128 Microsoft Excel 2010: Data Analysis and Business Modeling With a one-way data table, you can determine how changing one input changes any number of outputs. With a two-way data table, you can determine how changing two inputs changes a single output. This chapter’s three examples will show how easy it is to use a data table and obtain meaningful sensitivity results. Answers to This Chapter’s Questions I’m thinking of starting a store in the local mall to sell gourmet lemonade Before opening the store, I’m curious about how my prot, revenue, and variable costs will depend on the price I charge and the unit cost The work required for this analysis is in the le Lemonade.xlsx. (See Figures 17-1, 17-2, and 17-4.) The input assumptions are given in the range D1:D4. I assume that annual demand for lemonade (see the formula in cell D2) equals 65000–9000*price. (Chapter 79, “Estimating a Demand Curve,” contains a discussion of how to estimate a demand curve.) I’ve created the names in C1:C7 to correspond to cells D1:D7. I computed annual revenue in cell D5 with the formula demand*price. In cell D6, I computed the annual variable cost with the formula unit cost*demand. Finally, in cell D7, I computed prot by using the formula revenue–xed cost–variable cost. FIGURE 17-1 The nputs that change the protab ty of a emonade store. Suppose that I want to know how changes in price (for example, from $1.00 through $4.00 in $0.25 increments) affect annual prot, revenue, and variable cost. Because I’m changing only one input, a one-way data table will solve the problem. The data table is shown in Figure 17-2. Chapter 17 Sensitivity Analysis with Data Tables 129 FIGURE 17-2 One way data tab e w th vary ng pr ces. To set up a one-way data table, begin by listing input values in a column. I listed the prices of interest (ranging from $1.00 through $4.00 in $0.25 increments) in the range C11:C23. Next, I moved over one column and up one row from the list of input values, and there I listed the formulas I want the data table to calculate. I entered the formula for prot in cell D10, the formula for revenue in cell E10, and the formula for variable cost in cell F10. Now select the table range (C10:F23). The table range begins one row above the rst input; its last row is the row containing the last input value. The rst column in the table range is the column containing the inputs; its last column is the last column containing an output. After selecting the table range, display the Data tab on the ribbon. In the Data Tools group, click What-If Analysis, and then click Data Table. Now ll in the Data Table dialog box as shown in Figure 17-3. FIGURE 17-3 Creat ng a data tab e. For the column input cell, you use the cell in which you want the listed inputs—that is, the values listed in the rst column of the data table range—to be assigned. Because the listed inputs are prices, I chose D1 as the column input cell. After you click OK, Excel creates the one-way data table shown in Figure 17-4. 130 Microsoft Excel 2010: Data Analysis and Business Modeling FIGURE 17-4 One way data tab e w th vary ng pr ces. In the range D11:F11, prot, revenue, and variable cost are computed for a price of $1.00. In cells D12:F12, prot, revenue, and variable cost are computed for a price of $1.25, and on through the range of prices. The prot-maximizing price among all listed prices is $3.75. A price of $3.75 would produce an annual prot of $58,125.00, annual revenue of $117,187.50, and an annual variable cost of $14,062.50. Suppose I want to determine how annual prot varies as price varies from $1.50 through $5.00 (in $0.25 increments) and unit cost varies from $0.30 through $0.60 (in $0.05 incre- ments). Because here I’m changing two inputs, I need a two-way data table. (See Figure 17-5.) I list the values for one input down the rst column of the table range (I’m using the range H11:H25 for the price values) and the values for the other input in the rst row of the table range. (In this example, the range I10:O10 holds the list of unit cost values.) A two-way data table can have only one output cell, and the formula for the output must be placed in the upper-left corner of the table range. Therefore, I placed the prot formula in cell H10. FIGURE 17-5 A two way data tab e show ng prot as a funct on of pr ce and un t var ab e cost. Chapter 17 Sensitivity Analysis with Data Tables 131 I select the table range (cells H10:O25) and display the Data tab. In the Data Tools group, I click What-If Analysis and then click Data Table. Cell D1 (price) is the column input cell, and cell D3 (unit variable cost) is the row input cell. These settings ensure that the values in the rst column of the table range are used as prices, and the values in the rst row of the table range are used as unit variable costs. After clicking OK, we see the two-way data table shown in Figure 17-5. As an example, in cell K19, when we charge $3.50 and the unit variable cost is $0.40, the annual prot equals $58,850.00. For each unit cost, I’ve highlighted the prot- maximizing price. Note that as the unit cost increases, the prot-maximizing price increases as some of the cost increase is passed on to customers. Of course, I can only guarantee that the prot-maximizing price in the data table is within $0.25 of the actual prot-maximizing price. When you learn about the Excel Solver in Chapter 79, you’ll learn how to determine (to the penny) the exact prot-maximizing price. Here are some other notes on this problem: ■ As you change input values in a worksheet, the values calculated by a data table change, too. For example, if you increased xed cost by $10,000, all prot numbers in the data table would be reduced by $10,000. ■ You can’t delete or edit a portion of a data table. If you want to save the values in a data table, select the table range, copy the values, and then right-click and select Paste Special. Then choose Values from the Paste Special menu. If you take this step, how- ever, changes to your worksheet inputs no longer cause the data table calculations to update. ■ When setting up a two-way data table, be careful not to mix up your row and column input cells. A mix-up will cause nonsensical results. ■ Most people set their worksheet calculation mode to Automatic. With this setting, any change in your worksheet will cause all your data tables to be recalculated. Usually, you want this, but if your data tables are large, automatic recalculation can be in- credibly slow. If the constant recalculation of data tables is slowing your work down, click the File tab on the ribbon, click Options, and then click the Formulas tab. Then select Automatic Except For Data Tables. When Automatic Except For Data Tables is selected, all your data tables recalculate only when you press the F9 (recalculation) key. Alternatively, you can click the Calculation Options button (in the Calculation group on the Formulas tab) and then click Automatic Except For Data Tables. I am going to build a new house The amount of money I need to borrow (with a 15-year repayment period) depends on the price for which I sell my current house I’m also unsure about the annual interest rate I’ll receive when I close Can I determine how my monthly payments will depend on the amount borrowed and the annual interest rate? The real power of data tables becomes evident when you combine a data table with one of the Excel functions. In this example, we’ll use a two-way data table to vary two inputs (the amount borrowed and the annual interest rate) to the Excel PMT function and determine 132 Microsoft Excel 2010: Data Analysis and Business Modeling how the monthly payment varies as these inputs change. (The PMT function is discussed in detail in Chapter 10, “More Excel Financial Functions.”) Our work for this example is in the le Mortgagedt.xlst, shown in Figure 17-6. Suppose you’re borrowing money on a 15-year mortgage, where monthly payments are made at the end of each month. I’ve input the amount borrowed in cell D2, the number of months in the mortgage (180) in D3, and annual interest rate in D4. I’ve associated the range names in cells C2:C4 with the cells D2:D4. Based on these inputs, I compute the monthly pay- ment in D5 with the formula -PMT(Annual int rate/12,Number of Months,Amt Borrowed). FIGURE 17-6 You can use a data tab e to determ ne how mortgage payments vary as the amount borrowed and the nterest rate change. You think that the amount borrowed will range (depending on the price for which you sell your current house) between $300,000 and $650,000 and that your annual interest rate will range between 5 percent and 8 percent. In preparation for creating a data table, I entered the amounts borrowed in the range C8:C15 and possible interest rate values in the range D7:J7. Cell C7 contains the output you want to recalculate for various input combinations. Therefore, I set cell C7 equal to cell D5. Next I select the table range (C7:J15), click What-If Analysis on the Data tab, and then click Data Table. Because numbers in the rst column of the table range are amounts borrowed, the column input cell is D2. Numbers in the rst row of the table are annual interest rates, so our row input cell is D4. After you click OK, you see the data table shown in Figure 17-6. This table shows, for example, that if you borrow $400,000 at an annual rate of 6 percent, your monthly payments would be just over $3,375. The data table also shows that at a low interest rate (for example, 5 percent), an increase of $50,000 in the amount borrowed raises the monthly payment by around $395, whereas at a high interest rate (such as 8 percent), an increase of $50,000 in the amount borrowed raises the monthly payment by about $478. A major Internet company is thinking of purchasing another online retailer The retailer’s current annual revenues are $100 million, with expenses of $150 million Current projections indicate that the retailer’s revenues are growing at 25 percent per year and its expenses are growing at 5 percent per year We know projections might be in error, however, and we would like to know, for a variety of assumptions about annual revenue and expense growth, the number of years before the retailer will show a prot Chapter 17 Sensitivity Analysis with Data Tables 133 We want to determine the number of years needed to break even, using annual growth rates in revenue from 10 percent through 50 percent and annual expense growth rates from 2 percent through 20 percent. Let’s also assume that if the rm cannot break even in 13 years, we’ll say “cannot break even.” Our work is in the le Bezos.xlsx, shown in Figures 17-7 and 17-8. I chose to hide columns A and B and rows 16–18. To hide columns A and B, rst select any cells in columns A and B (or select the column headings), and then display the Home tab. In the Cells group, click Format, point to Hide & Unhide, and select Hide Columns. To hide rows 16–18, select any cells in those rows (or select the row headings) and repeat the previous procedure, selecting Hide Rows. Of course, the Format Visibility options also include Unhide Rows and Unhide Columns. If you receive a worksheet with many hidden rows and columns and want to quickly unhide all of them, you can select the entire worksheet by clicking the Select All button at the intersection of the column and row headings. Now selecting Unhide Rows and/or Unhide Columns will unhide all hidden rows and/or columns in the worksheet. In row 11, I project the rm’s revenue out 13 years (based on the annual revenue growth rate assumed in E7) by copying from F11 to G11:R11 the formula E11*(1+$E$7). In row 12, I project the rm’s expenses out 13 years (based on the annual expense growth rate assumed in E8) by copying from F12 to G12:R12 the formula E12*(1+$E$8). (See Figure 17-7.) FIGURE 17-7 You can use a data tab e to ca cu ate how many years t w take to break even. We would like to use a two-way data table to determine how varying the growth rates for revenues and expenses affects the years needed to break even. We need one cell whose value always tells us the number of years needed to break even. Because we can break even during any of the next 13 years, this might seem like a tall order. I begin by using in row 13 an IF statement for each year to determine whether we break even during the year. The IF statement returns the number of the year if we break even during the year or 0 otherwise. I determine the year we break even in cell E15 by simply adding together all the numbers in row 13. Finally, I can use cell E15 as the output cell for a two-way data table. I copy from cell F13 to G13:R13 the formula IF(AND(E11<E12,F11>F12),F10,0). This formula reects the fact that we break even for the rst time during a year if, and only if, during the previous year, revenues are less than expenses and during the current year, revenues are greater than expenses. If this is the case, the year number is entered in row 13; otherwise, 0 is entered. 134 Microsoft Excel 2010: Data Analysis and Business Modeling Now, in cell E15 I can determine the breakeven year (if any) with the formula IF(SUM(F13:R13)>0,SUM(F13:R13),”No BE”). If we do not break even during the next 13 years, the formula enters the text string “No BE”. I now enter the annual revenue growth rates (10 percent through 50 percent) in the range E21:E61. I enter annual expense growth rates (2 percent to 20 percent) in the range F20:X20. I ensure that the year-of-breakeven formula is copied to cell E20 with the formula E15. Next, I select the table range E20:X61, click What-If Analysis on the Data tab, and then click Data Table. I select cell E7 (revenue growth rate) as the column input cell and cell E8 (expense growth rate) as the row input cell. With these settings, I obtain the two-way data table shown in Figure 17-8. FIGURE 17-8 A two way data tab e. Note, for example, that if expenses grow at 4 percent a year, a 10-percent annual growth in revenue will result in breaking even in eight years, whereas a 50-percent annual growth in revenue will result in breaking even in only two years! Also note that if expenses grow at 12 percent per year and revenues grow at 14 percent per year, we will not break even by the end of 13 years. Problems 1. You’ve been assigned to analyze the protability of Bill Clinton’s autobiography. The following assumptions have been made: ❑ Bill is receiving a one-time royalty payment of $12 million. ❑ The xed cost of producing the hardcover version of the book is $1 million. ❑ The variable cost of producing each hardcover book is $4. ❑ The publisher’s net from book sales per hardcover unit sold is $15. ❑ The publisher expects to sell 1 million hardcover copies. ❑ The xed cost of producing the paperback is $100,000. ❑ The variable cost of producing each paperback book is $1. ❑ The publisher’s net from book sales per paperback unit sold is $4. ❑ Paperback sales will be double hardcover sales. Chapter 17 Sensitivity Analysis with Data Tables 135 Use this information to answer the following questions. ❑ Determine how the publisher’s before-tax prot will vary as hardcover sales vary from 100,000 through 1 million copies. ❑ Determine how the publisher’s before-tax prot varies as hardcover sales vary from 100,000 through 1 million copies and the ratio of paperback to hardcover sales varies from 1 through 2.4. 2. The annual demand for a product equals 500-3p+10a .5 , where p is the price of the product in dollars and a is hundreds of dollars spent on advertising the product. The annual xed cost of selling the product is $10,000, and the unit variable cost of pro- ducing the product is $12. Determine a price (within $10) and amount of advertising (within $100) that maximizes prot. 3. Reconsider our hedging example from Chapter 12, “IF Statements.” For stock prices in six months that range from $20 through $65 and the number of puts purchased varying from 0 through 100 (in increments of 10), determine the percentage return on your portfolio. 4. For our mortgage example, suppose you know the annual interest rate will be 5.5 percent. Create a table that shows for amounts borrowed from $300,000 through $600,000 (in $50,000 increments) the difference in payments between a 15-year, 20-year, and 30-year mortgage. 5. Currently, you sell 40,000 units of a product for $45 each. The unit variable cost of producing the product is $5. You are thinking of cutting the product price by 30 percent. You are sure this will increase sales by an amount from 10 percent through 50 percent. Perform a sensitivity analysis to show how prot will change as a function of the percentage increase in sales. Ignore xed costs. 6. Let’s assume that at the end of each of the next 40 years, you put the same amount in your retirement fund and earn the same interest rate each year. Show how the amount of money you will have at retirement changes as you vary your annual contribution from $5,000 through $25,000 and the rate of interest varies from 3 percent through 15 percent. 7. The payback period for a project is the number of years needed for a project’s future prots to pay back the project’s initial investment. A project requires a $300 million investment at Time 0. The project yields prot for 10 years, and Time 1 cash ow will be between $30 million and $100 million. Annual cash ow growth will be from 5 percent through 25 percent a year. How does the project payback depend on the Year 1 cash ow and cash ow growth rates? 8. A software development company is thinking of translating a software product into Swahili. Currently, 200,000 units of the product are sold per year at a price of $100 each. Unit variable cost is $20. The xed cost of translation is $5 million. Translating the product into Swahili will increase sales during each of the next three years by some 136 Microsoft Excel 2010: Data Analysis and Business Modeling unknown percentage over the current level of 200,000 units. Show how the change in prot resulting from the translation depends on the percentage increase in product sales. You can ignore the time value of money and taxes in your calculations. 9. The le Citydistances.xlsx gives latitude and longitude for several U.S. cities. There is also a formula that determines the distance between two cities by using a given latitude and longitude. Create a table that computes the distance between any pair of cities listed. 10. You have begun saving for your child’s college education. You plan to save $5,000 per year, and want to know for annual rates of return on your investment from 4 percent through 12 percent the amount of money you will have in the college fund after saving for 10–15 years. 11. If you earn interest at percentage rate r per year and compound your interest n times per year, then in y years $1 will grow to (1+(r/n)) ny dollars. Assuming a 10 percent annual interest rate, create a table showing the factor by which $1 will grow in 5–15 years for daily, monthly, quarterly, and semiannual compounding. 12. Assume I have $100 in the bank. Each year, I withdraw x percent (ranging from 4 percent through 10 percent) of my original balance. For annual growth rates of 3 percent through 10 percent per year, determine how many years it will take before I run out of money. Hint: You should use the IFERROR function (discussed in Chapter 12) because if my annual growth rate exceeds the withdrawal rate, I will never run out of money. 13. If you earn interest at an annual rate of x percent per year, then in n years $1 will become (1+x) n dollars. For annual rates of interest from 1 percent through 20 percent, determine the exact time (in years) in which $1 will double. 14. You are borrowing $200,000 and making payments at the end of each month. For an annual interest rate ranging from 5 percent through 10 percent and loan durations of 10, 15, 20, 25, and 30 years, determine the total interest paid on the loan. 15. You are saving for your child’s college fund. You are going to contribute the same amount of money to the fund at the end of each year. Your goal is to end up with $100,000. For annual investment returns ranging from 4 percent through 15 percent and number of years investing varying from 5–15 years, determine your required annual contribution. 16. The le Antitrustdata.xlsx gives the starting and ending years for many court cases. Determine the number of court cases active during each year. 17. You can retire at age 62 and receive $8,000 per year or retire at age 65 and receive $10,000 per year. What is the difference (in today’s dollars) between these two choices as you vary the annual rate at which you discount cash ows between 2 percent and 10 percent and vary age of death between 70 and 84? 137 Chapter 18 The Goal Seek Command Questions answered in this chapter: ■ For a given price, how many glasses of lemonade does a lemonade store need to sell per year to break even? ■ We want to pay off our mortgage in 15 years. The annual interest rate is 6 percent. The bank told us we can afford monthly payments of $2,000. How much can we borrow? ■ I always had trouble with “story problems” in high school algebra. Can Excel make solving story problems easier? The Goal Seek feature in Microsoft Excel 2010 enables you to compute a value for a worksheet input that makes the value of a given formula match the goal you specify. For example, in the lemonade store example in Chapter 17, “Sensitivity Analysis with Data Tables,” suppose you have xed overhead costs, xed per-unit costs, and a xed sales price. Given this information, you can use Goal Seek to calculate the number of glasses of lemonade you need to sell to break even. Essentially, Goal Seek embeds a powerful equation solver in your worksheet. To use Goal Seek, you need to provide Excel with three pieces of information: ■ Set Cell Species that the cell contains the formula that calculates the information you’re seeking. In the lemonade example, the Set Cell would contain the formula for prot. ■ To Value Species the numerical value for the goal that’s calculated in the Set Cell. In the lemonade example, because we want to determine the sales volume that represents the breakeven point, the To Value would be 0. ■ By Changing Cell Species the input cell that Excel changes until the Set Cell calculates the goal dened in the To Value cell. In the lemonade example, the By Changing Cell would contain annual lemonade sales. Answers to This Chapter’s Questions For a given price, how many glasses of lemonade does a lemonade store need to sell per year to break even? The work for this section is in the le Lemonadegs.xlsx, which is shown in Figure 18-1. As in Chapter 17, I’ve assumed an annual xed cost of $45,000.00 and a variable unit cost of $0.45. Let’s assume a price of $3.00. The question is how many glasses of lemonade do I need to sell each year to break even. [...]... worksheet), and Figure 19-2 shows the scenario report (contained in the Scenario Summary worksheet) 1 43 144 Microsoft Excel 2010: Data Analysis and Business Modeling FIGURE 19-1  The data on wh ch the scenar os are based FIGURE 19-2  The scenar o summary report To begin defining the best-case scenario, display the Data tab, and then click Scenario Manager on the What-If Analysis menu in the Data Tools... 138 Microsoft Excel 2010: Data Analysis and Business Modeling FIGURE 18-1  We use th s data to set up the Goa Seek feature to perform a breakeven ana ys s To start, insert any number for demand in cell D2 In the What-If Analysis group on the Data tab, click Goal Seek Now fill in the Goal Seek dialog box as shown in Figure... by each s nger 152 Microsoft Excel 2010: Data Analysis and Business Modeling How many songs were not sung by Eminem? To solve this problem, you need to know that Excel interprets the character combination as “not equal to.” The formula COUNTIF(Singer,”Eminem”), entered in cell C15, tells you that 837 songs in the database were not sung by Eminem, as you can see in Figure 20 -3 I need to enclose... column (column J) You can see that 16 ,33 3 160 Microsoft Excel 2010: Data Analysis and Business Modeling units of lip gloss were sold This is the net sales amount; transactions in which units of lip gloss were returned are counted as negative sales In a similar fashion, in cell B19 the formula SUMIF(Product,”lip gloss”,Dollars) tells you that a net amount of $49, 834 .64 worth of lip gloss was sold This... three columns and begins two columns to the right and one row above the current cell You can calculate the specified number of rows and columns you move from a reference cell by using other Excel functions The syntax of the OFFSET function is OFFSET(reference,rows moved,columns moved,height,width) 1 63 164 Microsoft Excel 2010: Data Analysis and Business Modeling ■ Reference is a cell or range of cells... during the winter, spring, summer, and fall quarters 10 Again using the file Makeup2007.xlsx, how much revenue was made on sales t ­ ransactions involving at least 50 units of makeup? 162 Microsoft Excel 2010: Data Analysis and Business Modeling 11 How many units of lip gloss did Cici sell in 2004? 12 What is the average number of units of foundation sold by Emilee? 13 What is the average dollar size... 146 Microsoft Excel 2010: Data Analysis and Business Modeling FIGURE 19-5  The Scenar o Manager d a og box d sp ays each scenar o you define FIGURE 19-6  Use the Scenar o Summary d a og box to se ect the resu t ce s for the summary report Because the result cells come from more than one range, I separated the ranges B17:F17 and B19 with a comma (I could also have used the Ctrl key to select and enter... the row containing the specified player’s name and then moves over 0 columns Because the reference consists of one cell, o ­ mitting the height and width arguments of the OFFSET function ensures that the range r ­ eturned by this formula is also one cell Thus, I pick up the player’s field goal percentage 166 Microsoft Excel 2010: Data Analysis and Business Modeling I often download software product sales... criteria, this is again a job for COUNTIFS Entering in cell C25 the formula COUNTIFS(Singer,”Madonna”,Minutes,”< 4”,Minutes,”> 3 ) counts all rows in which Madonna sang a song that was from three to four minutes long These are exactly 154 Microsoft Excel 2010: Data Analysis and Business Modeling the rows we want to count It turns out that Madonna sang 70 songs that were from three to four minutes long (My... range is omitted, it is assumed to be the same as range 157 158 Microsoft Excel 2010: Data Analysis and Business Modeling The rules for criteria you can use with the SUMIF function are identical to the rules used for the COUNTIF function For information about the COUNTIF function, see Chapter 20, “The COUNTIF, COUNTIFS, COUNT, COUNTA, and COUNTBLANK Functions.” The AVERAGEIF function has the syntax . two inputs (the amount borrowed and the annual interest rate) to the Excel PMT function and determine 132 Microsoft Excel 2010: Data Analysis and Business Modeling how the monthly payment varies. row 13; otherwise, 0 is entered. 134 Microsoft Excel 2010: Data Analysis and Business Modeling Now, in cell E15 I can determine the breakeven year (if any) with the formula IF(SUM(F 13: R 13) >0,SUM(F 13: R 13) ,”No. 128 Microsoft Excel 2010: Data Analysis and Business Modeling With a one-way data table, you can determine how changing one input changes any number of outputs. With a two-way data table,