# Discounted Cash Flow Valuation. Literature Review and Direction for Research Composed by Ngo Manh Duy

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1 Discounted Cash Flow Valuation Literature Review and Direction for Research Composed by Ngo Manh Duy

2 TABLE OF CONTENTS Acronyms DCF Valuation: definition and core theories DCF Valuation: Main Objective and Basic Steps Theories and gaps in each step: Methods Cash Flows Discount Rates Implementation Research objective and research questions Method and research value Reference

4 Definition of DCF valuation & Application Discounted Cash Flow (DCF) valuation is: a method of evaluating an investment opportunity by discounting predicted future cash flows generated by the investment at certain discount rates to find out the present value of the investment in monetary term Application: Mostly used in valuating securities (bonds or shares), companies and business projects. Valuation of bonds using DCF is simple and straightforward while DCF valuation of shares, companies and business projects is quite complex leading several issues for debates exploration.

5 1. DCF Model (Theory of Interest) by Fisher (1930): Two core theories: 1. DCF Model = ( + ) Where: PV 0 : Present value of cash flows (at time t = 0) CF t : Cash flow at time t k i : Discount rate or required rate of return for the period i n : Number of periods generating cash flows

6 2. Value Additivity principle Two core theories: 2. Value Additivity principle The summation of present values of cash flows divided from the same original cash flow will always equal the present value of the original. This principle is first demonstrated in MM Proposition I with tax of Modigliani and Miller (1958) : Where: V t : value of the firm at time t D t : value of debt at time t E t : value of equity at time t V t = D t + E t = Vu t + VTS t (1) Vu t : value of unlevered equity at time t (value of the firm when there is no leverage, i.e. 100% equity) VTS t : value of interest tax shield at time t

7 CCF = ECF + CFd = FCF + CFTS Two core theories: 2. Value Additivity principle V = E + D = Vu + VTS Where: CCF: Capital cash flow (all cash flows available to capital providers ) CFTS: generated from tax deduction on interest expenses) ECF: Equity cash flow (free cash flows to shareholders) CFd: Debt cash flow (cash flows to debtholders) FCF: Free cash flow (cash flows generated from business operation) CFTS: Cash flow from interest tax shield

8 Main objective & basis steps Objective of DCF valuation: Calculate shareholders (or investors ) equity value of the investmen. Basic steps of DCF valuation: 1. Choose a method (METHODS) 2. Calculate cash flows (CASH FLOWS) 3. Calculate discount rates (DISCOUNT RATES) 4. Implement discounting (IMPLEMENTATION)

9 12. RFadj CCF 1. APV 2. CCF Theories and 11. RFadj ECF 10. RFadj FCF 12 methods 3. FCFF 4. FCFE METHODS 9. BRadj CCF 5. EVA 8. BRadj ECF 7. BRadj FCF 6. RI Acronyms

10 METHODS 1 to 6 No. Method Cash flows Discount rate Implementation 1 Adjusted Present FCF, CFd, Ku, Kd Vu: discount FCF at Ku Value (APV) CFTS VTS: discount CFTS (at Ku or Kd or both depending the chosen theory) V = Vu + VTS D: discount CFd at Kd E = V D 2 Capital Cash Flow (CCF) 3 Free Cash Flow to Firm (FCFF) 4 Free Cash Flow to Equity (FCFE) CCF, CFd Kbt, Kd V: discount CCF at Kbt D: discount CFd at Kd E = V D FCF, CFd K, Kd V: discount FCF at K D: discount CFd at Kd E = V D ECF Ke E: discount ECF at Ke 5 Economic Value Added (EVA) EVA, CFd K, Kd V[EVA]: discount EVA at K V = Vbv + V[EVA] D: discount CFd at Kd E = V D Acronyms 6 Residual Income (RI) RI Ke V[RI]: discount RI at Ke E = Ebv + V[RI]

12 METHODS 10 to 12 No. Method Cash flows Discount rate Implementation 7 Risk free-adjusted FCF/Rf, CFd K, Rf, Kd FCF//Rf: obtained by adjusting FCF using K and Rf so Free Cash Flow (RFadj FCF) that discounting FCF//Rf at Rf will return V. V: discount FCF//Rf at Rf 8 Risk free-adjusted Equity Cash Flow (RF-adj ECF) 9 Risk free-adjusted Capital Cash Flow (RF-adj CCF) D: discount CFd at Kd E = V D ECF/Rf Ke, Rf ECF//Rf: obtained by adjusting ECF with Ke and Rf so that discounting ECF//Rf at Rf will return E. E: discount ECF//Rf at Rf CCF/Rf, CFd Kbt, Rf, Kd CCF//Rf: obtained by adjusting CCF using Kbt and Rf so that discounting CCF//Rf at Rf will return V. V: discount CCF//Rf at Rf D: discount CFd at Kd E = V D Acronyms

13 METHODS Summary APV and CCF were created by Myers (1974) and Arditti and Levy (1977) respectively why the rest were found by practitioners. The most popular method is FCFF which is sometimes referred as the textbook approach or the WACC approach. In the first 4 methods (APV, CCF, FCFF and FCFE), cash flows can be calculated independently of discount rates. The last 8 methods requires that discount rates and cash flows must be calculated at the same time. As long as Value Additivity principle is satisfied, there are no gaps in this literature regarding methods because all methods follow the same core theories and share the same inputs. Hence, if inconsistent results across methods in practice, it suggests that there are gaps in the last 3 steps.

14 13. RFadj CCF 1. FCF 2. CFTS Theories and CASH FLOWS 11. RFadj FCF 12. RFadj ECF 10. BRadj CCF 13 Cash Flows 3. CCF 4. CFd 5. ECF 9. BRadj ECF 6. EVA 8. BRadj FCF 7. RI

15 1. FCF t = EBIT t (1 T t ) Vbv t 2. CFTS t = T t I t = T t r t Dbv t-1 3. CCF t = FCF t + CFTS t = EBIT t (1 T t ) Vbv t + T t I t Theories and CASH FLOWS Formulas 4. CFd t = I t Dbv t 5. ECF t = CCF t CFd t = EBIT t (1 T t ) Vbv t (1 T t )I t + Dbv t 6. EVA t = EBIT t (1 T t ) K t Vbv t-1 7. RI t = EBIT t (1 T t ) (1 T t )I t Ke t Ebv t-1 8. FCF//Ku t = FCF t + V t-1 (Ku t K t ) 9. CCF//Ku t = CCF t + V t-1 (Ku t Kbt t ) 10. ECF//Ku t = ECF t + E t-1 (Ku t Ke t ) 11. FCF//Rf t = FCF t + V t-1 (Rf t K t ) 12. CCF//Rf t = CCF t + V t-1 (Rf t Kbt t ) 13. ECF//Rf t = ECF t + E t-1 (Rf t Ke t )

16 CASH FLOWS 3 approaches (assumptions) There are 3 different approaches which will lead to different cash flow results: 1. Constant debt and no growth (Modigliani and Miller 1958) 2. Constant debt ratio and perpetual growth (all other researchers including big names such as Hamada (1972), Myers (1974), Miles and Ezzell (1980), Fernández (2004), Damodaran (2008)) 3. Pro-forma financial statements (practitioners)

17 CASH FLOWS 3 approaches (assumptions) The first approach (constant debt, no growth) was too unrealistic to be applied in practice The second approach (constant debt ratio, perpetual growth): allows having discount rate unchanged but only takes advantage of the first year forecasted financial statements and forces all financial statements to grow at the same rate. Hence, it s still very unrealistic since it almost never happens in real business. The last approach (Pro-forma financial statement): Applies constant debt ratio and perpetual growth in stable period Uses budgeted financial statements and releases all assumptions in dynamic period.

18 CASH FLOWS Summary The third approach (used by practitioners) filled the gaps in the first 2 approaches. However, inconsistent results still occur due to: 1. Incorrect cash flow formulas 2. Incorrect discount rate formulas (tackled in DISCOUNT RATE step) 3. Improper implementation (tackled in IMPLEMENTATION step) The gap of this literature regarding cash flow is to reformulate cash flow formulas so that they are general enough to address almost all scenarios happening due to the dynamics of financial statement in the third approach.

19 1. Rf Theories and DISCOUNT RATES 6. Ke 5. Kbt 6 DISCOUNT RATES 2. Kd 3. Ku 4. K

20 DISCOUNT RATES Rf, Kd, Ku Beta approach: CAPM module of Sharpe (1964) Ku = Rf + BetaU MRP Top-down methods: (1) Regress market returns and stock return to obtain historical equity beta; (2) Unlever historical beta to acquire unlevered equity beta (BetaU) Bottom-up method: (1) Break down firm s overall operation to specific operations; (2) Find comparable BetaU for each operation; (3) Calculate weighted average BetaU of the firm Fama and French approach: Multi-factor model of Fama and French (1993) Acronyms

21 DISCOUNT RATES K, Kbt, Ke These discount rates must be calculated internally using the previous three discount rates and cash flow information. Those discount rate formulas are affected by: 1. Assumption of capital structure 2. Theory on which discount rate is chosen to discount cash flow of tax shield Acronyms

22 Theory Author Modigliani and Miller (1958) Fixed debt No growth Fixed ratio Constant growth debt Discount CFTS at Kd In 1 st In all period period Discount CFTS at Ku From 2 nd In all period period DISCOUNT RATES K, Kbt, Ke Luehrman (1997) Myers (1974) Harris and Pringle (1985) Kaplan and Ruback (1995) Miles and Ezzell (1985) Lewellen Emery (1986) and

23 DISCOUNT RATES K, Kbt, Ke Summary of theories Capital Structure assumption: As stated in CASH FLOW section, dynamic capital structure is the proper assumption for dynamic period while fixed capital structure is suitable for stable period. Theory on discount rate of CFTS: Discount CFTS at Kd (MM 1958): CFTS is one part of cash flow received by debtholders, hence, it should be discounted at cost of debt Kd. Discount CFTS at Ku (Myers 1974): Fixed debt ratio assumption leads to proportional adjustment of debt to firm value, hence, CFTS which arises from debt should have the same risk as the firm Ku. Discount CFTS at Kd in period 1 and at Ku from period 2 onward (Miles and Ezzell 1985): obtained through mathematic approach under fixed debt assumption. Author s view: MM s theory is straightforward and independent of capital structure. Theories of Myers and Miles and Ezzell s will lose their veracity when fixed debt ratio assumption is released.

24 DISCOUNT RATES Ke and K Formulas and gaps Cost of equity formula calculated through Ku and Kd Ke = Ku + (Ku Kd ) by MM (1958) Use fixed debt assumption under MM s theory Gap: Reformulate Ke under dynamic debt level and dynamic growth in all 3 theories. Weighted Average Cost of Capital formula calculated through Ke and Kd (must be used with a correct Ke formula) K = Ke E + 1 T Kd D E + D Popular textbook formula with no mathematic proof The gap was filled by Fernández (2003) with the following formula: K = Ke E + Kd D T r Dbv E + D

25 DISCOUNT RATES K Formulas and gaps Weighted Average Cost of Capital formula calculated through Ku and Kd (can be used alone) Ku (E +D D T ) + Kd D T T r Dbv K = E + D Found by Fernández (2003, 2004) but was proven incorrect by Fieten, Kruschwitz et al. (2005) and Cooper and Nyborg (2006) Gap: Find correct K formula calculated through Ku and Kd in all 3 theories of CFTS discount rate.

26 DISCOUNT RATES Kbt Formulas and gaps Before-tax Weighted Average Cost of Capital formula calculated through Ke and Kd (must be used with a correct Ke formula) Kbt = Ke E E + Kd D + D Found by Arditti and Levy (1977) with no mathematic proof but correct reasoning. Before-tax Weighted Average Cost of Capital formula calculated through Ku and Kd (can be used alone) Kbt = Ku with BetaU = BetaD + BetaE Proved by Ruback (2002) through beta formula under Myers theory Gap: Find correct Kbt formula calculated through Ku and Kd in MM s theory and Miles and Ezzell s theory.

27 IMPLEMENTA TION Inconsistent results across DCF methods were experienced in common practice along with violation of Value Additivity principle. Apart from reasons due existing gaps in step 2 and step 3 which were discussed before, improper implementation is one of the key reasons. In fact, considering all methods share the same input (evaluating the same asset) and the same core theories, the method should arrive at the same result.

28 IMPLEMENTA TION Researcher Findings Limitations Taggart Jr (1989) A consistent result in 3 methods: Fixed leverage APV, FCFF, FCFE Fixed discount rates Ku, Kd Shrieves and Wachowicz Jr (2001) Fernández (2003) A consistent result in 3 methods: FCFF, EVA, CCF A consistent result in 10 methods: APV, FCFF, FCFE, BR-adj FCF, BRadj ECF, RF-adj FCF, RF-adj ECF, CCF, EVA, RI Use textbook formula K No complex example testing Only try to prove the consistency of methods No discount rate formulas shown No testing Perpetual growth Proven errors in formula Use constant growth assumption in example Attempts and their limitation Oded and Michel (2007) A consistent result in 4 methods: APV, CCF, FCFE, FCFF Fixed leverage and rebalancing assumptions Constant growth Constant discount rates No complex example testing Massari, Roncaglio, and Zanetti (2008) Inconsistent results between APV and FCFF under perpetual growth assumptions Fixed leverage Perpetual growth Use textbook formula K

29 IMPLEMENTA TION Summary Fernández (2003) was able to filled most of the gaps in this literature by showing consistent results in 10 methods with Backward iteration method which was also applied by Miles and Ezzell (1985) However, he used incorrect formula, perpetual growth assumption and applied only his incorrectly-proven theory. Gap: Use correct cash flow formulas and discount rate formulas to demonstrate consistent results in 12 methods in 3 theories with dynamic debt and growth assumptions.

30 Research objectives Research questions Research objectives Under dynamic assumption of capital structure and growth: 1. Find generalised formulas for cash flows 2. Find generalized formulas for Ke, K and Kbt calculated through Ku and Kd under all 3 theories 3. Demonstrate consistent results in 12 methods under all 3 theories Research questions Under dynamic assumption of capital structure and growth: 1. What are the generalized formulas for cash flows? 2. What are the generalized formulas for Ke, K and Kbt calculated through Ku and Kd under all 3 theories? 3. How can one demonstrate consistent results in 12 methods under all 3 theories?

31 Method and Research value Method: Qualitative method with mathematic approach. Research value: Academic: Enhance the current literature of DCF valuation with more logical understanding, more general formulas and more suitable implementation. Practice: Allowing practitioners (investors, analyst, consultants etc) to make better investment decisions through making the popular DCF valuation much more reliable, logical and understandable/

32 References Arditti, F. D., & Levy, H. (1977). The weighted average cost of capital as a cutoff rate: a critical analysis of the classical textbook weighted average. Financial management, Cooper, I. A., & Nyborg, K. G. (2006). The value of tax shields IS equal to the present value of tax shields. Journal of Financial Economics, 81(1), Damodaran, A. (2008). Damodaran on valuation: John Wiley & Sons. Fama, E. F., & French, K. R. (1993). Common risk factors in the returns on stocks and bonds. Journal of Financial Economics, 33(1), Fernández, P. (2003). Equivalence of ten different methods for valuing companies by cash flow discounting. Paper presented at the EFMA 2004 Basel Meetings Paper. Fernández, P. (2004). The value of tax shields is NOT equal to the present value of tax shields. Journal of Financial Economics, 73(1), Fieten, P., Kruschwitz, L., Laitenberger, J., Löffler, A., Tham, J., Vélez-Pareja, I., & Wonder, N. (2005). Comment on The value of tax shields is NOT equal to the present value of tax shields. The Quarterly Review of Economics and Finance, 45(1), Fisher, I. (1930). The Theory of Interest New York: Macmillan. Gordon, M. J. (1962). The investment, financing, and valuation of the corporation: RD Irwin. Hamada, R. S. (1972). The effect of the firm's capital structure on the systematic risk of common stocks. The Journal of Finance, 27(2), Harris, R. S., & Pringle, J. J. (1985). Risk adjusted discount rates extensions from the average risk case. Journal of Financial Research, 8(3), Kaplan, S. N., & Ruback, R. S. (1995). The valuation of cash flow forecasts: An empirical analysis. The Journal of Finance, 50(4), Lewellen, W. G., & Emery, D. R. (1986). Corporate debt management and the value of the firm. Journal of Financial and Quantitative Analysis, 21(04), Luehrman, T. (1997). Using APV (adjusted present value): a better tool for valuing operations. Harvard business review, 75(3), 145. Massari, M., Roncaglio, F., & Zanetti, L. (2008). On the equivalence between the APV and the WACC approach in a growing leveraged firm. European financial management, 14(1), Miles, J. A., & Ezzell, J. R. (1985). Reformulating tax shield valuation: a note. The Journal of Finance, 40(5), Modigliani, F., & Miller, M. H. (1958). The cost of capital, corporation finance and the theory of investment. The American economic review, Myers, S. C. (1974). Interactions of corporate financing and investment decisions implications for capital budgeting. The Journal of Finance, 29(1), Oded, J., & Michel, A. (2007). Reconciling DCF valuation methodologies. Journal of Applied Finance, 17(2), 21. Ruback, R. S. (2002). Capital cash flows: a simple approach to valuing risky cash flows. Financial management, Sharpe, W. F. (1964). Capital asset prices: A theory of market equilibrium under conditions of risk*. The Journal of Finance, 19(3),

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