Interest rates, bill and bond valuation Chapter 6.

Interest rates, bill and bond valuation

Chapter 6

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 mean• Understand the impact of inflation on interest

rates• Understand the term structure of interest

rates and the determinants of bond yields

6-2 Copyright ©2011 McGraw-Hill Australia Pty LtdPPTs t/a Essentials of Corporate Finance 2e by Ross et al.Slides prepared by David E. Allen and Abhay K. Singh

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

6-3 Copyright © 2011 McGraw-Hill Australia Pty LtdPPTs t/a Essentials of Corporate Finance 2e by Ross et al.Slides prepared by David E. Allen and Abhay K. Singh

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’

• Face value– The principal amount that is repaid at the end of the

term. Also called par value.• Maturity– Date on which the principal amount is paid.


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

trF


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?– PV = 500 000/(1+0.06/365*90)=$492 125.98

• Calculator:– 0.2465 [N] (90/365)– 6[I/Y]– 500 000 [+/-][FV]– [CPT][PV]= 492 125.98


More on bill features• Three parties to a bill of exchange:

1. The drawer2. The acceptor3. 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 acceptor is liable to pay the face value of the bill to the current holder and will recover the money from the drawer.


More on bill features (cont.)

• Figure 6.1

• Figure 6.2


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.


Bond definitions

• Bond– Debt contract– Interest-only loan

• Par value (face value) ~ $1000• Coupon rate• Coupon payment• Maturity date• Yield to maturity


Key features of a bond

• Par value: – Face amount–Repaid at maturity –Assume $1000 for corporate bonds

• Coupon interest rate: – Stated interest rate –Usually = YTM at issue–Multiply by par value to get coupon

payment6-11

Copyright © 2011 McGraw-Hill Australia Pty LtdPPTs t/a Essentials of Corporate Finance 2e by Ross et al.Slides prepared by David E. Allen and Abhay K. Singh

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


Bond value


The bond-pricing equation

PV(Annuity) PV(lump sum)

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

t

t

r)(1

F

rr)(1

1-1

C Value Bond


Bond pricing—Calculator keys

[N]= Number of periods to maturity[I/Y]= Period interest rate = YTM[PV]= Present value = Bond value[PMT]= Coupon payment[FV]= Future value = Face value = Par value


Spreadsheet formulas

=FV(Rate,Nper,Pmt,PV,0/1) =PV(Rate,Nper,Pmt,FV,0/1)=RATE(Nper,Pmt,PV,FV,0/1)=NPER(Rate,Pmt,PV,FV,0/1)=PMT(Rate,Nper,PV,FV,0/1)

• Inside parens: (RATE,NPER,PMT,PV,FV,0/1)• ‘0/1’ Ordinary annuity = 0 (default)

Annuity due = 1 (must be entered)


Bond value─Example

• Barramundi Fishing Co. issue a bond with: – Face value = $1000– 10 years to maturity– Annual coupon = $80– Yield to maturity = 8%

• 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:

– PV of face value =1000/(1.08)10 = 463.19– PV of $80 annuity =80(1-1/1.0810)/0.08 = 536.18– Total = 463.19+536.18 = 1000


Megan Maniscalco

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Bond value─Example (cont.)Cash flow for Barramundi Co.


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• B = 100[1 – 1/(1.11)5] / .11 + 1000 / (1.11)5

• B = 369.59 + 593.45 = $963.04– Using the calculator:

• [N] = 5; I/Y = 11; [PMT] = 100; [FV] = 1000• [CPT] [PV] = -963.04

– Using Excel:• =PV(0.11, 5, 100, 1000, 0)


Valuing a premium bond with annual coupons

• Suppose you are looking at a bond that has a 10% annual coupon and a face value of $1000. There are 20 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– Using the calculator:

• [N ]= 20; [I/Y] = 8; [PMT]= 100; [FV] = 1000• [CPT][PV] = -1196.36

– Using Excel:• =PV(0.08, 20, 100, 1000, 0)


Graphical relationship between price and yield-to-maturity

600

700

800

900

1000

1100

1200

1300

1400

1500

0% 2% 4% 6% 8% 10% 12% 14%


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.– Why?– Selling at a discount, called a discount bond.

• If YTM < coupon rate, then par value < bond price.– Why?– Selling at a premium, called a premium bond.


The bond-pricing equationadjusted for semi-annual coupons

2t

2t

YTM/2)(1

F

YTM/2YTM/2)(1

1-1

2

C ValueBond

C = Annual coupon payment C/2 = Semi-annual coupon

YTM = Annual YTM (as an APR) YTM/2 = Semi-annual YTM

t = Years to maturity 2t = Number of 6-month periods to maturity

6-23Copyright © 2011 McGraw-Hill Australia Pty LtdPPTs t/a Essentials of Corporate Finance 2e by Ross et al.Slides prepared by David E. Allen and Abhay K. Singh

Semi-annual bondsExample 6.2

• Coupon rate = 7% - semi-annual• YTM = 8% (APR)• Maturity = 7 years– Number of coupon payments? (t or [N])• 14 = 2 x 7 years

– Semiannual coupon payment? (C or [PMT])• $35 = (7% x face value)/2

– Semiannual yield? (YTM or[I/Y])• 4% = 8%/2


Example 6.2 (cont.)• Semiannual coupon = $35• Semiannual YTM = 4%• Periods to maturity = 14• Bond value =

– 35[1 – 1/(1.04)14] / .04 + 1000 / (1.04)14 = 947.16

– Effective Annual Yield= (1+0.04)2-1=8.16%

t

t

YTM)(1

F

YTMYTM)(11

1-C ValueBond

Using the calculator:14 [N]4 [I/Y] 35 [PMT]1000 [FV][CPT][PV] -917.56Using Excel: =PV(0.08, 14, 70, 1000, 0)


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.


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.


Interest rate risk and time to maturityFigure 6.4


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]


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 $928.09.– Will the yield be more or less than 10%?

• Calculator solution:15 [N]928.09 [+/-][PV]1000 [FV]100 [PMT][CPT][I/Y] 11% Result = YTM

• Spreadsheet solution:– =RATE(15, 100, -928.09, 1000, 0)


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?

40 [N]1197.93 [+/-][PV]1000 [FV]50 [PMT][CPT][I/Y] 4%

YTM = 4%*2 = 8% (Result is doubled to get the annual YTM.)Excel solution =RATE(40, 50, -1197.93, 1000, 0) = 4%


Summary of bond valuationTable 6.1


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


Differences between debt and equity


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


Bond classifications• Registered vs bearer forms• Security

– Collateral─secured by financial securities– Mortgage─secured by real property, normally land or buildings– Debentures─unsecured– Notes─secured debt with original maturity less than 10 years

• Seniority– Senior versus junior, subordinated

• Repayment– Sinking fund

• The call provision• Protective covenant

– Negative covenant, positive covenant


Bond characteristics andrequired 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 bond


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.

6-38Copyright © 2011 McGraw-Hill Australia Pty LtdPPTs t/a Essentials of Corporate Finance 2e by Ross et al.Slides prepared by David E. Allen and Abhay K. Singh

Bond ratings—Speculative• Low grade

– Moody’s Ba, B ,Caa and Ca – Fitch BB, B, CCC and CC– S&P BB, B, CCC– Considered speculative with respect to capacity to pay.

The ‘B’ ratings are the lowest degree of speculation.• 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.


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


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.


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’.


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 returns.


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.


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 bonds.


http://asx.com.au/asx/markets/interestRateSecurityPrices.do

Treasury quotesTable 6.3


Treasury quotesExample 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.


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!


http://www.bloomberg.com/

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 inflation.


The Fisher effect

• The Fisher effect defines the relationship between real rates, nominal rates and inflation:

(1 + R) = (1 + r)(1 + h)R = nominal rate (quoted rate)r = real rate h = expected inflation rate

Approximation: R = r + h


The Fisher effectExample 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.


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


Upward-sloping yield curve—Figure 6.8A


Downward-sloping yield curve—Figure 6.8B


Government bond yield curve—Figure 6.9


http://www.bloomberg.com/markets/rates-bonds/government-bonds/australia/

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 required returns.


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 rates?• What factors determine the required return

on bonds?


Chapter 6

END

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Interest rates, bill and bond valuation Chapter 6.

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