Kd, Kps, Kce

1
LECTURE 4 (Chapter 6,7,10) Cost of Capital

• Kd, Kps, Kce
• CAPM, APT and FF 3-Factor Model
• WACC

2
Types of long-term capital

• Long-term debt
• Preferred stock
• Common equity

3
Terminologies

• Expected Rate of Return
• Investors return based on the actual market
  price.
• Required Rate of Return
• Investors return that can perfectly
  compensates for the risk that they takes.
• Cost of Capital
• Companys cost of raising capital,
  incorporating flotation cost and taxation.

4
I. Cost of Debt
5
Required rate of return for a debt security
ki k IP LP MRP DRP
6
Yield to Maturity the expected rate of return
earned on a bond held to maturity. Also called
promised yield. Whats the YTM on a 10-year,
9 annual coupon, 1,000 par value bond that
sells for 887?
7
INT
M
INT
...
V
?



B
?
?
?
?
?
?
N
N
1
k
k
1
1
1
k



d
d
d
90
1
000
90
,
...
887
?




?
?
?
?
?
?
1
10
10
1
1
k
k
1

k


d
d
d
INPUTS
10 -887 90 1000 N I/YR
PV PMT FV 10.91
OUTPUT
8
Cost of Debt
Corporate bond A 15-year, 12 semiannual bond
sells with net proceeds 1,153.72. Whats kd?
(tax rate is 40)
0
1
2
30
i ?
...
-60
-60 - 1,000
-60
1,153.72
30 1153.72 -60 -1000 5.0
x 2 kd 10
INPUTS
N
I/YR
PV
FV
PMT
OUTPUT
9

• Flotation costs are reflected. Use net price.
• Interest is tax deductible, so
• kd AT kd BT(1 - T)
• 10(1 - 0.40) 6.
• Use nominal rate.

10
Private debt A 10-year, 15 annual debt with
face value 600,000, and net proceeds 550,000.
Whats kd? (tax rate is 40)
0
1
2
10
i ?
...
-90,000
-90,000 -600,000
-90,000
550,000
10 550 -90 -600 kd
16.77
kd AT 16.77 (1-40) 10.06
INPUTS
N
I/YR
PV
FV
PMT
OUTPUT

11
II. Cost of Preferred Stock
12
Whats the cost of preferred stock? PP
113.10 10Q Par 100 F 2.
13
?
0
1
2
kps ?
...
-2.5
-2.5
113.1 -2
-2.5
14

• Flotation costs are reflected. Use net price.
• Preferred dividends are not tax deductible, so no
  tax adjustment.
• Use nominal rate.

15
II. Cost of Common Equity
16
Two Ways to Raise Common Equity

• Issue new shares of common stock.
• Reinvest earnings.

17
Why is there a cost for reinvested earnings?

• If earnings are not reinvested, they can paid out
  as dividends to investors, who could use the
  money to buy other securities and earn a return.
• Thus there is an opportunity cost if earnings are
  reinvested.

18
Cost of reinvested earnings vs. cost of common
stock

• Flotation cost

19
Three ways to determine the cost of common equity
1. DCF kce D1/NP0 g. 2. CAPM kce kRF
(kM - kRF)b kRF (RPM)b. 3. Own-Bond-Y
ield-Plus-Risk Premium kce kd RP.
20
Stock risk stand alone vs. well-diversifiable

• Stand alone stock risk
• measured by the standard deviation
• Well-diversifiable stock risk
• measured by the beta

21
Probability distribution
Stock X
Stock Y
Rate of return ()
50
15
0
-20

• Which stock is riskier? Why?

22
Assume the FollowingInvestment Alternatives
23
Calculate the expected rate of return on each
alternative.

k expected rate of return.

kHT 0.10(-22) 0.20(-2) 0.40(20)
0.20(35) 0.10(50) 17.4.
24

• HT has the highest rate of return.
• Does that make it best?

25
What is the standard deviationof returns for
each alternative?
26
HT ? ((-22 - 17.4)20.10 (-2 - 17.4)20.20
(20 - 17.4)20.40 (35 - 17.4)20.20
(50 - 17.4)20.10)1/2 20.0.
27
Expected Return versus Risk

• Which alternative is best?

28
Two-Stock Portfolios

• Two stocks can be combined to form a riskless
  portfolio if r -1.0.
• Risk is not reduced at all if the two stocks have
  r 1.0.
• In general, stocks have r ? 0.65, so risk is
  lowered but not eliminated.
• Investors typically hold many stocks.
• What happens when r 0?

29
Prob.
Large
2
1
0
15
Return
?1 ??35 ?Large ??20.
30
?p ()
Company Specific (Diversifiable) Risk
35
Stand-Alone Risk, ?p
20 0
Market Risk
10 20 30 40 2,000
Stocks in Portfolio
31
Market Risk vs. Firm Risk
Market (or non-diversifiable or systematic) risk
is that part of a securitys stand-alone risk
that cannot be eliminated by diversification. Fir
m-specific (or diversifiable or unsystematic)
risk is that part of a securitys stand-alone
risk that can be eliminated by diversification.
32
How is market risk measured for individual
securities?

• 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 stocks beta coefficient,
  which measures the stocks volatility relative to
  the market.
• What is the relevant risk for a stock held in
  isolation?

33
How are betas calculated?

• 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 stocks
  beta coefficient, or b.

34
Beta Illustration
35
Beta Illustration
For a similar example see pgs. 227-28 of the text.
36
How is beta interpreted?

• If b 1.0, stock has average risk.
• If b gt 1.0, stock is riskier than average.
• If b lt 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?

37
Expected Return versus Market Risk

• Which of the alternatives is best?

38
Use the SML to calculate eachalternatives
required return.

• The Security Market Line (SML) is part of the
  Capital Asset Pricing Model (CAPM).
• 
  
• SML ki kRF (RPM)bi .

39
The SML Equation

• The measure of risk used in the SML is the beta
  coefficient of company i, bi.
• Assume kRF 8 kM kM 15.
• RPM (kM - kRF) 15 - 8 7.

40
Required Rates of Return
kHT 8.0 (7)(1.29) 8.0 9.0
17.0.
kM 8.0 (7)(1.00) 15.0. kUSR 8.0
(7)(0.68) 12.8. kT-bill 8.0
(7)(0.00) 8.0. kColl 8.0
(7)(-0.86) 2.0.
41
Expected versus Required Returns

42
Arbitrage Pricing Theory (APT)

• The CAPM is a single factor model.
• The APT proposes that the relationship between
  risk and return is more complex and may be due to
  multiple factors such as GDP growth, expected
  inflation, tax rate changes, and dividend yield.

43
Required Return for Stock i under the APT
ki kRF (k1 - kRF)b1 (k2 - kRF)b2
... (kj - kRF)bj.
kj required rate of return on a portfolio
sensitive only to economic Factor j.
bj sensitivity of Stock i to economic
Factor j.
44
Fama-French 3-Factor Model

• Fama and French propose three factors
• The excess market return, kM-kRF.
• the return on, S, a portfolio of small firms
  (where size is based on the market value of
  equity) minus the return on B, a portfolio of big
  firms. This return is called kSMB, for S minus B.

45
Fama-French 3-Factor Model (Continued)

• the return on, H, a portfolio of firms with high
  book-to-market ratios (using market equity and
  book equity) minus the return on L, a portfolio
  of firms with low book-to-market ratios. This
  return is called kHML, for H minus L.

46
Required Return for Stock i under the
Fama-French 3-Factor Model
ki kRF (kM - kRF)bi (kSMB)ci (kHML)di bi
sensitivity of Stock i to the market return. ci
sensitivity of Stock i to the size factor. di
sensitivity of Stock i to the book-to-market
factor.
47
Whats the WACC?
WACC wdkd(1 - T) wpskps wceks
0.3(10)(0.6) 0.1(9) 0.6(14) 1.8 0.9
8.4 11.1.
48
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 ATT 9.8 Wal-Mart 9.8 Exxon
8.8 H. J. Heinz 8.5 BellSouth 8.2
49
What factors influence a companys WACC?

• Market conditions, especially interest rates and
  tax rates.
• The firms capital structure and dividend policy.
• The firms investment policy. Firms with riskier
  projects generally have a higher WACC.

50
Should the company use the composite WACC as the
hurdle rate for each of its projects?

• NO! The composite WACC reflects the risk of an
  average project undertaken by the firm.
  Therefore, the WACC only represents the hurdle
  rate for a typical project with average risk.
• Different projects have different risks. The
  projects WACC should be adjusted to reflect the
  projects risk.