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 CompanyBudgeted Income StatementFor the Year Ended December $31$SalesManufacturing expenses:$ $18,000,000$Variable$ $8,100,000$Fixed overhead$2,520,000$Gross margin$10,620,000$Selling and administrative$7,380,000$expenses:Commissions to agentsFixed marketing expenses$2,700,000126,000*$Fixed administrative expensesNet operating income$1,880,0004,706,000$Fixed interest expenses$2,674,000$Income before income taxes$630,0002,044,000$Income taxes $(30\%)$Net income$613,200$$ $1,430,800*$Primarily depreciation on storage facilities.As Barbara handed the statement to Karl Vecci, Pittman's president, she commented, "I went ahead and used the agents' $15\%$ commission rate in completing these statements, but we've just learned they refuse to handle our products next year unless we increase the commission rate to $20\%.""$That$\text{'}$s the last straw," Karl replied angrily. "Those agents have been demanding more and more, and this time they've gone too far.How can they possibly defend a $20\%$ commission rate?""They claim after paying for advertising, travel, and the other costs of promotion, there's nothing left over for profit," replied Barbara."That's ridiculous," retorted Karl. "And I also say it's time we dumped those guys and got our own sales force. Can you get your people to work up some cost figures for us to look at$?""$We$\text{'}$ve already worked them up$,"$ said Barbara. "Several companies we know of pay a $7\mathrm{.}5\%$ commission to their own salespeople, along with a small salary. Of course, we would have to handle all promotion costs, too. We figure our fixed expenses would increase by $$2,700,000$ per year, but that would be more than offset by the $$3,600,000(20\%\backslash$times $$18,000,000)$ we would avoid on agents' commissions."The breakdown of the $$2,700,000$ cost follows:Salaries:The breakdown of the $$2,700,000$ cost follows:Salaries:Sales managerSalespersonsTravel and entertainmentAdvertisingTotal$ $112,500675,000450,0001,462,500$$ $2,700,000$"Super," replied Karl. "And I noticed the $$2,700,000$ 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 $$82,800$ 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$\mathrm{.}2.$ 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$\mathrm{.}3.$ 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.PrintReferences$4.$ Compute the degree of operating leverage 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.