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Transcript of ACF2013 Session 03
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Applied Corporate Finance
Session 3:Interest Rates, Bond Valuation
and Stock Valuation
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1. Know the important bond features and bondtypes2. Understand bond values and why they fluctuate3. Understand bond ratings and what they mean4. Understand the impact of inflation on interest
rates5. Understand the term structure of interest rates
and the determinants of bond yields6. Understand how stock prices depend on future
dividends and dividend growth7. Be able to compute stock prices using the
dividend growth model
Learning outcomes
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Consider a bond with a coupon rate of 10% and annualcoupons. The par value is $1,000, and the bond has 5years to maturity. The yield to maturity is 11%. What isthe value of the bond? Using the formula:
B = PV of annuity + PV of lump sum B = 100[1 1/(1.11) 5] / .11 + 1,000 / (1.11) 5 B = 369.59 + 593.45 = 963.04
Suppose you are reviewing a bond that has a 10%annual coupon and a face value of $1000. There are20 years to maturity, and the yield to maturity is 8%.What is the price of this bond? Using the formula:
B = PV of annuity + PV of lump sum B = 100[1 1/(1.08) 20] / .08 + 1000 / (1.08) 20 B = 981.81 + 214.55 = 1196.36
Valuing a Discount Bond with Annual Coupons
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Relationship Between Price and Yield-to-maturity (YTM)for 8% bond
600
700
800
900
1000
1100
1200
1300
1400
1500
0% 2% 4% 6% 8% 10% 12% 14%
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B o n
d P r i c e
Yield-to-maturity (YTM)
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If YTM = coupon rate, then par value = bond price If YTM > coupon rate, then par value > bond price
Why? The discount provides yield above coupon rate Price below par value, called a discount bond
If YTM < coupon rate, then par value < bond price Why? Higher coupon rate causes value above par Price above par value, called a premium bond
Bond Prices: RelationshipBetween Coupon and Yield
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Find present values based on the paymentperiod How many coupon payments are there?
What is the semiannual coupon payment? What is the semiannual yield? B = 70[1 1/(1.08) 14] / .08 + 1,000 / (1.08) 14 =
917.56
Example 7.1
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Price Risk Change in price due to changes in interest rates Long-term bonds have more price risk than short-term bonds
(see page 223 for an example) Low coupon rate bonds have more price risk than high
coupon rate bonds Price risk is greater when the yield-to-maturity is low than
when the yield-to-maturity is high (Why? Look at the slope ofthe price and yield-to-maturity graph)
Reinvestment Rate Risk Uncertainty concerning rates at which cash flows can be
reinvested Short-term bonds have more reinvestment rate risk thanlong-term bonds
High coupon rate bonds have more reinvestment rate riskthan low coupon rate bonds
Interest Rate Risk
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Figure 7.2
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Yield to Maturity (YTM) is the rate implied bythe current bond price Finding the YTM requires trial and error if you do
not have a financial calculator and is similar tothe process for finding r with an annuity
If you have a financial calculator, enter N, PV,PMT, and FV, remembering the sign convention
(PMT and FV need to have the same sign, PV theopposite sign)
See examples 7.2 & 7.3 in text
Computing Yield to Maturity
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Suppose a bond with a 10% coupon rateand semiannual coupons, has a facevalue of $1,000, 20 years to maturity and
is selling for $1,197.93. Is the YTM more or less than 10%? What is the semiannual coupon payment? How many periods are there?
Using a financial calculator: N = 40; PV = -1,197.93; PMT = 50; FV = 1,000; CPT
I/Y = 4% (Is this the YTM?) YTM = 4%*2 = 8%
YTM with SemiannualCoupons
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Table 7.1
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Bonds of similar risk (and maturity) will bepriced to yield about the same return,regardless of the coupon rate
If you know the price of one bond, you canestimate its YTM and use that to find theprice of the second bond
This concept of pricing an asset based onthe price of a similar asset can be used tovalue other assets besides bonds
Bond Pricing Theorems
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There is a specific formula for findingbond prices on a spreadsheet PRICE(Settlement,Maturity,Rate,Yld,Redemption,
Frequency,Basis) YIELD(Settlement,Maturity,Rate,Pr,Redemption,Frequency,Basis)
Settlement and maturity need to be actual dates The redemption and Pr need to be input as % of par
value
Bond Prices with aSpreadsheet
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Differences BetweenDebt and Equity
Debt Not an ownership interest Creditors do not have
voting rights Interest is considered a
cost of doing business andis tax deductible Creditors have legal
recourse if interest orprincipal payments aremissed
Excess debt can lead tofinancial distress andbankruptcy
Equity Ownership interest Common stockholders
vote for the board ofdirectors and other issues
Dividends are notconsidered a cost of doingbusiness and are not taxdeductible
Dividends are not a liabilityof the firm, and
stockholders have no legalrecourse if dividends arenot paid
An all equity firm cannotgo bankrupt merely due todebt since it has no debt
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Contract between the company andthe bondholders that includes The basic terms of the bonds
The total amount of bonds issued A description of property used as
security, if applicable
Sinking fund provisions Call provisions Details of protective covenants
The Bond Indenture
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Registered vs. Bearer Forms Security
Collateral secured by financial securities
Mortgage secured by real property, normallyland or buildings
Debentures Unsecured debt (in US)
Secured debt (in UK) Notes unsecured debt with original maturity
less than 10 years
Seniority
Bond Classifications
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The coupon rate depends on the riskcharacteristics of the bond when issued
Which bonds will have the higher coupon,all else equal? Secured debt versus an unsecured debt Subordinated debt versus senior debt
A bond with a sinking fund versus one without A callable bond versus a non-callable bond
Bond Characteristics andRequired Returns
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The following are considered Investment Grade bonds1. High Grade
Moodys Aaa and S&P AAA capacity to pay is extremelystrong
Moodys Aa and S&P AA capacity to pay is very strong
2. Medium Grade Moodys A and S&P A capacity to pay is strong, but more
susceptible to changes in circumstances
Moodys Baa and S&P BBB capacity to pay is adequate,adverse conditions will have more impact on the firms abilityto pay
Anything below that are called Junk Bonds
Bond Ratings Investment Quality
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Low Grade Moodys Ba and B S&P BB and B Considered possible that the capacity to pay will
degenerate.
Very Low Grade Moodys C (and below) and S&P C (and below)
income bonds with no interest being paid, or in default with principal and interest in arrears
Page 234 shows the rating agencies in Asia Malaysia: RAM and MARC
Bond Ratings Speculative
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Make no periodic interest payments (coupon rate= 0%)
The entire yield-to-maturity comes from thedifference between the purchase price and thepar value
Cannot sell for more than par value Sometimes called zeroes, deep discount bonds,
or original issue discount bonds (OIDs) Treasury Bills and principal-only Treasury strips
are good examples of zeroes Zero-coupon bonds have no reinvestment
rate risk.
Zero Coupon Bonds
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Coupon rate floats depending on some indexvalue
Examples adjustable rate mortgages andinflation-linked Treasuries
There is less price risk with floating rate bonds The coupon floats, so it is less likely to differ
substantially from the yield-to-maturity
Coupons may have a collar the rate cannot goabove a specified ceiling or below a specifiedfloor
Floating-Rate Bonds
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Disaster bonds often issued by insurance companies
Income bonds Convertible bonds
bonds with warrant-like feature Put bonds There are many other types of provisions
that can be added to a bond and manybonds have several provisions it is important to recognize how these
provisions affect required returns
Other Bond Types
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Primarily over-the-counter transactionswith dealers connected electronically
Extremely large number of bond issues,
but generally low daily volume in singleissues Makes getting up-to-date prices difficult,
particularly on small company or municipal
issues Treasury securities are an exception
Bond Markets
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Highlighted quote in Figure 7.4
15 Nov 21 8.000 148.5000 148.5469 0.2656 2.59
What is the coupon rate on the bond? When does the bond mature? 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 theprevious day? What is the yield based on the ask price?
Treasury Quotations
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Clean price: quoted price Dirty price: price actually paid = quoted price plus
accrued interest Example: Consider a T-bond with a 4%
semiannual yield and a clean price of $1,282.50: Number of days since last coupon = 61 Number of days in the coupon period = 184 Accrued interest = (61/184)(.04*1000) = $13.26 Dirty price = $1,282.50 + $13.26 = $1,295.76
So, you would actually pay $ 1,295.76 for thebond
Clean vs. Dirty Prices
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Real rate of interest change in buyingpower
Nominal rate of interest quoted rate of
interest, change in actual number ofdollars The ex ante nominal rate of interest
includes our desired real rate of return plus
an adjustment for expected inflation
Inflation and Interest Rates
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The Fisher Effect defines the relationshipbetween real rates, nominal rates, andinflation
(1 + R) = (1 + r)(1 + h), where R = nominal rate r = real rate h = expected inflation rate
R = r + h + rh Approximation
R r + h
The Fisher Effect
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If we require a 10% real return and weexpect inflation to be 8%, what is thenominal rate?
R = (1.10)(1.08) 1 = .188 = 18.8% Approximation: R = 10% + 8% = 18% Because the real return and expected
inflation are relatively high, there issignificant difference between the actualFisher Effect and the approximation.
Example 7.5
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Term structure is the relationship between time tomaturity and yields, all else equal
It is important to recognize that we pull out theeffect of default risk, different coupons, etc.
Yield curve graphical representation of the termstructure Normal upward-sloping; long-term yields are higher
than short-term yields
Inverted downward-sloping; long-term yields are lowerthan short-term yields
Term Structure ofInterest Rates
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Figure 7.6 Downward-Sloping Yield Curve
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In addition to the above 3 factors, thefollowing are additional factors:1.Default risk premium remember bond
ratings2.Taxability premium remember municipalversus taxable3.Liquidity premium bonds that have morefrequent trading will generally have lowerrequired returns
Anything else that affects the risk of the cash flowsto the bondholders will affect the required returns
Factors Affecting BondYields
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Valuation of Shares
If you buy a share of stock, you canreceive cash in two ways The company pays dividends You sell your shares, either to another
investor in the market or back to thecompany
As with bonds, the price of the stockis the present value of theseexpected cash flows
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Developing The Model
You could continue to push back the year inwhich you will sell the stock
You would find that the price of the stock is really just the present value of all expected futuredividends
So, how can we estimate all future dividendpayments?
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)r (1D
...)r (1
D
)r (1D
)(1
D P
s3t
s
3t2t
s
2t1t
s
1tt
r
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Estimating Dividends: Special Cases Constant dividend
The firm will pay a constant dividend forever This is like preferred stock The price is computed using the perpetuity formula
Constant dividend growth The firm will increase the dividend by a constant percent
every period The price is computed using the growing perpetuity
model Supernormal growth
Dividend growth is not consistent initially, but settlesdown to constant growth eventually
The price is computed using a multistage model
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Zero Growth
If dividends are expected at regular intervalsforever, then this is a perpetuity and the presentvalue of expected future dividends can be foundusing the perpetuity formula P 0 = D / R
Suppose stock is expected to pay a $0.50dividend every quarter and the required return is
10% with quarterly compounding. What is theprice? P 0 = .50 / (0.1 / 4) = $20
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Constant Dividend Growth Model
Dividends are expected to grow at a constant percentper period. P 0 = D1 /(1+R) + D 2 /(1+R) 2 + D3 /(1+R) 3 + P 0 = D0(1+g)/(1+R) + D 0(1+g) 2/(1+R) 2 + D0(1+g) 3/(1+R) 3 +
With a little algebra and some series work, thisreduces to:
g-R Dg-R g)1(DP100
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Constant Dividend Growth Model Example 2
Suppose TB Pirates, Inc., is expected to pay a $2dividend in one year. If the dividend is expected togrow at 5% per year and the required return is 20%,what is the price?
Why isnt the $2 in the numerator multiplied by(1.05) in this example?
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33.130.05-0.2
2g-R
Dg-R
g)1(DP 100
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Stock Price Sensitivity to DividendGrowth Rate, g
D1 = $2; R = 20%
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Stock Price Sensitivity toRequired Return, R
D1 = $2; g = 5%
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Gordon Growth Company - I
Gordon Growth Company is expected to pay adividend of $4 next period, and dividends areexpected to grow at 6% per year. The requiredreturn is 16%. What is the current price?
Remember that we already have the dividendexpected next year, so we dont multiply thedividend by 1+g
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400.06-0.16
4g-R
Dg-R
g)1(DP 100
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Gordon Growth Company - II
What is the price expected to be in year 4?
What is the implied return given the change in price duringthe four year period?
Using financial calculator: -40 PV; 50.50 FV; 4 N; CPT I/Y= 6%
The price grows at the same rate as the dividends
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50.500.06-0.16
0.06)4(1g-R g)1(D
g-R D
P44
154
6%0.06r r)40(150.50
r)(1PP4
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N t t G th
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Nonconstant GrowthExample 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 P 2 = D3 / (R g) = 1.449 / (.2 - .05) = 9.66
Find the present value of the expected future cashflows
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8.670.2)(1
9.661.380.21
1.2R)(1
PDR 1
DP 22221
0
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Quick Quiz Part I
A company has just paid a dividend of $2. What isthe value of its stock if it expects to maintain thislevel of dividend every yea. Assume that therequired return is 15%.
$2/ ???? What if the company starts increasing dividendsby 3% per year, beginning with the next dividend?The required return stays at 15%. $2 ( ????
Why is the second value higher?
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See example 8.4 in pg. 267 Two-stage growth: p.268 & example
8.5 Try Problems 12 to 16 for interesting
variations of the standard model
Supernormal growth
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Using the Constant DGM to FindRequired Return, Dividend Yield,
Capital Gains Yield Start with the Constant DGM:
gPD
gP
g)1(D R
g-R D
g-R g)1(D
P
0
1
0
0
100
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Finding the Required Return
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Finding the Required Return,Dividend Yield, Capital Gains Yield -
ExampleSuppose a firms stock is selling for $10.50. It justpaid a $1 dividend, D 0, and dividends are expectedto grow at 5% per year.
What is the required return?
What is the dividend yield, D 1/P 0?
What is the capital gains yield?g =5%
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%1505.010.50
)05.01(1 g
Pg)1(D
R 0
0
10%10.50
0.05)1(1P
g)(1DPD
yielddiv0
0
0
1
bl k l
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Table 8.1 - Stock ValuationSummary
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Equity Valuation using Peer Multiples
1. P/E (Price-to-earnings) ratio trailing vs forward PE ratios often used to value IPO shares:
Based on comparable firms, estimate the appropriateP/E.
Multiply this by expected earnings to obtain an estimateof the stock price.
see pg. 272 for examples What are problems with PE method?
Often hard to find comparable firms. The average ratio from a sample of comparable firms
can have a wide range. Example: The average P/E ratio of comparable firms is 20 but the
range is from 10 to 50.
when profits are ve, PE ratio is meaningless
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Equity Valuation using Peer Multiples
2. Price-to-Sales MultiplesP/S ratio = price per share/ sales per sharefocuses on operating revenue so notinfluenced by one-off gains
3. Price-to-Cash Flow Multiple
useful to compare across countriessee airline example in pg 273
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Features of Common Stock
Voting Rights: Cumulative vs. straight voting
Proxy voting Classes of stock Other Rights
Share proportionally in declared dividends Share proportionally in remaining assets during
liquidation
Preemptive right first shot at new stock issue tomaintain proportional ownership if desired
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Features of Preferred Stock
Dividends Preferred dividend must be paid before
dividends can be paid to common stockholders Dividends are not a liability of the firm. Preferred dividends can be deferred
indefinitely Most preferred dividends are cumulative any
missed preferred dividends have to be paidbefore common dividends can be paid
Preferred stock generally do not carry votingrights
Similar to a perpetuity from a valuation point Is Preferred stock really Debt?
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Stock Market
Dealers vs. Brokers New York Stock Exchange (NYSE) Largest stock market in the world License holders (1,366)
Commission brokers Specialists Floor brokers Floor traders
Operations Floor activity
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NASDAQ
Not a physical exchange computer-basedquotation 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
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Bursa Malaysia and
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Bursa Malaysia andThe Singapore Exchange
Visit www.bursamalaysia.com Be familiar with the main features Source of much useful information Visit www.sgx.com.sg Select Prices from the menu on the left
Click on the following stocks to find the buy and sellquotes for selected stocks
SGX
Wilma DBS Bank
http://www.bursamalaysia.com/http://www.sgx.com.sg/http://www.sgx.com.sg/http://www.bursamalaysia.com/