Problem

You're considering certain equipment upgrades in your lab and you want to perform a net present worth analysis of the projected cash flow streams from these upgrades to determine which option presents the best alternative.

Solution

You can use the same techniques discussed in Recipe 14.6 to discount the projected cash flow streams in terms of present values. The option with the highest net present value is the best choice.

Discussion

Consider this example: you're currently running a numerical simulation laboratory that uses an aging supercomputer to run your simulations. You've forecast cash flows for your simulation services over the next five years. Now you're considering purchasing one of two candidate cluster-based systems that will boost your forecast cash flow over the next five years. These new clusters cost money, though, so you're not sure which one, if either, offers the best choice economically speaking. You need to decide whether to purchase system A, system B, or nothing at all.

Let's further assume that system A costs $250,000 and system B, which is somewhat more powerful than system A, costs $310,000. Also, at the end of the fifth year you can sell either system for salvage at 10% of its original cost.

You've worked out cash flow forecasts for these two options as shown in Figure 14-2.

The `No Upgrade` option means you don't upgrade your system, but instead continue offering services over the next five years using your current system. In this case, your cash flow is projected to decrease somewhat over the five-year period due to anticipated increases in operating and maintenance costs. Forecast cash flows for the system A option are expected to be fairly high, and the cash flow in the fifth year includes the 10% salvage value. Similarly, system B is expected to generate more cash flow due to its higher performance capabilities. The fifth-year cash flow value for system B also includes the 10% salvage value.

Examination of the net cash flow values shown in the `Total` row for the first three cash flow columns in the table in Figure 14-2 gives the impression that upgrading to system A offers the best choice. This is before discounting and figuring out the net present value of each option.

Figure 14-2. Net present worth example

Discounting these cash flows uses the same formulas shown in Recipe 14.6. The formulas in the last three cash flow columns, the discounted columns, are of the form `=PV($E$2,$B9,0,-C9,0)`, where the present value function, `PV`, is used to compute the present value of each year's cash flow amount for each option.

Net present values are represented by the totals for the last three discounted cash flow columns. Examining these totals reveals that purchasing system A is not the best option as originally thought. Instead the `No Upgrade` option offers the best alternative at this time. Upon viewing results like this, you might be inclined to hold off on your upgrade until new system prices come down a bit, in which case the net present worth analysis might yield different results. Other factors to consider include fluctuations in interest rates, as well as the declining cash flow of the old system as it ages further.

Excel offers a built-in function called `NPV` that computes the net present value of a series of cash flows given a discount rate (interest rate). Its syntax is `= NPV(`*rate*`,` *values*`)`, where ` rate` is the interest rate and

For example, to compute the net present value of the `No Upgrade` option, use the formula `=C8+NPV(E2,C9:C12)`. Notice that this formula discounts only the cash flow values for the second through fifth years. The first year, year 0, is then added to the discounted cash flow series to arrive at the net present value. Similarly, the formulas `=D8+NPV(E2,D9:D12)` and `=E8+NPV(E2,E9:E12)` compute the net present values for the system A and system B options, respectively. These three formulas yield the same net present value results computed using the `PV` function.

See Also

Check out Recipe 14.9 to learn how to compute internal rates of return for the options in this example.

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

Excel Scientific and Engineering Cookbook (Cookbooks (OReilly))

ISBN: 0596008791

EAN: 2147483647

EAN: 2147483647

Year: N/A

Pages: 206

Pages: 206

Authors: David M Bourg

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