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Pittman Company is a small but growing manufacturer of telecommunications equipment. The company has no sales force of its own; rather, it relies completely 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, has just prepared the company's budgeted income statement for next year as follows;

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 that 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 that after paying for advertising, travel, and the other costs of promotion, there's nothing left over for profit," replied Barbara.

"I say it's just plain robbery," 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

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"We've already worked them up$,"$ said Barbara. "Several companies we know about pay a $7\mathrm{.}5\%$ 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 $$2,400,000$ per year, but that would be more than offiset by the $$3,200,000(20\%$$$16,000,000)$ that 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 that 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."

"We've already worked them up$,"$ said Barbara. "Several companies we know about pay a $7\mathrm{.}5\%$ 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$ that 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 that 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:

a$.$ The agents' commission rate remains unchanged at $15\%.$

b$.$ The agents' commission rate is increased to $20\%.$

c$.$ The company employs its own sales force.

Assume that Pittman Company decides to continue selling through agents and pays the $20\%$ commission rate. Determine the dollar sales that would be required to generate the same net income as contained in the budgeted income statement for next year.

Determine the dollar sales at which net income would be equal regardless of whether Pittman Company sells through agents $($at a