Paychex (PAYX) is a services company specialized in staffing & outsourcing. Here we present a share pricing model for PAYX as based on decomposition into a weighed sum of two CPI components, time trend and free term. The final model includes the price index of food less beverages (FB) leading the share price by 3 months and the index of tenants’ and household insurance (THI). The most recent model uses the monthly closing price as of April 2011 and the CPI estimates published on April 14, 2011. Figure 1 depicts the evolution of the indices which provide the best fit model, i.e. the lowermost RMS residual error, between October 2010 and March 2011. The model is as follows:
PAYX (t) = -1.12(t-3) - 1.20THI(t-0) + 8.17(t-1990) + 255.59
where PAYX(t) is a share price in US dollars, t is calendar time. The observed and predicted models are depicted in Figure 2. The residual error is of $2.01 for the period between July 2003 and March 2011. Since the last three months in 2011 were characterized by a quick growth in the FB index one can expect a slight decrease in the share price in 2011 Q2.
Figure 1. Evolution of the price indices THI and FB.
Figure 2. Observed and predicted PAYX share prices.