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99Chapt
er
Chapt
er The Valuation and
Characteristics of Bonds
The Valuation and Characteristics of Bonds
Slides Developed by:
Terry FegartySeneca College
© 2006 by Nelson, a division of Thomson Canada Limited 2
Chapter 9: Outline (1)
• The Basis of Value• Bond Valuation
Terminology and Practice Finding the Yield Determining the Price of a Bond Solving Bond Problems with a Financial Calculator Maturity Risk Finding the Yield at a Given Price Reading Bond Quotations
© 2006 by Nelson, a division of Thomson Canada Limited 3
Chapter 9: Outline (2)
Call Provisions The Refunding Decision Risky Issues Institutional Characteristics of Bonds Kinds of Bonds Convertible Bonds Bond Indentures—Controlling Default Risk Bond Indentures
© 2006 by Nelson, a division of Thomson Canada Limited 4
Chapter 9: Outline (3)
• Appendix 9A: Leases Lease Financing Types of Leases Leases and Accounting Practices Leasing from the Perspective of the Lessor Residual Values Lease Versus Buy Analysis Advantages of Leasing Leveraged Leases Disadvantages to Leasing
© 2006 by Nelson, a division of Thomson Canada Limited 5
The Basis for Security Values
• Securities are worth the present value of the future cash income from them (intrinsic value) Should sell in financial markets for price
close to that value• However, I might think Security A has a different
intrinsic value then someone else thinks, because we have different estimates for the
• Discount rate • Expected future cash flows
© 2006 by Nelson, a division of Thomson Canada Limited 6
The Basis for Security Values
• 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 an ownership in a business
• A return—what investor receives divided by what he invests Debt investors receive interest
© 2006 by Nelson, a division of Thomson Canada Limited 7
The Basis for Security Values
• Rate of return—interest rate that equates the present value of its expected future cash flows with its current price PV of an amount to be received in 1 year:
Return is also known as • Yield• Interest
return1
FVPV
k
© 2006 by Nelson, a division of Thomson Canada Limited 8
Value of a Security: Example
Q. A financial asset is expected to generate a cash flow of $10,000 per year for five years. If the required return is 15%, what is the price of the asset now?E
xam
ple
© 2006 by Nelson, a division of Thomson Canada Limited 9
Value of a Security
0 1 2 3 4 5
$10K $10K $10K $10K $10K
PV
= $33,521.55
Exa
mpl
e
PV
A:
© 2006 by Nelson, a division of Thomson Canada Limited 10
Bond Terminology and Practice
• A bond issue represents borrowing from many lenders at one time under a single agreement
• Most bonds are purchased by institutional investors: banks, mutual funds, insurance companies, pension funds
© 2006 by Nelson, a division of Thomson Canada Limited 11
Bond Terminology and Practice
• A bond’s term (or maturity)—time from the present until principal is to be returned Bonds mature on last day of their term
• A bond’s face value (or par)—amount the firm intends to borrow (the principal) at the coupon rate of interest Denominations of $1,000 Bonds typically pay interest (coupon rate) every six
months Bonds are often non-amortized (meaning principal
is repaid only when the bond matures rather than being repaid in installments)
© 2006 by Nelson, a division of Thomson Canada Limited 12
Bond Valuation—Basic Ideas
• Adjusting to interest rate changes Bonds sold in both primary (original sale)
and secondary markets (subsequent trading among investors)
Interest rates change all the time Most bonds pay fixed interest rate
• What happens to the price of a bond paying a fixed interest rate in the secondary market when interest rates change?
© 2006 by Nelson, a division of Thomson Canada Limited 13
Bond Valuation—Basic Ideas
• Adjusting to interest rate changes Bond prices respond to changes in market
interest rates Bond prices and interest rates move in
opposite directions• When interest rates decline, prices of bonds go up;
when rates increase, prices go down• Price changes keep yields (returns) on seasoned
issues equal to yields on new issues of comparable risk and maturity
© 2006 by Nelson, a division of Thomson Canada Limited 14
Bond Valuation—Basic Ideas
• Bonds don’t generally sell for face values until close to maturity Sell for more or less than face value ($1000),
depending on where current interest rate is relative to their coupon rates
Bonds selling above face values—trading at a premium
Bonds selling below face value—trading at a discount
© 2006 by Nelson, a division of Thomson Canada Limited 15
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 ]
Payment = $ value of the interest paymentF = Face amount or principal repaymentk = (Yield-to-maturity (Required rate of return)n = Maturity (years)
© 2006 by Nelson, a division of Thomson Canada Limited 16
Figure 9.1: Cash Flow Time Line for a Bond
This is a
single sumThis is an ordinary annuity
© 2006 by Nelson, a division of Thomson Canada Limited 17
Figure 9.2: Bond Cash Flow and Valuation Concepts
© 2006 by Nelson, a division of Thomson Canada Limited 18
Determining the Price of a Bond
0 1 5 10
$100 a year for 10 years$100
$1,000$1,100
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:
Exa
mpl
e
In practice most bonds pay
interest semi-annually.
© 2006 by Nelson, a division of Thomson Canada Limited 19
Determining the Price of a Bond
• Interest Rates and Yields Coupon rate
• Determines size of interest payments
k—yield to maturity (YTM)• Long-term market yield on comparable bonds• Discount rate that makes present value of payments equal
to market price of bond
Current yield—annual interest payment divided by bond’s current price
© 2006 by Nelson, a division of Thomson Canada Limited 20
Solving Bond Problems with a Financial Calculator • Financial calculators have five time value
of money keys. For bond calculations: N—number of periods until maturity I/Y—yield-to-maturity (market interest rate) PV—price of bond FV—face value (par) of bond PMT—coupon interest payment per period
•With calculators that have sign convention, price (PV) of bond is entered as negative value
© 2006 by Nelson, a division of Thomson Canada Limited 21
Determining the Price of a Bond—Example
Q: The Emory Corporation issued an 8%, 25-year bond 15 years ago. The bond pays interest semiannually. 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?
Calculate the bond’s current yield.
Exa
mpl
e
© 2006 by Nelson, a division of Thomson Canada Limited 22
Determining the Price of a Bond—Example
A: We need to solve for the present value of the bond’s expected cash flows at today’s interest rate. We’ll use Equation 9.4 to do so:
Exa
mpl
e
B k, n k, nP [PVFA ] + [PVFFVM ]P T k represents the periodic current market interest rate,
or 10% 2.
n represents the number of
interest-paying periods until
maturity, or 10 years x 2 = 20.
The payment is 8% x $1,000, or $80 annually. However, it is
received in the form of $40
every six months.
The future value is the principal repayment of
$1,000.
© 2006 by Nelson, a division of Thomson Canada Limited 23
Determining the Price of a Bond—Example
A: Substituting the correct values into the equation gives us:
Exa
mpl
e
B 5%, 20 5%, 20P $40[PVFA ] + $1,000[PVF ]
$40[12.4622] + $1,000[0.3769]
$498.49 $376.90
$875.39
This is the price at which the bond must sell
to yield 10%. It is selling at a discount
because the current interest rate
is above the coupon rate.
The bond’s current yield is
$80 $875.39, or 9.14%.
This could also be calculated via a financial
calculator:N
I/Y
PMT
FV
20
5
40
1000
-875.39PV Answer
© 2006 by Nelson, a division of Thomson Canada Limited 24
Maturity Risk
• Relates to term of debt Longer term bonds fluctuate more in
response to changes in interest rates than shorter term bonds
• AKA price risk and interest rate risk• As time passes, if interest rates don’t
change, price of bond will approach par
© 2006 by Nelson, a division of Thomson Canada Limited 25
Table 9.1: Price Changes at Different Terms Due to an Interest Rate
Increase from 10% to 12%
© 2006 by Nelson, a division of Thomson Canada Limited 26
Finding the Yield at a Given Price
• To calculate bond yield based on current price, bond formula is;
B , n k, nkP PMT PVFA + FV PVF
Calculating yield Involves solving for k, which is complicated because it involves both an
annuity and a FVTo solve for k, use trial
and error, formula approach, a financial
calculator, or spreadsheet.
© 2006 by Nelson, a division of Thomson Canada Limited 27
Figure 9.3: Price Progression with Constant Interest Rate
© 2006 by Nelson, a division of Thomson Canada Limited 28
Example 9.2: Finding the Yield at a Given Price
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.)E
xam
ple
© 2006 by Nelson, a division of Thomson Canada Limited 29
Example 9.2: Finding the Yield at a Given Price
Exa
mpl
e
B k, n k, n
5, 32 5, 32
P PMT PVFA + FV PVF
$40 PVFA + $1,000 PVF
$40 15.8027 + $1,000 0.2099
$842.01
Clearly, 10% is not high enough.
Recalculating the price of the bond at
14% gives us $620.56, which means that 14%
is too high. The correct answer is 12%.
A: The bond is now selling below par. As interest rates rise, bond prices fall, so the yield must be above 8%. Using a guess of 10% and applying Equation 9.4 we obtain:
© 2006 by Nelson, a division of Thomson Canada Limited 30
Example 9.2: Formula Approach
Approximate Yield-to-Maturity =
For Example 9.2
1,000 71840
32YTM0.6 718 0.4 1,000
YTM = 5.875% × 2 = 11.75%
Exa
mpl
e
Principal payment - Price of bondNumber of years to maturity
Annual interest payment+(0.6 × Price of bond + (0.4 × Principal payment
© 2006 by Nelson, a division of Thomson Canada Limited 31
Example 9.2: Calculator Solution
N
PV
I/Y
PMT
FV
32
718
40
1000
6 × 2 = 12.0 Answer
Calculator
Exa
mpl
e
© 2006 by Nelson, a division of Thomson Canada Limited 32
Reading Bond Quotations
• Typical quote:
Issuer is Duke Energy Bond has a coupon rate of 6.375% (6 3/8 %) Bond matures in 2008 Current yield is 6.8% $40,000 dollars traded yesterday Closing price was $937.50 per $1,000 of face value Closing price was down $2.50 from the previous day
DukeEn 63/8 08 6.8 40 93¾ –1/4
© 2006 by Nelson, a division of Thomson Canada Limited 33
Call Provisions
• If interest rates have dropped substantially since a bond was originally issued, firm may wish to ‘refinance,’ or retire old, high interest bonds
• To ensure that corporation can refinance their bonds if they wish, corporation can make the bonds callable
© 2006 by Nelson, a division of Thomson Canada Limited 34
Call Provisions
• Call provisions allow bond issuers to retire bonds before maturity by paying call premium (penalty) to bondholders
• Many corporations offer deferred call period (meaning the bond won’t be called for at least x years after issue) Known as the call-protected period
© 2006 by Nelson, a division of Thomson Canada Limited 35
Call Provisions
• The Effect of A Call Provision on Price When valuing bond that is probably going to
be called when call-protected period is over• Cannot use traditional bond valuation procedure
• Cash flows will not be received through maturity because bond will probably be called
© 2006 by Nelson, a division of Thomson Canada Limited 36
Figure 9.5: The Call-Protected Period and a Declining Call Premium
© 2006 by Nelson, a division of Thomson Canada Limited 37
Figure 9.5: Valuation of a Bond Subject to Call
© 2006 by Nelson, a division of Thomson Canada Limited 38
Call Provisions
• Valuing the Sure-To-Be-Called Bond Requires that two changes be made to bond
valuation formula
nB k, k, nP PMT[PVFA ] + [PVFFV ]
n now represents the
number of periods until the bond is likely to
be called.
The future value becomes the call price (face value
plus call premium).
© 2006 by Nelson, a division of Thomson Canada Limited 39
The Refunding Decision
• When current interest rates fall below the coupon rate on bond, company has to decide whether or not to call in the issue Compare interest savings of issuing new
bond to costs of calling in old bond • Calling in old bond requires payment of call
premium• Issuing new bond to raise cash to pay off old bond
requires payment of administrative expenses and flotation costs
© 2006 by Nelson, a division of Thomson Canada Limited 40
Call Provisions
• Some issuers retire a portion of bond issue periodically
• Versus repaying entire issue at maturity• Often required by sinking funds
Does not require a call premium• Rather, those bondholders who must retire their
bond are determined by lottery
© 2006 by Nelson, a division of Thomson Canada Limited 41
Risky Issues
• Sometimes bonds sell for price far below intrinsic (calculated) values Investors worried that company may not be able to
pay promised cash flows
• Valuation model should determine price similar to the market price if the correct discount rate is used Riskier bonds should be discounted at higher interest
rate leading to a lower calculated price
© 2006 by Nelson, a division of Thomson Canada Limited 42
Institutional Characteristics of Bonds• Bearer bonds vs. registered bonds
Bearer bonds—interest payment is made to bearer of the bond
Registered bonds—interest payment is made to holder of record
• Registration, Transfer Agents, and Owners of Record Record of registered securities is kept by transfer
agent Payments are sent to owners of record as of the
dates the payments are due
© 2006 by Nelson, a division of Thomson Canada Limited 43
Kinds of Bonds
• Secured bonds and mortgage bonds Backed by collateral
• Debentures Unsecured bonds Pay higher interest
• Subordinated debentures Lower in priority than senior debt
• Junk bonds Issued by risky companies and pay high interest
rates
© 2006 by Nelson, a division of Thomson Canada Limited 44
Convertible Bonds
• Bonds exchangeable for a specified number of shares at option of bondholder Bondholders convert if price of shares rises enough
• Conversion ratio—number of shares that will be received for each bond
• Conversion price—implied share price if bond converted into certain number of shares Usually set 15-30% higher than share’s price when
bond issued
• Can usually be issued at lower coupon rates
© 2006 by Nelson, a division of Thomson Canada Limited 45
Bond Ratings—Assessing Default Risk• Bond rating agencies evaluate bonds
(and issuing firms) Assign a rating to each bond issued
• Ratings assess probability that issuers will default: fail to meet obligations
• 2 Canadian rating agencies Dominion Bond Rating Service S&P Ratings Direct Canada
© 2006 by Nelson, a division of Thomson Canada Limited 46
Table 9.2: DBRS and S&P Bond Ratings
© 2006 by Nelson, a division of Thomson Canada Limited 47
Bond Ratings—Assessing Default Risk
• Why Ratings Are Important Primary measure of the risk of default Basically determine rate at which firms can
borrow• Lower quality rating implies higher borrowing
rate
Many institutional investors are prohibited from buying below-investment-grade bonds
© 2006 by Nelson, a division of Thomson Canada Limited 48
Bond Ratings
• Interest rate spread between each bond rating is less during market expansions than during market contractions In recession marginal firms are more likely to fail,
making them riskier
Yie
ld
Yield Spread
© 2006 by Nelson, a division of Thomson Canada Limited 49
Bond Indentures—Controlling Default Risk• Bond indentures attempt to prevent
firms from becoming riskier after bonds are issued Include restrictive covenants such as:
• Avoiding high-risk businesses• Maintenance of debt management ratios• Restrictions on additional debt issues
Sinking funds require some repayment of bond principal before maturity
© 2006 by Nelson, a division of Thomson Canada Limited 50
Appendix 9-A: Lease Financing
• Lease—contract giving one party (lessee) the right to use an asset owned by another (lessor) for a periodic payment Long-term leases are effectively the same as debt
• Missed lease payments can cause the firm to fail just like a missed interest payment on debt
Corporations may lease automobiles, equipment and real estate
• Approximately 30% of all equipment today is leased
© 2006 by Nelson, a division of Thomson Canada Limited 51
Types of Leases
• For accounting purposes there are 2 types: Financing leases Operating leases
• Canadian accounting standards for leases are contained in the CICA handbook (CICA 3065)
© 2006 by Nelson, a division of Thomson Canada Limited 52
Types of Leases
• Financing Lease Sometimes called capital lease Initial term usually equal to expected
economic life of the asset Not cancelable by lessee Lessee responsible for maintenance,
insurance and property taxes Lessee effectively acquires ownership of the
leased asset
© 2006 by Nelson, a division of Thomson Canada Limited 53
Types of Leases
• Operating Lease Sometimes called service or maintenance
lease Term of lease is short (say 1-3 years)
• Less than economic life of the asset• For example, lease for photocopier
Usually cancelable by lessee on short notice Lessor maintains and services asset Lessor pays property taxes and insurance
© 2006 by Nelson, a division of Thomson Canada Limited 54
Leases and Accounting Practices
• According to the CICA, lease is financing lease if:
1. Lease will transfer legal ownership to the lessee at its end, either automatically or after making payment of a bargain purchase option at end of the lease, or
2. Lease term is longer than 75% of asset’s estimated economic
life, or
3. Present value of lease payments is more than 90% of asset’s fair market value at beginning of the lease
© 2006 by Nelson, a division of Thomson Canada Limited 55
Leases and Accounting Practices
• Financing Leases Firms are normally required to capitalize
financing leases on balance sheet• Value of leased assets in assets• Future lease payments in liabilities• Makes balance sheet similar to what it would have
been if asset purchased with borrowed money
© 2006 by Nelson, a division of Thomson Canada Limited 56
Leases and Accounting Practices
• Capitalized value of financing lease Equals present value of lease payments
• Interest rate is generally rate the lessee would pay if it were borrowing money when lease begins
• Both asset and liability are amortized (independently) over lease
© 2006 by Nelson, a division of Thomson Canada Limited 57
Example 9A.1: Leases and Accounting Practices
• Example of Reporting for Financing LeaseEmeral Inc.Balance Sheet($000)
Current assets $ 20 Current liabilities $ 10Leased crane 218 Lease obligation 218Capital assets 180 Long-term debt 90Total assets $418 Equity 100
Total debt & equity $418
Exa
mpl
e
© 2006 by Nelson, a division of Thomson Canada Limited 58
Leases and Accounting Practices
• Operating leases No balance sheet entries Lease payments are treated as expense Details must be listed in footnotes
© 2006 by Nelson, a division of Thomson Canada Limited 59
Leasing from the Perspective of the Lessor• Lessors are usually banks, finance companies
and insurance companies Companies buy equipment and lease it to customer
• Lease payments are calculated to provide given return to lessor Interest rate—lessor’s return or the rate implicit in
the lease
• Lessor holds legal title—can repossess assets if lessee defaults
• Lessors get better treatment in bankruptcy proceedings than lenders
© 2006 by Nelson, a division of Thomson Canada Limited 60
Residual Values
• Residual value—value of asset at end of lease term Lessee may exercise option to buy equipment Lessor may sell to someone else Asset may be re-leased (usually only with operating
leases)
• Makes lease pricing and return calculations more complex
• Often is important negotiating point between lessee and lessor
© 2006 by Nelson, a division of Thomson Canada Limited 61
Lease Vs. Buy—The Lessee’s Perspective• Broad financing possibilities
Equity Debt—available through bonds or banks Leasing—available through leasing
companies
• Should conduct a lease vs. buy comparison Choose the lowest cost (present value)
© 2006 by Nelson, a division of Thomson Canada Limited 62
Lease Versus Buy Analysis
• Approach:• Determine cash flows, after tax, if you
buy the asset• Determine cash flows, after tax, if you
lease the asset• Calculate present value of each
Discount rate is current rate on new long-term debt, after tax
• Choose option with lowest cost (present value)
© 2006 by Nelson, a division of Thomson Canada Limited 63
Lease Versus Buy Analysis
• Compare incremental cost of leasing versus borrowing and buying the asset
• Compare:
Present Value of Cost of Leasing
Present Value of Cost of Owning
against
© 2006 by Nelson, a division of Thomson Canada Limited 64
The Advantages of Leasing
• No money down Lenders typically require down payment
• lessors usually do not
• Restrictions Lenders usually require covenants/indentures
• lessors have few, if any, restrictions
• Easier credit with manufacturers/lessors Equipment manufacturers sometimes lease
their own products and will lease to marginally creditworthy customers
© 2006 by Nelson, a division of Thomson Canada Limited 65
The Advantages of Leasing
• Avoiding risk of obsolescence Lessee can return obsolete equipment at end of
lease
• Tax deduction for cost of land Lease payments for land are deductible
• No Capital Cost Allowance (tax amortization) for land
• Sale and leaseback Used to free up cash invested in real estate
• Tax advantages for marginally profitable companies (leveraged leases)
© 2006 by Nelson, a division of Thomson Canada Limited 66
Leveraged Leases
• Ability to amortize an asset reduces taxes• If company is not making profit (and not paying
taxes), amortization is not saving any money• Lessor buys equipment but borrows most of
cost (leveraged) Amortizes leased assets, deducts interest, and gains
tax benefits
• Lessor passes along some of tax benefits to lessee lower lease payments
© 2006 by Nelson, a division of Thomson Canada Limited 67
Disadvantages to Leasing
• May be more expensive than borrowing
• Lessor retains salvage value, including any capital gain
• May be difficult to obtain approval for modifications
• Often subject to cancellation penalty