Suppose the average daily float is $$6$ million with a weighted average delay of $5$ days.

a$.$ What is the total amount unavailable to earn interest?

b$.$ What is the NPV of a project that could reduce the delay by $4$ days if the cost is $$20$ million?

$4.$ A proposed single lockbox system will reduce collection time $3$ days on average.

Daily interest rate on T$-$bills $=0\mathrm{.}01\%.$

Average number of daily payments to the lockbox is $4,000.$

Average size of payment is $$500.$

The processing fee is $$0\mathrm{.}12$ per check plus $$10$ to wire funds each day.

What is the maximum investment that would make this lockbox system acceptable?