Introduction to Spreadsheet Modeling Chapter 2 Introduction to Spreadsheet Modeling

Introduction This book is all about spreadsheet modeling. By the time you are finished, you will have seen some reasonably complex—and realistic—models. Many of you will also be transformed into Excel “power” users. This chapter provides an introduction to Excel modeling and illustrates some interesting and relatively simple models. The chapter also covers the modeling process and includes some of the less well known, but particularly helpful, Excel tools that are available.

Basic spreadsheet modeling: Concepts and best practices Most mathematical models, including spreadsheet models, involve inputs, decision variables, and outputs. The inputs have given fixed values, at least for the purposes of the model. The decision variables are those a decision maker controls. The outputs are the ultimate values of interest; they are determined by the inputs and the decision variables. Spreadsheet modeling is the process of entering the inputs and decision variables into a spreadsheet and then relating them appropriately, by means of formulas, to obtain the outputs.

Concepts and best practices continued After the outputs are obtained, you can proceed in several directions. You might want to perform a sensitivity analysis to see how one or more outputs change as selected inputs or decision variables change. You might want to find the values of the decision variable(s) that minimize or maximize a particular output, possibly subject to certain constraints. You might also want to create charts that show graphically how certain parameters of the model are related. These operations are illustrated with several examples in this chapter.

Concepts and best practices continued You should construct your models with readability in mind, especially if the models are shared with others. Features that improve readability include: A clear, logical layout to the overall model Separation of different parts of a model, possibly across multiple worksheets Clear headings for different sections of the model and for all inputs, decision variables, and outputs Use of range names

Concepts and best practices continued Readability features continued: Use of boldface, italics, larger font size, coloring, indentation, and other formatting features Use of cell comments Use of text boxes for assumptions and explanations The formulas and logic in any spreadsheet model must be correct. Much of the power of spreadsheets derives from their flexibility. Plan ahead before diving in, and if your plan doesn’t look good after you start filling in the spreadsheet, revise your plan.

Cost projections In Example 2.2, a company wants to project its costs of producing products, given that material and labor costs are likely to increase through time. We build a simple model and then use Excel’s charting capabilities to obtain a graphical image of projected costs.

Breakeven analysis Many business problems require you to find the appropriate level of some activity. This might be the level that maximizes profit (or minimizes cost), or it might be the level that allows a company to break even—no profit, no loss. We discuss a typical breakeven analysis in Example 2.3.

Using Goal Seek From the data table in Example 2.3, we see that profit goes from negative to positive when the response rate is somewhere between 5% and 6%. Question 2 of the example asks for the exact breakeven point. This could be found with trial and error but is easy with Excel’s Goal Seek tool. Goal Seek is used to solve a single equation with a single unknown. In the example, the equation is Profit=0, and the single unknown is the response rate.

Using Goal Seek continued In Excel terminology, the unknown is called the changing cell because we are allowed to change it to make the equation true. To implement Goal Seek, select Goal Seek from the What-If Analysis dropdown in the Data ribbon and fill in the resulting dialog box as shown below.

Ordering with quantity discounts and demand uncertainty In Example 2.4, we again attempt to find the appropriate level of some activity: how much of a product to order when customer demand for the product is uncertain. Two important features of this example are the presence of quantity discounts and the explicit use of probabilities to model uncertain demand. Except for these features, the problem is very similar to the one discussed in Example 2.1.

Estimating the relationship between price and demand Example 2.5 illustrates a very important modeling concept: estimating relationships between variables by curve fitting. You will study this topic in much more depth in the discussion of regression in Chapter 14, but the ideas can be illustrated at a relatively low level by taking advantage of some of Excel’s useful features.

Estimating the relationship: The functions The three functions have some general properties that should be noted because of their widespread applicability. The linear function is the easiest. Its graph is a straight line. When x changes by 1 unit, y change by b units. The constant a is called the intercept, and b is called the slope

Estimating the relationship: The functions continued The power function is a curve except in the special case where the exponent b is 1 (then it is a straight line). The shape of the curve depends primarily on the exponent b. If b >1, y increases at an increasing rate as x increases. If 0 < b < 1, y increases, but at a decreasing rate, as x increases. If b < 0, y decreases as x increases. An important property of the power curve is that when x changes by 1%, y changes by a constant percentage, and this percentage is approximately equal to b%. For example, if y = 100x-2.35, then every 1% increase in x leads to an approximate 2.35% decrease in y.

Estimating the relationship: The functions continued The exponential function also represents a curve whose shape depends primarily on the constant b in the exponent. If b > 0, y increases as x increases. If b < 0, y decreases as x increases. An important property of the exponential function is that if x changes by 1 unit, y changes by a constant percentage, and this percentage is approximately equal to 100 x b%. Another important note about the equation is that it contains e, the special number 2.7182…. In Excel, e to any power can be calculated by the EXP function.

Estimating the relationship continued If we superimpose any one of these curves on the scatterplot for demand versus price, Excel will choose the best fitting curve of that type. Better yet if we check the Display Equation on Chart option, we see the equation of this best-fitting curve. Doing this for each type of curve we obtain the results in the following figures.

Best-fitting power curve

Best-fitting exponential curve

Estimating the relationship continued Each of these curves provides the best-fitting member of its “family” to the demand/price data, but which of these three is best overall? We answer this question by finding the mean absolute percentage error (MAPE) for each of the three curves. To do this, for any price in the data set and any of the three curves, we first predict demands by substituting the given price into the equation for the curve.

Estimating the relationship continued The predicted demand will typically not be the same as the observed demand, so we can calculate the absolute percentage error (APE) with the general formula Then we average these values of the APE for any curve to get its MAPE. We will consider the curve with the smallest MAPE as the best fit overall. Example calculations appear in Example 2.5.

Decisions involving the time value of money In many business situations, cash flows are received at different points in time, and a company must determine a course of action that maximizes the “value” of cash flows. Here are some examples: Should a company buy a more expensive machine that lasts for 10 years or a less expensive machine that lasts for 5 years? What level of plant capacity is best for the next 20 years? A company must market one of several midsize cars. Which car should it market?

Decisions involving the time value of money continued To make decisions when cash flows are received at different points in time, the key concept is that the later a dollar is received, the less valuable the dollar is. The value of the dollar at some time in the future is given by the equation: $1.00 x 1/(1+r) now = $1.00 a year from now The value 1/(1+r) is called the discount factor, and it is always less than 1.

Decisions involving the time value of money continued In general, if money can be invested at annual rate r compounded each year, then $1 received t years from now has the same value as 1(1+r)t dollars received today. If you multiply a cash flow received t years from now by 1(1+r)t to obtain its present value, then the total of these present values over all years is called the net present value (NPV) of the cash flows. The rate r (usually called the discount rate) used by major corporations generally comes from some version of the capital asset pricing model. Example 2.6 demonstrates this concept.

Conclusion The examples in this chapter provide a glimpse of things to come in later chapters. You have seen the spreadsheet modeling approach to realistic business problems, learned how to design spreadsheet models for readability, and explored some of Excel’s powerful tools, particularly data tables. In addition, at least three important themes have emerged from these examples: relating inputs and decision variables to outputs by means of appropriate formulas, optimization (for example, finding a “best” order quantity), and the role of uncertainty(uncertain response rate or demand).

Summary of key management science terms

Summary of key Excel terms

Summary of key Excel terms continued

End of Chapter 2