Question

1. A company is having a difficult time forecasting its cash balance levels. The company maintains $2,000 in the checking account at all times. A detailed study of past cash balances revealed that the standard deviation (б) in daily cash balances equals to $600. It is believed that the nature of the firm will not change and the volatility of cash balances is expected to continue in the future. The transaction costs average $85 and the marketable securities yield 6%. [Use 360-day year].

              a. What is the optimal return point for the firm?

              b. What is the upper limit?

              c .Draw your and explain the decisions that would be made using this model and the amount marketable securities that would bought and sold.

Answer 1

standard deviation (б) in daily cash balances equals to $600.

б = 600

Variance (v) = б^2 = 600^2 = 360,000

The transaction costs average = $85

Daily Interest Rate = Annual Rate / 360 = 6% / 360 = 0.000167

Spread (Z)

Z = 15,491.70 ~15,492

This is the difference between Upper Control and Lower Control

Lower Limit = Minimum Cash = 2000

Upper Limit = Minimum Cash + Spread = 2000 + 15,492 = 17,492

Return Point =  Minimum Cash + ( Spread / 3) = 2000 + ( 15,492 /03) = 7164

Ans a : What is the optimal return point for the firm = 7,164

Ans b : What is the upper limit = 17,492

Ans c :

If cash balance reach Upper Limit in checking account. Extra money will be invested in marketable securitie . When Cash balance is low i.e. t touches lower limit Invested Securities should be sold and maintain to Return Point.

Always after purchase or sales Cash balance reaches to return Point.

Y Axis : Cash Balance

X Axis - Time