The Determinants of the Market Interest Rate
Given the quoted (nominal) interest rate on a security:
rd = r* + IP + DRP + LP + MRP.
where:
rd
=
Required rate of return on a debt security.
- Also called quoted or nominal interest rate.
r*
=
Real risk-free rate
– rate of return on a riskless security if zero inflation is
expected. Rate of return on short-term Treasuries if no
inflation.
IP
=
Inflation premium
- the average expected inflation over the life of
security.
DRP =
Default risk premium.
- The risk that issuer will not pay interest or principal at
stated times.
Note: DRP= 0 for Treasury securities.
Note: DRP ↑s w/ riskiness of issuer.
LP
=
Liquidity (marketability) premium.
- controls for the fact that some securities can’t be
converted to cash on short notice.
LP is quite low for Treasury securities (not 0, since
there are transaction costs).
MRP =
Maturity risk premium.
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The nominal risk-free rate:
 rRF = r*+ IP
 rRF = Rate on Treasury securities.
Then: rd = rRF + DRP + LP + MRP.
Estimating IP:
Utilizes Treasury Inflation-Protected Securities (TIPS).
TIPS are indexed to inflation. How? The principal is periodically
adjusted to the CPI.
 The IP for a particular length maturity can be approximated as the
difference between the yield on a non-indexed Treasury security of
that maturity minus the yield on a TIPS of that maturity.
Bond Spreads, the DRP, and the LP
 A “bond spread” is often calculated as the difference between a
corporate bond’s yield and a Treasury security’s yield of the same
maturity. Therefore:
Spread = DRP + LP.
Note: Bond’s of large, strong companies often have very small LPs.
Bond’s of small companies often have LPs as high as 2%.
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Bond Ratings Provide One Measure of Default Risk
Investment Grade
Moody’s │ Aaa Aa A
Baa │
│
│
S&P
│AAA AA A BBB │
Junk Bonds
Ba B Caa Ca C D
BB
B CC
C D
Factors that affect default risk and bond ratings:
 Financial performance
 Debt ratio
 Coverage ratios, such as interest coverage ratio or EBITDA
coverage ratio
 Current ratios
Provisions in the bond contract
 Secured versus unsecured debt
 Senior versus subordinated debt
 Guarantee provisions
 Sinking fund provisions
 Debt maturity
 Earnings stability
 Regulatory environment
 Potential product liability
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The Maturity Risk Premium (MRP)
Interest Rate Risk - Change in price due to changes in interest rates
– Interest rates up, bond price down!
– Long-term bonds have more interest rate risk than shortterm bonds
• More-distant cash flows are more adversely affected by
an increase in interest rates
– Lower coupon rate bonds have more interest rate risk than
higher coupon rate bonds
•
More of the bond’s value is deferred to maturity (thus,
for a longer time) if the coupons are small
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Reinvestment rate risk - The risk that CFs will have to be reinvested in
the future at lower rates, reducing income.
 Illustration: Suppose you just won $500,000 playing the lottery.
You’ll invest the money and live off the interest. You buy a 1-year
bond with a YTM of 10%.
 Year 1 income = $50,000. At year-end get back $500,000 to
reinvest.
 If rates fall to 3%, income will drop from $50,000 to $15,000. Had
you bought 30-year bonds, income would have remained constant.
The Maturity Risk Premium
 Long-term bonds: High interest rate risk, low reinvestment rate
risk.
 Short-term bonds: Low interest rate risk, high reinvestment rate
risk.
 Nothing is riskless!
 Yields on longer term bonds usually are greater than on shorter
term bonds, so the MRP is more affected by interest rate risk than
by reinvestment rate risk.
Term Structure Yield Curve
 Term structure of interest rates: the relationship between interest
rates (or yields) and maturities.
 graph of the term structure is called the yield curve.
Relationship Between Treasury Yields and Corporate Yields
 Corporate yield curves are higher than that of the Treasury bond.
However, corporate yield curves are not necessarily parallel to the
Treasury curve.
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 The spread between a corporate yield curve and the Treasury
curve widens as the corporate bond rating decreases.
Bankruptcy
 Two main chapters of Federal Bankruptcy Act:
 Chapter 11, Reorganization
 Chapter 7, Liquidation
 Typically, company wants Chapter 11, creditors may prefer
Chapter 7.
If company can’t meet its obligations, it files under Chapter 11. That
stops creditors from foreclosing, taking assets, and shutting down the
business.
 Company has 120 days to file a reorganization plan.
 Court appoints a “trustee” to supervise reorganization.
 Management usually stays in control.
 Company must demonstrate in its reorganization plan that it is
“worth more alive than dead.”
 Otherwise, judge will order liquidation under Chapter 7.
If the company is liquidated, here’s the payment priority:
 Past due property taxes
 Secured creditors from sales of secured assets.
 Trustee’s costs
 Expenses incurred after bankruptcy filing
 Wages and unpaid benefit contributions, subject to limits
 Unsecured customer deposits, subject to limits
 Taxes
 Unfunded pension liabilities
 Unsecured creditors
 Preferred stock
 Common stock
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In a liquidation, unsecured creditors generally get zero. This makes
them more willing to participate in reorganization even though their
claims are greatly scaled back.
Various groups of creditors vote on the reorganization plan. If both the
majority of the creditors and the judge approve, company “emerges”
from bankruptcy with lower debts, reduced interest charges, and a
chance for success.
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CHAPTER 5
 Basic Stock Valuation




Topics in Chapter
Features of common stock
Determining common stock values
Efficient markets
Preferred stock
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Common Stock: Represents ownership.
 Ownership implies control.
o Stockholders (SHs) elect directors and directors hire
management.
 Since managers are “agents” of shareholders, their goal should be:
Maximize stock price.
 Preemptive Rights- current SHs have first dibs on new issued stock
→ managers can’t dilute 1. SHs share of ownership in firm or
2. stock prices
Classified Stock: stock that has special provisions.
 Could classify existing stock as founders’ shares, with voting rights
but dividend restrictions.
 New shares might be called “Class A” shares, with voting
restrictions but full dividend rights.
Tracking Stock
 The dividends of tracking stock are tied to a particular division,
rather than the company as a whole.
 Investors can separately value the divisions.
 Its easier to compensate division managers with the tracking stock.
 But tracking stock usually has no voting rights, and the financial
disclosure for the division is not as regulated as for the company.
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Initial Public Offering (IPO): when a firm “goes public”, the stock is
first offered to the public.
 Prior to an IPO, shares are typically owned by the firm’s managers,
key employees, and, in many situations, venture capital providers.
Seasoned Equity Offering (SEO): occurs when a company with public
stock issues additional shares.
 After an IPO or SEO, the stock trades in the secondary market, such
as the NYSE or Nasdaq.
Stock Valuation Notation:
Dt = expected dividend at end of year t. Exception: D0 is most recent
dividend (has already been paid).
Po = current market price of stock. Determined by marginal investors.
The same for all investors.
=expected price of stock at end of year t for a particular investor.
= individual investor's estimate of the intrinsic value of stock today.
Note: If ≥ P0 ==> investor will buy stock.
Equilibrium:
= P0 for marginal investors.
rs = required rate of return (the minimum acceptable return for the
marginal investor given the risk and return)
= investor's expected return.
= expected D1/P0 + expected (
Note: If
- P0)/P0
≥ rs ==> investor will buy stock.
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First Approach to Valuing Stock: DGM: a constant growth stock:
D1 = D0 (1+g)
D2 = D1 (1+g) = D0 (1+g) (1+g) = D0 (1+g)2
D3 = D2 (1+g) = D1 (1+g)2 = D0 (1+g)3 …
Intrinsic (Fundamental) Stock Value with constant growth:
= D0 (1+g) = D1
rs - g
rs – g
if g is constant and g < rs
 Dividend Growth and PV of Dividends: P0 = ∑(PVof Dt)
Ex: If D0 =2, g =6%, the beta for the firm is βfirm = 1.2, rRF = 7%, and
RPM = 5%. Use the SML to find the required rate of return (rs):
rs = rrf + (RPM) βfirm
= 7% + (5%) (1.2)
= 13 %
Find the Projected Dividends: D1, D2, D3.
Then: D1 = D0(1+g) = 2(1.06) = 2.12
D2 = D1(1+g) = 2.12(1.06) = 2.2472
D3 = D2(1+g) = 2.2472(1.06) = 2.3820
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Given: D0 = 2.00, rs = 13%, g = 6%. Find the intrinsic value,
= 2.12
.13 -.06
.
= 2.12 = $30.29
.07
Find the expected value one year from now:
 D1 will have been paid, so expected dividends are D2, D3, D4 and so
on.
Find the Expected Dividend Yield and Capital Gains Yield (Year 1)
Find the Total Year-1 Return, rs.
 Total return = Dividend yield + Capital gains yield.
= 7% + 6% = 13%.
= 13% = rs.
 For constant growth stock:
 Capital gains yield = 6% = g.
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Rearrange model to rate of return form:
Second Model for Valuing Stock: Constant Dividend Model:
If g = 0, the dividend stream is a perpetuity.
Used for Preferred Stock (a hybrid security).
- Similar to bonds in that preferred stockholders receive a fixed dividend
which must be paid before dividends can be paid on common stock.
- However, unlike bonds, preferred stock dividends can be omitted
without fear of pushing the firm into bankruptcy.
Ex: D = $2, rs =13%, find the intrinsic value.
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Third Model for Valuing Stock: Supernormal Growth Stock
To calculate the intrinsic value we have to find the PV of all expected future
dividends. Steps:
1. Calculate the required return if it is not given.
2. Compute the dividends until growth levels off (use g for each period)
3. Find the expected future price (stock price after g levels off)
4. Find the PV of expected future cash flows (include all future dividends
and expected future stock price then discount at rs).
Ex 1: If a stock has Supernormal growth of 30% for 3 years, and then
long-run constant g = 6%. Additionally, D0 = $2 and rs =13%.
1. Find the intrinsic value.
 Growth becomes constant after 3 years.
Nonconstant growth followed by constant growth:
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Notes:
- Current periods dividends have already been distribute ∴ not included.
- After the 3rd year, it is a constant growth stock
^
P3 =
D4
rs - g
and it must be discounted back to the PV.
Note: required return = Div. yield + Cap. Gains yield
Then:
CGY = RR – DY and DY = RR - CGY
Note: During nonconstant growth, dividend yield and capital gains
yield are not constant.
2. Back to our example: Find div. yield and CG Yield at t = 0.
3. Find Expected Dividend Yield and Capital Gains Yield when t = 4.
Note: After t = 3, g = constant = 6%, so the t = 4 capital gains yield =
6%.
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4. Is the stock price based on short-term growth?
 The current stock price is $54.11.
 The PV of dividends beyond year 3 is $46.11 (P3 discounted back
to t = 0).
 The percentage of stock price due to “long-term” dividends is:
Therefore, although the long-term growth rate is small, long term
dividends accounts for most of stock value.
Ex 2: Suppose g = 0 for t = 1 to 3, and then g is a constant 6%.
Additionally, D0 = $2 and rs =13%.
a. Find the intrinsic value.
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b. Find Dividend Yield and Capital Gains Yield (t = 0)
Dividend Yield = D1 / P0
c. Find Dividend Yield and Capital Gains Yield (t = 3)
Now have constant growth, so:
What if g < 0, would anyone buy the stock?
Yes, if intrinsic value > 0.
Ex 3: Suppose g = -6%, D0 = $2 and rs =13%.
a. Would anyone buy the stock? If so, at what price?
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b. Annual Dividend and Capital Gains Yields
Market Equilibrium
- In equilibrium, the expected price must equal the actual price.
In other words, the fundamental (or intrinsic) value must be
the same as the actual price.
Equilibrium:
If
= P0 for marginal investors.
> P0 ==> stock is a “bargain.” Investor will buy stock.
-- Actual price is lower than the fundamental value.
- Buy orders will exceed sell orders  P0 
the actual price will be bid up
If
< P0 ==> stock is “overpriced.” Stock owners will sell stock.
- Actual price is higher than the fundamental value.
- Sell orders will exceed buy orders  P0 
the actual price will be bid down
In equilibrium, expected returns must equal required returns:
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Efficient Market Hypothesis (EMH)
-Securities are normally in equilibrium and are “fairly priced.” One
cannot “beat the market” except through good luck or inside
information.
Weak-form EMH
Can’t profit by looking at past trends. A recent decline is no reason to
think stocks will go up (or down) in the future. Evidence supports
weak-form EMH, but “technical analysis” is still used.
Semistrong-form EMH
All publicly available information is reflected in stock prices, so it
doesn’t pay to pore over annual reports looking for undervalued stocks.
Largely true.
Strong-form EMH
All information, even inside information, is embedded in stock prices.
Not true—insiders can gain by trading on the basis of insider
information, but that’s illegal.
Markets are generally efficient because:
- 100,000 or so trained analysts--MBAs, CFAs, and PhDs-work for firms like Fidelity, Merrill, Morgan, and Prudential.
- These analysts have similar access to data and megabucks to
invest.
- Thus, news is reflected in P0 almost instantaneously.
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