Answer the question fully please!!!!! 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 $ $25,500,000$

Manufacturing expenses:

Variable $ $11,475,000$

Fixed overhead $3,570,00015,045,000$

Gross margin $10,455,000$

Selling and administrative expenses:

Commissions to agents $3,825,000$

Fixed marketing expenses $178,500*$

Fixed administrative expenses $2,180,0006,183,500$

Net operating income $4,271,500$

Fixed interest expenses $892,500$

Income before income taxes $3,379,000$

Income taxes $(30\%)1,013,700$

Net income $ $2,365,300$

$*$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. $$Several companies we know of pay a $7\mathrm{.}5\%$ commission to their own salespeople, along with a small salary. Of course, we would have to handle all promotion costs, too. We figure our fixed expenses would increase by $$3,825,000$ per year, but that would be more than offset by the $$5,100,000(20\%\backslash$times $$25,500,000)$ we would avoid on agents$$ commissions.$$

The breakdown of the $$3,825,000$ cost follows:

Salaries:

Sales manager $ $159,375$

Salespersons $956,250$

Travel and entertainment $637,500$

Advertising $2,071,875$

Total $ $3,825,000$

$$Super$,$ replied Karl. $$And I noticed the $$3,825,000$ equals what we$$re paying the agents under the old $15\%$ commission rate.$$

$$It$$s even better than that,$$ explained Barbara. $$We can actually save $$117,300$ a year because that$$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:

$1)$ 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.