BONDS VALUATION CHAPTER 7. Financial Market in the Financial System Financial Market – a market...

BONDS VALUATION

CHAPTER 7

Financial Market in the Financial System

Financial Market – a market where those who have excess funds and those who are in need of funds will meet to transact the financial assets that include both money and capital market securities.

4 main parties: households, business firms, foreigners and government.

2

SITI AISHAH BINTI KASSIM (FM2)

Characteristics of a Good Financial Market

Availability of information LiquidityPrice continuityTransaction costExternal efficiency or information

efficiency

3


Types of Securities Market

1. Money market Short-term securities which have maturity below than one-year.

2. Capital market Long-term securities which have maturity longer than one-year.

4


What is a Bond?

One of a debt financingA long term debt (fixed income security) in

which the issuer (borrower) has agreed to pay fixed income payments for a specified period and to repay a fixed amount of principal at maturity to the bondholder (lender).

Indenture – the contract between the issuer and the bondholder, which sets the obligations of the issuer.

5


Key Features of a Bond

Par value – face amount of the bond, which is paid at maturity (assume $1,000).

Coupon interest rate – a rate of interest payment for every bond issued and usually be converted into Ringgit amount by time the rate to the bond par value (CP = PV x CR)

Maturity date – years until the bond must be repaid.

Issue date – when the bond was issued.Yield to maturity – rate of return earned on

a bond held until maturity (also called the “promised yield”).

6


Bond Markets

Primarily traded in the over-the-counter (OTC) market.

Most bonds are owned by and traded among large financial institutions.

Full information on bond trades in the OTC market is not published, but a representative group of bonds is listed and traded on the bond division of the NYSE.

7


Callable bonds

Allow the issuer to redeem the bond at any time before the maturity date.

The bond will be call at premium price to compensate for the holders.

Issuer will call the bond when market interest rate decline – reduce it interest expenses and take the advantages of lower interest rate in the market.

8


Sinking Fund

Provision in the indenture to pay off a loan over its life rather than all at maturity. Failure to meet SF requirement causes bond default, may force firm into bankruptcy. Significant cash drain to firm.

Similar to amortization on a term loan. Reduces amount needed to retire the remaining debt at maturity.

Reduces risk to investor, shortens average maturity.

But not good for investors if rates decline after issuance.

9


Types of Bonds

A. Unsecured Bonds:Bonds that are not backed by an asset or collateral.

i. Debentures – unsecured long-term bondii. Subordinated Debentures – bonds that have a lower claim

on assets in the event of liquidation than do other senior debtholders.

iii. Income Bond – issued by firms facing financial difficulties or which are weak financially.

B. Secured Bonds:Bonds that are backed by an asset or collateral.

i. Mortgage Bond – secured by real estate or buildings, which are of higher value than the value of the mortgage bond issued.

ii. Collateral Trust Bond – secured by stock and/or bonds owned by the issuer.

iii. Equipment Trust Certificates – used to finance the purchase of ‘rolling stock’ such as trains, ships, boats and trucks.

10


Other Types of Bond Issues

Eurobonds – issued by an international borrower and sold to investors in countries with currencies other than currency in which the bond is denominated.

Junk Bonds – also called ‘high-yield securities’ because of the higher risks of default faced by the bondholders. Rated below BBB.

Zero (low) coupon bonds – known as original discount bond is sold at a large discount from par.

11


Rating the Bond

To provide the potential investor an objective form of risk analysis and evaluation on the quality of the bond and its issuer.

Rating Standard & Poor’s

Moody’s RAM

Highest AAA Aaa AAAAA Aa AAA A A

BBB Baa BBBBB Ba BBB B B

CCC Caa CCC Ca

Lowest C C D

12SITI AISHAH BINTI KASSIM (FM2)

Definition of Value

Book Value – the value of an asset shown on a firm’s balance sheet which is determined by its historical cost rather than its current worth.

Liquidation – the amount that could be realized if an asset is sold individually and not as part of a going concern.

Market Value – the observed value of an asset in the marketplace where buyers and sellers negotiate an acceptable price for the asset.

Intrinsic Value – the value based upon the expected cash flows from the investment, the riskiness of the asset, and the investor’s required rate of return.

13


Principles of Bond Price Behavior

When the required rate of return (k) differ from the bond’s coupon rate, the market value of the bond will differ from its par: When required rate of return (k) = coupon

interest rate, bond will sell at par. When required rate of return (k) > coupon

interest rate, bond will sell at a discount. When required rate of return (k) < coupon

interest rate, bond will sell at premium.

14


The Value of Financial Assets

nn

22

11

k)(1CF

... k)(1

CF

k)(1CF

Value

0 1 2 nk = ?%

CF1 CFnCF2Value

...


What is the value of a 10-year, 10% annual coupon bond, if kd = 10%? (coupon=10%x$1000=$100/year)

$1,000 V$385.54 $38.55 ... $90.91 V

(1.10)$1,000

(1.10)$100

... (1.10)$100

V

B

B

10101B

0 1 2 nKd = 10%

$100 $100 + $1,000$100VB = ?

...


Mathematical Calculation

Vb = CPN (PVIFA r%,n) + Par Value (PVIF r%,N)

= $100 (PVIFA10%,10) + $1000 (PVIF10%,10)

= $100(6.1446) + $1000(0.3855) = $614.46 + $385.50 = $1,000

*(If coupon rate = interest/discount rate (k) Vb = Par Value/Maturity Value =$1000)


Using a financial calculator to value a bond

This bond has a $1,000 lump sum due at t = 10, and annual $100 coupon payments beginning at t = 1 and continuing through t = 10, the price of the bond can be found by solving for the PV of these cash flows.

INPUTS

OUTPUT

N I/YR PMTPV FV

10 10 100 1000

-1000


An example:Increasing inflation and kd

Suppose inflation rises by 3%, causing kd = 13%. When kd rises above the coupon rate, the bond’s value falls below par, and sells at a discount.

INPUTS

OUTPUT

N I/YR PMTPV FV

10 13 100 1000

-837.21


What is the Vb if kd increases from 10% to 13%?

Vb = $100 (PVIFA13%,10) + $1000(PVIF13%,10)

= $100 (5.4262) + 1000 (0.2946) = $542.62 + $294.60 = $837.22 (bond sells at a discount)


An example:Decreasing inflation and kd

Suppose inflation falls by 3%, causing kd = 7%. When kd falls below the coupon rate, the bond’s value rises above par, and sells at a premium.

INPUTS

OUTPUT

N I/YR PMTPV FV

10 7 100 1000

-1210.71


What is the Vb if kd decreases from 10% to 7%?

Vb = $100 (PVIFA7%,10) + $1000(PVIF7%,10)

= $100 (7.0236) + $1000(0.5083) = $702.36 + $508.30 = $1,210.66 (bond sells at a

premium)


What is the YTM on a 10-year, 9% annual coupon, $1,000 par value

bond, selling for $887?

Must find the kd that solves this model.

10d

10d

1d

Nd

Nd

1d

B

)k(11,000

)k(1

90 ...

)k(190

$887

)k(1M

)k(1

INT ...

)k(1INT

V


Approximate YTM

AYTM (%) = I +(MV-Vb)/N

(MV + Vb)/2

ATYM =Approximate yield to maturity I = $Interest or $coupon interest (x%

of par value of $1000. Example, if coupon/interest is 9%, paid annually, I = 9% x 1000 = $90)MV = Maturity/Par value = $1000Vb = Value/Price of bond


Find the YTM on a 10-year, 9% annual coupon, $1,000 par value bond, selling

for $887

AYTM = I + (MV-Vb)/N(MV +Vb)/2

= $90 + ($1000 - $887)/10

($1000 + $887)/2 = 11%


Interpolation (to get exact rate)

kd Present Value

10% $90(PVIFA10%,10) +$1000(PVIF10%,10) = $938.51X% = $887.0011% $90(PVIFA11%,10) + $1000(PVIF11%,10) = $883.13 1%

Proportion = $938.51 - $887.00 = 0.93% $938.51 – $883.13

Therefore X = 10% + 0.93% = 10.93%


Current Yield, Capital Gains Yield and Expected Total Return

CGY

Expected

CY

Expected YTM return total Expected

price Beginningprice in Change

(CGY) yieldgains Capital

priceCurrent payment coupon Annual

(CY) eldCurrent yi


An example: Current and capital gains

yield

Find the current yield and the capital gains yield for a 10-year, 9% annual coupon bond that sells for $887, and has a face value of $1,000.

Current yield = $90 / $887= 0.1015 @

10.15%


Calculating Capital Gains Yield

YTM = Current yield + Capital gains yield

CGY = YTM – CY= 10.91% - 10.15%= 0.76%

Could also find the expected price one year from now and divide the change in price by the beginning price, which gives the same answer.


What is interest rate (or price) risk?

Interest rate risk is the concern that rising kd will

cause the value of a bond to fall.


What is reinvestment rate risk?

Reinvestment rate risk is the concern that kd will fall, and future CFs will have to be reinvested at lower rates, hence reducing income.

EXAMPLE: Suppose you just won $500,000 playing the lottery. You intend to invest the money and live off the interest.


Reinvestment rate risk example:

You may invest in either a 10-year bond or a series of ten 1-year bonds. Both 10-year and 1-year bonds currently yield 10%.

If you choose the 1-year bond strategy: After Year 1, you receive $50,000 in income and

have $500,000 to reinvest. But, if 1-year rates fall to 3%, your annual income would fall to $15,000.

If you choose the 10-year bond strategy: You can lock in a 10% interest rate, and $50,000

annual income.


Conclusions about interest rate and reinvestment rate

risk

CONCLUSION: Nothing is riskless!

Short-term AND/OR High coupon bonds

Long-term AND/OR Low coupon bonds

Interest rate risk

Low High

Reinvestment rate risk

High Low


Semiannual Bonds1. Multiply years by 2 : number of periods = 2n.2. Divide nominal rate by 2 : periodic rate (I/YR)

= kd / 2.

3. Divide annual coupon by 2 : PMT = ann cpn / 2.

INPUTS

OUTPUT

N I/YR PMTPV FV

2n kd / 2 cpn / 2 OKOK


What is the value of a 10-year, 10% semiannual coupon bond, if kd = 13%?

1. Multiply years by 2 : N = 2 * 10 = 20.

2. Divide nominal rate by 2 : I/YR = 13 / 2 = 6.5.

3. Divide annual coupon by 2 : PMT = 100 / 2 = 50.

INPUTS

OUTPUT

N I/YR PMTPV FV

20 6.5 50 1000

- 834.72


Semiannual Coupons/Interest

Vb = I/2(PVIFAr/2%,2N) + MV(PVIFr/2,2N)

Example: What is the price of a bond with coupon (interest) of 8.5% paid semi annually, remaining maturity of 12 years, and required rate of return is 10%?I=8.5% x $1000=$85; semi-annually=$42.50N= 12years x 2 = 24times; r = 10%/2 = 5%

Vb = $42.50(PVIFA5%,24) + $1000(PVIF5%,24) = $896.51


Semiannual BondsVb = PV (Coupon Payments) + PV (Par

Value)Vb = CPN PVIFA r/2%, 2N + 1000PVIF r/2%, 2N

2Vb = CPN (1 + r/2)2N – 1 + 1000

2 (r/2)(1 + r/2)2N (1 +

r/2)2N


Would you prefer to buy a 10-year, 10% annual coupon bond or a 10-year, 10%

semiannual coupon bond, all else equal?

The semiannual bond’s effective rate is:

10.25% > 10% (the annual bond’s effective rate), so you would prefer the semiannual bond.

10.25%12

0.1011

mi

1EFF%2m

Nom


If the proper price for this semiannual bond is $1,000, what would be the proper price for the annual coupon

bond?The semiannual coupon bond has an

effective rate of 10.25%, and the annual coupon bond should earn the same EAR. At these prices, the annual and semiannual coupon bonds are in equilibrium, as they earn the same effective return.INPUTS

OUTPUT

N I/YR PMTPV FV

10 10.25 100 1000

- 984.80


Yield to CallPrice of Bond:

Vb = I (PVIFAr%,N) + Call price(PVIFr%,N)

N= the number of years until the company can

call the bond.rd= yield to call


A 10-year, 10% semiannual coupon bond selling for $1,135.90 can be called in 4 years

for $1,050, what is its yield to call (YTC)?

The bond’s yield to maturity can be determined to be 8%. Solving for the YTC is identical to solving for YTM, except the time to call is used for N and the call premium is FV.

INPUTS

OUTPUT

N I/YR PMTPV FV

8

3.568

50 1050- 1135.90


Yield to call3.568% represents the periodic

semiannual yield to call.YTCNOM = kNOM = 3.568% x 2 = 7.137%

is the rate that a broker would quote.The effective yield to call can be

calculated YTCEFF = (1.03568)2 – 1 = 7.26%


If you bought these callable bonds, would you be more likely to earn the

YTM or YTC?

The coupon rate = 10% compared to YTC = 7.137%. The firm could raise money by selling new bonds which pay 7.137%.

Could replace bonds paying $100 per year with bonds paying only $71.37 per year.

Investors should expect a call, and to earn the YTC of 7.137%, rather than the YTM of 8%.


When is a call more likely to occur?

In general, if a bond sells at a premium, then (1) coupon > kd, so (2) a call is more likely.

So, expect to earn: YTC on premium bonds. YTM on par & discount bonds.


THE END

45


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BONDS VALUATION CHAPTER 7. Financial Market in the Financial System Financial Market – a market...

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