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Chapter 5 (Feb 16 and18)


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Chapter 5 (Feb 16 and18)

  1. 1. FIN 4453 Financial Models Spring 2010 Vladimir Gatchev CHAPTER 5: FINANCIAL FORECASTING (THIS LECTURE WILL BE COVERED IN TWO CLASSES) Forecasting is an important activity for a wide variety of business professionals. Nearly all of the decisions made by financial managers are made on the basis of forecasts of one type or another. For example, when we constructed the pro-forma Income Statement in Chapter 2 we had to make a forecast for the sales of the firm. In this chapter we will examine several methods of forecasting. We will also look at simple regression analysis, the backbone of many financial models. I. SIMPLE LINEAR REGRESSION A. The Basic Model Yt = α + β X t + ut % Simple? Linear? What is Yt ? What is X t ? February 16 and 18, 2010 1
  2. 2. What is ut ? Comes from … - Unpredictable effect Part of Y may not be predictable no matter how hard we try. - Measurement errors X and Y are measured with error so even if the actual Y is exactly equal to α + βX the measured Y is not exactly equal to α + βX. - Omitted variables Y = α + βX + δZ but we forget to put Z in the equation. What is α ? What is β ? B. Estimation of the Basic Model by the Method of Ordinary Least Squares The basic idea of a regression is to estimate the α and β parameters from a sample of data. This will give us α and β - the estimates of α and β . ˆ ˆ For any ˆ ˆ α and β we choose, we can calculate each residual (error). ˆ ˆ ( ut = Yt − α + βX t ˆ ) … here is a graphic representation of the Basic Model with four observations of X and Y. February 16 and 18, 2010 2
  3. 3. y y4 u4 ˆ ˆ ˆ y = α + βx u3 y3 y2 u2 u1 y1 x1 x2 x3 x4 x How do we find the line of best fit? ( ) n n 2 Sum of Squared Errors = ∑ u = ∑ Yt − α − βX t ˆ ˆ ˆ t 2 t =1 t =1 We want to find ˆ ˆ α and β so that the sum of squared errors is minimized. Thus the term Ordinary Least Squares (OLS). Solutions: ˆ α = Y − βX ˆ n ˆ ∑(X t − X )(Yt − Y ) Cov ( X , Y ) β= t =1 = Var ( X ) n ∑(X t =1 t − X )2 Y is the average Y and X is the average X. * Note that X cannot be a fixed number. February 16 and 18, 2010 3
  4. 4. C. The Overall Goodness of Fit Total Sum of Squares (TSS) Error Sum of Squares (ESS) Regression Sum of Squares (RSS) It is true that TSS = RSS + ESS. R2 = Interpretation of R2? D. Tests of whether the coefficients are different from 0. Test Statistic: February 16 and 18, 2010 4
  5. 5. II. THE PERCENT OF SALES METHOD OF FORECASTING A. Forecasting the Income Statement We already created a pro-forma Income Statement for Elvis Products International when we covered Chapter 2. Note that the Percent of Sales method, however, assumes that only Costs of Goods Sold and SG&A Expenses are a fixed percent of Sales. The rest of the items stay the same from 2009 to 2010, with the exception of Depreciation Expense. Depreciation Expense is $50,000 new investment / 10 years life. The idea behind the Percent of Sales method is that some items in the Income Statement are related to sales (like Costs of Goods Sold) and some are not strongly related to Sales, (like Depreciation and Interest Payments on Debt). So we do not always predict all items as a percent of Sales. When you re-do the pro-forma Income Statement, just make sure that you copy and paste the formulas for Net Income and other variables that are not numbers but are a function of the remaining variables. Here is the new pro-forma Income Statement. Make sure you compare it to the one presented in our previous lecture notes for Chapter 2. February 16 and 18, 2010 5
  6. 6. B. Forecasting the Balance Sheet We can forecast the balance sheet in exactly the same way as the Income Statement. The idea again is to use Sales and try to forecast the balance sheet items as a percent of Sales. If you remember, the common-size Balance Sheet presents everything as a percent of Total Assets so it is important to note that we cannot use the common-size Balance Sheet. 1. Forecasting Assets Here are the steps for forecasting the Assets of the Balance Sheet - We assume that the amount of cash in 2010 stays the same as in 2009. - Accounts Receivable is assumed to be a given percent of Sales. As a result, we need to calculate the average (Accounts Receivable / Sales) for 2008 and 2009. Then we multiply it by the forecasted Sales for 2010 from our pro- forma Income Statement. - Do the same for Inventory. - Plant and Equipment is assumed to grow by $50,000, while accumulated depreciation for 2010 equals accumulated depreciation for 2009 plus the depreciation expense for 2010 from the pro-forma Income Statement. The rest of the items are formulas. Here are the assets of the firm: February 16 and 18, 2010 6
  7. 7. 2. Forecasting Liabilities For our purposes here, we will distinguish the liabilities in a more convenient way. • Spontaneous sources of financing – these are the sources of financing that arise during the ordinary course in doing business. No firm can do without these financing sources. (e.g., accounts payable) • Discretionary sources of financing – the management of the firm can decide whether to have such liabilities or not. Not all firms need to have discretionary financing. (e.g., bank loans, bonds, stock) Here are the steps for forecasting the Liabilities and Equity of the Balance Sheet - Spontaneous sources of financing are a fixed percent of sales. These include Accounts Payable and Other Current Liabilities. - Discretionary sources are left unchanged (for now). These include Short-term Notes, Long-term Debt, and Common Stock. - Retained earnings for 2010 are equal to Retained Earnings for 2009 plus Net Income from 2010 (forecast) minus Dividends. Dividends for 2010 are assumed to be the same as in 2009. Here are the liabilities of the firm: February 16 and 18, 2010 7
  8. 8. 3. Discretionary Financing Needed (DFN) Note that our forecasted Balance Sheet does not balance. Assets are not equal to Liabilities and Equity. When Assets > Liabilities and Equity When Assets < Liabilities and Equity In this case we have a deficit of $38,120. What should we do with it? III. LINEAR TREND EXTRAPOLATION IN EXCEL First let’s plot Sales over time. Then we can use the TREND( ) function in Excel to predict the Sales for 2010 assuming that there is a trend in Sales. The TREND( ) function: February 16 and 18, 2010 8
  9. 9. IV. REGRESSION IN EXCEL We can use the regression approach discussed earlier, in order to: A. Predict Sales as a Function of Time Sales = α + β*Year February 16 and 18, 2010 9
  10. 10. B. Predict Costs of Goods Sold as a function of Sales. Cost of Goods Sold 4.00 3.50 3.00 2.50 2.00 m G O C S ) ( l i 1.50 1.00 1.00 2.00 3.00 4.00 5.00 Sales (mill) COGS = α + β*Sales February 16 and 18, 2010 10
  11. 11. Appendix: A Linear Regression Example We want to predict the annual expenditure for the maintenance of a given car (Toyota). The explanatory variable is the mileage of the car. 1. Let us first plot the two variables. The dependent variable (cost) goes on the Y-axis and the explanatory variable (mileage) goes on the X-axis. Annual Maintenance Cost $4,000 $3,500 $3,000 $2,500 $2,000 $1,500 $1,000 $500 M A C o u n c e a s t i l $0 - 10,000 20,000 30,000 40,000 50,000 60,000 70,000 80,000 Mileage You can see that maintenance costs increase with the mileage of the car. 2. Now let’s estimate the regression equation: COST = α + β × MILEAGE Regression Statistics Multiple R 92.65% R Square 85.85% Adjusted R Square 85.59% Standard Error 436.97 Observations 57 ANOVA df SS MS F Regression 1 63711096.36 63711096.36 333.67 Residual 55 10501754.90 190941.00 Total 56 74212851.26 Coefficients Standard Error t Stat P-value Intercept -796.07 134.74 -5.91 0.0000% Mileage 0.05 0.00 18.27 0.0000% February 16 and 18, 2010 11
  12. 12. … and on a graph: Milage Line Fit Plot $4,000 $3,500 $3,000 $2,500 $2,000 $1,500 $1,000 $500 M A C o u n c e a s $0 t i l -$500 - 10,000 20,000 30,000 40,000 50,000 60,000 70,000 80,000 -$1,000 Mileage 3. How would you interpret the α and β coefficient estimates? α = -796.07 β = 0.05 … interpretation? EXCEL TIPS To perform regression analysis, you need to install the Data Analysis ToolPak: Go to  Excel Options  Add-Ins and then click on Go under Manage Add Ins. Check the Analysis ToolPak To perform regression analysis: Go to Data and under the Analysis tab click on Data Analysis. Select Regression and click OK. February 16 and 18, 2010 12