ANÁLISIS Y DISCUSIÓN

If the firm wishes to hire a new employee, regardless of their rank in the company, they contribute some value to the company, referred to asθt , marginal value changes attributable to a change in the manager’s current ability, efforts, and/or decision making criteria. At this point, the model advances from the Arya et al (2004) model, as employee contribution to the company is divided into two parts: 1) incremental “sustainable” value, which will also be referred to as Θ_t; and 2) dependent “employee” value, which will be referred to as υ_t, which represents value added that relies on the employee, and is independent of φ . Practically, sustainable incremental value added refers to any incremental increases in value attributable to superior decision making, such as project selection, policy implementation or development of intellectual property (e.g. idea for a new product), etc. which will have a semi-permanent “footprint” on the firm. Other value

added by an employee however, is considered somewhat temporary as it is related to the individual’s personal attributes, knowledge or experience, e.g. he is effective at motivating other workers. So if the employee were to leave, this value would be lost. Although there is some overlap between attributes which contribute to both sustainable and temporary value (e.g. teacher could use knowledge and experience to help students year by year, and/or write a book), this possible overlap is dealt with in the model by the following

t t t

θ υ= + Θ (3.2)

The variable θt is slightly more complicated than other variables thus far, due to its relationship with other variables. From the firm’s perspective, the actual value that will be added by an employee is somewhat uncertain, particularly when there is incomplete information. Let us consider the actual value added, θ_t be a function of the employee’s perceived potential to add value, E

t

θ However, an employee may not actually produce

θt E

value depending on motivation for the employee. More detail regarding these incentives will be mentioned later in the chapter.

On top of the value created by an employee, there may be possible side benefits, depending on the form of compensation. In particular, compensation packages that include options will have a number of benefits, which will temporarily be referred to as

Bt, until further expansion of these different benefits.

With regards to value added to the firm, it will be assumed that all value to be added by current employees are not going to change value of the firm on their own accord, so that the impact of a new employee on a firm can be observed in isolation. Consequently the new formula for the value of the firm sees the addition of value added by employee plus any Bt side benefits less the cost of employing him/her, Ct.

As a side note, the following equation (3.3) is generalized, meant mainly for conceptual purposes, and will be expanded and developed throughout this section.

1 1 1

t t t t t t t t t

So although Ct is subtracted as if it were a simple dollar cost, it is not necessarily that simple to calculate. These costs, as well as a number of other benefits not covered in the general equation below, will be expanded on later also.

Strictly speaking φ_t is independent of θ_t+1 , as it represents expected value added independent of who is not employed by the firm at time = 0. However for future periods of φ_t+1, an employee is able to contribute Θ_t+1, “sustainable value” through project selection or policy implementation. In addition, φt+1 is susceptible to unexpected

changes, ε_t, to investments within the year. This gives us:

1

t t t t 1

φ₊ = + Θ +φ ε₊ (3.4)

t

Θ is also indirectly related to ωt due to the general risk and return relationship. As Θt represents changes in expected returns, these value adding decisions or investments will usually be associated with increased levels of market risk. However, there is only a general positive linear relationship, and thus can not be written explicitly. This is due to the selection of positive NPV projects, which provide excess returns above the expected risk adjusted return. Finally, it will be assumed that the firm does not pay dividends, so that any increases in value will be fully reflected in the stock price.

When attempting to reconcile this new model of future firm value to the random walk model, the main difference is that the random εt element is categorized into two different

sources, θ ω₀+ θ_t , contribute to the random components,with θ0 also relating to how the

long term expected return may change in the future. A more complicated model could be constructed by incorporating the CAPM into the calculation of φ0 on the basis of the

current expected market return, as well as splitting ωt into changes in the market return,

and unique firm risk.