Financial Analysis, Planning and Forecasting Theory and Application By Alice C. Lee San Francisco State University John C. Lee J.P. Morgan Chase Cheng F. Lee Rutgers University Chapter 11 Alternative Cost of Capital Analysis and Estimation

Outline  11.1 Introduction  11.2 Overview of Cost of Capital  11.3 Average earnings yield vs. current earnings yield method  11.4 Discounting cash-flow method  11.5 Weighted average cost of capital  11.6 The CAPM method  11.7 M&M’s cross-sectional method  11.8 Chase cost of capital  11.9 Summary and conclusion remarks  Appendix 11A. Derivative of the basic equilibrium market price of stock and its implications

11.3 Average earnings yield vs. current earnings yield method (11.1) (11.2) (11.3) The market value of the firm, V, can be defined as: where is the total expected future earnings and k is the cost of capital, then cost of capital can be estimated from Lintner (1963) derived the rule for the marginal cost-of-capital decision as: where r = the marginal internal rate of return, Y e = Y 0 /P 0 is the current earnings yield,Y 0 is current earnings per share, and P 0 is current price per share..

11.4Discounting cash-flow method (11.4), (11.5) Percentage change method Regression method where X t, X t-1 = earnings in year t, year (t -1), respectively, and is the estimate of the growth rate in period t.

11.4Discounting cash-flow method log EPS t = T, (0.026*) (0.020) log DPS t = T (0.145) (0.020) Where t-statistics are in parentheses and * indicated statistical significance under 5% significant level.

11.4Discounting cash-flow method TABLE 11.1 EPS and DPS of Johnson & Johnson ( ) * Standard errors are in parentheses. YearEPS t DPS t LogEPS t LogDPS t T

11.5Weighted average cost of capital (11.6) (11.6′) (11.7) Cost of debt

11.5Weighted average cost of capital (11.6′′) where M = Price at which the bond is sold in the market: M′ = Issue price of the bond (the price actually received by the issuing company); (M - M′) = Flotation cost; n = Life of the bond; C t = Interest expense per period on one bond. (11.6”’)

11.5Weighted average cost of capital (11.8) where M C = Market price of the convertible bond; C t = Interest payment on the convertible bond in period t; N = Time to conversion; V = Forecast value of the bond on termination.

11.5Weighted average cost of capital P N = P 0 (1 - C f ) (11.9) where P N = Net price of the stock, P 0 = Market price of the new stock, C f = Percentage flotation cost. P N = 22( ) = (11.10) Use P N into (11.5)

11.5Weighted average cost of capital TABLE 11.2 XYZ financing ComponentCalculationCost of Component Debt(no flotation cost)7.5% After tax(1-0.50)(7.5%)3.75% Debt (with flotation cost)7.87% After tax(1-0.50)(7.8%)3.9% Retained earnings10.0% New preferred stock10.125% New equity10.3%

11.5Weighted average cost of capital (11.11) (11.11a) (11.12)

Theoretical Justification of the WACC (11.13), (11.14) (11.15) (11.15’) (11.16)

Theoretical Justification of the WACC

(6.32) where V U = Market value of unlevered firm, = Corporate tax rate, = Capital gains tax rate, = Tax rate on ordinary income, D = Market value of debt.

11.6The CAPM method Fig Application of the asset-expansion criterion.

11.6The CAPM method (11.17) (11.18) where R j, R m, and ß j are defined in Chapter 6, E( )= The risk premium on a portfolio having a zero beta and zero dividend yield, E( ) = Expected rate of return on a hedge portfolio having zero beta and dividend yield of unity, d i = Dividend yield on stock i, and d m = Dividend yield on the market portfolio.

11.6The CAPM method TABLE 11.3 Means and standard deviations for three estimates of the cost of equity for the electric utility industry (standard deviations in parentheses) YearE/PKeKe RjRj (.0077).1033 (.0169).1054 (.0140) (.0077).1119 (.0186).1063 (.0149) (.0088).1340 (.0225).1209 (.0140) (.0092).1451 (.0283).1252 (.0143) (.0090).1576 (.0330).1010 (.0133) (.0091).1657 (.0354).1034 (.0152) (.0088).1891 (.0395).1285 (.0157) (.0119).2381 (.0566).1313 (.0156) (.0146).2009 (.0388).1258 (.0163) (.0166).1905 (.0350).1202 (.0159)

11.7M&M’s cross-sectional method  The cost of capital  Regression formulation and empirical results

11.7M&M’s cross-sectional method (11.19) where V = Sum of the market value of all securities issued by the firm, = Expected level of average annual earnings generated by current assets, = Corporate tax rate, = Cost of unlevered equity capital in a certain designated risk class, D = Market value of a firm’s debt The cost of capital

11.7M&M’s cross-sectional method V = S + D + P, (11.20) Where S = Common equity, D = Debt, P = Preferred equity (11.21) where = Change of market value of a firm, = S n + P + D = New investment in real asset, S 0 = Change in the market value of the shares held by the current owners of the firm, S n = Value of any new common stock issued, P = Value of any new preferred stock issued, D = Value of any new debt issued.

11.7 M&M’s cross-sectional method (11.22) (11.23) (11.24)

11.7 M&M’s cross-sectional method (11.25) (11.26) (11.27) (11.28a) (11.28b), (11.28c) Regression formulation and empirical results

11.7 M&M’s cross-sectional method (11.29), (11.30) (11.31) The integral yields (11.32) (11.33), (11.34), and (11.35)

11.7 M&M’s cross-sectional method (11.36) (11.37), (11.38) (11.39)

11.7 M&M’s cross-sectional method The direct least squares estimates k e with Constantk e without Constant The two-stage estimates k e with Constantk e without Constant DirectTwo-Stage

11.8Chase cost of capital V = E + D (11.40), (11.41) (11.42) NOPAT = C(E + D -  c D) (11.43) (11.44) (11.45)

11.8Chase cost of capital (11.46) (11.47) Y = R + ß(P) = 8% (5%) = 12.75%.

11.8Chase cost of capital (11.48) where = Marginal tax rate over the past five years; b = Interest rate on all debt over the past five years; D/E = Average total debt to total equity over the past five years. (Debt included capitalized leases, and equity includes deferred items and minority interest.)

11.8Chase cost of capital

11.9Summary and conclusion remarks Based upon the valuation models and capital-structure theories presented earlier, six alternative cost-of-capital determination and estimation methods are discussed in detail. These methods are (i) average earnings yield method, (ii) DCF method, (iii) WACC method, (iv) CAPM method, (v) M&M’s cross-section method, and (vi) Chase’s method. The interrelationship among different cost-of-capital estimation methods were explored in some detail. The relative advantages between different estimation methods were also indirectly explored. The six cost-of-capital estimation methods that were discussed in this chapter give managers enough background to choose the appropriate cost-of-capital estimation method for utility- regulation determination, capital-budgeting decisions, and financial planning and forecasting.

Appendix 11A. Derivative of the basic equilibrium market price of stock and its implications y d + d ln P t /d t = k t (11.A.1) where

Appendix 11A. Derivative of the basic equilibrium market price of stock and its implications (11.A.2)

Appendix 11A. Derivative of the basic equilibrium market price of stock and its implications (11.A.4) (11.A.5) (11.A.6)