Lecture Essentials of corporate finance (2/e) – Chapter 6: Interest rates and bond valuation

Chapter 6 introduces you to interest rates and bond valuation. In this chapter, you will learn: Know the important bond features and bond types, understand bond values and why they fluctuate, understand bond ratings and what they mean, understand the impact of inflation on interest rates, understand the term structure of interest rates and the determinants of bond yields.

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Interest rates, bill and bond

valuation

Chapter 6

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Key concepts and skills

• Know the important features and different types of bills and bonds

• Understand how bills and bonds are

valued and why they fluctuate

• Understand bond ratings and what they

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Chapter outline

• Bills of exchange and bill valuation

• Other short-term funding instruments

• Bonds and bond valuation

• More on bond features

• Bond ratings

• Some different types of bonds

• Bond markets

• Inflation and interest rates

• Determinants of bond yields

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Bills of exchange and bill

valuation

• A bill is defined as:

– ‘unconditional order in writing, addressed by one person to another, signed by the person giving it, requiring the person to whom it is addressed to

pay on demand, or at a fixed or determinable

future time, a sum certain in money to or to the

order of a specified person, or to bearer’

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Bill values and yields

• If a bill has:

– a face value of F paid at maturity

– t periods to maturity; and

– a yield of r per period

) 365

x 1

(

Value

Bill

t r

F

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Bill pricing—

Example

• Suppose the Edna Data Company was to issue a bill with a face value of $500 000 and 90 days to maturity, with a yield of

6.5% The acquirer of the bill will receive

$500 000 in 90 days’ time What would

this bill sell for?

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More on bill features

• Three parties to a bill of exchange:

1 The drawer

2 The acceptor

3 The discounter (or endorser)

• The amount of funds the drawer will receive

depends on the face value of the bill and the

prevailing market rates (discount rate)

• The original discounter may hold the bill to maturity

or sell it in the market before the maturity date

• At the maturity date, the current holder of the bill

will approach the acceptor for repayment The

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More on bill features (cont.)

• Figure 6.1

• Figure 6.2

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Other short-term funding instruments

• Promissory notes

– Promises to pay a lender an amount of

money in the future; and

– issued for short terms

• Bank overdraft

– An agreement under which a firm is

authorised to overdraw its bank account

up to a specified amount.

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Key features of a bond

• Par value:

– Face amount

– Assume $1000 for corporate bonds

• Coupon interest rate:

– Stated interest rate

– Usually = YTM at issue

– Multiply by par value to get coupon

payment

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Key features of a bond

(cont.)

• 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

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The bond-pricing equation

PV(Annuity) PV(lump sum)

C = Coupon payment; F = Face value, r=

t

r) (1

F r

r) (1

1

1 C Value

Bond

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Bond pricing—Calculator

keys

[N]= Number of periods to maturity

[I/Y]= Period interest rate = YTM

[PV]= Present value = Bond value

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• 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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• What would this bond sell for?

• Bond involves an annuity of $80 in form of coupon for 10 years and $1000 as final payment.

• Using the formula:

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Bond value─ Example (cont.)

Cash flow for Barramundi Co.

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Valuing a discount bond with

annual coupons

• Consider a bond with a coupon rate of 10%

and coupons paid annually The par value is

$1000 and the bond has 5 years to maturity

The yield to maturity is 11% What is the value

of the bond?

– Using the formula:

• B = PV of annuity + PV of lump sum

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Valuing a premium bond with

– Using the formula:

• B = PV of annuity + PV of lump sum

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Graphical relationship between price and yield-to-

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Bond prices: Relationship

between coupon and yield

• If YTM = coupon rate, then par value = bond price.

• If YTM > coupon rate, then par value > bond price.

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The bond-pricing equation

adjusted for semi-annual

coupons

2t

YTM/2) (1

F YTM/2

YTM/2) (1

1 -

1 2

C Value

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• $35 = (7% x face value)/2 – Semiannual yield? (YTM

PPTs t/a Essentials of Corporate Finance 2e by Ross et al.

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F YTM

YTM) (1

1 1-

C Value Bond

Using the calculator:

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Interest rate risk

• Price risk

– Change in price owing 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 (cont.)

• 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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Interest rate risk and time to maturity

Figure 6.4

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Computing yield to maturity

(YTM)

• Yield-to-maturity is the rate implied by the current bond price.

• Finding the YTM is a process of trial and

error if you do not have a financial

calculator, and is similar to the process for finding r with an annuity.

• 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]

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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

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YTM with semi-annual

coupons

• Suppose a bond with a 10% coupon rate and

semi-annual 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 semi-annual coupon payment?

– How many periods are there?

Excel solution =RATE(40, 50, -1197.93, 1000, 0) = 4%

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Summary of bond valuation

Table 6.1

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Spreadsheet strategies

• There is a specific formula for finding

bond 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 given as % of par value

• Double-click on the Excel icon for an

example

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Differences between debt and

equity

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The bond trust deed

• The trust deed is the written legal

agreement between the corporation (the

borrower) and its creditors The document 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

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Bond classifications

• Registered vs bearer forms

• Security

– Collateral─secured by financial securities

– Mortgage─secured by real property, normally land or

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Bond characteristics and

required returns

• Coupon rate

– (risk characteristics of the bond when

issued)

– Usually ≈ yield at issue

• Which bonds will have the higher

coupon, all else equal?

– Secured debt versus a note

– Subordinated note versus senior debt

– A bond with a sinking fund versus one

without

– A callable bond versus a non-callable 6-37

PPTs t/a Essentials of Corporate Finance 2e by Ross et al.

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Bond ratings─Investment

quality

• High grade

– Moody’s Aaa, Fitch AAA and S&P

AAA─capacity to pay is extremely strong.

– Moody’s Aa, Fitch AA and S&P AA─capacity

to pay is very strong.

• Medium grade

– Moody’s A, Fitch A and S&P A─capacity to

pay is strong, but more susceptible to

changes in circumstances.

– Moody’s Baa, Fitch BBB and S&P

BBB─capacity to pay is adequate, adverse

conditions will have more impact on the firm’s ability to pay.

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• Very low grade

– Moody’s C, Fitch C and S&P C—income bonds

with no interest being paid.

– Moody’s D, Fitch DDD, DD and D, and S&P D—in default with principal and interest in arrears.

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Government bonds

• Treasury securities

• Bank bills—pure discount debt with

original maturity of one year or less

• State government securities

• Debt of state and local governments

• Varying degrees of default risk, rated

similar to corporate debt

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Zero coupon bonds

• Make no periodic interest payments

– (coupon rate = 0%)

• The entire yield-to-maturity comes from

the difference between the purchase price and the face value.

• Cannot sell for more than face value.

• Sometimes called zeroes, or deep

discount bonds.

• Bank bills are good examples of zeroes.

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Floating rate bonds

• Coupon rate floats depending on some

index value.

• Examples—adjustable rate mortgages

and inflation-linked bonds.

• 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 go above a specified ‘ceiling’ or

below a specified ‘floor’.

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Other bond types

• Subordinated bonds

• Convertible bonds

• Put bond

• There are many other types of

provisions that can be added to a bond and many bonds have several

provisions—it is important to recognise how these provisions affect required

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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 is difficult,

particularly on small company or

municipal issues.

• Treasury securities are an exception.

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Bond price reporting

• Corporate bond market associated with Australian Securities Exchange (ASX).

• Click on information; which leads to

Detailed search—prices, charts and

announcements section for interest rate and hybrid security prices.

• The chart gives the buy/bid, sell/ask

prices and other figures for corporate

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Treasury quotes

Table 6.3

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Treasury quotes

Example 6.5

• In Table 6.3, for bond maturing Feb-2017

– Coupon rate?

– Yield to maturity based on ask price (sell price)?

– Bond trading at discount?

• Bond we are looking at:

6.00% Feb-17 5.250 1208 11748

– YTM at last sale = 5.25% (Sale price > Face value)

– Bond’s years to maturity = 7 (Assume today as 15/02/2010) – Coupon rate = 6% (half yearly) = $3

– YTM = 5.25/2=2.625

– PV=3[1-1/(1+0.02625)14]/0.02625+100/

(1.02625)14=104.346

• The bond maturing in April 2020 is selling at discount.

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Work the Web—Example

• Bond quotes are available online.

• One good site is Bloomberg.com.

• Go to Bloomberg’s website.

• Follow the bond search.

• Search a bond issue and see what you can find!

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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

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The Fisher effect

• The Fisher effect defines the

relationship between real rates,

nominal rates and inflation:

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The Fisher effect

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 a

significant difference between the actual

Fisher effect and the approximation.

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Determinants of bond yields Term structure of interest rates

• Term structure is the relationship between time to maturity and yields, all else being equal.

• It is important to recognise that we pull out the effect of default risk, different coupons, etc.

• Yield curve—graphical representation of

the term structure

– Normal—upward-sloping, long-term yields are higher than short-term yields

– Inverted—downward-sloping, long-term yields are lower than short-term yields

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Upward-sloping yield curve—

Figure 6.8A

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Downward-sloping yield curve

—Figure 6.8B

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Government bond yield curve

—Figure 6.9

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Factors affecting 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

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Quick quiz

• How do you find the value of a bond and

why do bond prices change?

• What is a bond trust deed and what are

some of its important features?

• What are bond ratings and why are they

important?

• How does inflation affect interest rates?

• What is the term structure of interest

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Chapter 6

END

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