Selling Price and Income Statement for Maximum Profit In the preceding discussions, we assumed that the number of units ABC can sell is not affected by the

selling price—that is, ABC can sell any number of units at any price it chooses to charge. Actually, in the absence of a monopoly, the number of units a company can sell depends very much on the selling price. The higher the price, the fewer the units that can be sold, and the more customers will buy from competitors who offer similar products at lower prices. Setting a product’s selling price involves inputs from both a firm’s sales and marketing division and either its purchasing department or its operations or production division. The selling price needs to consider the effect of selling price on the number of units that can be sold and their cost to produce or acquire.

To explore the effect of selling price on the maximum profit and values in a company’s income statement, copy Figure 10-8 to a new worksheet. Label the new worksheet Figure 10-9. Let us assume that the firm’s marketing division has done some customer research and, as a result, has concluded that the effect of selling price on the number of units that can be sold is as given in Table 10-1.

Figure 10-9 shows the new worksheet with values from Table 10-1 entered in Cells B41:B46 and D41:D46. We need to use this information to link the number of units sold (Cell B33) to the selling price (Cell B32). We will do this by creating a regression equation that expresses the number of units sold as a function of the selling price. The technique for creating the regression equation is the same as we used to create forecasting models in Chapters 3. However, instead of forecasting annual revenues as a function of the year, our units-sold/price model will forecast the number of units sold as a function of the selling price.

The first step in developing the regression model for forecasting the number of units sold as a function of the selling price is to decide whether to use a linear, quadratic, exponential or other type of model. As in Chapter 3, we can create a scatter diagram of the data and insert different types of trend lines until we get a satisfactory match between the inserted trend line and the data.

At the left of the data in Figure 10-9 is a scatter diagram of the values, with a quadratic (or second- order polynomial) trend line inserted, along with the regression equation and its coefficient of determina- tion. The match looks good.

Table 10-1

Effect of Selling Price on the Number of Units That Can be Sold Unit Selling Price

Number of Units That Can be Sold

330 ❧ Corporate Financial Analysis with Microsoft Excel ® Figure 10-9

Income Statement at Optimum Selling Price

1 ABC COMPANY

2 Income Statement for the Year Ended Dec. 31, 20X2 3 Dollar values are in $ thousand, except for per share and unit selling price.

4 Total Operating Revenues (or Total Sales Revenues)

5 Less: Cost of Goods Sold (COGS)

Maximum Gross Profits 6 Gross Profits

7 Less: Operating Expenses 8 Selling Expenses

9 General and Administrative Expenses (G&A)

10 Depreciation Expense

11 Fixed Expenses

12 Total Operating Expenses

13 Net Operating Income

14 Other Income

15 Earnings before Interest and Taxes (EBIT)

16 Less: Interest Expense 17 Interest on Short-Term Notes

18 Interest on Long-Term Borrowing

19 Total Interest Expense

20 Earnings before Taxes (EBT)

21 Less: Taxes 22 Current

24 Total Taxes (rate = 40%)

25 Earnings after Taxes (EAT)

26 Less: Preferred Stock Dividends

27 Net Earnings Available for Common Stockholders

28 Earnings per Share (EPS), 100,000 shares outstanding

29 Retained Earnings

Optimum selling price 31 Information added to determine selling price for maximum profit

30 Dividends Paid to Holders of Common Stock

32 Unit Selling Price

Entry in Cell B33 is 33 Number of Units Sold

=E50+D50*B32+C50*B32^2. 34 COGS, as percent of Sales

35 Break-Even Point, units

New break-even point (units and $) 36 Break-Even Point, sales in $ thousand

for optimum selling price

37 Derivation of Quadratic Regression Equation 38 for Forecasting the Number of Units Sold from the Unit Selling Price

39 Units Sold Error, 40 130,000

SP, $

SP^2

Data Forecast Units 41

Average error = 48 90,000 49 50 80,000

LINEST Output

51 NUMBER OF UNITS SOLD 70,000 79.77 3,998.2 49,357.0 52

1,965.0 #N/A 53 60,000

3 #N/A 54 $20

2.505E+09 1.16E+07 #N/A 55

56 SELLING PRICE, $/UNIT

Profit, Break-Even, and Leverage ❧ 331 To use Excel’s LINEST command to determine the parameters for the quadratic model, we first

need to add values for the squares of the selling prices in Cells C41:C46. To do this, enter =B41^2 in Cell C41 and copy it to C42:C46. Then use Excel’s LINEST command to evaluate the parameters for the quadratic equation. To do this, drag the mouse to select Cells C50:E54 and type =LINEST(D41:D46, B41:C46,1,1). Press the Control/Shift/Enter keys to enter LINEST. Our “forecasting” model is now expressed by the equation

Y =− , 99 120 2 22 006 80 . + , . X − 555 23 . X 2

where Y = number of units sold, X = selling price (in dollars), and the values of the three coefficients are in Cells E50, D50, and C50.

Validate this model in the same way as any other forecasting models—that is, by showing that the average forecast error is zero and the errors scatter randomly. To forecast units sold, enter =$E$50+$D$50*B41+$C$50*B41^2 in Cell E41 and copy the entry to E42:E46. To calculate errors, enter =D41-E41 in Cell F41 and copy the entry to F42:F46. To calculate the average error, enter =AVERAGE(F41:F46) in Cell F47. By examining the sequence of errors in Cells F41 to F46, you should

be able to recognize that their scatter is random. (If you need a picture to recognize this, prepare a chart with the values in Cells F41:F46 plotted on the Y-axis against those in Cells B41:B46 on the X-axis.) The agreement between forecast values for the units sold and the estimates from the marketing division for the number of units that can be sold at different selling prices appears satisfactory; it is within the errors we might expect for the estimates from the marketing division.

The next step is to link our model to the income statement. To do this, enter a trial value for selling price in Cell B32. The trial value will be changed later, so don’t hesitate to enter a value. (The value 24 would be a good choice, but other values would be satisfactory.) To calculate the number of units that can be sold at the selling price in Cell B32, enter =E50+D50*B32+C50*B32^2 in Cell B33. (Recall that the operating revenues in Cell B4 is the product of the values in Cells B32 and B33.)

We now use Excel’s Solver tool to change the trial value in Cell B32 to the value that will maximize the Gross Profits in Cell B6. Figure 10-10 shows the settings. Executing Solver produces the results shown in Figure 10-9.

The results in Figure 10-9 show that the optimum selling price is $23.94/unit (Cell B32). At this selling price, sales will be an estimated 109,517 units (Cell B33). The combination of this selling price and number of units sold gives total operating revenues of $2,621,600 (Cell B4) and maximum gross profits of $1,450,800 (Cell B6). The break-even point at this selling price is 49,445 units (Cell B35), which is well below the 109,517 we can expect to sell. Figure 10-9 also shows, for example, that at this selling price the EBIT is $795,800 dollars and the earnings per share is $3.46.

Selling Price and Income Statement for Maximum Profit In the preceding discussions, we assumed that the number of units ABC can sell is not affected by the