Chapter 6: Bond Valuation and Interest Rates

Chapter 6
Interest Rates and Bond Valuation
SLO: Synthesize and apply financial data to Bonds and Stock
Valuations
©2020 McGraw-Hill Education. All rights reserved. Authorized
only for instructor use in the classroom. No reproduction or
further distribution permitted without the prior written consent
of McGraw-Hill Education.
1
Key Concepts and Skills
After studying this chapter, you should be able to:
Identify important bond features and types of bonds.
Describe bond values and why they fluctuate.
Discuss bond ratings and what they mean.
Evaluate the impact of inflation on interest rates.
Explain the term structure of interest rates and the determinants
of bond yields.
©2020 McGraw-Hill Education
6-‹Nº›
Chapter Outline
6.1Bonds and Bond Valuation.
6.2More on Bond Features.
6.3Bond Ratings.
6.4Some Different Types of Bonds.

6.5Bond Markets.
6.6Inflation and Interest Rates.
6.7Determinants of Bond Yields.
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Bond Definitions
Bond.
Debt contract.
Interest-only loan.
Par value (face value) approximately $1,000.
Coupon rate.
Coupon payment.
Maturity date.
Yield to maturity.
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Key Features of a Bond 1
Par value:
Face amount.
Re-paid at maturity.
Assume $1,000 for corporate bonds.
Coupon interest rate:
Stated interest rate.
Usually = YTM at issue.
Multiply by par value to get coupon payment.
6-‹Nº›

Key Features of a Bond 2
Maturity:
Years until bond must be repaid.
Yield to maturity (YTM):
The market required rate of return for bonds of similar risk and
maturity.
The discount rate used to value a bond.
Return if bond held to maturity.
Usually = coupon rate at issue.
Quoted as an APR.
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Bond Value
Bond Value = PV(coupons) + PV(par).
Bond Value = PV(annuity) + PV(lump sum)
Remember:
As interest rates increase present values decrease.
As interest rates increase, bond prices decrease
and vice versa.
6-‹Nº›
The Bond-Pricing Equation
PV(Annuity)
PV(lump sum)
C = Coupon payment; F = Face value
Return to Quiz

6-‹Nº›
Texas Instruments BA-II Plus
N= number of periods to maturity.
I/Y= period interest rate = YTM.
PV= present value = bond value.
PMT= coupon payment.
FV= future value = face value = par value.
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Spreadsheet Formulas
=FV(Rate,Nper,Pmt,PV,0/1).
=PV(Rate,Nper,Pmt,FV,0/1).
=RATE(Nper,Pmt,PV,FV,0/1).
=NPER(Rate,Pmt,PV,FV,0/1).
=PMT(Rate,Nper,PV,FV,0/1).
Inside parens: (RATE,NPER,PMT,PV,FV,0/1).
“0/1” Ordinary annuity = 0 (default).
Annuity Due = 1 (must be entered).
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Pricing Specific Bonds on the TI BAII+
Bond Worksheet: 2nd BOND (above “9”).
SDT CPN RDT RV ACT 2/Y YLD PRI.
SDT = Actual Settlement date (enter MM.DDYY).
CPN = Annual rate in %.
RDT = Actual Redemption (maturity) date.
RV = Redemption value as a % of par.

ACT = ACT/360 day count setting.
2/Y = 2/Y – 1/Y coupons per year.
YLD = Yield to redemption.
PRI = Dollar price per $100 of par value.
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Pricing Specific Bonds in Excel
=PRICE(Settlement,Maturity,Rate,Yld,Redemption,
Frequency,Basis).
=YIELD(Settlement,Maturity,Rate,Pr,Redemption,
Frequency,Basis).
Settlement = actual date as a serial number.
Maturity = actual date as a serial number.
Redemption and Pr(ice) = % of par value.
Rate (coupon) and Yld = annual rates as decimals.
Frequency = # of coupons per year.
Basis = day count convention (enter “2” for ACT/360).
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Valuing a Discount Bond with Annual Coupons
Coupon rate = 10%
Annual coupons
Par = $1,000
Maturity = 5 years
YTM = 11%5N11I/Y100PMT1000FVCPT PV= − 963.04
Using the calculator:

Using the formula:
B = PV(annuity) + PV(lump sum)
B = 369.59 + 593.45 = 963.04
Using Excel: =PV(0.11, 5, 100, 1000, 0)
Bond”
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Valuing a Premium Bond with Annual Coupons
Coupon rate = 10%
Annual coupons
Par = $1,000
Maturity = 20 years
YTM = 8%20N8I/Y100PMT1000FVCPT PV= − 1196.36
Using the calculator:
Using the formula:
B = PV(annuity) + PV(lump sum)
B = 981.81 + 214.55 = 1196.36
Using Excel: =PV(0.08, 20, 100, 1000, 0)
Note:
Bond”
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Graphical Relationship Between Price and Yield-to-Maturity

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Bond Prices: Relationship
Between Coupon and Yield
Coupon rate =
“Discount bond” … Why?
“Premium bond” … Why?
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Bond Value ($) versus Years Remaining to Maturity
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The Bond-Pricing Equation
Adjusted for Semiannual Coupons
-annual couponYTM =
-annual YTMt =
-month
periods to maturity
6-‹Nº›

Semiannual Bonds
Example 6.1
Coupon rate = 14% − Semiannual.
YTM = 16% (APR).
Maturity = 7 years
Number of coupon payments? (2t or N).
14 = 2 × 7 years.
Semiannual coupon payment? (C/2 or PMT).
$70 = (14% × Face Value)/2.
Semiannual yield?(YTM/2 or I/Y).
8% = 16%/2
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Example 6.1
Semiannual coupon = $70.
Semiannual yield = 8%.
Periods to maturity = 14.
Bond value =
70[1 – 1/(1.08)14] / .08 + 1000 / (1.08)14 = 917.56.
Using Excel: =PV(0.08, 14, 70, 1000, 0).
Using the calculator:14N8I/Y70PMT1000FVCPT PV= −917.56
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Interest Rate Risk 1
Price Risk.

Change in price due to changes in interest rates.
Long-term bonds have more price risk than short-term bonds.
Low coupon rate bonds have more price risk than high coupon
rate bonds.
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Interest Rate Risk 2
Reinvestment Rate Risk.
Uncertainty concerning rates at which cash flows can be
reinvested.
Short-term bonds have more reinvestment rate risk than long-
term bonds.
High coupon rate bonds have more reinvestment rate risk than
low coupon rate bonds.
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Figure 6.2
Access the text alternative for these images
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Computing Yield-to-Maturity (YTM)
Yield-to-maturity (YTM) = the market required rate of return
implied by the current bond price
With a financial calculator,
Enter N, PV, PMT, and FV.
Remember the sign convention.

PMT and FV need to have the same sign (+).
PV the opposite sign (−).
CPT I/Y for the yield.
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YTM with Annual Coupons
Consider a bond with a 10% annual coupon rate, 15 years to
maturity and a par value of $1000. The current price is $928.09.
Will the yield be more or less than
928.09PV (enter as a negative)
Using Excel: =RATE(15, 100, −928.09, 1000, 0).
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YTM with Semiannual Coupons 1
Suppose a bond with a 10% coupon rate and semiannual
coupons, has a face value of $1000, 20 years to maturity and is
selling for $1197.93.
Is the YTM more or less than 10%?
What is the semiannual coupon payment?
How many periods are there?
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YTM with Semiannual Coupons 2
Suppose a bond with a 10% coupon rate and semiannual
coupons, has a face value of $1,000, 20 years to maturity and is
selling for $1,197.93.40N1197.93PV

(negative)1000FV50PMTCPT PV4% (= ½ YTM)
YTM = 4%*2 = 8%
Using Excel: =RATE(40, 50, −1197.93, 1000, 0) = 4%.
NOTE: Solving a semi-annual payer for YTM results in a 6-
month yield.
The calculator & Excel solve what you enter.
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Table 6.1
TABLE 6.1 Summary of bond valuation
Finding the value of a bond
Bond value = C × [1 − 1/(1 + r)t]/r + F/(1 + r)t
where:
C = Coupon paid each period
r = Rate per period
t = Number of periods
F = Bond’s face value
Finding the yield on a bond
Given a bond value, coupon, time to maturity, and face value, it
is possible to find the implicit discount rate, or yield to
maturity, by trial and error only. To do this, try different
discount rates in the preceding formula until the calculated bond
value equals the given bond value. Remember that increasing
the rate decreases the bond value.
6-‹Nº›
Debt or Equity
Debt.
Not an ownership interest.
No voting rights.

Interest is tax-deductible.
Creditors have legal recourse if interest or principal payments
are missed.
Excess debt can lead to financial distress and bankruptcy.
Equity.
Ownership interest.
Common stockholders vote to elect the board of directors and
on other issues.
Dividends are not tax deductible.
Dividends are not a liability of the firm until declared.
Stockholders have no legal recourse if dividends are not
declared.
An all-equity firm cannot go bankrupt.
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The Bond Indenture
“Deed of Trust”
Contract between issuing company and
bondholders includes:
Basic terms of the bonds.
Total amount of bonds issued.
Secured versus Unsecured.
Sinking fund provisions.
Call provisions.
Deferred call.
Call premium.
Details of protective covenants.
Return to Quiz
6-‹Nº›

Bond Classifications
Registered versus Bearer Bonds.
Security.
Collateral – secured by financial securities.
Mortgage – secured by real property, normally land or
buildings.
Debentures – unsecured.
Notes – unsecured debt with original maturity less than 10
years.
Seniority.
Senior versus Junior, Subordinated.
6-‹Nº›
Bond Characteristics and
Required Returns
Coupon rate.
Usually ≈ yield at issue.
Which bonds will have the higher coupon, all else equal?
Secured debt versus a debenture.
Subordinated debenture versus senior debt.
A bond with a sinking fund versus one without.
A callable bond versus a non-callable bond.
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Bond Ratings – Investment Quality
High Grade.
Moody’s Aaa and S&P AAA – capacity to pay is extremely
strong.
Moody’s Aa and S&P AA – capacity to pay is very strong.

Medium Grade.
Moody’s A and S&P A – capacity to pay is strong, but
more susceptible to changes in circumstances.
Moody’s Baa and S&P BBB – capacity to pay is adequate,
adverse conditions will have more impact on the firm’s ability
to pay.
Return to Quiz
6-‹Nº›
Bond Ratings – Speculative
Low Grade.
Moody’s Ba, B, Caa and Ca.
S&P BB, B, CCC, CC.
Considered speculative with respect to capacity to pay. The “B”
ratings are the lowest degree of speculation.
Very Low Grade.
Moody’s C and S&P C – income bonds with no interest being
paid.
Moody’s D and S&P D – in default with principal and interest
in arrears.
6-‹Nº›
Government Bonds 1
Municipal Securities.
Debt of state and local governments.
Varying degrees of default risk, rated similar to corporate debt.
Interest received is tax-exempt at the federal level.
Interest usually exempt from state tax in issuing state.

6-‹Nº›
Government Bonds 2
Treasury Securities = Federal government debt.
Treasury Bills (T-bills).
Pure discount bonds.
Original maturity of one year or less.
Treasury notes.
Coupon debt.
Original maturity between one and ten years.
Treasury bonds.
Coupon debt.
Original maturity greater than ten years.
6-‹Nº›
Example 6.4
A taxable bond has a yield of 8% and a municipal bond has a
yield of 6%
If you are in a 40% tax bracket, which bond do you prefer?
8%(1 − .4) = 4.8%.
The after-tax return on the corporate bond is 4.8%, compared to
a 6% return on the municipal.
At what tax rate would you be indifferent between the two
bonds?
8%(1 − T) = 6%.
T = 25%.
6-‹Nº›
Zero Coupon Bonds

Make no periodic interest payments (coupon rate = 0%).
Entire yield-to-maturity comes from the difference between the
purchase price and the par value (capital gains).
Cannot sell for more than par value.
Sometimes called zeroes, or deep discount bonds.
Treasury Bills and U.S. Savings bonds are good examples of
zeroes.
6-‹Nº›
Floating Rate Bonds
Coupon rate floats depending on some index value.
Examples – adjustable rate mortgages and inflation-linked
Treasuries.
Less price risk with floating rate bonds.
Coupon floats, so is less likely to differ substantially from the
yield-to-maturity.
Coupons may have a “collar” – the rate cannot go above a
specified “ceiling” or below a specified “floor.”
6-‹Nº›
Other Bond Types
Structured notes.
Convertible bonds.
Put bonds.
Many types of provisions can be added to a bond.
Important to recognize how these provisions affect required
returns.
Who does the provision benefit?

6-‹Nº›
Bond Markets
Primarily over-the-counter transactions with dealers connected
electronically.
Extremely large number of bond issues, but generally low daily
volume in single issues.
Getting up-to-date prices difficult, particularly on small
company or municipal issues.
Treasury securities are an exception.
6-‹Nº›
Work the Web Example
Bond information is available online.
One good site:
http://finra-markets.morningstar.com/BondCenter/Default.jsp
Click on this link to go to the site.
Use “Quick Bond Search” to observe the yields for various bond
types, and the shape of the yield curve.
6-‹Nº›
Corporate Bond Quotations
ABC 8.375 Jul 15, 2033 100.641 8.316 362 30 763,528
What company are we looking at?
What is the coupon rate? If the bond has a $1000 face value,
what is the coupon payment each year?
When does the bond mature?
What was the trading volume on that day?
What is the quoted price? (Ask price).

How does the bond’s yield compare to a comparable
Treasury note/bond?
8.316 = Last yield.
362 = basis point difference versus 30-yr T-Bond.
6-‹Nº›
Treasury Quotations 1
FIGURE 6.3 Sample Wall Street Journal U.S. Treasury note and
bond prices
U.S. Treasury Quotes
Treasury note and bond data are representative over-the-counter
quotations as of 3 p.m. Eastern
time.MaturityCouponBidAskedChgAsked
Yield1/31/20191.50099.546999.5625−0.00782.20512/31/20212.
12597.890697.90630.07032.7491/31/20221.50095.656395.6719
0.05472.7622/28/20232.62599.210999.22660.11722.8019/30/20
231.37592.796992.81250.11722.8472/29/20242.12596.117296.1
3280.14842.8647/31/20242.12595.734495.75000.11722.8871/31
/20252.50097.632897.64840.19532.8924/30/20252.87599.83599
9.85160.21092.89911/15/20266.500126.6406126.65630.31252.9
062/15/20295.250120.9453121.00780.40632.9415/15/20306.250
132.8984132.96090.46882.949
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FIGURE 6.3 Sample Wall Street Journal U.S. Treasury note and
bond prices (Continued)
U.S. Treasury Quotes
Treasury note and bond data are representative over-the-counter
quotations as of 3 p.m. Eastern

time.MaturityCouponBidAskedChgAsked
Yield2/15/20364.500120.9375121.00000.56252.9645/15/20375.
000129.0938129.15630.66412.97311/15/20394.375121.3047121
.36720.69533.0145/15/20404.375121.5313121.59380.75003.021
8/15/20413.750111.6875111.75000.75003.0405/15/20423.00099
.187599.21880.72663.0462/15/20433.125101.1641101.19530.73
443.0562/15/20443.625110.0313110.06250.68753.0568/15/2046
2.25084.679784.71090.60163.0645/15/20473.00098.757898.789
10.69533.0635/15/20483.125101.1875101.21880.74223.062
Source: www.wsj.com, 6/14/2018.
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Highlighted quote in Figure 6.3.
5/15/20306.250132.8984132.96090.46882.949
When does the bond mature?
What is the coupon rate on the bond?
What is the bid price? What does this mean?
What is the ask price? What does this mean?
How much did the price change from the previous day?
What is the YTM based on Ask price?
6-‹Nº›
5/15/20306.250132.8984132.96090.46882.949
Maturity = May 15, 2030.
Coupon rate = 6.250% per year.
Bid price = 132.8984% of par.
Price at which dealer is willing to buy from you.
Ask price = 132.9609% of par.

Price at which dealer is willing to sell to you.
Bid-Ask Spread = Dealer’s profit.
Change = ask price is up .4688% since the previous day.
Asked Yield = 2.949%.
6-‹Nº›
Quoted Price versus Invoice Price
Quoted bond prices = “clean” price.
Net of accrued interest.
Invoice Price = “dirty” or “full” price.
Price actually paid.
Includes accrued interest.
Accrued Interest.
Interest earned since last coupon payment is owed to bond seller
at time of sale.
6-‹Nº›
Inflation and Interest Rates
Real rate of interest.
= Change in purchasing power.
Nominal rate of interest.
= Quoted rate of interest.
= Change in purchasing power and inflation.
The ex ante nominal rate of interest includes our desired real
rate of return plus an adjustment for expected inflation.
6-‹Nº›

The Fisher Effect
The Fisher Effect defines the relationship between real rates,
nominal rates and Inflation.
(1 + R) = (1 + r)(1 + h).
R = nominal rate (Quoted rate).
r = real rate.
h = expected inflation rate.
Approximation: R = r + h.
Return to Quiz
6-‹Nº›
Example 6.6
If we require a 10% real return and we expect inflation to be
8%, what is the nominal rate?
R = (1.1)(1.08) – 1 = .188 = 18.8%.
Approximation: R = 10% + 8% = 18%.
Because the real return and expected inflation are relatively
high, there is significant difference between the actual Fisher
Effect and the approximation.
6-‹Nº›
Term Structure of Interest Rates
Term structure: The relationship between time to maturity and
yields, all else equal.
The effect of default risk, different coupons, etc., has been
removed.
Yield curve: Graphical representation of the term structure.
Normal = upward-
Inverted = downward-
Return to Quiz

6-‹Nº›
Figure 6.5 A: Upward-Sloping Yield Curve
6-‹Nº›
Figure 6.5 B: Downward-Sloping Yield Curve
6-‹Nº›
Figure 6.6: Treasury Yield Curve
More information can be found at this link.
6-‹Nº›
Factors Effecting Required Return
Default risk premium – bond ratings.
Taxability premium – municipal versus taxable.
Liquidity premium – bonds that have more frequent trading will
generally have lower required returns.
Maturity premium – longer term bonds will tend to have higher

required returns.
Anything else that affects the risk of the cash flows to the
bondholders will affect the required returns.
Return to Quiz
6-‹Nº›
Quick Quiz
How do you find the value of a bond and why do bond prices
change? (Slide 6.8).
What is a bond indenture and what are some of the important
features? (Slide 6.30).
What are bond ratings and why are they important? (Slide
6.33).
How does inflation affect interest rates? (Slide 6.50).
What is the term structure of interest rates?(Slide 6.52).
What factors determine the required return on bonds? (Slide
6.56).
6-‹Nº›
Chapter 6
END
Accessibility Content:
Text Alternatives for Images

1-‹Nº›
Figure 6.2 Text Alternative
This graph has the interest rate (percent) on the x-axis and the
bond value (in dollars) on the y-axis. The x-axis goes from zero
to twenty counting by fives. The y-axis goes from zero to
$2,000 counting by $500. The graph displays two intersecting
curves. The curve for the 1-year bond is so slight that it almost
looks like a line with a slight negative slope. If interest rates
are 5%, a 1-year bond with a 10% rate has a value of $1,047.62.
If interest rates are 20%, a 1-year bond with a 10% rate has a
value of $916.67. The curve for a 30-year bond is much steeper.
If interest rates are 5%, a 30-year bond with a 10% rate has a
value of $1768.62. If interest rates are 20%, a 30-year bond
with a 10% rate has a value of $502.11.
Return to slide containing original image
1-‹Nº›
Figure 6.5 A: Upward-Sloping Yield Curve Text Alternative
Both graphs have the x-axis labeled as "time to maturity" with
no values indicated on the axis. The y-axis is labeled "interest
rate" also with no labeled values. In both graphs the real rate is
plotted first as a horizontal line about one-quarter of the way up
the y-axis. In the upward-sloping term structure, the line
indicating the inflation premium is vertically higher than the
real rate, and has a positive slope, showing that inflation is
anticipated to increase over time. Starting at the same location
on the y-axis and increasing in a concave down fashion is a
curve that describes the interest rate risk premium. As the
inflation premium increases, so does the interest rate premium,

but at a less rapid rate over time. Overall, in the upward-sloping
term structure, the nominal interest rate increases.
In the downward-sloping term structure graph, the line
indicating the inflation premium intersects the y-axis as high as
possible for the unmarked axis and decreases over time in a
linear manner indicating that inflation is anticipated to decrease
over time. Starting at the same location on the y-axis and
decreasing in a concave down fashion is a curve that describes
the interest rate risk premium. Overall, in the downward-sloping
term structure the nominal interest rate decreases.
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Figure 6.6: Treasury Yield Curve
Text Alternative
The x-axis shows maturity dates in 1 mo, 3 mo, 6 mo, 1yr, 2 yr,
3 yr, 5 yr, 7 yr, 10 yr, 20 yr, and 30 yr. The y-axis shows yield
% for zero to 3 percent in 0.5% increments. Both nominal and
real plots are shown. The nominal plot starts at 1.4 for 1 month
and steadily rises to 3.0% for 30 yr on Date 2/1/2018. The real
plot starts at 0.6% for 5 yr and rises to 0.85% for 30 yr.
1-‹Nº›
Bond PriceYou are looking at a bond that has 25 years to
maturity. The coupon rate is 9% and coupons are paid
semiannually. The yield-to-maturity is 8%. What is the current
price?Settlement Date:09/15/05(Choose a date)Maturity
Date:09/15/30(Choose a date 25 years after settlement)Coupon
Rate:9%(Same as .09, needs to be annual rate)YTM:8%(Same as
.08, needs to be annual rate)Face Value (% of par):100Coupons

per year:2Price(% of
par):110.7410923083Formula:=PRICE(B3,B4,B5,B6,B7,B8)
YieldYou are looking at a bond that has 25 years to maturity.
The coupon rate is 9% and coupons are paid semiannually. The
current price is $950. What is the yield to maturity?Settlement
Date:03/15/02(Choose a date)Maturity Date:03/15/27(Choose a
date 25 years after settlement)Coupon Rate:9%(Same as .09,
needs to be annual rate)Bond Price (% of par):95Face Value (%
of par):100Coupons per year:2Yield to maturity:9.53%(The
answer is returned as a decimal; format the cell to get a
percent.)Formula:=YIELD(B3,B4,B5,B6,B7,B8)
TVMYou are looking at a bond that has 25 years to maturity.
The coupon rate is 9% and coupons are paid semiannually. The
yield-to-maturity is 8%. What is the current
price?RATE4.00%(8%/2)NPER50(25*2)PMT4.5(9%*100/2)FV1
00(Using 100 par so that PV will give price as % of
par)Price$110.74Formula: -PV(B3,B4,B5,B6)You are looking at
a bond that has 25 years to maturity. The coupon rate is 9% and
coupons are paid semiannually. The current price is $950. What
is the yield to maturity?NPER50(25*2)PMT4.5(9%*100/2)PV-
95(Entered as a % of par and negative for sign
convention)FV100YTM9.53%(Returns as a whole percent,
format to get decimal
places)Formula:=2*RATE(B11,B12,B13,B14)(Have to multiply
by 2 because it returns a semiannual rate)
Chapter 7
Equity Markets and Stock Valuation
SLO: Synthesize and apply financial data to Bonds and Stock
Valuations

1
Key Concepts and Skills
Understand how stock prices depend on future dividends and
dividend growth.
Be able to compute stock prices using the dividend growth
model.
Understand how corporate directors are elected.
Understand how stock markets work.
Understand how stock prices are quoted.
7-‹Nº›
Chapter Outline
7.1Common Stock Valuation.
7.2Some Features of Common and Preferred Stock.
7.3The Stock Markets.
7-‹Nº›
Cash Flows for Stockholders
If you own a share of stock, you can receive cash in two ways.
The company pays dividends.
You sell your shares, either to another investor in the market or
back to the company.
As with bonds, the price of the stock is the present value of
these expected cash flows.
Dividends → cash income.

Selling → capital gains.
7-‹Nº›
One-Period Example 1
Suppose you are thinking of purchasing the stock of Moore Oil,
Inc.
You expect it to pay a $2 dividend in one year.
You believe you can sell the stock for $14 at that time.
You require a return of 20% on investments of this risk.
What is the maximum you would be willing to pay?
7-‹Nº›
One-Period Example 2
D1 = $2 dividend expected in one year.
R = 20%.
P1 = $14.
CF1 = $2 + $14 = $16.
Compute the PV of the expected cash flows.
7-‹Nº›
Two-Period Example
What if you decide to hold the stock for two years?
D1 = $2.00CF1 = $2.00.
D2 = $2.10.
P2 = $14.70.

Now how much would you be willing to pay?
CF2 = $2.10 + $14.70 = $16.80
7-‹Nº›
Three-Period Example
What if you decide to hold the stock for three years?
D1 = $2.00 CF1 = $2.00.
D2 = $2.10CF2 = $2.10.
D3 = $2.205.
P3 = $15.435.
Now how much would you be willing to pay?
CF3 = $2.205 + $15.435 = $17.640
7-‹Nº›
Three-Period Example
Using TI BAII + Cash Flow Worksheet
Cash Flows:CF0=0CF1=2.00CF2=2.10CF3=17.64DisplayYou
EnterCF C000Enter, DownC012Enter, DownF011Enter,
DownC022.10Enter, DownF021Enter, DownC0317.64Enter,
DownF031Enter, Down NPVI20Enter, Down CPTNPV 13.33
7-‹Nº›

Developing the Model
You could continue to push back when you would sell the stock.
You would find that the price of the stock is really just the
present value of all expected future dividends.
7-‹Nº›
Stock Value = PV of Dividends
How can we estimate all future dividend
payments?
7-‹Nº›
Estimating Dividends Special Cases
Constant dividend/Zero Growth.
Firm will pay a constant dividend forever.
Like preferred stock.
Price is computed using the perpetuity formula.
Constant dividend growth.
Firm will increase the dividend by a constant percent every
period.
Supernormal growth.
Dividend growth is not consistent initially, but settles down to
constant growth eventually.

7-‹Nº›
Zero Growth
Dividends expected at regular intervals
forever = perpetuity.
P0 = D / R
Suppose stock is expected to pay a $0.50 dividend every quarter
and the required return is 10% with quarterly compounding.
What is the price?
7-‹Nº›
Constant Growth Stock
One whose dividends are expected togrow forever at a constant
rate, g.
D1 = D0(1 + g)1
D2 = D0(1 + g)2
Dt = D0(1 + g)t
D0 = Dividend JUST PAID.
D1 to Dt = Expected dividends.
7-‹Nº›
Projected Dividends
D0 = $2.00 and constant g = 6%.
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.

7-‹Nº›
Dividend Growth Model
“Gordon Growth Model”
7-‹Nº›
DGM: Example 1
Suppose Big D, Inc. just paid a dividend of $.50. It is expected
to increase its dividend by 2% per year. If the market requires a
return of 15% on assets of this risk, how much should the stock
be selling for?
D0= $0.50
g = 2%
R = 15%
7-‹Nº›
DGM: Example 2
Suppose TB Pirates, Inc. is expected to pay a $2 dividend in one
year. If the dividend is expected to grow at 5% per year and the
required return is 20%, what is the price?
D1 = $2.00
g = 5%
r = 20%

7-‹Nº›
Stock Price Sensitivity to Dividend Growth, g
7-‹Nº›
Stock Price Sensitivity to Required Return, R
7-‹Nº›
Example 7.3
Gordon Growth Company I
Gordon Growth Company is expected to pay a dividend of $4
next period and dividends are expected to grow at 6% per year.
The required return is 16%.
What is the current price?
7-‹Nº›
Example 7.3
Gordon Growth Company II 1

What is the price expected to be in year 4?
7-‹Nº›
Example 7.3
Gordon Growth Company II 2
What is the implied return given the change in price during the
four year period?
50.50 = 40(1 + return)4; return = 6%
4 N; −40 PV; 50.50 FV; 0 PMT; CPT I/Y = 6%
The price grows at the same rate as dividends.
7-‹Nº›
Constant Growth Model Conditions
Dividend expected to grow at g forever.
Stock price expected to grow at g forever.
Expected dividend yield is constant.
Expected capital gains yield is constant and
equal to g.
Expected total return, R, must be > g.
Expected total return (R):
= expected dividend yield (DY).
+ expected growth rate (g).
= dividend yield + g.
7-‹Nº›

Nonconstant Growth
Suppose a firm is expected to increase dividends by 20% in one
year and by 15% in two years. After that dividends will increase
at a rate of 5% per year indefinitely. If the last dividend was $1
and the required return is 20%, what is the price of the stock?
Remember that we have to find the PV of all expected future
dividends.
7-‹Nº›
Nonconstant Growth –
Solution
Compute the dividends until growth levels off.
D1 = 1(1.2) = $1.20.
D2 = 1.20(1.15) = $1.38.
D3 = 1.38(1.05) = $1.449.
Find the expected future price at the beginning of the constant
growth period:
P2 = D3 / (R – g) = 1.449 / (.2 − .05) = 9.66.
Find the present value of the expected future cash flows.
P0 = 1.20 / (1.2) + (1.38 + 9.66) / (1.2)2 = 8.67.

7-‹Nº›
Nonconstant + Constant Growth 1
Basic PV of all Future Dividends Formula
Dividend Growth Model
7-‹Nº›
Nonconstant + Constant Growth 2
+

7-‹Nº›
Nonconstant Growth Followed by Constant Growth
7-‹Nº›
Quick Quiz: Part 1
What is the value of a stock that is expected to pay a constant
dividend of $2 per year if the required return is 15%?
What if the company starts increasing dividends by 3% per year
beginning with the next dividend? The required return remains
at 15%.
7-‹Nº›

Using the DGM to Find R
Start with the DGM:
Rearrange and solve for R:
7-‹Nº›
Finding the Required Return
Example 1
A firm’s stock is selling for $10.50. They just paid a $1
dividend and dividends are expected to grow at 5% per year.
What is the required return?
7-‹Nº›
Example 2
P0 = $10.50.

D0 = $1.
g = 5% per year.
7-‹Nº›
Example 3
P0 = $10.50.
D0 = $1.
g = 5% per year.
What is the dividend yield?
1(1.05) / 10.50 = 10%.
What is the capital gains yield?
g = 5%.

Dividend Yield
Capital Gains
Yield
7-‹Nº›
Valuation Using Multiples
For stocks that don’t pay dividends (or have erratic dividend
growth rates), we can value them using the price-earnings (PE)
ratio and/or the price-sales ratio:
Price at time t = Pt
= Benchmark PE ratio × Earnings per sharet
Price at time t = Pt
= Benchmark price-sales ratio × Sales per sharet
The price-sales ratio can be especially useful when earnings are
negative.
7-‹Nº›

Valuation Using Multiples
Example
Suppose we are trying to value the company Inactivision, a
video game developer that does not pay dividends. If the
appropriate industry PE for this type of company is 20 and you
predict earnings to be $2.50 per share for the coming year, then
the forecasted stock price for a year from now, or target price,
is the following:
Target price = 20 × $2.50 = $50
7-‹Nº›
Table 7.1
TABLE 7.1 Summary of stock valuation
The general case
In general, the price today of a share of stock, P0, is the present
value of all of its future dividends, D1, D2, D3, … :
where R is the required return.
Constant growth case
If the dividend is constant and equal to D, then the price can be
written as:

If the dividend grows at a steady rate g, then the price can be
written as:
This result is called the dividend growth model.
Nonconstant Growth
If the dividend grows steadily after t periods, then the price can
be written as:
where:
The required return, R, can be written as the sum of two things:
R = D1 / P0 + g
where D1/P0 is the dividend yield and g is the capital gains
yield (which is the same thing as the growth rate in dividends
for the steady growth case).
Valuation Using Comparables
For stocks that don’t pay dividends (or have erratic dividend
growth rates), we can value them using the PE ratio and/or the
price-sales ratio:
Pt = Benchmark PE ratio × EPSt

Pt = Benchmark price – sales ratio × Sales per sharet
7-‹Nº›
Features of Common Stock 1
Voting Rights.
Stockholders elect directors.
Cumulative voting versus Straight voting.
Boards are often staggered, or “classified.”
Proxy voting.
Classes of stock.
Founders’ shares.
Class A and Class B shares.
Return to Quick Quiz
7-‹Nº›
Features of Common Stock 2
Other Rights.
Share proportionally in declared dividends.
Share proportionally in remaining assets during liquidation.

Preemptive right.
Right of first refusal to buy new stock issue to maintain
proportional ownership if desired.
7-‹Nº›
Dividend Characteristics
Dividends are not a liability of the firm until declared by the
Board of Directors.
A firm cannot go bankrupt for not declaring dividends.
Dividends and Taxes.
Dividends are not tax deductible for firm.
Taxed as ordinary income for individuals.
Dividends received by corporations have a minimum 70%
exclusion from taxable income.
7-‹Nº›
Features of Preferred Stock
Dividends.

Must be paid before dividends can be paid to common
stockholders.
Not a liability of the firm.
Can be deferred indefinitely.
Most preferred dividends are cumulative.
Missed preferred dividends have to be paid before common
dividends can be paid.
Preferred stock generally does not carry voting rights.
7-‹Nº›
The Stock Markets
Primary versus Secondary Markets.
Primary = new-issue market.
Secondary = existing shares traded among investors.
Dealers versus Brokers.
Dealer: Maintains an inventor.
Ready to buy or sell at any time.
Think “Used car dealer.”
Broker: Brings buyers and sellers together.
Think “Real estate broker.”

7-‹Nº›
New York Stock Exchange (NYSE)
NYSE.
Merged with Euronext in 2007.
NYSE Euronext merged with the American Stock Exchange in
2008.
Members (Historically).
Buy a trading license (own a seat).
Designated market makers, DMMs (formerly known as
“specialists”).
Floor brokers.
Supplemental liquidity providers (SLPs).
7-‹Nº›
NYSE Operations
Operational goal = attract order flow.
NYSE DMMs:
Assigned broker/dealer.
Each stock has one assigned DMM.

All trading in that stock occurs at the “DMM’s post.”
Trading takes place between customer orders placed with the
DMMs and “the crowd.”
“Crowd”= Floor brokers and SLPs.
7-‹Nº›
NASDAQ
NASDAQ OMX (merged 2007).
Computer-based quotation system.
Multiple market makers.
Electronic Communications Networks.
Three levels of information.
Level 1 – median quotes, registered representatives.
Level 2 – view quotes, brokers & dealers.
Level 3 – view and update quotes, dealers only.
Large portion of technology stocks.
7-‹Nº›
ECNs

Electronic Communications Networks provide direct trading
among investors.
Developed in late 1990s.
ECN orders transmitted to NASDAQ.
Observe live trading online at Batstrading.com.
7-‹Nº›
Reading Stock Quotes
What information is provided in the stock quote?
Click on this link to go to Bloomberg for current stock quotes.
7-‹Nº›
Work the Web
Not only are stock price quotes readily available online. Some
online trading sites display their “order book” or “limit order
book” live online.
The BATS Exchange was one of these websites until it was

purchased by the CBOE in 2016.
Follow this link to see current buy and sell orders for Microsoft
(MSFT).
7-‹Nº›
Quick Quiz: Part 2 1
You observe a stock price of $18.75. You expect a dividend
growth rate of 5% and the most recent dividend was $1.50.
7-‹Nº›
Quick Quiz: Part 2 2
What are some of the major characteristics of common stock?
(Slide 38 and Slide 39).
What are some of the major characteristics of preferred stock?

(Slide 41).
7-‹Nº›
Chapter 7
END
Accessibility Content:
Text Alternatives for Images
1-‹Nº›
Reading Stock Quotes Text Alternative
Data are listed and graphed and include previous close, open,
bid, ask, day's range, 52-week range, ex-dividend date, and so

on.
1-‹Nº›

Chapter 6: Bond Valuation and Interest Rates

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