“Lather, Rinse, Repeat: How We Discount the Terminal Value” Seth Fliegler, MBA, CVA, CFE

ather, rinse, repeat….lather, rinse Equation 1 Equation 2 repeat. Quite often there are ac- Stage 1 Stage 2 tions that we perform simply be- CF1 CFn(1+g) Lcause we are trained to do so and they PV = CF1 CF2 CFn k - g have been executed repeatedly. Often- c PV = + + ...+ + times, these actions are completed with- (1+k) (1+k)2 (1+k)n (1+k)n out any thought given as to their deriva- PV = Present value PV = Present value tion because the reasoning was learned CF = Free cash flow CF = Free cash flow many years prior, if at all. At a training c = capitalization rate k = Discount rate class I recently attended, one such type n = Number of periods in the discrete projection period of repeated action was brought into the g = Long-term growth rate into perpetuity spotlight: in generating the present val- ue of a terminal value in a discounted cash flow analysis, why does a valuation counted Cash Flow Method1 (Equation the time value of money and the non- analyst discount the terminal value back 2). In the Capitalization Method, a sin- diversifiable risk of the cash flows); and using the last year of the projection pe- gle, anticipated cash flow is converted to 2) the present value of the estimated ter- riod rather than the year after the last present value through the divisor called minal value (the value of operating cash projected year? That is, if the last projec- a capitalization rate. flows expected to be realized subsequent

tion year is “n,” why isn’t the terminal Specifically, the cash flow (CF1) is the to the projection period). Algebraically, year value discounted by “n+1”? The cash flow expected in the period imme- the present value of an entity using a immediate response appeared to be lath- diately following the valuation date. If discounted cash flow model is shown in er, rinse, repeat—in other words, that the valuation date is time “0,” then the Equation 2 above.2 is just how it is done. This article aims cash flow applied in the capitalization The last portion of Equation 2 (Stage

to provide a brief explanation to valua- method is CF1, the cash flow in period 2) reflects the terminal value. A valua- tion analysts as to the reasoning behind 1. Further, these cash flows are expected tion analyst can arrive at the terminal the process of discounting the terminal to reflect stable, long-term growth. The value in a variety of ways, including the value and to provide a fresh reminder of capitalization rate, “c,” is the rate at capitalization of ongoing economic in- why it is we do what we do. which the cash flow in period “1” is dis- come (e.g., a Gordon Growth Model) or counted to the valuation date. an estimated market multiple of the pro- The Income Approach and Under the Discounted Cash Flow jected economic income for the last year Present Value Method, the value of a business is esti- to the projection period. In the equa- The Income Approach to valuation mated as the sum of two components: 1) tion above, a Gordon Growth Model provides for two principal methods of the present value of expected future op- is applied, which essentially inserts the determining value based on future eco- erating cash flows for a finite projection capitalization model described above nomic benefits: 1) the Capitalization period (discounted at a rate that reflects (Equation 1) at the end of the discrete Method (Equation 1), and 2) the Dis- 1 The Excess Earnings Method, which combines the Income 2 For further analysis, see, Shannon P. Pratt, and Alina V. Nic- Approach and the Asset Approach, is another commonly ulita, Valuing a Business: The Analysis and Appraisal of Closely used valuation method applying the Income Approach. Held Companies, McGraw Hill, Fifth Edition, Chapter 10.

Fourth Quarter 2014 I BUSINESS APPRAISAL PRACTICE I 2 1 The Value Of Computer Software: When Does The Intangible Become Tangible

projection period of the discounted cash very beginning of the subsequent pro- nal value and the last discrete projection flow model. This process is sometimes jection period. period (i.e., as of December 31, 2005) referred to as the Two-Stage Model (the To simplify, if the last discrete projec- will be discounted using the same num- first stage being the discrete projection tion period (n) in Equation 2 is assumed ber of periods (i.e., 6 periods) back to the period [Stage 1] and the second being to be the valuation date, then the ter- valuation date, January 1, 2000. the terminal value generated through minal value (Stage 2) simply becomes the capitalization model [Stage 2]). Equation 1: Conclusion Yet it is the use of “n” in the denomi- CF1 The terminal value in a discounted cash Terminal Value = nator of the terminal value in Equation c flow model can be viewed as the capital- 2 that had generated much consternation ization model attached to a discrete pro- and reflects the present value of the fu- (and today is accepted as given). If the ter- jection period. Since the terminal value ture cash flows as of the last period of minal value reflects the cash flow of the reflects future cash flows as of that last the discrete projection period (i.e., n). last year of the projection period times projection period, the terminal value and However, since the valuation date in the growth rate (i.e., CF (1+g)), why the last discrete projection period are dis- n Equation 2 is at some time period prior isn’t this value discounted back by “n+1” counted by the same number of projec- to the last discrete projection period, rather than just “n”? For example, if the tion periods. Valuation analysts can now both the last discrete projection period valuation date is January 1, 2000 and the comfortably project, discount, and repeat and the terminal value are discounted discrete projection period ends Decem- knowing why it is we do what we do. back to the valuation date using the ber 31, 2005, why is the terminal value same number of periods (i.e., n).3 In discounted from December 31, 2005 (n) Seth Fliegler, MBA, CVA, CFE, is a director in the keeping with the example above where and not December 31, 2006 (n+1)? Morristown, New Jersey, office of Duff & the discrete projection period extends to Phelps, LLC. Mr. Fliegler is part of the Dispute The answer lies in the fact that Equa- December 31, 2005, the terminal value is Consulting practice and has more than 15 tion 2 assumes that the terminal value calculated to be the present value of the years of experience assisting clients in business reflects cash flows received just after the valuation and economic and financial future cash flows essentially as of Decem- last discrete projection period. In other analyses particularly within the financial ber 31, 2005. As a result, both the termi- words, the terminal value cash flows are services industry. Mr. Fliegler advises clients on topics related to valuation, solvency, received at the very end of the last pro- commercial and economic damages, and jection period or, said differently, at the 3 For additional resources, see Shannon P. Pratt and Roger fraud investigations. He can be reached at J. Grabowski, Cost of Capital: Applications and Examples, Wiley, Fifth Edition, 48. [email protected].

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22 I BUSINESS APPRAISAL PRACTICE I Fourth Quarter 2014