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:

Pittman Company

Budgeted Income Statement

For the Year Ended December $31$

Sales $ $26,000,000$

Manufacturing expenses:

Variable $ $11,700,000$

Fixed overhead $3,640,00015,340,000$

Gross margin $10,660,000$

Selling and administrative expenses:

Commissions to agents $3,900,000$

Fixed marketing expenses $182,000*$Footnote asterisk

Fixed administrative expenses $2,200,0006,282,000$

Net operating income $4,378,000$

Fixed interest expenses $910,000$

Income before income taxes $3,468,000$

Income taxes $(30\%)1,040,400$

Net income $ $2,427,600$

$*$Footnote asteriskPrimarily 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 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 look at$?$

$$We$$ve already worked them up$,$ said Barbara. $$Several companies we know about pay a $7\mathrm{.}5\%$ commission to their own salespeople, along with a small salary. Of course, we would have to handle all promotion costs, too. We figure our fixed expenses would increase by $$3,900,000$ per year, but that would be more than offset by the $$5,200,000(20\%\backslash$times $$26,000,000)$ that we would avoid on agents$$ commissions.$$

The breakdown of the $$3,900,000$ cost follows:

Salaries:

Sales manager $ $162,500$

Salespersons $975,000$

Travel and entertainment $650,000$

Advertising $2,112,500$

Total $ $3,900,000$

$$Super$,$ replied Karl. $$And I noticed that the $$3,900,000$ equals what we$$re paying the agents under the old $15\%$ commission rate.$$

$$It$$s even better than that,$$ explained Barbara. $$We can actually save $$119,600$ a year because that$$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 maCompute Pittman Company$$s break$-$even point in dollar sales for next year assuming:

Please solve

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

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

The company employs its own sales force.