Title: Chapter 5: How to value bonds and stocks
1Chapter 5 How to value bonds and stocks
- Corporate Finance
- Ross, Westerfield, and Jaffe
2Outline
- 5.1 Bonds
- 5.2 Bond pricing
- 5.3 Bond concepts and reporting
- 5.4 Dividend discount model (DDM)
- 5.5 Stock market reporting
3Announcement
- Cancelled Your group needs to submit a typed
report for mini-case Stock Valuation at Ragan
Thermal Systems, p. 159, after we finish this
chapter.
4Notations, I
- 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.
5Notations, II
- 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.
6How to value bonds
- 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 PVs. - Thus, for a typical bond, PV PVannuity
PVprincipal.
7Bond pricing formula
- 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.
8Bond example, I
- 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.
9Semiannual payments
- 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.
10Bond example, II
- 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.
11Bond example, III
- 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.
12YTM example
- 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 ().
13Bond price and YTM
- 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.
14Bond markets
- Trading is inactive for corporate bonds
typically, trading occurs in OTC
(over-the-counter not exchange) Illiquid. - Trading is active for U.S. government debt
instruments. This sector has many international
participants, e.g., Chinese Central Bank.
15Bond reporting
- 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/Defaul
t.aspxority)
16A FINRA bond quotation
- Issue IBM.GT IBM 8.375 11/01/2019
- Rating -------------------Last Sale
---------------------------- - Moody's/SP/Fitch Date Price
Yield - A1 / A / AA- 05/02/2007 125.00
5.569263 - This TRACE quotation was retrieved on 05/15/2007.
- 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.
17Bond features, I
- 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 (gt 10 years) and note (lt 10 years) an
unsecured debt. - Sinking fund an account managed by the bond
trustee for early bond redemption.
18Bond features, II
- 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 lenders interest. - Treasury notes (2-10 years) and bonds (gt10
years) long-term debt securities issued by the
U.S. federal government.
19Bond features, III
- 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 holders option.
20Dividends as cash flows
- 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 flowscash 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.
21But the problems are
- 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.
22How about those no-dividend firms?
- 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.
23Infinite terms?
- 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.
24Zero-growth DDM
- 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 GEs future
dividends. The applicable discount rate is 10. - PV 2 / 10 20.
25Constant-growth DDM
- 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).
26Constant-growth DDM example
- 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.
27Multiple-stage DDM model
- 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.
28Multiple-stage example, I
- 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.
29Multiple-stage example, II
30Quality of inputs
- 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.
31Sensitivity
- You should change some of the parameters in the
previous Excel sheet to see the sensitivity of PV
with respect to changes in these parameters. - You would notice that PV is most sensitive to 2
parameters (1) cost of equity (i), i.e., the
discount rate, and (2) the long term growth rate,
i.e., the growth rate (g) after year 5.
32Cost of equity, i
- We will talk about the determination of required
return (i) in Chapter 10 Risk and Return. The
cost of equity is directed to the risk level of
the investment (project) because for a risky
project one would require a higher return
risk-return tradeoff. - In real life, the i estimates from practitioners
tend not to be too far away from one another.
33Long-term growth rate, g, I
- In contrast, the g estimates from practitioners
can have a wide range, particularly in the times
when the market is extremely optimistic or
pessimistic. - Empirical evidence indicates that the
relationship between past and future growth rates
is weak. This means that it is dangerous to
simply extrapolate past dividends (earnings, cash
flows) trends into the future to obtain the
future growth rate. - The game of guessing g -- the wild west.
- 2 cents the simple math in p. 141 is probably
not useful in real life.
34Mad money CNBC and alike
35P/E ratio, I
- 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.
36P/E ratio, II
- 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 SP 500 but
once they beat the SP 500, they tend to have
extremely good performance. - An effective, widely-used communication tool
because of its simplicity.
37Stock market reporting (WSJ), I
- This quotation was retrieved from WSJ on
05/15/2007. - STOCK SYM CLOSE NET CHG
- GenMotor GM 30.62 1.16
38Stock market reporting (WSJ), II
- Yesterdays (05/14/2007) closing price 30.62.
- Yesterdays closing price is higher than the
closing price of the previous trading day by
1.16.
39Let us work on this
- Q2, P. 154. Microhard has issued a bond with the
following characteristics (1) par 1000, (2)
time to maturity 20 years, (3) coupon rate 8
(4) semiannual payments. What is the price of
the bond if the YTM is (a) 10, and (b) 6?
40Mini-case report due
- Cancelled Please submit your report for
mini-case Stock Valuation at Ragan Thermal
Systems, p. 159, in 1 week. - For this assignment, you need equation (5.8), p.
141. The following reading in the textbook will
help you pp. 136-151. - Please be prepared to contribute to our
discussions on this mini-case.