Financial Analysis, Planning and Forecasting Theory and Application Chapter 12 Alternative Cost of Capital Analysis and Estimation By Cheng F. Lee Rutgers University, USA John Lee Center for PBBEF Research, USA

Outline 12.1 Introduction 12.2 Overview of Cost of Capital 12.3 Average earnings yield vs. current earnings yield method 12.4 Discounting cash-flow method 12.5 Weighted average cost of capital 12.6 The CAPM method 12.7 M&M’s cross-sectional method 12.8 Chase cost of capital 12.9 Summary Appendix 12A. Derivative of the basic equilibrium market price of stock and its implications

12.3 Average earnings yield vs. current earnings yield method (12.1) (12.2) (12.3) 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, Ye = Y0/P0 is the current earnings yield,Y0 is current earnings per share, and P0 is current price per share..

12.4 Discounting cash-flow method (12.4), (12.5) Percentage change method where Xt, Xt-1 = earnings in year t, year (t -1), respectively, and is the estimate of the growth rate in period t. Regression method

12.4 Discounting cash-flow method log EPSt = 0.910 + 0.015T, (0.026*) (0.020) log DPSt = -0.137 + 0.022T (0.145) (0.020) Where t-statistics are in parentheses and * indicated statistical significance under 5% significant level.

12.4 Discounting cash-flow method TABLE 12.1 EPS and DPS of Johnson & Johnson (1995-2006) * Standard errors are in parentheses. Year EPSt DPSt LogEPSt LogDPSt T 1995 3.72 1.28 1.314 0.247 1 1996 2.17 0.74 0.775 -0.308 2 1997 2.47 0.85 0.904 -0.163 3 1998 2.27 0.97 0.820 -0.030 4 1999 3.00 1.09 1.099 0.086 5 2000 3.45 1.24 1.238 0.215 6 2001 1.87 0.70 0.626 -0.357 7 2002 2.20 0.80 0.788 -0.229 8 2003 2.42 0.93 0.884 -0.078 9 2004 2.87 1.10 1.054 0.091 10 2005 3.50 1.253 0.243 11 2006 3.76 1.46 1.324 0.375 12

12.5 Weighted average cost of capital (12.6) (12.6′) (12.7) Cost of debt

12.5 Weighted average cost of capital (12.6′′) 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; Ct = Interest expense per period on one bond. (12.6”’)

12.5 Weighted average cost of capital (12.8) where MC = Market price of the convertible bond; Ct = Interest payment on the convertible bond in period t; N = Time to conversion; V = Forecast value of the bond on termination.

12.5 Weighted average cost of capital PN = P0(1 - Cf) (12.9) where PN = Net price of the stock, P0 = Market price of the new stock, Cf = Percentage flotation cost. PN = 22(1 - 0.05) = 20.90. Use PN into (12.5) (12.10)

12.5 Weighted average cost of capital TABLE 12.2 XYZ financing Component Calculation Cost of Component Debt(no flotation cost) 7.5% After tax (1-0.50)(7.5%) 3.75% Debt (with flotation cost) 7.87% (1-0.50)(7.8%) 3.9% Retained earnings 10.0% New preferred stock 10.125% New equity 10.3%

12.5 Weighted average cost of capital (12.11) (12.11a) (12.12)

12.5.1 Theoretical Justification of the WACC (12.13), (12.14) (12.15) (12.15’) (12.16)

12.5.1 Theoretical Justification of the WACC

12.5.1 Theoretical Justification of the WACC (7.32) where VU = Market value of unlevered firm, = Corporate tax rate, = Capital gains tax rate, = Tax rate on ordinary income, D = Market value of debt.

12.6 The CAPM method Fig. 12.1 Application of the asset-expansion criterion.

12.6 The CAPM method (12.17) (12.18) where Rj, Rm, and ßj 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, di = Dividend yield on stock i, and dm = Dividend yield on the market portfolio.

12.6 The CAPM method Year E/P Ke Rj 1967 .0558 (.0077) .1033 (.0169) .1054 (.0140) 1968 .0589 .1119 (.0186) .1063 (.0149) 1969 .0663 (.0088) .1340 (.0225) .1209 1970 .0713 (.0092) .1451 (.0283) .1252 (.0143) 1971 .0752 (.0090) .1576 (.0330) .1010 (.0133) 1972 .0788 (.0091) .1657 (.0354) .1034 (.0152) 1973 .0880 .1891 (.0395) .1285 (.0157) 1974 .1031 (.0119) .2381 (.0566) .1313 (.0156) 1975 .1115 (.0146) .2009 (.0388) .1258 (.0163) 1976 .1167 (.0166) .1905 (.0350) .1202 (.0159) TABLE 12.3 Means and standard deviations for three estimates of the cost of equity for the electric utility industry (standard deviations in parentheses)

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

12.7 M&M’s cross-sectional method 12.7.1 The cost of capital (12.19) 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.

12.7 M&M’s cross-sectional method (12.21) where = Change of market value of a firm, = Sn + P + D = New investment in real asset, S0 = Change in the market value of the shares held by the current owners of the firm, Sn = Value of any new common stock issued, P = Value of any new preferred stock issued, D = Value of any new debt issued. V = S + D + P, (12.20) Where S = Common equity, D = Debt, P = Preferred equity

12.7 M&M’s cross-sectional method (12.22) (12.23) (12.24)

12.7 M&M’s cross-sectional method 12.7.2 Regression formulation and empirical results (12.25) (12.26) (12.27) (12.28′) (12.28′′), (12.28′′′)

12.7 M&M’s cross-sectional method (12.29), (12.30) (12.31) The integral yields (12.32) (12.33), (12.34) and (12.35)

12.7 M&M’s cross-sectional method (12.36) (12.37), (12.38) (12.39)

12.7 M&M’s cross-sectional method The direct least squares estimates ke with Constant ke without Constant 1957 0.0637 0.0625 1956 0.0641 0.0602 1954 0.0730 0.0521 The two-stage estimates ke with Constant ke without Constant 1957 0.0617 0.0621 1956 0.0641 0.0599 1951 0.0552 0.0508 Direct Two-Stage 1957 0.164 0.004 1956 0.057 0.054 1954 0.274 0.072

12.8 Chase cost of capital V = E + D (12.40), (12.41) (12.42) NOPAT = C(E + D - cD) (12.43) (12.44) (12.45)

12.8 Chase cost of capital (12.46) (12.47) Y = R + ß(P) = 8% + 0.95(5%) = 12.75%.

12.8 Chase cost of capital (12.45′) 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.)

12.8 Chase cost of capital

12.9 Summary 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.

yd + d ln Pt/dt = kt (12.A.1) where Appendix 12A. Derivative of the basic equilibrium market price of stock and its implications yd + d ln Pt/dt = kt (12.A.1) where

Appendix 12A. Derivative of the basic equilibrium market price of stock and its implications

Appendix 12A. Derivative of the basic equilibrium market price of stock and its implications