Incorporating the Effect of Number of Units on the Unit Cost of Goods Sold on Profits and Leverage

As production and sales volume increase, a product’s unit cost generally decreases. The cost of goods sold may be lowered, for example, by taking advantage of volume discounts for purchasing raw materials and supplies in larger quantities, by training workers to work more efficiently, by better management of inventories, or from other payoffs for operating on a larger scale.

The following example analyzes the effect of scale on values in the income statement and a firm’s operating leverage.

Example 10.2: For purposes of illustration, suppose we start with the conditions shown in Figure 10-9 for the maximum profit for the ABC Company. The unit cost under these conditions is $10.69, which can be determined by dividing the value for COGS in Cell B5 ($1,170,800) by the number of units in Cell B33 (109,517). Call these values the base values. Now suppose that each increase of 1000 units above the base value of 109,517 units reduces the unit cost by $0.25 below the base value of $10.69.

What will be the optimum selling price if the company takes advantage of the reduction in cost by increas- ing the number of goods it produces? How does this affect the value of COGS and other items on the income statement? Assume there is no change in fixed costs.

Solution: Figure 10-14 is a spreadsheet solution. To create this spreadsheet (while saving Figure 10-9), copy Figure 10-9 to a new worksheet. Insert new Rows 37 and 38. Compute the unit costs in Cell B37 by the entry =B5/B33. Compute the operating leverage in Cell B39 by the entry =(B4-B5)/B15. Then copy all entries in Column B to Column C.

As in Figure 10-9, the number of units sold (Cell C33) is determined by the selling price (C32) and is calculated from the values of the parameters in Cells C52:E52 of the LINEST output. (If the parameters of the quadratic equation that relates the number of units sold to the selling price was not entered in Cell B33 as absolute references with $ signs, you will need to correct these entries after copying to Cell C33 so that the value 109,517 appears in Cell C33. This value will change when Column C is edited.)

We are now ready to edit Column C to take into account the reduction in cost due to volume discounts. To evaluate the effect of the number of units sold in Cell C33 on the unit cost, enter $0.25 in Cell C38 and change the entry in Cell C37 to =B37-C38*(C33-B33)/1000. To link the number of units sold and the unit cost to the total cost of goods sold (i.e., to COGS), change the entry in Cell C5 to =C33*C37. To calculate COGS as a percent of sales, change the entry in Cell C34 to =C5/C4.

To find the selling price that maximizes the profit, use Solver with a target of maximizing Cell C6 by changing Cell C32. The result is a selling price of $22.30/unit, which gives a sales volume of 115,534 units (Cell C33), a unit cost of $9.19 (Cell C37).

Note that the number of units has increased by 6,017 units (or approximately 6,000 units) and the unit cost has decreased by $1.50, which is a decrease of $0.25 per 1000 units. This confirms the correctness of our entry in Cell C37.

Also, note that, although the sales revenue (Cell C4) decreases from the base value as a result of decreas- ing the selling price, the cost of goods sold (Cell C5) is less, the number of units sold (C33) is more, and the financial payoffs (C6, C15, C20, C24, C27, and C36) are greater. The operating leverage drops to 1.76 (Cell C39), a reduction of 3.35 percent from the base optimum. All of these are favorable results from reducing the selling price. The break-even point (Cell C35) is slightly greater.

The percentage changes are evaluated in Column D by entering =(C4-B4)/B4 in Cell D4 and copying to the cells below. Note that unit cost is reduced by 14.07 percent (Cell D37) as a result of the increased number of units sold.

(Continued)

338 ❧ Corporate Financial Analysis with Microsoft Excel ®

Figure 10-14

Income Statement with the Addition of the Effect of Number of Units Sold on the Cost of Goods Sold

1 ABC COMPANY

2 Income Statement for the Year Ended December 31, 20X2

Dollar values are in $ thousand except for per share and

3 per unit values.

4 Total Operating Revenues (or Total Sales Revenues)

5 Less: Cost of Goods Sold (COGS)

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

30 Dividends Paid to Holders of Common Stock

31 Information Added to Determine Selling Price for Maximum Profit.

32 Unit Selling Price for Maximum EBIT

33 Number of Units Sold

34 COGS, as Percent of Sales

35 Break-Even Point (EBIT = 0), Units

36 Break-Even Point (EBIT = 0), Sales in $ Thousands

37 Unit Cost

38 Reduction in Unit Cost per 1,000 Units

39 Degree of Operating Leverage

40 Derivation of Quadratic Regression Equation 41 for Forecasting the Number of Units Sold from the Unit Selling Price (SP)

42 Units Sold Error, 43 130,000

Forecast units 44 45 120,000

Average error = 52 70,000

LINEST Output 53 NUMBER OF UNITS SOLD

Y = –99,120 + 22,007X – 555.2X^2

56 UNIT SELLING PRICE

3 #N/A 57

2.51E+09 11583168

#N/A

Profit, Break-Even, and Leverage ❧ 339

Incorporating the Effect of Number of Units on the Unit Cost of Goods Sold on Profits and Leverage