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LECTURE 3 Cost of Capital
- WACC
- kd, kps, kce
- CAPM
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Enterprise Value of a Corporation
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Types of long-term capital
Long-term debt
Preferred stock
Common equity
WACC = wdkd(1 - T) + wpskps + wcekce
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Terminologies
Rate of Return:
An investor’s return from an investment.
Cost of Capital:
A company’s cost of raising capital.
I. Cost of Debt
Yield to Maturity: the expected rate of return earned on a bond (or a loan) held to maturity. Also called “promised yield.”
What’s the YTM on a 10-year, 9% annual coupon, $1,000 par value bond that sells for $887?
5
10 -887 90 1000
N I/YR PV PMT FV
10.91
V
INT
k
M
k
B
d
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d
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1
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INT
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k
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887
90
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000
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1
10
10
k
k
d
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90
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k
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INPUTS
OUTPUT
...
6
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-60
-60 - 1,000
-60
0
1
2
30
i = ?
30 1153.72 -60 -1000
5.0% x 2 = kd = 10%
N
I/YR
PV
FV
PMT
1,153.72
...
INPUTS
OUTPUT
Cost of Debt
[Corporate bond] A 15-year, 12% semiannual bond sells with price $1,153.72. What’s kd? (tax rate is 40%)
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- Interest is tax deductible, so
kd AT = kd BT(1 - T)
= 10%(1 - 0.40) = 6%.
- Use nominal rate.
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What’s the cost of preferred stock?
Pps = $111.10; 10%Q; Par = $100.
II. Cost of Preferred Stock
-2.5
-2.5
0
1
2
kps = ?
+111.1
...
-2.5
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- Preferred dividends are not tax deductible, so no tax adjustment.
- Use nominal rate.
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Two ways to raise common equity:
- Issue new shares of common stock.
- Reinvest earnings.
Cost difference: flotation cost.
Why is there a cost of reinvested earnings?
III. Cost of Common Equity
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Ways to determine the
cost of common equity
1. DCF: kce = D1/P0 + g.
2. CAPM: kce= kRF + (kM - kRF)b
= kRF + (RPM)b.
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- Stand alone stock risk:
measured by the standard deviation
- Well-diversifiable stock risk:
measured by the beta
Stock risk:
stand alone vs. well-diversifiable
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Volatility of an Equally Weighted Portfolio versus the Number of Stocks
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Market Risk vs. Firm Risk
Market (or non-diversifiable or systematic) risk:
is that part of a security’s stand-alone risk that cannot be eliminated by diversification.
Firm-specific (or diversifiable or unsystematic) risk:
is that part of a security’s stand-alone risk that can be eliminated by diversification.
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- Market risk, which is relevant for stocks held in well-diversified portfolios, is defined as the contribution of a security to the overall riskiness of the portfolio.
- It is measured by a stock’s beta coefficient, which measures the stock’s volatility relative to the market.
What is the relevant risk for a stock held in isolation?
How is market risk measured for individual securities?
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b = (kce- kRF)/(kM - kRF)
- If b = 1.0, stock has average risk.
- If b > 1.0, stock is riskier than average.
- If b < 1.0, stock is less risky than average.
- Most stocks have betas in the range of 0.5 to 1.5.
Can a stock have a negative beta?
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How are betas calculated?
- kce= kRF + (kM - kRF)b = kRF + (RPM)b CAPM
= (1-b) kRF + b kM
- Run a regression with returns on the stock in question plotted on the Y axis and returns on the market portfolio plotted on the X axis.
- The slope of the regression line, which measures relative volatility, is defined as the stock’s beta coefficient, or b.
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Beta Illustration
Sheet7
SUMMARY OUTPUT | ||||||||
Regression Statistics | ||||||||
Multiple R | 0.4933156243 | |||||||
R Square | 0.2433603052 | |||||||
Adjusted R Square | 0.159289228 | |||||||
Standard Error | 0.0237005529 | |||||||
Observations | 11 | |||||||
ANOVA | ||||||||
df | SS | MS | F | Significance F | ||||
Regression | 1 | 0.0016259983 | 0.0016259983 | 2.8946971211 | 0.1230816184 | |||
Residual | 9 | 0.0050554459 | 0.0005617162 | |||||
Total | 10 | 0.0066814442 | ||||||
Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | |
Intercept | -0.0164600154 | 0.0074495346 | -2.2095360774 | 0.0544864623 | -0.0333120462 | 0.0003920154 | -0.0333120462 | 0.0003920154 |
S&P Ret | 0.7581862916 | 0.4456299418 | 1.7013809453 | 0.1230816184 | -0.2498994414 | 1.7662720246 | -0.2498994414 | 1.7662720246 |
Chart1
-0.0180995475 |
0.0291666667 |
-0.0338621833 |
-0.0079868452 |
-0.0042105263 |
-0.0425531915 |
-0.0424619344 |
-0.0172813488 |
0.011942845 |
-0.0399577409 |
-0.0551493063 |
Sheet1
Week of | GE | S&P | S&P Ret | GE Ret |
27-Aug-01 | 41.23 | 1161.51 | -1.98% | -1.81% |
20-Aug-01 | 41.99 | 1184.93 | 1.98% | 2.92% |
13-Aug-01 | 40.80 | 1161.97 | -2.46% | -3.39% |
13-Aug-01 | 42.23 | 1191.29 | 0.09% | -0.80% |
6-Aug-01 | 42.57 | 1190.16 | -1.99% | -0.42% |
30-Jul-01 | 42.75 | 1214.35 | 0.71% | -4.26% |
23-Jul-01 | 44.65 | 1205.82 | -0.42% | -4.25% |
16-Jul-01 | 46.63 | 1210.85 | -0.40% | -1.73% |
9-Jul-01 | 47.45 | 1215.68 | 2.11% | 1.19% |
2-Jul-01 | 46.89 | 1190.59 | -2.76% | -4.00% |
25-Jun-01 | 48.84 | 1224.38 | -0.08% | -5.51% |
18-Jun-01 | 51.69 | 1225.35 |
Sheet2
Sheet3
Sheet4
Sheet5
Sheet6
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Beta Illustration
Sheet7
SUMMARY OUTPUT | ||||||||
Regression Statistics | ||||||||
Multiple R | 0.4933156243 | |||||||
R Square | 0.2433603052 | |||||||
Adjusted R Square | 0.159289228 | |||||||
Standard Error | 0.0237005529 | |||||||
Observations | 11 | |||||||
ANOVA | ||||||||
df | SS | MS | F | Significance F | ||||
Regression | 1 | 0.0016259983 | 0.0016259983 | 2.8946971211 | 0.1230816184 | |||
Residual | 9 | 0.0050554459 | 0.0005617162 | |||||
Total | 10 | 0.0066814442 | ||||||
Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | |
Intercept | -0.0164600154 | 0.0074495346 | -2.2095360774 | 0.0544864623 | -0.0333120462 | 0.0003920154 | -0.0333120462 | 0.0003920154 |
S&P Ret | 0.7581862916 | 0.4456299418 | 1.7013809453 | 0.1230816184 | -0.2498994414 | 1.7662720246 | -0.2498994414 | 1.7662720246 |
Chart1
-0.0180995475 |
0.0291666667 |
-0.0338621833 |
-0.0079868452 |
-0.0042105263 |
-0.0425531915 |
-0.0424619344 |
-0.0172813488 |
0.011942845 |
-0.0399577409 |
-0.0551493063 |
Sheet1
Week of | Open | High | Low | GE | S&P | S&P Ret | GE Ret | |
27-Aug-01 | 42 | 42.56 | 41.15 | 41.23 | 1161.51 | -0.0197648806 | -0.0180995475 | |
20-Aug-01 | 41 | 42.26 | 40.29 | 41.99 | 1184.93 | 0.0197595463 | 0.0291666667 | |
13-Aug-01 | 42.5 | 43.11 | 40.35 | 40.8 | 1161.97 | -0.0246119753 | -0.0338621833 | |
13-Aug-01 | 42.5 | 43.11 | 42.02 | 42.23 | 1191.29 | 0.0009494522 | -0.0079868452 | |
6-Aug-01 | 42.4 | 42.85 | 41.26 | 42.57 | 1190.16 | -0.0199201219 | -0.0042105263 | |
30-Jul-01 | 44.55 | 44.9 | 41.9 | 42.75 | 1214.35 | 0.0070740243 | -0.0425531915 | |
23-Jul-01 | 46.5 | 46.62 | 43.15 | 44.65 | 1205.82 | -0.0041541066 | -0.0424619344 | |
16-Jul-01 | 47.15 | 47.5 | 45.4 | 46.63 | 1210.85 | -0.003973085 | -0.0172813488 | |
9-Jul-01 | 46.9 | 47.75 | 44.3 | 47.45 | 1215.68 | 0.0210735854 | 0.011942845 | |
2-Jul-01 | 48.7619 | 50.0378 | 46.6 | 46.89 | 1190.59 | -0.0275976413 | -0.0399577409 | |
25-Jun-01 | 51.5329 | 52.44 | 47.2369 | 48.8416 | 1224.38 | -0.0007916106 | -0.0551493063 | |
18-Jun-01 | 48.8416 | 52.2606 | 48.3831 | 51.6924 | 1225.35 |
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Sheet6
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Average Betas for Stocks by Industry and the Betas of a Selected Company in Each Industry
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Use the SML to calculate each
alternative’s required return.
- The Security Market Line (SML) is part of the Capital Asset Pricing Model (CAPM), illustrating the relation between required rate of return and beta.
- SML: ki = kRF + (RPM)bi .
Intercept is kRF and slope is RPM .
- The measure of risk used in the SML is the beta coefficient of company i, bi.
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Expected Returns, Volatility, and Beta
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Estimating the Cost of Equity
Problem:
- The equity beta for Johnson & Johnson (ticker: JNJ) is 0.67. The yield on ten-year treasuries is 3%, and you estimate the market risk premium to be 6%. Further, Johnson & Johnson issues dividends at an annual rate of $2.16. Its current stock price is $60.50, and you expect dividends to increase at a constant rate of 4% per year. Estimate J&J’s cost of equity in two ways.
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1. CAPM: kce= kRF + (kM - kRF)b
= kRF + (RPM)b
= 3% + 0.67 × 6%
= 7.0%.
- DCF: kce = D1/P0 + g
= 2.16/60.5+4%=7.6%.
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Finally, What’s WACC?
WACC = wdkd(1 - T) + wpskps + wcekce
= 0.3(10%)(0.6) + 0.1(9%) + 0.6(14%)
= 1.8% + 0.9% + 8.4% = 11.1%.
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WACC Estimates for Some Large
U. S. Corporations
Company WACC
Intel 12.9%
General Electric 11.9
Motorola 11.3
Coca-Cola 11.2
Walt Disney 10.0
AT&T 9.8
Wal-Mart 9.8
Exxon 8.8
H. J. Heinz 8.5
BellSouth 8.2
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What factors influence a company’s WACC?
- Market conditions, especially interest rates and tax rates.
- The firm’s capital structure and dividend policy.
- The firm’s investment policy. Firms with riskier projects generally have a higher WACC.
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- Key Assumptions
- Average Risk
- We assume initially that the market risk of the project is equivalent to the average market risk of the firm’s investments
- Constant Debt-Equity Ratio
- We assume that the firm adjusts its leverage continuously to maintain a constant ratio of the market value of debt to the market value of equity
- Limited Leverage Effects
- We assume initially that the main effect of leverage on valuation follows from the interest tax deduction and that any other factors are not significant at the level of debt chosen
Using the WACC to Value a Project
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Suppose DuPont is considering acquiring Weyerhaeuser, a company that is focused on timber, paper, and other forest products
- Weyerhaeuser faces different market risks than DuPont does in its chemicals business
- DuPont’s WACC would be inappropriate for valuing Weyerhaeuser
- Instead, DuPont should calculate and use Weyerhaeuser’s WACC of 8.8% when assessing the acquisition
WACC of a New Acquisition
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Now assume DuPont decides to create a forest products division internally, rather than buying Weyerhaeuser.
- What should the cost of capital for the new division be?
- If DuPont plans to finance the division with the same proportion of debt as is used by Weyerhaeuser, then DuPont would use Weyerhaeuser’s WACC as the WACC for its new division
Divisional WACC
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Compare rate of return and cost of capital
Cost of debt and cost of preferred stock
Beta versus sigma, market risk versus firm specific risk
Cost of common equity (CAPM and DCF)
WACC
Lecture Highlights
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Calculate a beta, Ks, Kd and WACC for your company.
You may use and/or review the sample spreadsheet “proforma” provided on the course Titanium website.
Project
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Week ofGES&PS&P RetGE Ret
27-Aug-0141.231161.51-1.98%-1.81%
20-Aug-0141.991184.931.98%2.92%
13-Aug-0140.801161.97-2.46%-3.39%
13-Aug-0142.231191.290.09%-0.80%
6-Aug-0142.571190.16-1.99%-0.42%
30-Jul-0142.751214.350.71%-4.26%
23-Jul-0144.651205.82-0.42%-4.25%
16-Jul-0146.631210.85-0.40%-1.73%
9-Jul-0147.451215.682.11%1.19%
2-Jul-0146.891190.59-2.76%-4.00%
25-Jun-0148.841224.38-0.08%-5.51%
18-Jun-0151.691225.35
Regression of GE's Weekly Returns on the S&P 500
Returns: 6/18/01 to 8/27/01
y = - 0.0165+
0.76
X
R
2
= 0.2434
-0.06
-0.04
-0.02
0
0.02
0.04
-0.04-0.03-0.02-0.0100.010.020.03
GE RetLinear (GE Ret)