Financial Analysis, Planning and Forecasting Theory and Application Chapter 7 Valuation and Capital Structure: Theory and application By Cheng F. Lee Rutgers University, USA John Lee Center for PBBEF Research, USA

Outline 7.1 Introduction 7.2 Bond valuation 7.3 Common-stock valuation 7.4 Financial leverage and its effect on EPS 7.5 Degree of financial leverage and combined effect 7.6 Optimal capital structure 7.7 Possible reasons for optimal capital structure 7.8 Summary Appendix 7A. Convertible Security Valuation Theory Appendix 7B. Derivation of DOL, DFL, and CML

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

7.1 Introduction (7.1) 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.

7.2 Bond valuation Perpetuity Term bonds Preferred stock

7.2 Bond valuation (7.2) where n = Number of periods to maturity, CFt = Cash flow (interest and principal) received in period t, kb = Required rate-of-return for bond.

7.2 Bond valuation (7.3) (7.4) where It = Coupon payment, coupon rate X face value, p = Principal amount (face value) of the bond, n = Number of periods to maturity.

7.2 Bond valuation TABLE 7.1 Convertible bond: conversion options Advantages Purchase Price Of Bond Gain 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%. 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.

7.2 Bond valuation (7.5) where dp = Fixed dividend payment, coupon X par on face value of preferred stock; kp = Required rate-of-return on the preferred stock.

7.3 Common-stock valuation Inflation and common-stock valuation Growth opportunity and common-stock valuation

7.3 Common-stock valuation where P0 = Present value, or price, of the common stock per share, dt = Dividend payment, k = Required rate of return for the stock, assumed to be a constant term, Pn = Price of the stock in the period when sold.

7.3 Common-stock valuation (7.6b) (7.6c)

7.3 Common-stock valuation (7.7) where gs = Growth rate of dividends during the super-growth period, n = Number of periods before super-growth declines to normal, gn = Normal growth rate of dividends after the end of the super-growth phase, r = Internal rate-of-return.

7.3 Common-stock valuation where dt = Dividend payment per share in period t, p = Proportion of earnings paid out in dividends (the payout ratio, 0  p  1.0), EPSt = earnings per share in period t.

7.3 Common-stock valuation (7.8) Where Qt = Quantity of product sold in period t, Pt = Price of the product in period t, Vt = Variable costs in period t, F = Depreciation and interest expenses in period t, = Firm tax rate.

7.3 Common-stock valuation where

7.3 Common-stock valuation (7.9) where = Current expected earnings per share, b = Investment (It) as a percentage of total earnings (Xt), r = Internal rate of return V0 and k = Current market value of a firm and the required rate of return, respectively.

7.3 Common-stock valuation (7.9b)

7.4 Financial leverage and its effect on EPS 7.4.1 Measurement 7.4.2 Effect

7.4 Financial leverage and its effect on EPS (7.10) where ke = 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.

7.4 Financial leverage and its effect on EPS (7.11) (7.10a) (7.12a)

7.4 Financial leverage and its effect on EPS (7.12b) (7.10b) (7.13)

7.4 Financial leverage and its effect on EPS (7.14) (7.15a) (7.15b)

7.4 Financial leverage and its effect on EPS (7.16) (7.17) (7.18a)

7.4 Financial leverage and its effect on EPS (7.18b) (7.18c) (7.18d)

7.4 Financial leverage and its effect on EPS Figure 7.1

7.4 Financial leverage and its effect on EPS (7.19) (7.20)

7.5 Degree of financial leverage and combined effect (7.21) (7.22) (7.23)

7.5 Degree of financial leverage and combined effect

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

7.6.1 Overall Discussion

7.6 Optimal capital structure (7.24) (7.25) (7.26)

7.6 Optimal capital structure (7.27) (7.28) (7.29)

7.6 Optimal capital structure (7.30) (7.31)

7.6 Optimal capital structure TABLE 7.3 Valuation of two companies in accordance with Modigliani and Miller’s Proposition 1 Initial Disequilibrium Final Equilibrium Company 1 2 Total Market Value ( ) Debt ( ) Equity ( ) Expected Net Operating Income ( ) Interest ( ) Net Income ( ) Cost of Common Equity ( ) Average Cost of Capital ( ) $500 500 50 10.00% $600 300 21 29 9.67% 8.34% $550 550 9.09% 250 11.6%

7.6 Optimal capital structure (7.32) (7.33) (7.34)

7.6 Optimal capital structure Fig. 7.3 Aggregated supply and demand for corporate bonds (before tax rates). From Miller (1977). Reprinted by permission.

7.6 Optimal capital structure (7.35) (7.36)

7.6 Optimal capital structure (7.37) (7.38)

The traditional Approach of Optimal Capital Structure Bankruptcy Cost 7.7 Possible Reason for Optimal Capital Structure The traditional Approach of Optimal Capital Structure Bankruptcy Cost Agency Cost

7.7 Possible Reason for Optimal Capital Structure (7.39) (7.40)

Possibility of Optimal Debt Ratio when Bankruptcy Allowed

Possibility of Optimal Debt Ratio when Bankruptcy Allowed

7.8 Summary 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.

Appendix 7A. Convertible security valuation theory Where FV = the face value of the bond; I = the periodic coupon payment; k = the investor’s required rate-of-return; and n = the number of periods until the maturity of the issue.

Appendix 7A. Convertible security valuation theory

Appendix 7A. Convertible security valuation theory Where

Appendix 7A. Convertible security valuation theory Therefore: (7.A.5) (7.A.6)

Appendix 7A. Convertible security valuation theory

Appendix 7A. Convertible security valuation theory

Appendix 7A. Convertible security valuation theory

Appendix 7A. Convertible security valuation theory

Appendix 7B. Derivation of DOL, DFL, and CML I. DOL II. DFL III. DCL (degree of combined leverage)

Appendix 7B. Derivation of DOL, DFL, and CML I. DOL Let Sales = P×Q′ EBIT = Q (P – V) – F Q′ = new quantities sold The definition of DOL can be defined as:

Appendix 7B. Derivation of DOL, DFL, and CML I. DOL

Appendix 6B. Derivation of DOL, DFL, and CML II. DFL Let i = interest rate on outstanding debt D = outstanding debt (or iD = interest payment on 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:

Appendix 7B. Derivation of DOL, DFL, and CML II. DFL

Appendix 7B. Derivation of DOL, DFL, and CML II. DFL

Appendix 7B. Derivation of DOL, DFL, and CML III. DCL (degree of combined leverage) = DOL × DFL