# Breakeven Analysis Project

#### Summary

The project requires students to use basic programming skills in MATLAB to write a program that will perform a breakeven analysis for a proposed new elephant house at the local zoo. Students are given parameters for calculating construction costs using three different options for materials and construction methods. The program should determine the expected return on investment and the time to break even for a single construction option chosen by the user. The construction costs are considered the initial fixed costs. The particular construction materials selected will affect the variable costs for operating the new enclosure as well as the revenue that can be expected, which is based on visitor response.

## Learning Goals

Use a menu choice and user inputs to pull data from a cell array and calculate initial construction costs (fixed costs), variable operating costs, including unit conversions, and revenue predicted. Formatted output is used to send calculated values to the command window. Two plots are to be created, based upon which material the user choices, one plotting cost and revenue and one plotting profits, both indicating the breakeven time.

Students use basic problem-solving skills to gain an understanding of economic impacts involved with choices an engineering firm might be asked to consider. Basic programming skills are used to facilitate problem solving, visualize comparisons, and communicate results. Each team submits only one code, so teamwork skills are presented in order to learn to communicate and come to agreement on everything from the basic algorithm to the colors used to present the graphs. A Teamwork Guide is provided as reference for basic teamwork skills: Student Teamwork Guide.

**Categories of Learning Objectives for Breakeven Analysis Project: **

PS problem solving

ML MATLAB skills

BE engineering economics of breakeven analysis

TW teamwork

CS communication skills

**Specific Goals of the Project / Course**

PS - Express observations in appropriate units and perform conversions when necessary, importance of units in solving complex equations

CS - Graphical representation and interpretation of data.

PS / CS / BE - Use graphical techniques to create "proper" plots and determine graphical solutions to problems.

PS / TW / BE - Formulate and justify a solution to an engineering problem within a team structure

PS / ML - Formulate algorithmic steps into code utilizing input instructions, formatted output, and plots.

ML - Read, write, interpret, and debug MATLAB programs and functions.

ML / CS - Proper documentation, including description of variables and general housekeeping (clearing workspace, command window, closing figure windows)

PS / BE - Trace the value of variables through MATLAB program execution. Verify output against a manually calculated solution.

PS / ML / BE - Use MATLAB to enhance problem solution techniques, including entering and formatting data; including mathematical; create and format data into graphs.

## Context for Use

This project is assigned late in the semester in the freshman-level Engineering Problem Solving course, which is a high enrollment, prerequisite course at a large public university. Students work in teams of 3 to complete the project during one week. We have assigned teams based on performance on the first exam in the class, but other methods may be used to create teams. All class time (approximately 3 hours) for the week is devoted to working on the project and it is submitted on Saturday night by 10 pm. Breakeven analysis is the context for students to combine programming skills learned up to that point and produce a program that integrates data types, input and output statements, calculations, and plots. Student must be familiar with the terminology for economic analysis, including fixed costs, variable costs, revenue, profit, and breakeven point. The project is fairly easily adaptable to other engineering work involving similar economic analysis.

## Description and Teaching Materials

The project is introduced at the beginning of Project Week and students work together in their assigned teams to finish by the end of the week. A companion to the Student Teamwork Guide, Instructor Guide, is also available with case studies, class exercises, and lesson plans for anyone interested in enhancing and assessing teamwork.The project does not have to be completed as a team project and can be assigned to individual students. If teamwork is a goal, additional instruction can be given regarding how to work well in a team environment, what makes a good team member, and how to resolve conflict.

Breakeven Analysis Project (Acrobat (PDF) 226kB Sep8 20)

## Teaching Notes and Tips

Many teams complete the project within the 3-hour class time and do not need to work on it outside of class. Students may need help writing the equations for revenue and for costs in terms of time. Once the equations are determined, the breakeven time is found easily by setting revenue equal to cost, which is where the plotted lines cross.

Total Cost = Variable Cost * Quantity + Fixed Cost

Revenue = Selling Price * Quantity

Profit = Revenue – Total Cost

Breakeven when Total Cost = Revenue, set equations equal and solve for Quantity

Breakeven Quantity = Fixed Cost / (Selling Price – Variable Cost)

For this project, students are required to create a vector for time in years: YearVector = [1:NumYears], where NumYears is specified by user input. The equations for breakeven analysis must be modified to be functions of time.

Total Cost = (Variable Cost/week) * (Number of Weeks/Year) * YearVector + Fixed Cost

Revenue = (Revenue/week) * (Number of Weeks/Year) * YearVector

Profit = Revenue – Total Cost

Breakeven Weeks = Fixed Cost / ( Revenue/week – Variable Cost/week)

**MATLAB skills used in this project**

Basic programming rules

- Commenting / documentation
- Clear; clc; close all
- Describe variables and units
- Syntax and order of execution

Create variables, understand data types, scalars, strings, vectors (matrix with single row or single column), cell arrays

User input with input command, menu command

Problem solving, write equations to calculate new values and unit conversions

Use dot operator to perform element-wise multiplication

Use colon to pull column as list of menu options, use menu choice as index to pull correct information from cell array

Formatted output to table, use control characters %s, %f, %e and control decimal places, use \n and \t

Create plots, figure windows, multiple data series in a single window, markers, lines, graphing properties

Proper plot rules:

- Experimental data – must be represented with markers
- Theoretical data – must be represented by lines
- More than one data series requires:
- Markers with different colors and different marker styles
- Lines with different colors and different line styles
- Legend

- All plots require:
- Axis labels – xlabel, ylabel
- Axis limits – axis ([ ])
- Grid – grid on
- Title – only required if problem statement gives title

## Assessment

A rubric is provided to student graders in order to keep grading focused on the desired outcomes and so that grading is consistent across approximately 1200 students (400 projects) each semester. The MATLAB code solution is also provided as well as a Word document that includes the output and graphs for each case. The rubric does not assess teamwork skills.

## References and Resources

Stephan, E. A., Bowman, D. R., Park, W. J., Sill, B. L., & Ohland, M. W. (2018). 11.6 Graphical Solutions. In Thinking like an engineer: An active learning approach (pp. 382-388). NY, NY: Pearson.

This is the textbook used in the course, and the specific chapter introduces the economic terms for costs and revenue. It includes the breakeven point, which is the graphical solution for where the cost and revenue lines cross.

Clark, Andrew M., et al. "Teamwork: An Open Access Practical Guide." *Teamwork An Open Access Practical Guide*, Mavs Open Press, 25 Aug. 2020, uta.pressbooks.pub/teamworkstudent/.

Clark, Andrew M., et al. "Teamwork: An Open Access Practical Guide – Instructor Companion." *Teamwork An Open Access Practical Guide – Instructor Companion*, Mavs Open Press, 25 Aug. 2020, uta.pressbooks.pub/teamworkinstructorguide/.

Additionally, the following links are videos on YouTube that provide the background information on the Engineering Economics of Breakeven Analysis. These could be used in place of the specific textbook referenced above.

Genreneaus, (2020, June). *2.9 Chapter 2: Break-even Analysis* [Video]. YouTube. https://www.youtube.com/watch?v=tXI3Qdu_Qt8

Alanis Business Academy, (2013). *How to Conduct a Breakeven Analysis *[Video]. YouTube. https://www.youtube.com/watch?v=tXI3Qdu_Qt8

maxus knowledge, (2014, January 23). *Break even analysis – Graphical method *[Video]. YouTube. https://www.youtube.com/watch?v=fQZEDv0pMlc