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 Average earnings yield vs. current earnings yield method  11.3 Discounting cash-flow method  11.4 Weighted average cost of capital  11.5 The CAPM method  11.6 M&M’s cross-sectional method  11.7 Chase cost of capital  11.8 Summary and conclusion remarks  Appendix 11A. Derivative of the basic equilibrium market price of stock and its implications  Appendix 11B. Cummins and Lee’s composite cost of capital estimation model

11.2 Average earnings yield vs. current earnings yield method (11.1) (11.2) (11.3)

11.3Discounting cash-flow method (11.4) (11.5)

11.3Discounting cash-flow method

log EPS t = T, (0.026) (0.004) log DPS t = T (0.145) (0.020)*

11.3Discounting 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

11.4Weighted average cost of capital  Theoretical justification of the WACC

11.4Weighted average cost of capital (11.6) (11.6′)

11.4Weighted average cost of capital (11.7)

11.4Weighted 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.

11.4Weighted average cost of capital (11.6′′′)

11.4Weighted 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.

11.4Weighted 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( ) =

11.4Weighted average cost of capital (11.10)

11.4Weighted 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%

11.4Weighted average cost of capital (11.11) (11.11a) (11.12)

11.4Weighted average cost of capital (11.13) (11.14) (11.15)

11.4Weighted average cost of capital (11.15′) (11.16)

11.4Weighted average cost of capital

(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.

11.5The CAPM method Fig Application of the asset-expansion criterion.

11.5The 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.

11.5The 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)

11.6M&M’s cross-sectional method  The cost of capital  Regression formulation and empirical results

11.6M&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.

11.6M&M’s cross-sectional method V = S + D + P, (11.20) where S = Common equity, D = Debt, P = Preferred equity,

11.6 M&M’s cross-sectional method (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.

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

11.6 M&M’s cross-sectional method (11.25) (11.26) (11.27)

11.6 M&M’s cross-sectional method (11.28a) (11.28b) (11.28c)

11.6 M&M’s cross-sectional method (11.29) (11.30) (11.31)

11.6 M&M’s cross-sectional method (11.32) (11.33)

11.6 M&M’s cross-sectional method (11.34) (11.35)

11.6 M&M’s cross-sectional method (11.36)

11.6 M&M’s cross-sectional method (11.37) (11.38) (11.39)

11.6 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

11.6 M&M’s cross-sectional method DirectTwo-Stage

11.7Chase cost of capital (11.40) V = E + D (11.41) (11.42)

11.7Chase cost of capital NOPAT = C(E + D -  c D) (11.43) (11.44) (11.45)

11.7Chase cost of capital (11.46) (11.47) Y = R + ß(P) = 8% (5%) = 12.75%.

11.7Chase 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.)

11.7Chase cost of capital

11.8Summary 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)

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