# FINANCIAL ENGINEERING CHEN 320 Team 9 Anna Burgess Allen Messina Chadley Box Omar Ahmed Michael Li 1 Figure 1: An engineer uses simple arrhythmic math.

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FINANCIAL ENGINEERING CHEN 320 Team 9 Anna Burgess Allen Messina Chadley Box Omar Ahmed Michael Li 1 Figure 1: An engineer uses simple arrhythmic math programs on MATLAB to see the stability of his project http://www.mathworks.com/products/connections/images/main/36879_main_Thetaris_image_sm.jpg

Outline  Introduction into Financial Engineering  Purpose  Methodology  Defining Financial Indicators  Decision Tree  Optimizing indicators for use in Matlab  Everyday Project Examples  Drawing conclusions  Improvements upon the research 2 http://sfi.epfl.ch/files/content/sites/sfi/files/MFE- Home.jpg Figure 2: Engineers discussing the process for completing the project in a plant Figure 3: By following these steps, it will lead you to financial success of your projects http://www.flickr.com/photos/ac wa/3650209755/

Introduction Engineers need to understand the importance of having financial stability before performing a project.  Financial Indicators help management determine the profitability of a project and help them compare between multiple projects to determine which projects to take on. 3 http://www.12manage.com/images/picture_cost_b enefit_analysis.gif Figure 5: Determining the financial indicators can be compared to weighing the costs and benefits. If the costs are too large or the indicators do not meet requirements set by the company the project is not profitable. Figure 4: In any business, value, profit, and success will come with following these indicators. http://certifiedhosting.com/hosting-resource- center/wp-content/uploads/2010/10/value.jpg

Purpose The objective of this presentation is to showcase the importance of engineers knowing the line of profitable projects to costly, unaffordable projects. Without that information, the project could make the company lose assets, prevent them from pursuing future projects, or, worst of all, send the company into bankruptcy. However, all of these hardships can be avoided by answering these questions:  How much will the project cost?  How long after the project is completed will the product start paying back the money put in?  Does the project have longevity and future worth? 4 Figure 6: If the project does not offer a profit, the project is not worth the money. http://mybec.org/wp-content/uploads/2012/06/profit-720x720.jpg http://www.thedigeratilife.com/images/bills.gif Figure 7: If the project is done without knowing the profit it could cause the company to go into debt or loss of assets

Methodology The method to complete this project involves these steps:  Read and analyze the article of Investments for Engineers  Read economics and numerical textbooks to learn more about the particular terms used in the article  Create a process of determining whether a project is a good investment  The process: 5 Understand each financial indicator Calculate all financial indicators Conclude whether the project is profitable Figure 8: A method could be seen as one of the tasks in completing any project Figure 9: Process Diagram http://thinkingfutures.net/wp-content/uploads/2010/10/method.jpg

The List of Financial Indicators: 1. DISCOUNTED CASH FLOW (DCF) 2. NET PRESENT VALUE (NPV) 3. INTERNAL RATE OF RETURN (IRR) 4. RETURN ON INVESTMENT (ROI) 5. PAYBACK PERIOD 6 http://us.123rf.com/400wm/400/400/janpietruszk/janpietruszk1003/janpietruszk100300485/6537558- financial-indicators.jpg Figure 10: Financial indicators combine the value of business, planning, and finance in order to have financial success.

1. Discounted Cash Flow (DCF)  A dollar in the future is generally worth less than a dollar today; this effect is called the time value of money  A net cash flow (NCF) is the amount of income from a project received in one year after the expenses and taxes are paid  Due to the time value of money, the NCFs must be discounted back to the value of a dollar today in order to properly interpret a project  DCF’s can be manipulated by changing the discount rate and time period  The value of a NCF in today’s dollar amount is the DCF 7 http://cbrownley.wordpress.com/2011/04/ 10/time-value-of-money/ Figure 11: The graph is a visual representation of how money put into a project loses its value. Starting with \$10,000 at present day the value of the money decreases with the added years. Therefore, the cost of the project will increase as the years follow.

2. Net Present Value (NPV)  NPV is simply the sum of the DCF’s  Generally when choosing between two projects, the one with the higher NPV must be chosen, but it is important to compare the projects based on the same term, discount rate, and risk  However, the project term, discount rate, and net cash flows can each be difficult to predict in some cases due to necessary assumptions that may prove to be inaccurate later on  The discount rate can be manipulated to reflect the relative risk of each project to help evaluate them 8 n=number of years DCF=cash flow Figure 12: This is the formula on how to calculate the NPV. The NPV tells how much your plant, well, or piece of equipment is worth if the project is done by adding up all the DCFs or cash that it makes the company with this project implemented.

3. Internal Rate of Return (IRR)  The IRR is the discount rate for a project which results in an NPV of 0, or the case of breaking even  Generally, if the actual discount rate of a project is below the IRR then a project will be profitable  However, if the cash flows change in such a way that the NPV’s fluctuate between positive and negative values over the course of the project (non- normal cash flows), then IRR becomes ineffective  IRR can be calculated by trial and error, iterations, directly, or using a spreadsheet, but mainly depends on the method used to discount the cash flows 9 Figure 13: With the NPV information, graph the yearly NPV against a rising discount rate. The intersection of those two values will give the IRR, which is how long until the project breaks even with the invested money for the project.

4. Return on Investment (ROI)  ROI is the percent of profit per cost of the project: ROI= Profit/Capital investment *100%  Each company uses its own interpretation of profit (before or after tax) and capital investment (value can be taken at various points in time)  An acceptable ROI for a project varies based on factors like company size, economic conditions, competition, cost of borrowing, etc. 10 http://www.rms.net/roi_investreturn.gif Figure 14: This picture gives a visual representation of what ROI is by showing that internally there are costs and benefits of the project that must be considered. After those values are known a simple division of profit and capital investment determines the ROI of the project.

5. Payback Period  Payback Period is the time required for the sums of the cash flows to meet or exceed the initial capital investment  There are two types of payback periods: Simple Payback Period, which uses NCF’s, and Discounted Payback Period, which uses DCF’s  Payback Period helps indicate of the riskiness of a project  Shorter payback periods allow for sooner recovery of capital and less time exposure to risks 11 http://pmstudy.com/blog/wp-content/uploads/2012/11/Payback-Period.jpg Figure 15: This image represents what all companies want to know: when will they get their money back. The term for this is payback period.

Decision Tree 12 Is the project a good investment? Is the NPV a positive value? No: Project is not financially stable Yes: Is the IRR greater than an established minimum acceptable value? No: Project is not financially stable Yes: Is the Payback Period within an acceptable time frame? No: Project is not financially stable Yes: Project is financially stable Figure 16:

Analysis & Optimization 1. NPV - A positive NPV reflects a profitable project that will add value to the firm while a negative NPV reflects a project that will be unprofitable 2. IRR - The IRR must be greater than an established minimum acceptable value. This value is decided by the company or group in charge of the project. 3. ROI - A good starting point for ROI is around 30% 4. Payback Period- A shorter payback period is preferable With these indicators met and acceptable for the company or group, the project is more likely to be a reliable investment. 13 http://elliottanalysis.com/wp-content/uploads/2013/07/Reward-Risk-Ratio.png Figure 17: Minimizing risk in an investment can result in profit.

Programs of the Financial Indicators 14 Figure 18: We created four programs that directly calculate DCF, NPV, ROI, and Payback Period http://core3solutions.com/web/wp-content/uploads/2011/06/Programing.jpg

Discounted Cash Flow Program clear all clc prompt='What is the interest rate?'; r=input(prompt) prompt='What is the time in years?'; n=input(prompt) prompt='What is the net cash flow?'; c=input(prompt) % Discounted Cash Flow Calculation DCF= c/(1+r)^(n) 15 Figure 19: DCF Program

Net Present Value Program  function [NPV]=npvvalue(k,NCF)  % Input:  % NCF = an array of the net cash flows starting at time 0  % k = return rate  % Output:  % NPV = the net present value for the given k and NCF array  format bank  n=1;  while n<=length(NCF)  DCF(n)=NCF(n)/(1+k/100)^(n-1);  n=n+1;  end  NPV=sum(DCF);  nform=[0:(length(NCF)-1)];  table=[nform' DCF']  end 16 Figure 20

Return of Investment Program clc prompt='What is your profit?'; P=input(prompt) prompt='What is your capital investment?'; CI=input(prompt) % Percent Return on Investment Calculation ROI=(P/CI)*100 17 Figure 21: ROI Program

IRR Program 18 Figure 22 function [IRR, fx, ea, iter] = NCFbisect(func,xl,xu,NCF,es,maxit) % bisect: root location zeroes % [root, fx, ea, iter] = bisect(func, xl, xu, es, maxit, p1, p2,...): % uses bisection method to find the root of func % input : % func = name of function % xl, xu = lower and upper guesses % es = desired relative error (default = 0.0001%) % maxit = maxiumum allowable iterations (default = 50) % p1,p2,... = additional parameters used by func % output : % root = real root % fx = function value at root % ea = approximate relative error (%) % iter = number of iterations % Input: % NCF = an array of the net cash flows starting at time 0 % k = return rate

19 IRR Program [cont.] Figure 23 % Output: % NPV = the net present value for the given k and NCF array %NPV=sum(DCF); if nargin<4, error('at least 3 input arguments required'), end test=func(xl, NCF)*func(xu,NCF); if test>0, error('no sign change'), end if nargin<5|isempty(es), es=0.0001; end if nargin<6|isempty(maxit), maxit=50; end iter=0; xr=xl; ea=100; while (1) xrold=xr; xr=(xl+xu)/2; iter=iter+1; if xr~=0, ea=abs((xr-xrold)/xr)*100; end test=func(xl,NCF)*func(xr,NCF); if test < 0 xu=xr; elseif test>0

20 IRR Program [cont.] Figure 24 xl=xr; else ea=0; end if ea =maxit,break,end end IRR=xr;fx=func(xr,NCF); xval=linspace(0,50); i=1; while i<=length(xval) yval(i)=func(xval(i),NCF); i=i+1; end plot(xval,yval,IRR,0,'o','markerfacecolor','k') grid on title('Plot of r vs. NCF') xlabel('r') ylabel('NCF')

Payback Period Program clc prompt='What is your initial investment?'; I=input(prompt) prompt='What is your annual cash flow?'; C=input(prompt) % Payback Period Calculation P=I/C 21 Figure 25: PBP Program

Common Examples for Calculating Financial Indicators 22 http://clomedia.com/articles/view/avoiding-the-trickle-of-a-leaking-pipeline http://www.scmp.com/sites/default/files/styles/980w/public/2013/07/31/04ac0abd8b9b60dd023e6 d7ec827e97.jpg?itok=fgvNDzkV Figure 26: With this pipe leak, a decision needs to be made on whether the company can afford a new pipe or if it is more profitable to create a new design for the pipeline. Figure 27: This plant fire has destroyed a section of the plant. Financial indicators need to be calculated on whether the company can afford to rebuild this section or cut this section out of the plant completely.

Current Day Example 23 http://jto.s3.amazonaws.com/wp-content/uploads/2013/10/p1- fukushima-z-20131010.jpg Figure 28: This image shows a storage tank leak. The tank was filled with a radioactive coolant, so the decision has to be made on whether there are sufficient funds to replace the tank. A plant has shut down because there is a leak in one of the collection tanks. Should the tank be replaced or should the fluid be rerouted to the other tank on site?

DCF Example 24 Figure 29: The DCF has a discount rate of 0.1, 10 years, and cash flow of 8000 dollars. What is the interest rate?.1 r = 0.1000 What is the time in years?10 n = 10 What is the cash flow?8000 c = 8000 DCF = 3.08435e+003

Investment= -\$40,000 DCF1=\$7272.73 DCF2=\$6611.57 DCF3=\$6010.52 : DCF10=\$3084.35 Today: Year 0 C1= \$8,000 C2= \$8,000 C3= \$8,000 Year 1 Year 2 Year 3 Year 10 C10= \$8000 Discount rate= 10% 10% Example Discounted Cash Flow (DCF) 25 Figure 30: This shows the cash flow of \$8000 dollars over 10 years

NPV 10 26 Figure 31: This is the NPV of ten years. With a positive value, the NPV is acceptable by most companies.

IRR 27 Figure 32: The IRR is the intersection of the Discounted Rate and NPV. In this example, it occurs at (15.10,0). This means that our project is fundable because our interest rate is at 10%. IRR (15.10, 0) Interest Rate (10, 0.915654)

Example: ROI 28 Figure 33: ROI is 26.4% with an expected profit of \$10,569.90 and capital investment of \$40000. This RIO value is acceptable because the value is close to expected value of 30%. What is your profit?10569.90 P = 1.0570e+004 What is your capital investment?40000 CI = 40000 ROI = 26.4247

Example of Payback Period 29 Figure 34: With the 40,000 dollar investment and a cash flow of \$8,000, the payback period will be in 5 years. What is your initial investment?40000 I = 40000 What is your annual cash flow?8000 C = 8000 P = 5

Results:  NPV was a positive value ✔  IRR was greater than interest rate ✔  ROI was favorable ✔  Payback Period was reasonable ✔ With all four financial indicators having favorable results, the project can be deemed feasible investment. The tank should be replaced. 30 http://www.intergraph.com/assets/images/tank.jpg Figure 35: New Storage Tank

Improvements on the Paper 31 Figure 36: Change is necessary to improve what was discussed in the Investments paper. http://www.undermyhat.org/blog/wp- content/uploads/2010/04/Change-ahead-sign-652x250- 642x250.jpg?cda6c1 To improve this paper, six programs were developed to gather more information on whether the investment would be profitable. One program finds the interest rate for a certain DCF, and the other five programs are used to determine the accurate cost and the worth of the project once completed.

Calculating Interest rate (r) for a certain DCF 32 Figure 37: Interest Rate Program function [ r ] = solveR(DF,n) r=fzero(@(x) DF-(exp(x)- 1)*(exp(-x*n))/x,3); end

Calculating Compound Interest 33 Figure 38: Compound Interest Program function A = comp_int(P, r, n, t) % A=comp_int(P,r,n,t) function to calculaate compount interest % Input: % P=principal investment % r=interest rate % n=compound times per year % t=time in years % Output: % A=ending balance A = P*(1 + r/n)^(n*t);

Calculating Simple Interest 34 Figure 39: Simple Interest Program function A=simp_int(P,r,t) % A=simp_int(P,r,t): function to calculate simple interest % Input: % P=principle investment % r=interest rate % t=time in years % Output: % A=ending balance A=P+P*r*t

Calculating Continuous Compounding Interest 35 Figure 40: Continuous Compound Interest Program function A=cont_comp(P,r,t) % A=cont_comp(P,r,t): function to compute continuously compounding interest % Input: % P=principle investment % r=interest rate % t=time in years % Ouput: % A=ending balance A=P*exp(r*t)

Calculating Annual Payments 36 Figure 41: Annual Payments Program function annualpayments(P,i,n) % annualpayments(P,i,n): function to yield annual payments to pay off initial % loan % Input: % P=principle loan % i=interest rate % n=number of years nn=1:n; % Number of years increasing by one A=P*((i*(1+i).^nn)./((1+i).^nn- 1)); % Equation to calculate annual payments using given parameters y=[nn;A]; % Output: % y=matrix of years and payments fprintf('\n nn A\n'); fprintf('%5d%14.2f\n',y);

Calculating Future Worth 37 Figure 42: Future Worth Program function futureworth(P,i,n) % futureworth(P,i,n): function to yield annual future worth of initial % investement % Input: % P=principle investment % i=interest rate % n=number of years nn=0:n; % Numer of years increasing by one F=P*(1+i).^nn; % Equation of future worth using given parameters y=[nn;F]; % Output: % y=matrix of years and investments fprintf('Year Future Worth'); fprintf('%5d%14.2f\n',y);

Future Improvements  Utilize past investment models to determine their usability in the future  Research more precise equations for numerical approximations 38 http://bit.ly/LTmTwL Figure 43: The best way to come off of a failure in a project is to learn from those mistakes and make sure your future projects do not follow the same path. http://i.dailymail.co.uk/i/pix/2013/06/15/article- 2342090-1A4E6269000005DC-570_634x476.jpg Figure 44: By not investing in the right equipment, the company lost a major plant.

Conclusion  Financial indicators are very important when analyzing capital investments  Using the programs we have created, we can make estimations about which projects to pursue 39 http://www.glasbergen.com/wp-content/gallery/financial-cartoons/toon796.gif Figure 45: Without doing the process of financial indicators for the project, you could land your company into a large debt. Therefore, take the time to calculate all cost and benefits of the project before starting the work.

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