The Casablanca Piano Company is currently holding \($800,000\) in cash. It projects that over the next year its cash outflows will exceed its cash inflows by \($345,000\) per month. Each time securities are bought or sold through a broker, the company pays a fee of \($500.\) The annual interest rate on money-market securities is 7 percent.

a. How much of this cash should be retained and how much should be used to increase the company’s holdings of marketable securities?

b. After the initial investment of excess cash, how many times during the next 12 months will securities be sold?