounded}\right)\end{array}$

The number of break-even for Mini Sander is 34,211.