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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 6 Valuation and Capital Structure: Theory and application 1

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Outline 6.1Introduction 6.2Bond valuation 6.3Common-stock valuation 6.4Financial leverage and its effect on EPS 6.5Degree of financial leverage and combined effect 6.6Optimal capital structure 6.7Summary and remarks Appendix 6A. Derivation of Dividend Discount Model Appendix 6B. Derivation of DOL, DFL, and CML Appendix 6C. Convertible security valuation theory 2

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6.1Introduction Components of capital structure Opportunity cost, required rate- of-return, and the cost of capital 3

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6.1Introduction (6.1) where = Expected rate of return for asset j, = Return on a risk-free asset, = Market risk premium, or the difference in return on the market as a whole and the return on a risk-free asset, = Beta coefficient for the regression of an individual’s security return on the market return; the volatility of the individual security’s return relative to the market return. 4

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6.2Bond valuation Perpetuity Term bonds Preferred stock 5

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6.2Bond valuation (6.2) where n = Number of periods to maturity, CF t = Cash flow (interest and principal) received in period t, k b = Required rate-of-return for bond. 6

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6.2Bond valuation (6.3) (6.4) where I t = Coupon payment, coupon rate X face value, p = Principal amount (face value) of the bond, n = Number of periods to maturity. 7

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6.2Bond valuation TABLE 6.1 Convertible bond: conversion options Advantages Purchase Price Of BondGain (1)Conversion to stock if price rises above $25. (2)Interest payment if stock price remains less than $25. (3)Interest payment versus stock dividend. $1000 Sell 40 shares at $30, = $1,200, for a return of 12%. $100 per year, for a return of 10% Dividend must rise to $2.50 per share before return on stock = 10%. 8 The results in this table are based on a $1000 face-value bond with 10% coupon rate, convertible to 40 shares of stock at $25 each.

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6.2Bond valuation (6.5) where d p = Fixed dividend payment, coupon X par on face value of preferred stock; k p = Required rate-of-return on the preferred stock. 9

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6.3Common-stock valuation Valuation Inflation and common-stock valuation Growth opportunity and common-stock valuation 10

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6.3Common-stock valuation (6.6a) where P 0 = Present value, or price, of the common stock per share, d t = Dividend payment, k = Required rate of return for the stock, assumed to be a constant term, P n = Price of the stock in the period when sold. 11

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6.3Common-stock valuation (6.6b) (6.6c) 12

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6.3Common-stock valuation (6.7) where g s = Growth rate of dividends during the super-growth period, n = Number of periods before super-growth declines to normal, g n = Normal growth rate of dividends after the end of the super-growth phase, r = Internal rate-of-return. 13

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6.3Common-stock valuation where d t = Dividend payment per share in period t, p = Proportion of earnings paid out in dividends (the payout ratio, 0 p 1.0), EPS t = earnings per share in period t. 14

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6.3Common-stock valuation (6.8) Where Q t = Quantity of product sold in period t, P t = Price of the product in period t, V t = Variable costs in period t, F = Depreciation and interest expenses in period t, = Firm tax rate. 15

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6.3Common-stock valuation (6.8a) where 16 The equation (6.8) is related to operating-income hypothesis which has been discussed in chapter 5 on pages 158-160.

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6.3Common-stock valuation (6.9) where = Current expected earnings per share, b = Investment (I t ) as a percentage of total earnings (X t ), r = Internal rate of return V 0 and k = Current market value of a firm and the required rate of return, respectively. 17

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6.3Common-stock valuation (6.9a) (6.9b) 18

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6.4 Financial leverage and its effect on EPS 6.4.1 Measurement 6.4.2 Effect 19

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6.4 Financial leverage and its effect on EPS (6.10) where k e = Return on equity, r = Return on total assets (return on equity without leverage) i = Interest rate on outstanding debt, D = Outstanding debt, E = Book value of equity. 20

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6.4 Financial leverage and its effect on EPS (6.11) (6.10a) (6.12a) 21

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6.4 Financial leverage and its effect on EPS (6.12b) (6.10b) (6.13) 22

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6.4 Financial leverage and its effect on EPS (6.14) (6.15a) (6.15b) 23

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6.4 Financial leverage and its effect on EPS (6.16) (6.17) (6.18a) 24

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6.4 Financial leverage and its effect on EPS (6.18b) (6.18c) (6.18d) 25

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6.4 Financial leverage and its effect on EPS Figure 6.1 26

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6.4 Financial leverage and its effect on EPS (6.19) (6.20) 27

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6.5 Degree of financial leverage and combined effect (6.21) (6.22) (6.23) 28

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6.5 Degree of financial leverage and combined effect 29

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6.6Optimal capital structure Overall discussion Arbitrage process and the proof of M&M Proposition I 30

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6.6.1 Overall Discussion 31

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6.6Optimal capital structure (6.24) (6.25) (6.26) 32

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6.6Optimal capital structure (6.27) (6.28) (6.29) 33

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6.6Optimal capital structure (6.30) (6.31) 34

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6.6Optimal capital structure TABLE 6.2 Valuation of two companies in accordance with Modigliani and Miller’s Proposition 1 Initial DisequilibriumFinal Equilibrium Company 1 Company 2 Company 1 Company 2 Total Market Value ( ) Debt ( ) Equity ( ) Expected Net Operating Income ( ) Interest ( ) Net Income ( ) Cost of Common Equity ( ) Average Cost of Capital ( ) $500 0 500 50 0 50 10.00% 0 1 10.00% $600 300 50 21 29 9.67% 8.34% $550 0 550 50 0 50 9.09% 0 1 9.09% $550 300 250 50 21 29 11.6% 9.09% 35

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6.6Optimal capital structure (6.32) (6.33) (6.34) 36

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6.6Optimal capital structure Fig. 6.2 Aggregated supply and demand for corporate bonds (before tax rates). From Miller, M., “Debt and Taxes,” The Journal of Finance 29 (1977): 261-275. Reprinted by permission. 37

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6.6Optimal capital structure (6.35) (6.36) 38

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6.6Optimal capital structure (6.37) (6.38) 39

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The traditional Approach of Optimal Capital Structure Bankruptcy Cost Agency Cost 6.6 Possible Reason for Optimal Capital Structure 40

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Possibility of Optimal Debt Ratio when Bankruptcy Allowed 41

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6.7Summary and remarks In this chapter the basic concepts of valuation and capital structure are discussed in detail. First, the bond-valuation procedure is carefully discussed. Secondly, common-stock valuation is discussed in terms of (i) dividend-stream valuation and (ii) investment-opportunity valuation. It is shown that the first approach can be used to determine the value of a firm and estimate the cost of capital. The second method has decomposed the market value of a firm into two components, i.e., perpetual value and the value associated with growth opportunity. The criteria for undertaking the growth opportunity are also developed. An overall view on the optimal capital structure has been discussed in accordance with classical, new classical, and some modern finance theories. Modigliani and Miller’s Proposition I with and without tax has been reviewed in detail. It is argued that Proposition I indicates that a firm should use either no debt or 100 percent debt. In other words, there exists no optimal capital structure for a firm. However, both classical and some of the modern theories demonstrate that there exists an optimal capital structure for a firm. In summary, the results of valuation and optimal capital structure will be useful for financial planning and forecasting. 42

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Appendix 6A. Convertible security valuation theory (6.A.1) where P = Market value of the convertible bond, r = Coupon rate on the bond, F = Face value of the bond, P 0 = Initial market value, k i = Effective rate of interest on the bond at the end of the period m (now), n = Original maturity of the bond, m = Number of periods since the bond was issued, j = Number of periods from the time the bond was issued till the time of conversion, F’= Value of the stock on date of conversion, t = Marginal corporate tax rate. 43

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Appendix 6A. Convertible security valuation theory Fig. 6.A.1 Hypothetical model of a convertible years’ bond. (From Brigham, E. F. “An analysis of convertible debentures: theory and some empirical evidence,” Journal of Finance 21 (1966), p. 37) Reprinted by permission. 44

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Appendix 6A. Convertible security valuation theory (6.A.2) (6.A.2a) (6.A.2b) (6.A.3) 45

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Appendix 6A. Convertible security valuation theory (6.A.4) (6.A.4′) (6.A.5) (6.A.6) 46

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Appendix 6A. Convertible security valuation theory (6.A.6′) (6.A.7) (6.A.8) 47

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Appendix 6A. Convertible security valuation theory (6.A.9) (6.A.10) (6.A.11) 48

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Appendix 6B. Derivation of DOL, DFL, and CML I. DOL II. DFL III. DCL (degree of combined leverage) 49

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Appendix 6B. Derivation of DOL, DFL, and CML Let Sales = P×Q′ EBIT = Q (P – V) – F Q′ = new quantities sold The definition of DOL can be defined as: I. DOL 50

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Appendix 6B. Derivation of DOL, DFL, and CML I. DOL 51

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Appendix 6B. Derivation of DOL, DFL, and CML II. DFL Let i = interest rate on outstanding debt D = outstanding debt N = the total number of shares outstanding τ = corporate tax rate EAIT = [Q(P – V)– F– iD] (1–τ) The definition of DFL can be defined as: (or iD = interest payment on debt ) 52

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Appendix 6B. Derivation of DOL, DFL, and CML II. DFL 53

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Appendix 6B. Derivation of DOL, DFL, and CML II. DFL 54

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Appendix 6B. Derivation of DOL, DFL, and CML III. DCL (degree of combined leverage) = DOL × DFL 55

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Appendix 6C. Derivation of Dividend Discount Model I. Summation of infinite geometric series II. Dividend Discount Model 56

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Appendix 6C. Derivation of Dividend Discount Model S = A + AR + AR 2 + … + AR n −1 (6.C.1) RS = AR + AR 2 + … + AR n −1 + AR n (6.C.2) S − RS = A − AR n 57

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Appendix 6C. Derivation of Dividend Discount Model (6.C.3) S ∞ = A + AR + AR 2 +…+ AR n −1 +…+ AR ∞, (6.C.4) (6.C.5) 58

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Appendix 6C. Derivation of Dividend Discount Model (6.C.6) or (6.C.7) 59

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