Model Answer
0 min readIntroduction
Effective cash management is crucial for organizational liquidity and profitability. The Miller-Orr model, developed by Merton Miller and Dan Orr in 1966, provides a framework for determining the optimal cash balance a firm should maintain. It balances the costs associated with holding cash (opportunity cost) against the costs of converting marketable securities into cash (transaction cost). This model is particularly relevant in situations where firms experience predictable cash flows and can accurately estimate these costs. Understanding this model is vital for financial managers aiming to optimize their working capital.
The Miller-Orr Model: A Detailed Explanation
The Miller-Orr model is a probabilistic model that aims to minimize the total cost of cash management. It assumes that cash flows are not constant but vary randomly. The model suggests that a firm should maintain a buffer stock of cash to meet unexpected disbursements. This buffer stock is determined by balancing two key costs:
1. Transaction Costs
Transaction costs are the expenses incurred when a firm sells marketable securities to obtain cash. These costs include brokerage fees, bid-ask spreads, and potential price discounts due to selling securities quickly. The model assumes that the larger the cash disbursement, the higher the transaction cost.
2. Opportunity Costs
Opportunity costs represent the return a firm forgoes by holding cash instead of investing it in other profitable ventures, such as marketable securities. This cost is directly related to the interest rate that could be earned on alternative investments. The higher the interest rate, the greater the opportunity cost of holding cash.
Determining the Appropriate Cash Balance
The Miller-Orr model uses the following formula to determine the optimal cash balance (CB):
CB = √ (2 * r * D) / k
- CB = Optimal cash balance
- r = Average daily cash disbursement
- D = Daily variation in cash disbursements (standard deviation)
- k = Interest rate earned on marketable securities (daily rate)
The formula indicates that the optimal cash balance increases with both the average daily cash disbursement (r) and the variability of cash disbursements (D). Conversely, the optimal cash balance decreases as the interest rate on marketable securities (k) increases. The model essentially finds the point where the expected transaction costs equal the expected opportunity costs.
Practical Application and Considerations
The Miller-Orr model is most effective when:
- Cash flows are predictable, allowing for accurate estimation of 'r' and 'D'.
- Transaction costs are clearly defined and quantifiable.
- The firm has access to a liquid market for marketable securities.
However, the model has limitations. It assumes a normal distribution of cash flows, which may not always be the case. It also doesn't account for factors like credit lines or overdraft facilities that can reduce the need for a large cash buffer. Furthermore, the model doesn't consider the potential benefits of holding cash for strategic purposes, such as taking advantage of unexpected investment opportunities.
Example: A company has average daily disbursements of ₹50,000 (r), a standard deviation of ₹10,000 (D), and can earn a daily interest rate of 0.05% (k). Using the formula, the optimal cash balance would be: CB = √ (2 * 50,000 * 10,000) / 0.0005 = ₹447,213.60
Conclusion
The Miller-Orr model provides a valuable framework for optimizing cash balances by balancing transaction and opportunity costs. While it relies on certain assumptions and has limitations, it remains a foundational concept in cash management. Modern firms often supplement this model with more sophisticated techniques, such as economic order quantity (EOQ) for cash and just-in-time inventory management principles, to further refine their cash management strategies. Effective implementation requires accurate data and a thorough understanding of the firm’s specific cash flow patterns.
Answer Length
This is a comprehensive model answer for learning purposes and may exceed the word limit. In the exam, always adhere to the prescribed word count.