Branch banks must keep enough money on hand to satisfy customers' cash demands.
Suppose that the daily demand for cash at a branch of University Bank follows a
lognormal distribution with means and standard deviation summarized as follows
in $ s:
An armored truck delivers cash to this bank once a week. The manager of the bank
can order any amount of cash she desires for this delivery. Of course, running out of
cash in any week is very undesirable as customers of the bank expect to be able to
withdraw their deposits on demand. Of course, keeping excessive cash reserves
would guard against this happenstance. However, cash is a noninterest earning
asset, so there is an opportunity cost for holding excess cash reserves.
a Suppose the bank manager follows the practice of ordering enough cash to
start each week with a balance of $ Create a spreadsheet model to track
the daily cash balance throughout the week.
b What is the probability that the bank will run out of money at some point
during the week?
