TIE2140 / IE2140e Engineering Economy Tutorial 6 (Lab 2) Engineering-Economic Decision Making Process using EXCEL Solutions Guide by Wang Xin, Hong Lanqing & Mei Wenjie 1. Learning Objectives In this lab-based tutorial, you will learn how to: 1. Develop a basic deterministic financial after-tax cash flow model using Excel 2. Perform One-Way Range Sensitivity Analysis using Sensit (Tornado and Spider Diagrams) 3. Perform Break-Even Analysis using Rainbow Diagrams (and Goal Seek) 4. Perform Probabilistic Risk Analysis using Monte Carlo Simulation using @Risk. 5. Interpret Risk Profile and determine risk measures. 2. Problem Description A company plans to invest in a flexible manufacturing system (FMS) to mass produce a new product for the market. The relevant information including base estimates for production quantity, price, fixed & variable costs, direct & indirect costs, etc are given in the table below: Variables Base Value 1 Number of pieces produced/year 550,000 2 Selling Price $ 12.00 3 Variable labor cost/part $ 2.20 4 Variable material cost/part $ 1.50 5 Annual overhead $ 2,250,000 6 Annual tooling costs $ 450,000 7 Annual inventory costs $ 150,000 8 Investment Cost $ 7,500,000 9 Useful system life 10 years 10 Salvage value $ 500,000 11 Depreciation scheme 3-Year Capital Allowance 12 Corporate tax rate 17% 13 MARR 15% The company is not sure what to do, and you have been engaged as a consultant to help and advice the company on the feasibility and risk of investing in this project. soln-tut6-lab-2-1
3. Hand-on Exercises and Solutions 3.1 Base Model Development & Analysis a. Using Excel, perform ATCF analysis to determine the After-Tax PW for the proposed investment based on the base estimates and a study period of 10 years. You may use the Excel template provided. b. Is the project economically feasible based on the base estimates? First, open the ie2140-17-tut-06-lab2-templates and go to the Base Model sheet. The uncertain variables, fixed parameters and their base values are already inputted in the Excel sheet. Then, conduct the After-Tax Cash Flow Analysis. First, input the investment cost of Year 0, which equals to B12, the investment cost. Then we move on to the first year: Annual revenue = number of pieces produced/year selling price, i.e., -$B$5*$B$6, here, we press F4 to fix the values. Labor cost = number of pieces produced/year variable labor cost/part, i.e., -$B$5*$B$7. Material cost = number of pieces produced/year variable material cost/part, i.e., -$B$5*$B$8. Overheads = - annual overheads, i.e., -$B$9. Tooling cost = - annual tooling costs, i.e., -$B$10. Inventory cost = - annual inventory costs, i.e., -$B$11. After input all the related values of Year 1, we select all of them, put the mouse on the lower right corner where there is a + sign, and then drag to the right side and obtain values from Year 2 to Year 10. Investment Cost of Year 0, -B12 drag to the right side Then we input the investment cost of Year 10, B13. Investment Cost of Year 10, B13 Then we move to the depreciation. In this project, the 3-year CA is used, so the depreciation is investment cost divided by 3, i.e., $B$12/3. After inputting all the related values, we go to FORMULAS Calculate now, all other numbers are updated accordingly. soln-tut6-lab-2-2
Or you could click Calculate Options Automatic, then next time Excel would update the calculation automatically. In the after tax cash flow (ATCF), we could see that there are two cash flow in Year 10, so we need to add them up to be the total cash flow in Year 10, L42 + M42. Then we use the NPV function to calculate the after-tax PW, where After-tax PW = Year 0 cash flow + NPV (after tax MARR, cash flow from Year 1 to Year 10) Then, we get the after-tax PW = $716,918.53. Since the after-tax PW is greater than zero, the project is feasible. We can also obtain after-tax IRR of the project using IRR function. As the IRR function does not allow separate entries of cash flows, we need to develop a compacted ATCF array that has a single cash flow in Year 10 equal to L42+M42. The After-Tax IRR can be obtained using IRR function, which is 17.60%. The project is feasible as it is larger than MARR. soln-tut6-lab-2-3
3.2 One-Way Range Sensitivity Analysis The management is not very comfortable with the results as the company does not have any previous experience in operating an FMS, and there are uncertainties in the many of the variables base values. It is proposed that sensitivity analyses be performed on the base model to raise the company s confidence. Expert s estimates of the possible range of values for each of the uncertain input variables are given in the table below: Uncertain Variables Low Value Base Value High Value 1 Number of pieces produced/year 500,000 550,000 600,000 2 Selling Price $ 10.00 $ 12.00 $ 14.00 3 Variable labor cost/part $ 2.10 $ 2.20 $ 2.30 4 Variable material cost/part $ 1.25 $ 1.50 $ 1.75 5 Annual overhead $ 2,000,000 $ 2,250,000 $ 2,500,000 6 Annual tooling costs $ 425,000 $ 450,000 $ 475,000 7 Annual inventory costs $ 130,000 $ 150,000 $ 170,000 8 Investment Cost $ 7,400,000 $ 7,500,000 $ 7,600,000 9 Salvage value $ 475,000 $ 500,000 $ 525,000 a. Perform one-way range sensitivity analysis by generating Tornado and Spider Diagrams using the Sensit software. Interpret the results. b. Which are the sensitive variables? c. Which are the insensitive variables? In the second part, instead of having just one base value, each variable now has its low value and high value. To perform one-way range sensitivity analysis, we need to add in macros. We go back to the folder of templets, double click the Sensit-XXX-Trial-Addin-XXXX, and add the macro into Excel. Then we could find ADD-INS in the menu bar. soln-tut6-lab-2-4
To conduct the sensitivity analysis, we move to the Sensitivity Model. Here we can also find the correct answer of the first question. First, we click the Senslt Trial Tornado-Spider option, and click OK. Here, to input the input variables, we click the drop-down list, and select all the names of uncertain variables, $A$5 to $A$13. click soln-tut6-lab-2-5
Then, click the right side and back to the main menu. click to go back By the same procedure, we input the value of the input variables, $B$5 to $B$13. In the right side, One Extreme is the low value, so we select $D$5 to $D$13. The Base Case is the middle column, $E$5 to $E$13, and Other Extreme is all the high values, $F$5 to $F$13. As for the Cells for Output Variable, it is the After-Tax PW, $A$45, whose value is $B$45. After select all the related variables, we click both the Tornado Chart and Spider Chart, then click on OK. After running the macros, we obtain the Tornado Chart and Spider Chart. In the Tornado Chart, it has a summary table of all the relevant information. soln-tut6-lab-2-6
For each of the variables, we have the low, base and high values. Excel calculates the corresponding PW, and then draws the Tornado Chart. It is shown that the Selling Price is the most sensitive, we define the first five variables as the sensitive variables. The Salvage value is the least sensitive. soln-tut6-lab-2-7
The Spider PW output file contains a summary table and the spider diagram. All variables were sorted in descending order of sensitivity. As shown in the table and figure, the Selling Price is the most sensitive. We define the first five variables as the sensitive variables. The Salvage value is the least sensitive. 3.3 Break-Even Analysis a. Plot a Rainbow Diagram to determine the break-even the number of pieces produced and sold for the project to be feasible. What is the break-even value? How will the change in the production will affect our decision? b. Plot a Rainbow Diagram to determine the break-even the price of product for the project to be feasible. What is the break-even value? Now we go back to the sensitivity model, and click the Sensit Trial One-Input Plot. In case a, the only variable that is changing is the number of pieces produced/year, so we input the corresponding label $A$5 and value $B$5. For the range of the input value, the Start is the lower bound, which is 500,000. The Stop is the upper bound, $600,000. The maximum step (number of calculation point) in Excel is 32,000. In each point, Excel calculates the corresponding After-Tax PW. soln-tut6-lab-2-8
the number of pieces produced/year After-Tax PW After click OK, we obtain the rainbow diagram. To find the break-even point which PW = 0, we choose DESIGN Add Chart Element Gridlines to add Gridlines to add major and minor gridline into the diagram. soln-tut6-lab-2-9
We can see that the break-even point is about $530,000. In case b, we perform the rainbow diagram to determine the break-even the price of product for the project to be feasible. The procedure is the same as case a. We get the rainbow diagram as below, and the breakeven point is about $ 11.7. The exact break-even values of the number of pieces produced and the price of product are 529,264 and 11.69, which can be obtained using the Goal Seek function. soln-tut6-lab-2-10
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3.4 Probabilistic Risk Analysis using Monte Carlo Simulation a. Risk Profile Generation: For each of the sensitive variables identified in the previous step, access their respective probability distribution, and perform Monte Carlo simulations on them (while keeping the non-sensitive variables at their base values) to generate the risk profile for the project s after-tax PW. Hint: You may assume the followings distributions if needed: Variable Distribution Parameters 1 Number of pieces produced/year Uniform Integer (500,000, 600,000) 2 Selling Price Normal (Truncated) µ = $12.00 σ = $1.000 3 Variable labor cost/part Normal (Truncated) µ = $2.20 σ = $0.050 4 Variable material cost/part Normal (Truncated) µ = $1.50 σ = $0.125 5 Annual overhead Uniform ($2,000,000, $2,500,000) You may assume that although the above variables are currently uncertain, each of them has the same value over the 10 years study period. b. Risk Profile: What are the mean and standard deviation of the After-tax PW of the project? c. Downside Risk: What is the probability that the project will be economically infeasible based on aftertax PW? d. Upside Potentials: i. What is the probability that project will achieve after-tax PW $3 million? ii. What is the probability that project will achieve after-tax PW $4 million? e. Project Value-at-Risk: Value-at-Risk (VaR) is a popular measure for investment risk. It indicates the maximum loss an investment may incur at a certain level of confidence (e.g. 90%, 95%). i. What is the project s present-value-at-risk at 90% confidence? ii. What is the project s present-value-at-risk at 95% confidence? Optional Homework f. Perform Monte Carlo Simulation using After-Tax IRR as the output measure and interpret the risk profile generated. In this question, we move to the Probabilistic Model. The distribution of variables are already inputted in the Excel sheet. We will use @Risk to do the probabilistic analysis. Simply search @Risk in your computer. Double click the icon. Click Close when you see the following dialog. soln-tut6-lab-2-12
If @Risk is successfully loaded, you will see @Risk in the menu bar. In the probabilistic analysis, each uncertain variable has a distribution. So we need to use Excel to generate random numbers for each variable according to its distribution. To define a uniform integer distribution for the number of pieces produced per year, we first click cell B5. Then click Define Distributions. The uniform integer function can be found in the Discrete group of functions. Click IntUniform and click Select Distribution. soln-tut6-lab-2-13
We then input parameter references by clicking the small data icon shown below. Min and Max should contain cell I5 and J5, respectively. Then click the icon in the upper right corner to go back and then click Ok. soln-tut6-lab-2-14
Most of distributions can be input in a similar way while the truncated normal distribution requires more effort. To define a truncated normal distribution for the selling price, we first find a normal distribution and then specify limits. Click B6. Go to Define Distributions. Find normal distribution under Common or Continuous and then click Select Distribution. Click small arrow next to Parameter and select Truncation Limits and Values. Click OK. soln-tut6-lab-2-15
Besides mu and sigma, you will see there are two more entries (Trunc. Min and Trunc.Max) to specify. Again, click the icon at the bottom right corner. soln-tut6-lab-2-16
Mu, Sigma, Trunc.Min, Trunc.Max should correspond to cell I6, J6, K6, and L6, respectively. Then click the icon in the upper right corner to go back and then click OK. Distributions for variable labor cost and material cost per part can be defined similarly as selling price. Or you can click cell B6, move mouse to the bottom right corner until a cross sign appears. Then drag all the way down to cell B8. In this way, you copy the formula in B6 to B7 and B8. The uniform distribution for the annual overhead is defined as below. soln-tut6-lab-2-17
Note that we have provided formula for all variables so that you can check whether your input is correct or not. As we would like to see the risk profile for the project s after-tax PW, we next add After-Tax PW as the output. Click cell B45, click Add Output in the menu, and click OK. soln-tut6-lab-2-18
Note that you can add After-Tax IRR as the output simultaneously to see its risk profile. Before running the simulation, it is highly suggested checking model inputs and outputs carefully. You can do this by clicking Model Window. As can be seen, there are five inputs corresponding to five random variables and two outputs of interest. soln-tut6-lab-2-19
Then click Start Simulation to run the simulation. Simulation results will be shown in a separate window and you can always view the results by clicking Browse Results in the menu. The expected value and standard deviation of the After-tax PW of the project are $716,580.87 and $2,340,310.78. soln-tut6-lab-2-20
Downside Risk: The probability that the project will be economically infeasible based on after-tax PW is about 39.2%. soln-tut6-lab-2-21
Upside Potentials: The probability that project will achieve after-tax PW $3 million is 17.3%. The probability that project will achieve after-tax PW $4 million is 8.7%. soln-tut6-lab-2-22
Project Value-at-Risk: The project s equivalent present value-at-risk at 90% confidence is -2.33 million dollars. The project s equivalent present value-at-risk at 95% confidence is -3.07 million dollars. soln-tut6-lab-2-23
To generate excel report, you can click Excel Reports in the menu bar or the icon at bottom left of the result window. soln-tut6-lab-2-24