Solving Inverse Problems
Problem
You want to solve a problem in reverse. For example, referring to the net present worth example discussed in Recipe 14.8, you might want to find what annual cash flow value would make one upgrade option the more attractive alternative.
Solution
Use Goal Seek or Solver to iteratively find a solution. See Chapters 9 and 13 for an in-depth discussion and examples of using Goal Seek and Solver.
Discussion
Let's reconsider the example discussed in Recipe 14.8. Earlier it was found that the No Upgrade option yielded the highest net present worth. Now the question is what annual cash flow would be required for, say, the system A option to yield a net present worth equal to or greater than the No Upgrade option. You can solve this problem with just a few small changes to the spreadsheet shown earlier in Figure 14-2. All you have to do is add a new value in a cell that represents the assumed annual cash flow for system A. Then you need to revise the cash flow values shown in the undiscounted cash flow column for system A to refer to the new assumed value. Finally, you can use Goal Seek to iteratively find the assumed cash flow value while setting the net present worth value for system A to that of the No Upgrade option. Figure 14-3 shows the result of this exercise.
Cell E3 contains the new assumed annual cash flow value for system A. After running Goal Seek as discussed a moment ago, the resulting value is $88,607, and you can see that the net present worth values for the No Upgrade and System A options in cells F13 and G13, respectively, are the same. Therefore, in order for system A to be the more attractive option, your annual cash flow for that option must exceed $88,607.
The only changes I made to the original spreadsheet to find this solution are as follows:
- I added a value in cell E3 to hold the assumed annual cash flow value for system A.
- I added a text label in cell D3.
- I changed cells D9, D10, and D11 from hardcoded values to the cell formula =E3.
- I changed the formula in cell D12 from =85000+0.1*ABS(D8) to =E3+0.1*ABS(D8).
After making these changes, I ran Goal Seek to set cell G13 to a value of 85,575 by changing the value in cell E3. The result is as shown in Figure 14-3.
Figure 14-3. Net present worth example revisited
See Also
Be sure to read Chapter 9 to learn a lot more about using Solver and Goal Seek.
Using Excel
- Introduction
- Navigating the Interface
- Entering Data
- Setting Cell Data Types
- Selecting More Than a Single Cell
- Entering Formulas
- Exploring the R1C1 Cell Reference Style
- Referring to More Than a Single Cell
- Understanding Operator Precedence
- Using Exponents in Formulas
- Exploring Functions
- Formatting Your Spreadsheets
- Defining Custom Format Styles
- Leveraging Copy, Cut, Paste, and Paste Special
- Using Cell Names (Like Programming Variables)
- Validating Data
- Taking Advantage of Macros
- Adding Comments and Equation Notes
- Getting Help
Getting Acquainted with Visual Basic for Applications
- Introduction
- Navigating the VBA Editor
- Writing Functions and Subroutines
- Working with Data Types
- Defining Variables
- Defining Constants
- Using Arrays
- Commenting Code
- Spanning Long Statements over Multiple Lines
- Using Conditional Statements
- Using Loops
- Debugging VBA Code
- Exploring VBAs Built-in Functions
- Exploring Excel Objects
- Creating Your Own Objects in VBA
- VBA Help
Collecting and Cleaning Up Data
- Introduction
- Importing Data from Text Files
- Importing Data from Delimited Text Files
- Importing Data Using Drag-and-Drop
- Importing Data from Access Databases
- Importing Data from Web Pages
- Parsing Data
- Removing Weird Characters from Imported Text
- Converting Units
- Sorting Data
- Filtering Data
- Looking Up Values in Tables
- Retrieving Data from XML Files
Charting
- Introduction
- Creating Simple Charts
- Exploring Chart Styles
- Formatting Charts
- Customizing Chart Axes
- Setting Log or Semilog Scales
- Using Multiple Axes
- Changing the Type of an Existing Chart
- Combining Chart Types
- Building 3D Surface Plots
- Preparing Contour Plots
- Annotating Charts
- Saving Custom Chart Types
- Copying Charts to Word
- Recipe 4-14. Displaying Error Bars
Statistical Analysis
- Introduction
- Computing Summary Statistics
- Plotting Frequency Distributions
- Calculating Confidence Intervals
- Correlating Data
- Ranking and Percentiles
- Performing Statistical Tests
- Conducting ANOVA
- Generating Random Numbers
- Sampling Data
Time Series Analysis
- Introduction
- Plotting Time Series Data
- Adding Trendlines
- Computing Moving Averages
- Smoothing Data Using Weighted Averages
- Centering Data
- Detrending a Time Series
- Estimating Seasonal Indices
- Deseasonalization of a Time Series
- Forecasting
- Applying Discrete Fourier Transforms
Mathematical Functions
- Introduction
- Using Summation Functions
- Delving into Division
- Mastering Multiplication
- Exploring Exponential and Logarithmic Functions
- Using Trigonometry Functions
- Seeing Signs
- Getting to the Root of Things
- Rounding and Truncating Numbers
- Converting Between Number Systems
- Manipulating Matrices
- Building Support for Vectors
- Using Spreadsheet Functions in VBA Code
- Dealing with Complex Numbers
Curve Fitting and Regression
- Introduction
- Performing Linear Curve Fitting Using Excel Charts
- Constructing Your Own Linear Fit Using Spreadsheet Functions
- Using a Single Spreadsheet Function for Linear Curve Fitting
- Performing Multiple Linear Regression
- Generating Nonlinear Curve Fits Using Excel Charts
- Fitting Nonlinear Curves Using Solver
- Assessing Goodness of Fit
- Computing Confidence Intervals
Solving Equations
- Introduction
- Finding Roots Graphically
- Solving Nonlinear Equations Iteratively
- Automating Tedious Problems with VBA
- Solving Linear Systems
- Tackling Nonlinear Systems of Equations
- Using Classical Methods for Solving Equations
Numerical Integration and Differentiation
- Introduction
- Integrating a Definite Integral
- Implementing the Trapezoidal Rule in VBA
- Computing the Center of an Area Using Numerical Integration
- Calculating the Second Moment of an Area
- Dealing with Double Integrals
- Numerical Differentiation
Solving Ordinary Differential Equations
- Introduction
- Solving First-Order Initial Value Problems
- Applying the Runge-Kutta Method to Second-Order Initial Value Problems
- Tackling Coupled Equations
- Shooting Boundary Value Problems
Solving Partial Differential Equations
- Introduction
- Leveraging Excel to Directly Solve Finite Difference Equations
- Recruiting Solver to Iteratively Solve Finite Difference Equations
- Solving Initial Value Problems
- Using Excel to Help Solve Problems Formulated Using the Finite Element Method
Performing Optimization Analyses in Excel
- Introduction
- Using Excel for Traditional Linear Programming
- Exploring Resource Allocation Optimization Problems
- Getting More Realistic Results with Integer Constraints
- Tackling Troublesome Problems
- Optimizing Engineering Design Problems
- Understanding Solver Reports
- Programming a Genetic Algorithm for Optimization
Introduction to Financial Calculations
- Introduction
- Computing Present Value
- Calculating Future Value
- Figuring Out Required Rate of Return
- Doubling Your Money
- Determining Monthly Payments
- Considering Cash Flow Alternatives
- Achieving a Certain Future Value
- Assessing Net Present Worth
- Estimating Rate of Return
- Solving Inverse Problems
- Figuring a Break-Even Point
Index
EAN: 2147483647
Pages: 206
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- The Evolution of IT Governance at NB Power
