Bond Valuation and Interest Rates 5

8/13/2019 Bond Valuation and Interest Rates 5

1/29

Bond Valuation and InterestRates


2/29

CHAPTER 6 Bond Valuation and Interest Rates 6 - 2

The Basic Structure of Bonds

What is a bond?

a bond is any debt instrument that promises a

fixed income stream to the holder Fixed income securities are often classified

according to maturity, as follows:

Less than one yearBills or Paper

1 year < Maturity < 7 yearsNotes

< 7 yearsBonds


3/29



A typical bond has the followingcharacteristics:

A fixed face or par value, paid to the holder of the

bond, at maturity A fixed coupon, which specifies the interest payable

over the life of the bond Coupons are usually paid either annually or semi-annually

A fixed maturity date


4/29


Bond indenture - the contract between theissuer of the bond and the investors who hold it

The market price of a bond is equal to the

present value of the payments promised by thebond



5/29


The Basic Structure of BondsCash Flow Pattern for a Traditional Coupon-Paying Bond

0 1 2 3 n

I I I I I

F

FIGURE 6-1

I = interest payments, and F = principal repayment


6/29


Cash Flow Pattern of a Bond

The Purchase Price or Market Price of a bond is simply the present

value of the cash inflows, discounted at the bonds yield-to-maturity

0 2 3 4 n1

Coupon Coupon Coupon Coupon Coupon +

Face Value

Purchase

Price

Cash Inflows

to the Investor

Cash Outflows

to the Investor


7/29


Term-to-maturitythe time remaining to thebonds maturity date

Coupon ratethe annual percentage interestpaid on the bonds face value; to calculate the

dollar value of the annual coupon, multiply thecoupon rate by the face value If the coupon is paid twice a year, divide the annual

coupon by two

Example: A $1,000 bond with an 8% coupon rate willhave an $80 coupon if paid annually or a $40 couponif paid semi-annually



8/29


Bond Valuation

The value of a bond is a function of:

Par value

Term to maturity Coupon rate

Investors required rate of return (discount rate is also

known as the bonds yield to maturity)


9/29


Bond Valuation: Example

What is the market price of 15-years,$1,000 bond with a 10% coupon, if the

bonds yield-to-maturity is 10%?


10/29


Bond ValueGeneral Formula

[ 6-1]


11/29


12/296 - 12


VB= 100* 7.6061 + 1000* 0.2394 = 760.61+ 239.4= 784.55 $


13/29

6 - 13



14/29

6 - 14


1- INT= 1000 *8%= 80$N= 19 yearsM= 1000Kd= 6%VB= 80/(1+6%) + 1000 /(1+6%)VB= 80 * 11.1581+ 100 * 0.3305= 1223.148$

19 19

2- INT= 1000 *8%= 80$N= 19 years

M= 1000Kd= 10%VB= 80/(1+10%) + 1000 /(1+10%)VB= 80 * 8.3649+ 100 * 0.1635= 832.692$

19 19


15/29


Factors Affecting Bond PricesBond Price-Yield Curve

Market Yield (%)

FIGURE 6-2

Price($)

When interest rates increase, bond prices fall


16/29




17/29




18/29


The relationship between the coupon rate and thebonds yield-to-maturity (YTM) determines if the bondwill sell at a premium, at a discount, or at par

If Then Bond Sells at a:

Coupon < YTM Market < Face Discount

Coupon = YTM Market = Face Par

Coupon > YTM Market > Face Premium

Factors Affecting Bond Prices


19/29

CHAPTER 6 Bond Valuation and Interest Rates6 - 19

Bond Valuation: Semi-Annual Coupons

So far, we have assumed that all bonds haveannual pay coupons. While this is true for manybonds, it is not true for other bond issues, whichhave coupons that are paid semi-annually

To adjust for semi-annual coupons, we mustmake three changes:

Size of the coupon payment (divide by 2)

Number of periods (multiply by 2) Yield-to-maturity (divide by 2)


20/29


For example, suppose you want to value a 5-years, $10,000 Government ofCanada bond with a 4% coupon, paid twice a year, given a YTM of 6%.

INT /2=( 10000 *4%)/2= 400/2= 200$N * 2=5 * 2=10M= 10000

Kd /2= 6% /2= 3%

VB= 200/(1+3%) + 10000 /(1+3%)VB= 200 * 8.5302+ 10000 * 0.7441 = 9147.04$

10 10


21/29



There are three factors that affect the pricevolatility of a bond

Yield to maturity

Time to maturity Size of coupon


22/29


Bond Yields

Yield-to-maturity (YTM)the discount rate usedto evaluate bonds

The yield earned by a bond investor who: Purchases the bond at the current market price Held the bond to maturity

Reinvested all of the coupons at the YTM

Is the bonds Internal Rate of Return (IRR)


23/29


24/29


Factors Affecting Bond PricesPrice and Yield: 25 Year Bond, 10% Coupon

Price/Yield Relationship

0

50

100

150

200

250

300

350

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29

Percent YTM

P

rice

per$100

ofFa

ce

Value


25/29



Time to maturity

Long bonds have greater price volatility than shortbonds

The longer the bond, the longer the period for which thecash flows are fixed

Size of coupon

Low coupon bonds have greater price volatility

than high coupon bonds High coupons act like a stabilizing device, since a greater

proportion of the bonds total cash flows occur closer to

today & are therefore less affected by a change in YTM


26/29


Interest Rate Risk & Duration

The sensitivity of bond prices to changes ininterest rates is a measure of the bondsinterest rate risk

A bonds interest rate risk is affected by: Yield to maturity

Term to maturity

Size of coupon

These three factors are all captured in onenumber called duration


27/29


Duration

Duration is a measure of interest rate risk

The higher the duration, the more sensitive thebond is to changes in interest rates

A bonds duration will be higher if its: YTM is lower

Term to maturity is longer

Coupon is lower


28/29

6 - 28



29/29

6 - 29


Bond Valuation and Interest Rates 5

Documents

Transcript of Bond Valuation and Interest Rates 5