1. 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

2. 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

3. 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..

4. 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

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

6. 12.4 Discounting cash-flow method
TABLE EPS and DPS of Johnson & Johnson ( )
* 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

7. 12.5 Weighted average cost of capital
(12.6)
(12.6′)
(12.7)
Cost of debt

8. 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”’)

9. 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.

10. 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( ) =
Use PN into (12.5)
(12.10)

11. 12.5 Weighted average cost of capital
TABLE 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. 12.5 Weighted average cost of capital
(12.11)
(12.11a)
(12.12)

13. 12.5.1 Theoretical Justification of the WACC
(12.13), (12.14)
(12.15)
(12.15’)
(12.16)

14. 12.5.1 Theoretical Justification of the WACC

15. 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.

16. 12.6 The CAPM method
Fig Application of the asset-expansion criterion.

17. 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.

18. 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)

19. 12.7 M&M’s cross-sectional method
The cost of capital
Regression formulation and empirical results

20. 12.7 M&M’s cross-sectional method
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.

21. 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

22. 12.7 M&M’s cross-sectional method
(12.22)
(12.23)
(12.24)

23. 12.7 M&M’s cross-sectional method
Regression formulation and empirical results
(12.25)
(12.26)
(12.27)
(12.28′)
(12.28′′), (12.28′′′)

24. 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)

25. 12.7 M&M’s cross-sectional method
(12.36)
(12.37), (12.38)
(12.39)

26. 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

27. 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)

28. 12.8 Chase cost of capital
(12.46)
(12.47)
Y = R + ß(P)
= 8% (5%) = 12.75%.

29. 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.)

30. 12.8 Chase cost of capital

31. 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.

32. 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

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

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