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Part $1$

Float$$ Simon Corporation has daily cash receipts of $$$$50$ comma $000.$ A recent analysis of its collections indicated that$$ customers' payments were in the mail an average of $4\mathrm{.}0$ days. Once$$ received, the payments are processed in $3\mathrm{.}0$ days. After payments are$$ deposited, it takes an average of $2\mathrm{.}5$ days for these receipts to clear the banking system.

a$.$How much collection float$($in days$)$ does the firm currently$$ have?

b$.$If the$$ firm's opportunity cost of capital is $9\%,$ would it be economically advisable for the firm to pay an annual fee of $ $16$ comma $000$ to reduce collection float by $3$days$?$ Explain why or why not.

c$.$What would the$$ company's opportunity cost have to be to make the $ $16$ comma $000$ fee$$ worthwhile?