Harrison Printing has projected its sales for the first eight months of $2014$ as$$ follows:$$

Harrison collects $20$ percent of its sales in the month of the$$ sale, $50$ percent in the month following the$$ sale, and the remaining $30$ percent two months following the sale. During November and December of$2013,$ Harrison's sales were $$220,500$ and $$$$175,500,$ respectively.

Harrison purchases raw materials two months in advance of its sales equal to $65$ percent of their final sales price. The supplier is paid one month after delivery. $$ Thus, purchases for April sales are made in February and payment is made in March.

In$$ addition, Harrison pays $$$$10,200$ per month for rent and $$$$19,000$ each month for other expenditures. Tax prepayments of $$22,500$ are made each quarter beginning in March. The$$ company's cash balance as of December$31,2013,$ was $$$$22,100$; a minimum balance of $$$$20,000$ must be maintained at all times to satisfy the$$ firm's bank line of credit agreement. Harrison has arranged with its bank for$$ short$-$term credit at an interest rate of $12$ percent per annum$(1$ percent per$$ month$)$ to be paid monthly. Borrowing to meet estimated monthly cash needs takes place at the end of the$$ month, and interest is not paid until the end of the following month. $$ Consequently, if the firm were to need to borrow $$50,000$ during the month of$$ April, then it would pay $$500(50,000\backslash$times $0\mathrm{.}12\backslash$times $1/12)$ in interest during May. $$ Finally, Harrison follows a policy of repaying its outstanding$$ short$-$term debt in any month in which its cash balance exceeds the minimum desired balance of $$$$20,000.$

a$.$Harrison needs to know what its cash requirements will be for the next six months so$$ that, if$$ necessary, it can renegotiate the terms of its$$ short$-$term credit agreement with its bank. To analyze this$$ problem, the firm plans to evaluate the impact of a plus or minus $20\%\backslash$pm $20\%$ variation in its monthly sales efforts. Prepare a$$ seven$-$month cash budget for Harrison and use it to evaluate the$$ firm's cash needs.$($Note$$: You will need to prepare the cash budgets for three$$ scenarios: most likely$($sales given in January $$100,900$ May $$274,200$

February $$120,700$ June $$199,100$

March $$149,200$ July $$200,500$

April $$299,000$ August $$180,700),$ worst case$($sales down by $20\%),$ and best case$($sales up by $20\%)$

b$.$Harrison has a $$$$199,000$ note due in June. Will the firm have sufficient cash to repay the$$ loan?