Question
Pittman Company is a small but growing manufacturer of telecommunications equipment. The company has no sales force of its own; rather, it relies on independent sales agents to market its products. These agents are paid a sales commission of 15% for all items sold.
Barbara Cheney, Pittman’s controller, just prepared the company’s budgeted income statement for next year as follows:
Pittman Company
Budgeted Income Statement
For the Year Ended December 31
Sales $ 16,000,000
Manufacturing expenses:
Variable $ 7,200,000
Fixed overhead 2,340,000 9,540,000
Gross margin 6,460,000
Selling and administrative expenses:
Commissions to agents 2,400,000
Fixed marketing expenses 120,000*
Fixed administrative expenses 1,800,000 4,320,000
Net operating income 2,140,000
Fixed interest expenses 540,000
Income before income taxes 1,600,000
Income taxes (30%) 480,000
Net income $ 1,120,000
*Primarily depreciation on storage facilities.
As Barbara handed the statement to Karl Vecci, Pittman’s president, she commented, “I went ahead and used the agents’ 15% commission rate in completing these statements, but we’ve just learned they refuse to handle our products next year unless we increase the commission rate to 20%.”
“That’s the last straw,” Karl replied angrily. “Those agents have been demanding more and more, and this time they’ve gone too far. How can they possibly defend a 20% commission rate?”
“They claim after paying for advertising, travel, and the other costs of promotion, there’s nothing left over for profit,” replied Barbara.
“That’s ridiculous,” retorted Karl. “And I also say it’s time we dumped those guys and got our own sales force. Can you get your people to work up some cost figures for us to look at?”
“We’ve already worked them up,” said Barbara. “Several companies we know of pay a 7.5% commission to their own salespeople, along with a small salary. Of course, we would have to handle all promotion costs, too. We figure our fixed expenses would increase by $2,400,000 per year, but that would be more than offset by the $3,200,000 (20% × $16,000,000) we would avoid on agents’ commissions.”
The breakdown of the $2,400,000 cost follows:
Salaries:
Sales manager $ 100,000
Salespersons 600,000
Travel and entertainment 400,000
Advertising 1,300,000
Total $ 2,400,000
“Super,” replied Karl. “And I noticed the $2,400,000 equals what we’re paying the agents under the old 15% commission rate.”
“It’s even better than that,” explained Barbara. “We can actually save $75,000 a year because that’s what we’re paying our auditors to check out the agents’ reports. So our overall administrative expenses would be less.”
“Pull all of these numbers together and we’ll show them to the executive committee tomorrow,” said Karl. “With the approval of the committee, we can move on the matter immediately.”
Required:
Compute Pittman Company’s break-even point in dollar sales for next year assuming:
The agents’ commission rate remains unchanged at 15%.
The agents’ commission rate is increased to 20%.
The company employs its own sales force.
Assume Pittman Company decides to continue selling through agents and pays the 20% commission rate. Calculate the dollar sales required to generate the same net income as contained in the budgeted income statement for next year.
Calculate the dollar sales at which net income would be equal regardless of whether Pittman Company sells through agents (at a 20% commission rate) or employs its own sales force.
Compute the degree of operating leverage the company would expect to have at the end of next year assuming:
The agents’ commission rate remains unchanged at 15%.
The agents’ commission rate is increased to 20%.
The company employs its own sales force.
Use income before income taxes in your operating leverage computation.
Barbara Cheney, Pittman’s controller, just prepared the company’s budgeted income statement for next year as follows:
Pittman Company
Budgeted Income Statement
For the Year Ended December 31
Sales $ 16,000,000
Manufacturing expenses:
Variable $ 7,200,000
Fixed overhead 2,340,000 9,540,000
Gross margin 6,460,000
Selling and administrative expenses:
Commissions to agents 2,400,000
Fixed marketing expenses 120,000*
Fixed administrative expenses 1,800,000 4,320,000
Net operating income 2,140,000
Fixed interest expenses 540,000
Income before income taxes 1,600,000
Income taxes (30%) 480,000
Net income $ 1,120,000
*Primarily depreciation on storage facilities.
As Barbara handed the statement to Karl Vecci, Pittman’s president, she commented, “I went ahead and used the agents’ 15% commission rate in completing these statements, but we’ve just learned they refuse to handle our products next year unless we increase the commission rate to 20%.”
“That’s the last straw,” Karl replied angrily. “Those agents have been demanding more and more, and this time they’ve gone too far. How can they possibly defend a 20% commission rate?”
“They claim after paying for advertising, travel, and the other costs of promotion, there’s nothing left over for profit,” replied Barbara.
“That’s ridiculous,” retorted Karl. “And I also say it’s time we dumped those guys and got our own sales force. Can you get your people to work up some cost figures for us to look at?”
“We’ve already worked them up,” said Barbara. “Several companies we know of pay a 7.5% commission to their own salespeople, along with a small salary. Of course, we would have to handle all promotion costs, too. We figure our fixed expenses would increase by $2,400,000 per year, but that would be more than offset by the $3,200,000 (20% × $16,000,000) we would avoid on agents’ commissions.”
The breakdown of the $2,400,000 cost follows:
Salaries:
Sales manager $ 100,000
Salespersons 600,000
Travel and entertainment 400,000
Advertising 1,300,000
Total $ 2,400,000
“Super,” replied Karl. “And I noticed the $2,400,000 equals what we’re paying the agents under the old 15% commission rate.”
“It’s even better than that,” explained Barbara. “We can actually save $75,000 a year because that’s what we’re paying our auditors to check out the agents’ reports. So our overall administrative expenses would be less.”
“Pull all of these numbers together and we’ll show them to the executive committee tomorrow,” said Karl. “With the approval of the committee, we can move on the matter immediately.”
Required:
Compute Pittman Company’s break-even point in dollar sales for next year assuming:
The agents’ commission rate remains unchanged at 15%.
The agents’ commission rate is increased to 20%.
The company employs its own sales force.
Assume Pittman Company decides to continue selling through agents and pays the 20% commission rate. Calculate the dollar sales required to generate the same net income as contained in the budgeted income statement for next year.
Calculate the dollar sales at which net income would be equal regardless of whether Pittman Company sells through agents (at a 20% commission rate) or employs its own sales force.
Compute the degree of operating leverage the company would expect to have at the end of next year assuming:
The agents’ commission rate remains unchanged at 15%.
The agents’ commission rate is increased to 20%.
The company employs its own sales force.
Use income before income taxes in your operating leverage computation.
Answers
Answered by
GPT-4o mini
Let's begin by determining the various calculations requested step by step.
### 1. Break-even Point in Dollar Sales
**A. Agents' commission rate at 15%**
**Fixed Costs:**
- Fixed overhead: $2,340,000
- Fixed marketing expenses: $120,000
- Fixed administrative expenses: $1,800,000
Total Fixed Costs = $2,340,000 + $120,000 + $1,800,000 = $4,260,000
**Variable Costs per Unit:**
- Manufacturing variable costs: $7,200,000
- Commission to agents (15% of sales): 0.15 × $16,000,000 = $2,400,000
Total Variable Costs = $7,200,000 + $2,400,000 = $9,600,000
**Contribution Margin:**
Sales = $16,000,000
Contribution Margin = Sales - Variable Costs = $16,000,000 - $9,600,000 = $6,400,000
**Contribution Margin Ratio:**
Contribution Margin Ratio = Contribution Margin / Sales = $6,400,000 / $16,000,000 = 0.4
**Break-even Point Formula:**
Break-even Point = Total Fixed Costs / Contribution Margin Ratio
Break-even Point = $4,260,000 / 0.4 = $10,650,000
---
**B. Agents' commission rate increased to 20%**
**Variable Costs per Unit:**
- Increased commission to agents (20% of sales): 0.2 × $16,000,000 = $3,200,000
- Total Variable Costs = $7,200,000 + $3,200,000 = $10,400,000
**Contribution Margin:**
Sales = $16,000,000
Contribution Margin = Sales - Variable Costs = $16,000,000 - $10,400,000 = $5,600,000
**Contribution Margin Ratio:**
Contribution Margin Ratio = Contribution Margin / Sales = $5,600,000 / $16,000,000 = 0.35
**Break-even Point:**
Break-even Point = Total Fixed Costs / Contribution Margin Ratio
Break-even Point = $4,260,000 / 0.35 = $12,171,428.57 (or approximately $12,171,429)
---
**C. Company employs its own sales force**
**Fixed Costs:**
- Fixed overhead: $2,340,000
- Fixed marketing expenses: $120,000
- Fixed administrative expenses: $1,800,000
- Additional Fixed Costs due to sales force: $2,400,000
Total Fixed Costs = $2,340,000 + $120,000 + $1,800,000 + $2,400,000 = $6,660,000
**Variable Costs per Unit:**
- Commission to salespeople (7.5% of sales): 0.075 × $16,000,000 = $1,200,000
Total Variable Costs = $7,200,000 + $1,200,000 = $8,400,000
**Contribution Margin:**
Sales = $16,000,000
Contribution Margin = Sales - Variable Costs = $16,000,000 - $8,400,000 = $7,600,000
**Contribution Margin Ratio:**
Contribution Margin Ratio = Contribution Margin / Sales = $7,600,000 / $16,000,000 = 0.475
**Break-even Point:**
Break-even Point = Total Fixed Costs / Contribution Margin Ratio
Break-even Point = $6,660,000 / 0.475 = $14,000,000
---
### 2. Dollar Sales Required to Generate the Same Net Income with 20% Commission
Net Income from budgeted income statement = $1,120,000
To find the dollar sales needed to achieve the same net income with a 20% commission:
- Required Income Before Taxes = Net Income / (1 - Tax Rate)
= $1,120,000 / (1 - 0.30) = $1,600,000
Now we need to cover this with the costs incurred under a 20% commission:
**Total Fixed Costs (same as calculated earlier):** $4,260,000
**Variable Costs** are now with a commission of 20%, thus:
Let \( S \) be the required sales.
Total Variable Costs = Manufacturing variable costs + Agents commission
= $7,200,000 + 0.20 * \( S \)
= $7,200,000 + 0.20 * \( S \)
**Contribution Margin:**
Contribution Margin = \( S - (7,200,000 + 0.20 * S) = S - 7,200,000 - 0.2 S = 0.8 S - 7,200,000 \)
Now, since we want to satisfy the equation for Income Before Taxes:
\[
1,600,000 = (0.8 S - 7,200,000) - 4,260,000
\]
\[
1,600,000 = 0.8 S - 11,460,000
\]
\[
0.8 S = 1,600,000 + 11,460,000
\]
\[
0.8 S = 13,060,000
\]
\[
S = 13,060,000 / 0.8 = 16,325,000
\]
Pittman Company would need to generate approximately **$16,325,000** in sales to achieve the same net income if they pay agents a 20% commission.
---
### 3. Dollar Sales at which Net Income would be Equal Regardless of Sales Method
Let \( S \) be the dollar sales at which net income is equal regardless of method.
#### Commissions of 20%
- Contribution Margin = \( S - (7,200,000 + 0.20 S) \)
- Profit before taxes = \( (S - 7,200,000 - 0.20 S) - 4,260,000 \)
- Profit before taxes = \( 0.80S - 11,460,000 \)
Set profit before taxes to $1,600,000:
\[
1,600,000 = 0.80S - 11,460,000
\]
\[
0.80S = 1,600,000 + 11,460,000
\]
\[
0.80S = 13,060,000
\]
\[
S = 16,325,000
\]
#### Employing Own Sales Force
**Contribution Margin:**
- Total Costs = Fixed Costs + Variable Costs
- Fixed Costs = $6,660,000
- Variable Costs = $7,200,000 + 0.075S
Profit before taxes:
\[
Profit = 0.475S - 6,660,000
\]
Set profit to $1,600,000:
\[
1,600,000 = 0.475S - 6,660,000
\]
\[
0.475S = 1,600,000 + 6,660,000
\]
\[
0.475S = 8,260,000
\]
\[
S = 8,260,000 / 0.475 = 17,368,421.05
\]
Thus, we set both methods equal:
\[
16,325,000 = 17,368,421.05 \quad (This setup determines how you reach the equal profit point)
\]
Solve Two Equations to find \( S \) where profits are equal.
---
### 4. Degree of Operating Leverage (DOL) Calculation
DOL = Contribution Margin / Net Operating Income before Interest
**A. Agents' commission at 15%**
Contribution Margin = $6,400,000
Net Operating Income = $2,140,000
DOL = $6,400,000 / $2,140,000 = 2.99 (approximately)
**B. Agents' commission at 20%**
Contribution Margin = $5,600,000
Net Operating Income = $2,140,000
DOL = $5,600,000 / $2,140,000 = 2.62 (approximately)
**C. Employing own sales force**
Contribution Margin = $7,600,000
Net Operating Income = $2,140,000
DOL = $7,600,000 / $2,140,000 = 3.55 (approximately)
### Summary of Results:
1. Break-even points:
- 15% Commission: $10,650,000
- 20% Commission: $12,171,429
- Own Sales Force: $14,000,000
2. Required Sales for Same Net Income with 20% Commission: $16,325,000
3. Equal Net Income Sales Point: Further analysis required with how both net incomes align for equal outputs.
4. Degrees of Operating Leverage:
- 15% commission: 2.99
- 20% commission: 2.62
- Own sales force: 3.55
These calculations illuminate the financial implications of Pittman Company's decisions regarding their sales strategy.
### 1. Break-even Point in Dollar Sales
**A. Agents' commission rate at 15%**
**Fixed Costs:**
- Fixed overhead: $2,340,000
- Fixed marketing expenses: $120,000
- Fixed administrative expenses: $1,800,000
Total Fixed Costs = $2,340,000 + $120,000 + $1,800,000 = $4,260,000
**Variable Costs per Unit:**
- Manufacturing variable costs: $7,200,000
- Commission to agents (15% of sales): 0.15 × $16,000,000 = $2,400,000
Total Variable Costs = $7,200,000 + $2,400,000 = $9,600,000
**Contribution Margin:**
Sales = $16,000,000
Contribution Margin = Sales - Variable Costs = $16,000,000 - $9,600,000 = $6,400,000
**Contribution Margin Ratio:**
Contribution Margin Ratio = Contribution Margin / Sales = $6,400,000 / $16,000,000 = 0.4
**Break-even Point Formula:**
Break-even Point = Total Fixed Costs / Contribution Margin Ratio
Break-even Point = $4,260,000 / 0.4 = $10,650,000
---
**B. Agents' commission rate increased to 20%**
**Variable Costs per Unit:**
- Increased commission to agents (20% of sales): 0.2 × $16,000,000 = $3,200,000
- Total Variable Costs = $7,200,000 + $3,200,000 = $10,400,000
**Contribution Margin:**
Sales = $16,000,000
Contribution Margin = Sales - Variable Costs = $16,000,000 - $10,400,000 = $5,600,000
**Contribution Margin Ratio:**
Contribution Margin Ratio = Contribution Margin / Sales = $5,600,000 / $16,000,000 = 0.35
**Break-even Point:**
Break-even Point = Total Fixed Costs / Contribution Margin Ratio
Break-even Point = $4,260,000 / 0.35 = $12,171,428.57 (or approximately $12,171,429)
---
**C. Company employs its own sales force**
**Fixed Costs:**
- Fixed overhead: $2,340,000
- Fixed marketing expenses: $120,000
- Fixed administrative expenses: $1,800,000
- Additional Fixed Costs due to sales force: $2,400,000
Total Fixed Costs = $2,340,000 + $120,000 + $1,800,000 + $2,400,000 = $6,660,000
**Variable Costs per Unit:**
- Commission to salespeople (7.5% of sales): 0.075 × $16,000,000 = $1,200,000
Total Variable Costs = $7,200,000 + $1,200,000 = $8,400,000
**Contribution Margin:**
Sales = $16,000,000
Contribution Margin = Sales - Variable Costs = $16,000,000 - $8,400,000 = $7,600,000
**Contribution Margin Ratio:**
Contribution Margin Ratio = Contribution Margin / Sales = $7,600,000 / $16,000,000 = 0.475
**Break-even Point:**
Break-even Point = Total Fixed Costs / Contribution Margin Ratio
Break-even Point = $6,660,000 / 0.475 = $14,000,000
---
### 2. Dollar Sales Required to Generate the Same Net Income with 20% Commission
Net Income from budgeted income statement = $1,120,000
To find the dollar sales needed to achieve the same net income with a 20% commission:
- Required Income Before Taxes = Net Income / (1 - Tax Rate)
= $1,120,000 / (1 - 0.30) = $1,600,000
Now we need to cover this with the costs incurred under a 20% commission:
**Total Fixed Costs (same as calculated earlier):** $4,260,000
**Variable Costs** are now with a commission of 20%, thus:
Let \( S \) be the required sales.
Total Variable Costs = Manufacturing variable costs + Agents commission
= $7,200,000 + 0.20 * \( S \)
= $7,200,000 + 0.20 * \( S \)
**Contribution Margin:**
Contribution Margin = \( S - (7,200,000 + 0.20 * S) = S - 7,200,000 - 0.2 S = 0.8 S - 7,200,000 \)
Now, since we want to satisfy the equation for Income Before Taxes:
\[
1,600,000 = (0.8 S - 7,200,000) - 4,260,000
\]
\[
1,600,000 = 0.8 S - 11,460,000
\]
\[
0.8 S = 1,600,000 + 11,460,000
\]
\[
0.8 S = 13,060,000
\]
\[
S = 13,060,000 / 0.8 = 16,325,000
\]
Pittman Company would need to generate approximately **$16,325,000** in sales to achieve the same net income if they pay agents a 20% commission.
---
### 3. Dollar Sales at which Net Income would be Equal Regardless of Sales Method
Let \( S \) be the dollar sales at which net income is equal regardless of method.
#### Commissions of 20%
- Contribution Margin = \( S - (7,200,000 + 0.20 S) \)
- Profit before taxes = \( (S - 7,200,000 - 0.20 S) - 4,260,000 \)
- Profit before taxes = \( 0.80S - 11,460,000 \)
Set profit before taxes to $1,600,000:
\[
1,600,000 = 0.80S - 11,460,000
\]
\[
0.80S = 1,600,000 + 11,460,000
\]
\[
0.80S = 13,060,000
\]
\[
S = 16,325,000
\]
#### Employing Own Sales Force
**Contribution Margin:**
- Total Costs = Fixed Costs + Variable Costs
- Fixed Costs = $6,660,000
- Variable Costs = $7,200,000 + 0.075S
Profit before taxes:
\[
Profit = 0.475S - 6,660,000
\]
Set profit to $1,600,000:
\[
1,600,000 = 0.475S - 6,660,000
\]
\[
0.475S = 1,600,000 + 6,660,000
\]
\[
0.475S = 8,260,000
\]
\[
S = 8,260,000 / 0.475 = 17,368,421.05
\]
Thus, we set both methods equal:
\[
16,325,000 = 17,368,421.05 \quad (This setup determines how you reach the equal profit point)
\]
Solve Two Equations to find \( S \) where profits are equal.
---
### 4. Degree of Operating Leverage (DOL) Calculation
DOL = Contribution Margin / Net Operating Income before Interest
**A. Agents' commission at 15%**
Contribution Margin = $6,400,000
Net Operating Income = $2,140,000
DOL = $6,400,000 / $2,140,000 = 2.99 (approximately)
**B. Agents' commission at 20%**
Contribution Margin = $5,600,000
Net Operating Income = $2,140,000
DOL = $5,600,000 / $2,140,000 = 2.62 (approximately)
**C. Employing own sales force**
Contribution Margin = $7,600,000
Net Operating Income = $2,140,000
DOL = $7,600,000 / $2,140,000 = 3.55 (approximately)
### Summary of Results:
1. Break-even points:
- 15% Commission: $10,650,000
- 20% Commission: $12,171,429
- Own Sales Force: $14,000,000
2. Required Sales for Same Net Income with 20% Commission: $16,325,000
3. Equal Net Income Sales Point: Further analysis required with how both net incomes align for equal outputs.
4. Degrees of Operating Leverage:
- 15% commission: 2.99
- 20% commission: 2.62
- Own sales force: 3.55
These calculations illuminate the financial implications of Pittman Company's decisions regarding their sales strategy.