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Random Utility Theory



RANDOM UTILITY THEORY

DEFINITION
It is assumed that the source of stochasticity is due to errors made by the analyst in developing the model. Here the assumption is that while humans are deterministic and rational utility maximizes, analysts are unable to understand and model fully all of the relevant factors that affect human behavior. The individual is assumed to be all-knowing and rational and selects the alternative with the highest utility. However, the utilities are not known to the analyst with certainty and are therefore treated by the analyst as random variables. This is called the random utility approach. The value of the random utility approach is that it provides a link with behavioral theory one from microeconomics.

EXPLANATION WITH EXAMPLE
Random utility theory posits that people generally choose what they prefer, and where they do not, this can be explained by random factors. For example, a person may choose their preferred cold drinks   9 out of 10 times and on the 10th occasion, they choose something else due to some random factor.
The term 'random' in this instance has a very precise meaning. The variations in behavior due to randomness must not be explainable. That is, if it is known that the reason that the consumer deviated from their preferred cold drinks on the 10th occasion is that it was out of stock then this is not a random phenomenon.
Random utility theory is not an accurate description of human behavior. Nevertheless, checking that models of behavior are consistent with random utility theory provides is a way of checking that the models do not have silly and inconsistent assumptions.
Utility theory, which random utility theory is a special case of, has been criticized on the basis that it implies people are overly rational (i.e., that they have an 'irrational passion for dispassionate rationality'). However, although such an assumption is commonly made in situations where random utility theory is assumed, such an assumption is not a part of utility theory, as utility theory can readily be understood as the idea that people behave in line with self-interest where self-interest reflects peoples' needs to save time and economize on effort.


TRADE OF THEORY
DEFINITION
The trade-off theory states that the optimal capital structure is a trade-off between interest tax shields and cost of financial distress
Value of firm = Value if all-equity financed + PV(tax shield) - PV(cost of financial distress)

EXPLANATION
The trade-off theory can be summarized graphically. The starting point is the value of the all-equity financed firm illustrated by the black horizontal line in Figure. The present value of tax shields is then added to form the red line. Note that PV(tax shield) initially increases as the firm borrows more until additional borrowing increases the probability of financial distress rapidly. In addition, the firm cannot be sure to benefit from the full tax shield if it borrows excessively as it takes positive earnings to save corporate taxes. The cost of financial distress is assumed to increase with the debt level.
The cost of financial distress is illustrated in the diagram as the difference between the red and blue curves. Thus, the blue curve shows firm value as a function of the debt level. Moreover, as the graph suggests an optimal debt policy exists which maximized firm value.


[TRADE OF THEORY GRAPH]


As companies grow and continue to operate, they must decide how to fund their various projects and operations as well as how to pay employees and keep the lights on. While sales revenues are key source of income, most companies also seek capital from investors or lenders as well. But what is the right mix of equity stock sold to investors and bonds sold to creditors? Capital structure theory is the analysis of this key business question.

The net income approach, static trade-off theory, and the pecking order theory are two financial principles that help a company choose its capital structure. Each plays a role in the decision-making process depending on the type of capital structure the company wishes to achieve. The pecking order theory, however, has been empirically observed to be most used in determining a company's capital structure.

SUMMARY:
Capital structure refers to the mix of revenues, equity capital, and debt that a firm uses to fund its growth and operations.
Several economists have devised approaches to identify and optimize the ideal capital structure for a firm.
Here, we look at three popular methods: 
  1. Net income approach; 
  2. Static trade-off theory; 
  3. Pecking order theory.

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