Quantitative Financial Valuation

The initial step in the valuation process. In order to forecast cash flows, it is important to:

• Precisely define the components of cash flow.
• Develop statistical tools to aid in forecasting cash flows.
• Analyze different types of annuities, which are structured series of cash flows.

We mathematically derive the cash flow statement as the result of creating and manipulating a series of accounting equations and identities. This should give the appraiser a much greater depth of understanding of how cash flows derive from and relate to the balance sheet and income statement. It may help eliminate errors made by appraisers who perform discounted cash flow analysis using shortcut or even incorrect definitions of cash flow.

In Chapter 2, we demonstrate in detail:

• How appraisers can use regression analysis to forecast sales and expenses, the latter by far being the more important use of regression.
• When and why the common practice of not using more than five years of historical data to prevent using stale data may be wrong.
• How to use regression analysis in valuation using publicly traded guideline companies information. While this is not related to forecasting sales and expenses, it fits in with our other discussions about using regression analysis.

When using publicly traded guideline companies of widely varying sizes, ordinary least squares (OLS) regression will usually fail, as statistical error is generally proportional to the market value (size) of the

guideline company. However, there are simple transformations the appraiser can make to the data that will (1) enable him or her to minimize the negative impact of differences in size and (2) still preserve the very

important benefit we derive from the variation in size of the publicly traded guideline companies, as we discuss in the chapter. The final result is valuations that are more reliable, realistic, and objective.

Most electronic spreadsheets provide a least squares regression that is adequate for most appraisal needs. I am familiar with the regression tools in Microsoft Excel.

Historically, ADFs have not been used much in business valuation and thus, have had relatively little importance. Their importance is growing, however, for several reasons. They can be used in:

• Calculating the present value of annuities, including those with constant growth. This application has become far more important since the Mercer Quantitative Marketability Discount Model requires an ADF with growth.
• Valuing periodic expenses such as moving expenses, losses from lawsuits, etc.
• Calculating the present value of periodic capital expenditures with growth, e.g., what is the PV of keeping one airplane of a certain class in service perpetually.
• Calculating loan payments.
• Calculating loan principal amortization.
• Calculating the present value of a loan. This is important in calculating the cash equivalency selling price of a business, as seller financing typically takes place at less-than-market rates. The present value of a loan is also important in ESOP valuations.