Question

Khan industries experiences regular cash flows of $50,000 per day as it expands its chain of cheap beer joints across the country to help spread happiness, and joy. The firm incurs a transaction cost of $100 when it sells its marketable securities and earns 6 percent on its marketable securities portfolio. What is the optimal amount?

Answer 1

Cash Flow per day = $50,000

Transaction cost on selling its marketable securities = $100

Return of marketable securities = 6%

Optimal Amount of cash balance = square root of ((2*C*T)/i) =

where C = Annual Cash = $50,000*365

T = Transaction costs

i = 6%

Optimal Amount of cash balance = square root of ((2*$50000*365*100)/6%) or ((2*$50000*365*100)/6%) ^(1/2)

= $246,644

Optimal Amount = $246,644

Since the daily balance is $50,000, the optimal amount will last for only 4.9 days (5 days = $246,644/$50,000) after which the account needs to be re-filled.