**Author** David Graser, Yavapai College, Prescott, AZ (David.Graser@yc.edu)

**Abstract**

These two group projects are design to get teams delving into the financial data for large corporations. Using data for the price and earnings over several quarters, teams construct linear models and then a corresponding rational model for the PE ratio. For the first project, students find the long term behavior of the rational model using a limit at infinity.

In the second project, student expand their model by utilizing quadratic models for either the price of earnings. once a satisfactory model is found, they calculate the instantaneous rate of change using derivatives.

- Content Area -Applied Calculus
- Time Frame – 3 to 4 weeks with mini-lectures for each project
- Published – June 22, 2015
- Keywords -limits at infinity, rational model, instantaneous rate of change, derivative

**Project Content**

**Scaffolding Resources for Project 1**

**Technology Assignment: Find a Company and Its Financial Data**

The goal of this assignment is to help teams find potential securities for this project. Each team member will choose a different security based on the criteria in the Project Letter. Once theyhave completed this assignment, theinstructor will help teamsto choose the best security from the several theteammates have chosen. Each team member will choose a company and gather its data as demonstrated below for Verizon.

Teams will complete the assignment in a shared Google Sheet. This will make sure that teammates and you can see your work at any time.

**Technology Assignment: Calculate Linear Models for Price and Earnings**

In the tech assignment above, each team member gathered data for a different security. Before starting this assignment, each team member should look at the feedback from theinstructor. This feedback should indicate which of the securities would be best to proceed with for the rest of the project.

In this assignment, each teammate will need to find the equation of a line that passes through two of the data points for the price data and another line that passes through two of the data points for the earnings data. Each team member should work with DIFFERENT pairs of points. For instance, one team member might work with the first and fourth pair of points and another might work with the first two points. Teammatesneed to communicate which pair of point you will do to the rest of your team.

Teams should complete this assignment in the shared Google Sheet for theteam so that each of them can easily see your work.

**Technology Assignment: Find and Graph the PE Ratio Model**

At this point in the project, each team member should have a linear function that passes through a pair of the price data points and another linear function that passes through a pair of the earnings data points. Since each of team memberused a different pair of points, theyshould all have different linear functions.

In this technology assignment, each team memberwill put theirfunctions together in a rational function. They will graph this function along with theirPE ratio data to make sure it corresponds correctly.

As with earlier assignments, the work will be put in a shared Google Sheet. Once the teamhave all finished this assignment, theyneed to pick which of the models is best. This is where the percent error will come in handy. Then they must use the very best model to determine the long term value of the PE ratio.

**Scaffolding Resources for Project 2**

**Technology Assignment: Find a Regression Model for the Price and Earnings**

In this tech assignment, teams will complete the first part of the second project. In this project, teams will need to find linear models for price and earnings as well as quadratic models for price and earnings.

The video below illustrates how to do this in Google Sheets.

**Technology Assignment: Calculate a Rational Model for the PE Ratio**

After the previous tech assignment, teams should have produced four regression models for theirfinancial data. In this assignment, teams willput together four rational models of the PE ratio. Teamsshould communicate to determine who will do which model: linear/linear, linear/quadratic, quadratic/linear, or quadratic/ quadratic.

**Notes**

- It is best to complete both the first project only or both projects since the process of collecting the data is in a tech assignment for the first project. However, the first tech assignment could be added to the second project making it a stand alone project.