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The Valuation and Characteristics of Bonds
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The Basis of Value
A security’s value is equal to the present value of its expected cash flows.
A security should sell in financial markets for a price close to that value Differences of opinion exist about a security’s price
because of different assumptions about cash flows and interest rates for PV calculations
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The Basis for Value
Investing Using a resource to benefit
the future rather than for current satisfaction Putting money to work to
earn more money Common types of
investments Debt—lending money Equity—buying
ownership in a business
Return
What the investor receives for making an investment
For a 1 year investment the rate of return =
$ received / $ invested
Debt investors receive interest
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The Basis for Value
Rate of return is the interest rate that equates the present value of an investment’s expected future cash flows with its current price
Return is also known as Yield Interest
Debt investments only
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Bond Valuation
Bonds represent a debt relationship in which the issuing company borrows and the buyers lend. A bond issue represents borrowing
from many lenders at one time under a single agreement
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Bond Terminology and Practice
A bond’s term (or maturity) is the time from the present until the principal is returned Bonds mature on the last day of their term A bond’s term gets shorter as it ages
A bond’s face (or par) value represents the amount the firm intends to borrow (the principal) at the coupon rate of interest Bonds are non-amortized debt - the entire principal is
repaid at maturity
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The Coupon Rate
Coupon Rate – the fixed rate of interest paid by a bond Doesn’t change over the bond’s life
In the past, bonds had “coupons” attached, today they are “registered”
Most bonds pay coupon interest semiannual
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Bond Valuation—Basic Ideas
Adjusting to Interest Rate Changes Bonds are originally sold in the primary
market and trade subsequently among investors in the secondary market.
Although bonds have fixed coupons, market interest rates constantly change. What happens to the price of a bond paying a fixed
interest rate in the secondary market when interest rates change?
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Bond Valuation—Basic Ideas
Buy a 20 year, $1000 par bond with a 10% coupon rate for $1,000. It promises 20 years of coupon payments of $100 each, and a principal
repayment of $1,000 after 20 years
Needing cash, you sell it early. Assume interest rates have risen and the market rate of return is 11% Investors can now buy new bonds with an 11% coupon rate for $1,000 so
they will not pay $1000 for your bond – but they will buy it for less than $1,000
Bond prices and interest rates move in opposite directions
Bonds adjust to changing yields by changing price Selling at a Premium – bond price above face value Selling at a Discount – bond price below face value
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Determining the Price of a Bond
0 1 5 10
$100a year for 10 years
$100
$1,000
$1,100
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Q:A bond has 10 years to maturity, a par value of $1,000, and a coupon rate of 10%. What cash flows are expected from the bond?
A:
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Determining the Price of a Bond
The Bond Valuation Formula The price of a bond is the present value of a
stream of interest payments plus the present value of the principal repayment
k,n
Interest payments are annuities--can usethe present value of an annuity form
Principal repayment is a lump sum in ula:
PMT[PVFA
the futur
]
B PV(princiPV(interest payme pal repaymP +nt ) es nt)
k, n
e--can use the future value formula:FV[PVF ]
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Cash Flow Time Line for a Bond Figure 7.1
This is an ordinary annuity. This is a
single sum.
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Determining the Price of a Bond
Two Interest Rates and One More Coupon Rate
Determines the size of the interest payments
k—the current market yield on comparable bonds The discount rate that makes the present value of the payments
equal to the price of the bond in the market AKA yield to maturity (YTM)
Current yield — annual interest payment divided by bond’s current price
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Solving Bond Problems with a Financial Calculator
Financial calculators have five time value of money keys
With a bond problem, all five keys are used n—number of periods until maturity I/Y—market interest rate PV—price of bond FV—face value (par) of bond PMT—coupon interest payment per period
With calculators that have a sign convention the PMT and FV must be of one sign while the PV will be the other sign
The unknown is either interest rate or present value (Price)
Sophisticated calculators have a ‘bond’ mode allowing easy calculations dealing with accrued interest
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Determining the Price of a Bond Example 7.1
Q: The Emory Corporation issued an 8%, 25-year bond 15 years ago. At the time of issue it sold for its par (face) value of $1,000. Comparable bonds are yielding 10% today. What must Emory’s bond sell for in today’s market to yield 10% (YTM) to the buyer? Assume the bond pays interest semiannually. Also calculate the bond’s current yield.
Exa
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Bond Example Continued Example 7.1
A: Substituting the correct values into the equation gives us:
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This can also be calculated via a financial calculator:
N
PV
PMT
FV
I/Y
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Maturity Risk Revisited
Relates to term of the debt Longer term bond prices fluctuate more in
response to changes in interest rates than shorter term bonds
AKA price risk and interest rate risk
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Price Changes at Different Terms due to an Interest Rate Increase
from 8% to 10% Table 7.1
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Finding the Yield at a Given Price
Calculate a bond’s yield assuming it is selling at a given price
Trial and error – guess a yield – calculate price – compare to price given
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Finding the Yield at a Given PriceExample 7.3
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Q: The Benson Steel Company issued a 30-year bond 14 years ago with a face value of $1,000 and a coupon rate of 8%. The bond is currently selling for $718. What is the yield to an investor who buys it today at that price? (Assume semiannual interest.)
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Call Provisions
If interest rates fall, a firm may wish to retire old, high interest bonds “Refinance” with new lower interest debt
To ensure their ability to refinance bonds, corporations make bonds ‘callable’ Call provision gives right to pay off the bond early
Investors don’t like calls – lose high interest So issuers and investors Compromise
Call provisions usually have a call premium Call protection means the bond won’t be called for a
certain number of years.
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The Refunding Decision
When current interest rates fall below the bond’s coupon rate, a firm must decide whether to call in the issue Compare interest savings to the cost of making
the call: Call premium – extra payment to bond holders Flotation costs – incurred in issuing new bonds,
includes brokerage fees, administrative expenses, printing, etc.
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Dangerous Bonds with Surprising Calls
Bonds can have obscure call features buried in their contract terms.
Most common type – a sinking fund provision – requires an issuer to call in and retire a fixed percentage of the issue each year Usually no call premium Determined by lottery
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Convertible Bonds
Unsecured bonds exchangeable for a fixed number of shares of stock at the bondholder's discretion Bondholders can participate in the stock’s price appreciation
Conversion ratio - the number of shares of stock received for each bond
Conversion price - the implied stock price if bond is converted into a certain number of shares Usually set 15-30% above the stock’s market value when the
bond is issued
Usually issued at lower coupon rates
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Advantages of Convertible Bonds
To Issuing Companies
Convertible features are “sweeteners” enabling a risky firm to pay a lower interest rate
Viewed as a way to sell equity at a price above market
Usually have few or no restrictions
To Buyers
Offer the chance to participate in stock price appreciation
Offer a way to limit risk associated with a stock investment
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Forced Conversion
A firm may want bonds converted eliminates interest payments on bond strengthens balance sheet don’t want conversion at very high stock prices
Convertible bonds are always issued with call features which can be used to force conversion
Issuers generally call convertibles when stock prices rise to 10-15% above conversion prices
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Effect on Earnings Per Share—Diluted EPS
Upon conversion convertible bonds cause dilution in EPS EPS drops due to the increase in the number of
shares of stock
Thus outstanding convertibles represent a potential to dilution of EPS
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Exa
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Q: Montgomery Inc. is a small manufacturer of men’s clothing with operations in Southern California. It issued 2,000 convertible bonds in 1999 at a coupon rate of 8% and a par value of $1,000. Each bond is convertible into Montgomery’s common stock at $40 per share. Management expected the stock price to rise rapidly after the convertible was issued and lead to a quick conversion of the bond debt into equity. However, a recessionary climate has prevented that from happening, and the bonds are still outstanding. In 2003 Montgomery had net income of $3 million. One million shares of its stock were outstanding for the entire year, and its marginal tax rate is 40%. Calculate Montgomery’s basic and diluted EPS.
A: Basic EPS is the firm’s net income divided by the number of shares outstanding, or $3,000,000 ÷ 1,000,000 = $3.00.
Effect on Earnings Per Share—Diluted EPS
Example 7.7
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Effect on Earnings Per Share—Diluted EPS
Example 7.7
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Diluted EPS assumes all convertible bonds are converted at the beginning of the year. Two adjustments need to be made:
Add the number of newly converted shares to the denominator:
Shares exchanged: Bond’s par ÷ Conversion price = $1,000 ÷ $25 = 40
Since each bond can be converted into 40 shares of stock and there are 2,000 bonds, the newly converted shares totals 80,000, or 40 x 2,000, bringing the total number of shares outstanding to 1,080,000.
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Institutional Characteristics of Bonds
Registration, Transfer Agents, and Owners of Record
Classify bonds as either bearer or registered bonds. Bearer bonds — interest payment is made to the bearer of the
bond Registered bonds — interest payment is made to the holder of
record Owners of registered bonds are recorded with a
transfer agent. Keeps track of bonds for issuing companies Sends payments to owners of record Transfers ownership when bond is sold to another investor
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Kinds of Bonds
Secured bonds and mortgage bonds Backed by the value of specific assets - collateral
Debentures Unsecured bonds issued with higher
interest rates Subordinated debentures
Lower in priority than senior debt Junk bonds
Issued by risky companies and pay high interest rates
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Bond Ratings—Assessing Default Risk
Bonds are assigned quality ratings reflecting their probability of default. Higher ratings mean lower default probability
Bond rating agencies (such as Moody’s, S&P) evaluate bonds (and issuers), and assign a rating Examine the financial and market conditions
of the issuer
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Bond Ratings—Assessing Default Risk
Why Ratings Are Important Ratings are the primary measure of the default
risk associated with bonds The rating determines the rate at which the
firm can borrow A lower quality rating implies a higher borrowing rate A differential exists between the rates required on high
and low quality issues.
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Moody’s and S&P Bond Ratings Table 7.2
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Bond Indentures—Controlling Default Risk
Bond indentures attempt to prevent firms from becoming riskier after bonds are purchased by including restrictive covenants: Preclude entering high risk businesses Limit further borrowing Require certain financial ratios
Safety is also provided by sinking funds Provide money for repayment of bond principal
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The Advantages of Leasing Appendix 7-A
No money down Lenders generally require a down payment lessors usually do not
Restrictions Lenders require covenants/indentures, lessors have few,
if any, restrictions
Easier credit with manufacturers/lessors Equipment manufacturers may lease their own products
and will sometimes lease to marginally creditworthy customers
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The Advantages of Leasing Appendix 7-A
Avoiding the risk obsolescence Short leases transfer this risk to lessors
Tax deducting the cost of land If real estate is leased - the lease payment can be
deducted as an expense If land is owned - it is not depreciable
Increasing liquidity—the sale and leaseback A firm may sell an asset to a financial institution and
lease back the same asset — frees up cash Tax advantages for marginally profitable
companies