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 $ $24,500,000$

Manufacturing expenses:

Variable $ $11,025,000$

Fixed overhead $3,430,00014,455,000$

Gross margin $10,045,000$

Selling and administrative expenses:

Commissions to agents $3,675,000$

Fixed marketing expenses $171,500*$

Fixed administrative expenses $2,140,0005,986,500$

Net operating income $4,058,500$

Fixed interest expenses $857,500$

Income before income taxes $3,201,000$

Income taxes $(30\%)960,300$

Net income $ $2,240,700$

$*$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 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. $$Several companies we know about pay a $7\mathrm{.}5\%$ commission to their own salespeople, along with a small salary. Of course, we would have to handle all promotion costs, too. We figure our fixed expenses would increase by $$3,675,000$ per year, but that would be more than offset by the $$4,900,000(20\%\backslash$times $$24,500,000)$ that we would avoid on agents$$ commissions.$$

The breakdown of the $$3,675,000$ cost follows:

Salaries:

Sales manager $ $153,125$

Salespersons $918,750$

Travel and entertainment $612,500$

Advertising $1,990,625$

Total $ $3,675,000$

$$Super$,$ replied Karl. $$And I noticed that the $$3,675,000$ equals what we$$re paying the agents under the old $15\%$ commission rate.$$

$$It$$s even better than that,$$ explained Barbara. $$We can actually save $$112,700$ a year because that$$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.

$2.$ 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.

$3.$ Determine 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.

$4.$ Compute the degree of operating leverage that the company would expect to have at the end of 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.

Use income before income taxes in your operating leverage computation