Chapters 8 & 9: How to value bonds and stocks Corporate Finance

Chapters 8 & 9: How to value
bonds and stocks
Corporate Finance
Ross, Westerfield, and
Jaffe
Outline
1. Bonds
2. Bond pricing
3. Bond concepts and reporting
4. Dividend discount model (DDM)
5. Stock market reporting
What is a bond?
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https://www.youtube.com/watch?v=O2IiwstF
_UE
Notations, I
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Bonds: debt securities with long-term
maturities, typically longer than 1 year.
Coupon, typically C = C1 = C2 = … = CN: the
stated interest payment made on a bond.
Par (face) value (FV): the principal value of a
bond; by default, $1,000.
Maturity (N): specified date on which the
principal is paid.
Notations, II
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–
–
–
–
Coupon rate: annual coupon / FV.
Yield to maturity (YTM): the rate required in the
market on a bond.
Market decides.
Time varying.
Related to default risk.
If coupons are paid out annually, i = YTM. If
coupons are paid out semiannually, i = YTM/2.
How to value bonds
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Note that the cash flows of a typical bond
consists of two cash flow streams: (1) an
annuity of coupon payments, and (2) a final
principal.
Recall that the PV of multiple cash flows is
simply the sum of individual PV’s.
Thus, for a typical bond, PV = PVannuity +
PVprincipal.
Bond pricing formula
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PV = PVannuity + PVprincipal = C  { [ 1 – 1 / (1 +
i)N ] / i } + FV / (1 + i)N.
Of course, we can also use a financial
calculator to do the job.
Note that computation itself is rather
straightforward. The difficult part is to
correctly figure out the values of parameters.
Bond example, I
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Suppose that VTcredit Inc. is going to issue a bond.
The maturity is 25 years. The average YTM on
similar issues is 10%. A series of $120 as coupons
is paid out annually. The face value is $1,000. What
is the fair price of the bond?
Formula: PV = = C  { [ 1 – 1 / (1 + i)N ] / i } + FV / (1
+ i)N = $120  { [ 1 – 1 / (1 + 10%)25 ] / 10% } +
$1,000 / (1 + 10%)25 = $1,181.54.
Calculator: 120 PMT; 1000 FV; 25 N; 10 I/Y; CPT
PV. The answer is: PV = -1,181.5408.
Semiannual payments
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Most corporate bonds pay coupons
semiannually. The principle of calculation is
the same.
But remember: the time frequency of i and
N must be the same.
Bond example, II
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Suppose that VTcredit Inc. is going to issue a bond.
The maturity is 25 years. The average YTM on
similar issues is 10%. A series of $60 as coupons is
paid out semiannually. The face value is $1,000.
What is the fair price of the bond?
Formula: PV = = C  { [ 1 – 1 / (1 + i)N ] / i } + FV / (1
+ i)N = $60  { [ 1 – 1 / (1 + 5%)50 ] / 5% } + $1,000 /
(1 + 5%)50 = $1,182.56.
Calculator: 60 PMT; 1000 FV; 50 N; 5 I/Y; CPT PV.
The answer is: PV = -1,182.5593.
Bond example, III
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Suppose that Northern Inc. bonds have a
$1,000 face value. Annual coupon is $100.
The bonds mature in 20 years. YTM = 10%.
What is the bond price?
Calculator: 100 PMT; 1000 FV; 20 N; 10 I/Y;
CPT PV. The answer is: PV = -1,000.
Lesson: if payment rate equals to discount
rate, the bond price is simply the FV.
YTM example
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Northern Inc. issued 12-year bonds 2 years
ago at a coupon rate of 8.4%. The bonds
make semiannual payments. If these bonds
currently sell for 110% of par value, what is
the YTM?
Calculator: 42 PMT; 1000 FV; 20 N; -1100
PV; CPT I/Y. The answer is: I/Y = 3.4966.
YTM = 2 × 3.4966 = 6.9932 (%).
Bond price and YTM
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Recall from Chapter 4: Holding time period
constant – the higher the interest (discount)
rate, the smaller the PV.
Because YTM is closely related to discount
rate, one would expect that YTM is
negatively related to bond price.
That is, market interest rates rise  yield
(YTM) increases  bond price falls.
YTM and bond price
Bond Value
1300
When the YTM < coupon, the bond
trades at a premium.
1200
When the YTM = coupon, the
bond trades at par.
1100
1000
800
0
0.01
0.02
0.03
0.04
0.05
0.06 0.07
6 3/8
0.08
0.09
0.1
Discount Rate
When the YTM > coupon, the bond trades at a discount.
Bond markets
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Trading is inactive for corporate bonds;
typically, trading occurs in OTC (over-thecounter; not exchange); Illiquid.
Trading is active for U.S. government debt
instruments. This sector has many
international participants, e.g., Chinese
Central Bank.
Bond rating
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Junk bonds: rating at BB or below by S&P;
rating at Ba or below by Moody’s.
Investment-quality bonds: rating at BBB or
above by S&P; rating at Baa or above by
Moody’s.
P. 251
Bond reporting
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WSJ used to publish corporate bond
quotation for the 40 most active corporate
bonds; but not anymore.
Bond trading information can be found at
FINRA (Financial Industry Regulatory
Authority)
http://cxa.marketwatch.com/finra/MarketData/
Default.aspx
A FINRA bond quotation
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Issue: IBM.GT IBM 8.375 11/01/Year T + 12
Rating -------------------Last Sale ---------------------------Moody's/S&P/Fitch Date
Price
Yield
A1 / A+ / AA05/02/Year T 125.00 5.569263
This TRACE quotation was retrieved on 05/15/Year T.
This issue pays coupons semiannually: 05/01 and 11/01.
I/Y = YTM / 2 = 2.7846.
Coupon rate = 8.375%. So, the semiannual payment is
$41.875.
Calculator: 25 N; 2.7846 I/Y; 1000 FV; 41.875 PMT; CPT PV.
The answer is: PV = -1,250.2572, which is 125.02572% of par.
Bond features, I
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Indenture: The written agreement between
the corporation and the lender detailing the
terms of the debt issue.
Collateral: the asset pledged on a debt.
Debenture (> 10 years) and note (< 10
years): an unsecured debt.
Sinking fund: an account managed by the
bond trustee for early bond redemption.
Bond features, II
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Call bond: a bond that allows the firm to repurchase
or “call” part or all of the bond issue at stated prices
over a specific period.
Put bond: a bond that allows the holder to force the
issuer to buy the bond back at a stated price.
Protective covenant: a part of the indenture limiting
certain actions that might be taken during the term of
the loan, usually to protect the lender’s interest.
Treasury notes (2-10 years) and bonds (>10 years):
long-term debt securities issued by the U.S. federal
government.
Bond features, III
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Municipal bonds (munis): debt securities issued by
state and local governments.
Zero coupon bond: a bond that makes no coupon
payments, thus initially priced at a deep discount.
Floating-rate bond: a bond whose coupon payments
are adjustable.
Convertible bond: a bond that can be swapped for a
fixed number of shares of stock anytime before
maturity at he holder’s option.
Inflation and interest rates
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Inflation erodes purchasing power
Nominal rate (R): the percentage change in
the number of dollars you have.
Real rate (r): the percentage change in how
much you can buy with your dollars.
Fisher effect/equation: (1 + R) = (1 + r) × (1
+ h), where h is the inflation rate.
Nominal rate
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Suppose that the real risk-free rate is 2.5%
and the inflation rate is expected to be 4.7%.
What rate would you expect to see on a 1year T-bill?
(1 + R) = (1 + r) × (1 + h)
(1 + R) = (1 + 2.5%) × (1 + 4.7%)  R =
7.32%.
Dividends as cash flows
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For bond pricing, we just discounted coupons and
par (2 types of cash flows) to arrive at the PV.
For stock pricing, this course focuses on one
particular type of cash flows—cash dividends.
Discounting dividends makes sense because
dividends are the only types of cash flows that
investors can actually receive from the firm.
When dividends are used as cash flows for
discounting, we need to use cost of equity, i.e., the
required rate demanded by shareholders, as the
applicable discount rate.
But the problems are:
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Discounting all (possibly infinite terms)
dividends to arrive at PV (fundamental value
of the stock) is theoretically correct.
However, the problems are: (1) cash flows
are uncertain; we usually plug in a series of
estimates as if they were certain, (2) the
required rate of return is unknown and
frequently time unstable, (3) the life of the
security is actually unknown.
How about those no-dividend firms?
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About 50% of U.S. publicly traded firms do not pay
dividends.
However, the valuation concept is the same, except
that some of the early dividend payments are zero.
After all, there should be expectations that at some
point the firm will start paying dividends. Otherwise,
the investment will have no value.
Of course, it is often difficult to forecast when these
firms will pay dividends and how much will they pay.
Infinite terms?
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The fundamental value of a stock is the PV of
its future dividends.
Because a firm can possibly live forever, thus
we are discounting an infinite number of cash
flows.
To make the calculation doable, we need to
make some assumptions.
Zero-growth DDM
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The easiest assumption one can make is to assume
that there is no growth in dividends, i.e., D1 = D2 = …
= D.
Because this is a perpetuity, the pricing is rather
straightforward: PV = D / i.
Suppose that GE paid $2 dividend per share last
year. Investors expect no growth in GE’s future
dividends. The applicable discount rate is 10%.
PV = $2 / 10% = $20.
Constant-growth DDM
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Another easy assumption one can make is to
assume that there is a constant growth rate,
g, in dividends, i.e., D1 = D0 × (1 + g), D2 =
D0 × (1 + g)2, etc.
That is, this is a growing perpetuity.
Recall from Chapter 4, the PV of a growing
perpetuity is: PV = D1 / (i – g).
Constant-growth DDM example
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Vermont Financial Inc. paid a dividend of $1
last year. The constant growth rate of
dividends is 5%, and the required rate of
return is 10%.
PV = [D0 × (1 + g)] / (i – g) = [$1 × (1 +
5%)] / (10% – 5%) = $21.
Multiple-stage DDM model
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This model allows different growth rates for
different stages.
Typically, it takes care of recent, supernormal
growth.
There are formulas for PV. However, they do
not look neat.
Let us use Excel to visualize the discounting
process.
Multiple-stage example, I
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HP has a cost of equity at 14%. HP just paid
an annual dividend of $2.
The expected dividend growth rate between
year 1-3 is 25%. The expected dividend
growth rate between year 4-5 is 15%. The
expected dividend growth rate for year 6 and
afterwards is 5%.
Multiple-stage example, II
Year Dividend Growth rate Discount rate
PV5
PV
0
2
0.14
1
2.5
0.25
2.1929825
2
3.125
0.25
2.404586
3
3.90625
0.25
2.6366075
4
4.492188
0.15
2.6597356
5
5.166016
0.15
60.2701823 33.985511
6
5.424316
0.05
43.879422
Quality of inputs
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The above stock pricing examples seem
quite simple. In reality, stock valuation is
extremely difficult. The difficulty does not
arise from the calculation itself, but from the
uncertainty associated with model inputs
(estimates).
Professional investors compete on the
quality of inputs.
Estimating g
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There are potentially many ways to estimate
g.
One possible way is to use the industry’s
long-term average growth rate.
Another way: g = retention ratio × ROE
(return on equity).
Retention ratio = (NI – dividends) / NI.
ROE = NI / equity.
P/E ratio, I
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The ratio of the current market price per
share to the expected next-12-month
earnings per share (or the current annual
earnings per share).
When the expected next-12-month EPS is
used, this P/E ratio is also called “forward
P/E ratio.”
The level of P/E ratio is related to growth
potential. A stock with higher expected
growth potential tends to have a higher P/E
ratio.
P/E ratio, II
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Embedded in the seemingly high prices of
those high PE stocks are expectations that
in the aggregate are unlikely to be met. You
should expect a high strikeout rate.
Example: During 1996-2000, only 1/3 of all
high PE, high-tech stocks have higher
returns than the S&P 500; but once they
beat the S&P 500, they tend to have
extremely good performance.
An effective, widely-used communication
tool because of its simplicity.
Stock market reporting (WSJ)
STOCK
SYM CLOSE
NET CHG
GenMotor GM
30.62
1.16
 Yesterday’s closing price: $30.62.
 Yesterday’s closing price is higher than the
closing price of the previous trading day by
$1.16.
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Review: Let us work on this
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Q2, P. 267. Microhard has issued a bond
with the following characteristics: (1) par:
$1000, (2) time to maturity: 15 years, (3)
coupon rate: 7%; (4) semiannual payments.
What is the price of the bond if the YTM is (a)
7%, and (b) 9%?
End-of-chapter
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Chapter 8: Concept questions: 1-17;
Questions and problems: 1-10, 14-17, and
21-23.
Chapter 9: Concept questions: 1-10;
Questions and problems: 1-9, 12-14, and19.