9 9 Chapter The Valuation and Characteristics of Bonds Slides Developed by: Terry Fegarty Seneca College

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



Call Provisions The Refunding Decision Risky Issues Institutional Characteristics of Bonds Kinds of Bonds Convertible Bonds Bond Indentures—Controlling Default Risk Bond Indentures



• 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


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



• 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



• 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


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


Value of a Security

0 1 2 3 4 5

$10K $10K $10K $10K $10K

PV

= $33,521.55

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PV

A:


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


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)


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?



• 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



• 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


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)


Figure 9.1: Cash Flow Time Line for a Bond

This is a

single sumThis is an ordinary annuity


Figure 9.2: Bond Cash Flow and Valuation Concepts



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:

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In practice most bonds pay

interest semi-annually.



• 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


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


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.

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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:

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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.



A: Substituting the correct values into the equation gives us:

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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


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


Table 9.1: Price Changes at Different Terms Due to an Interest Rate

Increase from 10% to 12%


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.


Figure 9.3: Price Progression with Constant Interest Rate


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


Example 9.2: Finding the Yield at a Given Price

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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:


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%

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Principal payment - Price of bondNumber of years to maturity

Annual interest payment+(0.6 × Price of bond + (0.4 × Principal payment


Example 9.2: Calculator Solution

N

PV

I/Y

PMT

FV

32

718

40

1000

6 × 2 = 12.0 Answer

Calculator

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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


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


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


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


Figure 9.5: The Call-Protected Period and a Declining Call Premium


Figure 9.5: Valuation of a Bond Subject to Call


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).


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


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


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


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


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


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


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


Table 9.2: DBRS and S&P Bond Ratings


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


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


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


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


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)


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


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


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



• 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



• 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


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

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• Operating leases No balance sheet entries Lease payments are treated as expense Details must be listed in footnotes


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


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


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)


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)


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


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


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)


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


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

Documents

9 9 Chapter The Valuation and Characteristics of Bonds Slides Developed by: Terry Fegarty Seneca College