Baumol’s Model: Assume that Everyman’s Bookstore uses up cash at a steady rate of $200,000 a year. The interest rate is 2 percent and each sale of securities costs $20.a) What it the economic level of cash that the store should convert from marketable securities at a time?

Question

b) How many times a year should the store sell securities? c) What is its average cash balance? d) What it the annual opportunity cost of holding cash for the store? e) What is the annual cost of trading

Answer 1

Baumol's Model is a cash management model that helps a company determine the optimal amount of cash to convert from marketable securities and the frequency of those conversions. Here are the calculations based on the information given:

Given Data

• Cash demand (D) = $200,000 per year
• Interest rate (i) = 2% = 0.02
• Cost of selling securities (T) = $20 per transaction

a) Economic Level of Cash to Convert (\( C^* \))

The formula for the economic level of cash to convert from marketable securities is:

\[ C^* = \sqrt{ \frac{2DT}{i} } \]

Substituting the given values into the formula:

\[ D = 200,000, \quad T = 20, \quad i = 0.02 \]

\[ C^* = \sqrt{ \frac{2 \times 200,000 \times 20}{0.02} } \]

\[ C^* = \sqrt{ \frac{8,000,000}{0.02} } \]

\[ C^* = \sqrt{400,000,000} \]

\[ C^* = 20,000 \]

b) Number of Times a Year the Store Should Sell Securities (\( N \))

The number of times the store should convert cash from marketable securities is given by:

\[ N = \frac{D}{C^*} \]

Substituting our values:

\[ N = \frac{200,000}{20,000} \]

\[ N = 10 \]

c) Average Cash Balance (\( C_{avg} \))

The average cash balance can be calculated as:

\[ C_{avg} = \frac{C^*}{2} \]

Substituting our value for \( C^* \):

\[ C_{avg} = \frac{20,000}{2} \]

\[ C_{avg} = 10,000 \]

d) Annual Opportunity Cost of Holding Cash

The opportunity cost of holding cash is given by:

\[ OC = C_{avg} \times i \]

Substituting the values we found:

\[ OC = 10,000 \times 0.02 \]

\[ OC = 200 \]

e) Annual Cost of Trading

The annual cost of trading can be calculated as:

\[ TC = N \times T \]

Substituting our values:

\[ TC = 10 \times 20 \]

\[ TC = 200 \]

Summary of Results

• a) Economic Level of Cash to Convert: $20,000
• b) Number of Times the Store Should Sell Securities: 10 times per year
• c) Average Cash Balance: $10,000
• d) Annual Opportunity Cost of Holding Cash: $200
• e) Annual Cost of Trading: $200

This analysis provides Everyman’s Bookstore with a structured way to manage cash efficiently, minimizing costs associated with holding cash and converting securities.