1. 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

2. 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

3. 7.1 Introduction Components of capital structure
Opportunity cost, required rate-of-return, and the cost of capital

4. 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.

5. 7.2 Bond valuation
Perpetuity
Term bonds
Preferred stock

6. 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. 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.

8. 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.

9. 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.

10. 7.3 Common-stock valuation
Inflation and common-stock valuation
Growth opportunity and common-stock valuation

11. 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.

12. 7.3 Common-stock valuation
(7.6b)
(7.6c)

13. 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.

14. 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.

15. 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.

16. 7.3 Common-stock valuation
where

17. 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.

18. 7.3 Common-stock valuation
(7.9b)

19. 7.4 Financial leverage and its effect on EPS
7.4.1 Measurement
7.4.2 Effect

20. 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.

21. 7.4 Financial leverage and its effect on EPS
(7.11)
(7.10a)
(7.12a)

22. 7.4 Financial leverage and its effect on EPS
(7.12b)
(7.10b)
(7.13)

23. 7.4 Financial leverage and its effect on EPS
(7.14)
(7.15a)
(7.15b)

24. 7.4 Financial leverage and its effect on EPS
(7.16)
(7.17)
(7.18a)

25. 7.4 Financial leverage and its effect on EPS
(7.18b)
(7.18c)
(7.18d)

26. 7.4 Financial leverage and its effect on EPS
Figure 7.1

27. 7.4 Financial leverage and its effect on EPS
(7.19)
(7.20)

28. 7.5 Degree of financial leverage and combined effect
(7.21)
(7.22)
(7.23)

29. 7.5 Degree of financial leverage and combined effect

30. 7.6 Optimal capital structure
Overall discussion
Arbitrage process and the proof of M&M Proposition I

31. 7.6.1 Overall Discussion

32. 7.6 Optimal capital structure
(7.24)
(7.25)
(7.26)

33. 7.6 Optimal capital structure
(7.27)
(7.28)
(7.29)

34. 7.6 Optimal capital structure
(7.30)
(7.31)

35. 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%

36. 7.6 Optimal capital structure
(7.32)
(7.33)
(7.34)

37. 7.6 Optimal capital structure
Fig. 7.3 Aggregated supply and demand for corporate bonds (before tax rates). From Miller (1977). Reprinted by permission.

38. 7.6 Optimal capital structure
(7.35)
(7.36)

39. 7.6 Optimal capital structure
(7.37)
(7.38)

40. 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

41. 7.7 Possible Reason for Optimal Capital Structure
(7.39)
(7.40)

42. Possibility of Optimal Debt Ratio when Bankruptcy Allowed

43. Possibility of Optimal Debt Ratio when Bankruptcy Allowed

44. 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.

45. 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.

46. Appendix 7A. Convertible security valuation theory

47. Appendix 7A. Convertible security valuation theory
Where

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

49. Appendix 7A. Convertible security valuation theory

50. Appendix 7A. Convertible security valuation theory

51. Appendix 7A. Convertible security valuation theory

52. Appendix 7A. Convertible security valuation theory

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

54. 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:

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

56. 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:

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

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

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