Frandson$$s Farm Supply, Inc. has been trying to determine the optimal cash balance level for the firm. The firm$$s Chief Financial Officer, Andy Mays, has selected the Baumol Model for this analysis. Data which he has assembled on Frandson$$s Farm Supply, Inc. for use in the Baumol Model includes the following. Annual disbursements for the firm are expected to be $$200,000.$ The firm$$s investment broker charges $$25$ per securities transaction. Short$-$term investment interest rates are $14$ percent.

a$.$ What should the optimal cash balance $($ C$*)$ 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 cash replenishment orders to its investment broker will Frandson$$s Farm Supply have in a year, assuming the model$$s assumptions are valid?

d$.$ What will the total costs be for the year, including both $$opportunity cost$$ and $$trading cost$?$

$33.34.$ The State Bank of Middleton is planning to make a regular, $$simple interest$$ loan to Acme Manufacturing, Inc. The loan value is $$35,000$ and the nominal annual interest rate is $4\mathrm{.}5\%.$ Interest on this loan will be paid each month. Assume a $360-$day year, and a $30-$day month.

a$.$ Based on this information, calculate the daily interest rate on this loan:

b$.$ Then, calculate the interest charge on this loan that will be due each month:

$35.36.$ Mindy and Mark Anderson have been offered an add$-$on interest installment loan for a vehicle purchase by their bank, First Premier Bank. They are planning to purchase a used SUV and repay the loan in $12$ equal monthly installments. The nominal, annual interest rate on this loan is $8\mathrm{.}5\%.$ The Anderson$$s are planning to borrow $$12,000$ for this vehicle.

a$.$ Calculate the total annual interest cost on this add$-$on interest loan:

b$.$ Mindy and Mark will only have the use of the full $$12,000$ during the first month of this loan. During the final month, only $1/12$ of the original loan of $$12,000$ would be outstanding. Based on this information, calculate the $$approximate annual interest rate$$ on this add$-$on interest loan:

$37.40.$ Assume that you are given the following information for Ressler Restaurant Supply

Company for the glass measuring cups that they carry in inventory:

$25,500$ measuring cups are sold per year.

$$ The cost to place an order from the vendor $($including employee wages and benefits and computer time and postage$)$ is $$24$;

$$ The carrying cost per measuring cup is $$1\mathrm{.}05$ per year.

a$.$ Given the above information, calculate the $$Economic Order Quantity$($EOQ$)$ for the measuring cup that Ressler Restaurant Supply currently carries in inventory.

b$.$ Calculate the $$Total Annual Ordering Cost$$ for the measuring cup item, based on the EOQ order quantity that you calculated in Part A above.

c$.$ Calculate the $$Total Annual Carrying Cost$$ for the measuring cup item, based on the EOQ order quantity that you calculated in Part A above.

d$.$ Why are the $$Total Annual Ordering Cost$$ value that you calculated in Part B above and the $$Total Annual Carrying Cost$$ value that you calculated in Part C above equal to one another for the measuring cup item?