$1.$ The assistant treasurer of Monroe Tires, Inc., is trying to determine what the appropriate cash return level should be$.$ The company$$s cash balances have been fluctuating wildly because of unpredictable and wide$-$ranging receipts and disbursements. The best estimate of annual disbursements is $$5,000,000.$ The investment broker charges $$75$ per securities transaction. Short$-$term investment interest rates are $12$ percent. The company does not mind a $$0$ cash balance but does not want the balance to be negative.

a$.$ What should the cash return level be$,$ according to the Baumol model? b$.$ What will the average cash balance be if the company$$s cash outflows fit the assumptions of the Baumol model?

c$.$ How many security sales will Monroe have in a year, assuming the model$$s assumptions are valid? d$.$ What will the total period costs be for a year? e$.$ Do you recommend that Monroe use the Baumol model? Why or why not?

$2.$ Assess your results from the previous problem using sensitivity analysis. What conclusions do you reach based on your analysis? How might Monroe use this information?