Definition

The Concept of Q ratio was introduced by James Tobin in 1969 to predict the firm’s profitable investment.

The formal definition of Q Ratio is as Follows :

Q Ratio = Firm’s Market Value / Firm’s Replacement Cost

The implication is, if Q > 1, it is worthy to be invested in the firm.

Concept

In particular, the Q ratio has been used as a measure of firm’s intangible asset. The use of Q for measuring intangible value is based on the assumption that the Long Run Equilibrium Market value must be equal to the replacement value of its assets, given a Q value close to unity.

The advantage of using Tobin’s Q is that the difficult problem of estimating either rate of return or marginal cost is avoided.

On the other hand, for Q to be meaningfull, one needs accurate measures of both the market value and replacement cost of a firm’s assets.

It is usually possible to get an accurate estimate for the market value of a firm’s assets by summing the values of the securities that a firm has issued , such as stocks and bonds.

It is much more difficult to obtain an estimate of the replacement costs of its assets, unless the used equipments still exists in the market.

Moreover, expenditures on advertising & research and development create intangible assets that may be hard to value.

Typically, researchers who construct Tobin’s Q ignore the replacement costs of these intangible assets in their calculations. For that reason, Q typically exceeds 1.

Expandable Concept

Tobin’s Q has been used as a proxy variable of many corporate phenomena such as the Information Technology (IT) investments, & research and development.

Tobin’s Q also used as a measure of the capitalized value of monopoly rents.

We also wish to use the concept of Tobin’s Q in the Talent Management.

Tobin’s Q in talent Management

Q ratio in Talent management = Overall Employees Benefits / Total Hiring Cost

A new hire ideally ramps up to full productivity over months, going through on-boarding, induction, on-job training, certification etc. During all of that time, an employee deliveres no value, they just prepare to start work.

So, total cost of hiring comprise of the following :

Total Hiring Cost = Cost of Job posting + Interview Cost + Cost of reference Check + Cost of relocation + Cost of Training + Cost of Losses of existing Employees + Cost of Overtime Expenses + Cost of yearly Bonus + Cost of Salary Increase + Cost of Salary

At time zero, costs are very high. The cost gradually decreases and productivity increases over time.

In this model, I have taken some assumptions, which may differ organization to organization.

But, here, my main aim is to prepare a model to measure the value of the employee from the company perspective.That means, when and how the overall Employee Benefits shows greater than the Total hiring cost or Q > 1 and what is the pattern of Tobin’s Q Curve.

Assumptions

  1. In this model, after about a year, the main monthly expense is salary & overhead.
  2. In this model, an employee takes a year to ramp up to full productivity.
  3. Though, we should use different models for different jobs, here, we assume that, all jobs are identicals.

Variables and assumed values

max.yrs = 5 # max number of years to show on plot
max.benefit = 1.5   # year at which employee delivers fully-trained value (asymptote) 
cost.ramp = 1.5 # higher numbers speed up time before costs = salary
cost.scale = 3      # higher numbers increase height of original training costs
salary = 0.5        # monthly salary as a percent of fully trained value delivered to company

Employee Value

set up data frame with time series in months

emp.value = as.data.frame(0:(max.yrs*12)/12)
names(emp.value)= "tenure.yrs"

Employee Benefits

set up Benefit Function, modeled as a Sigmoid

emp.value$benefit = 1/(1+exp(-(emp.value$tenure.yrs/max.benefit*12-6)))
plot(emp.value$benefit, type="l")

Employee Costs

set up Cost Function, modeled as a Gompertz

emp.value$cost = exp(-exp(cost.ramp * emp.value$tenure.yrs))*cost.scale + salary
plot(emp.value$cost, type="l")

Tobin’s Q

Now diagramatic representation of Tobin’s Q

TobinQ=emp.value$benefit/emp.value$cost
plot(TobinQ, type="l")