chapter 6 valuing bonds. copyright ©2014 pearson education, inc. all rights reserved.6-2 6.1 bond...

Chapter 6

Valuing Bonds

Copyright ©2014 Pearson Education, Inc. All rights reserved. 6-2

6.1 Bond Cash Flows, Prices, and Yields

• Bond Terminology– Bond Certificate

• States the terms of the bond– Maturity Date

• Final repayment date– Term

• The time remaining until the repayment date– Coupon

• Promised interest paymentsCoupon Rate Face Value

Number of Coupon Payments per Year

CPN


Zero-Coupon Bonds

• Zero-Coupon Bond– Does not make coupon payments– Always sells at a discount (a price lower than

face value), so they are also called pure discount bonds

– Treasury Bills are U.S. government zero-coupon bonds with a maturity of up to one year.

– Brokerage houses can “create” zero coupon treasury securities.


Zero-Coupon Bonds (cont'd)

• Suppose that a one-year, risk-free, zero-coupon bond with a $100,000 face value has an initial price of $96,618.36. The cash flows would be:

– Although the bond pays no “interest,” your compensation is the difference between the initial price and the face value.


Alternative Example 6.1

• Problem– Suppose that the following zero-coupon bonds

are selling at the prices shown below per $100 face value. Determine the corresponding yield to maturity for each bond.

Maturity 1 year 2 years 3 years 4 years

Price $98.04 $95.18 $91.51 $87.14


Alternative Example 6.1 (cont'd)

• Solution:

1/2

1/3

1/4

YTM (100 / 98.04) 1 0.02 2%YTM (100 / 95.18) 1 0.025 2.5%YTM (100 / 91.51) 1 0.03 3%YTM (100 / 87.14) 1 0.035 3.5%


Zero-Coupon Bonds

• Risk-Free Interest Rates– Spot Interest Rate

• Another term for a default-free, zero-coupon yield– Zero-Coupon Yield Curve

• A plot of the yield of risk-free zero-coupon bonds as a function of the bond’s maturity date


Coupon Bonds

• Coupon Bonds– Pay face value at maturity– Pay regular coupon interest payments

• Treasury Notes– U.S. Treasury coupon security with original

maturities of 1–10 years• Treasury Bonds

– U.S. Treasury coupon security with original maturities over 10 years



The U.S. Treasury has just issued a ten-year, $1000 bond with a 4% coupon and semi-annual coupon payments. What cash flows will you receive if you hold the bond until maturity?


Bond Valuation

• Primary Principle:– Value of financial securities = PV of expected

future cash flows • Bond value is, therefore, determined by the

present value of the coupon payments and par value.

• Interest rates are inversely related to present (i.e., bond) values.


Coupon Bonds (cont'd)

• Yield to Maturity– The YTM is the single discount rate that equates

the present value of the bond’s remaining cash flows to its current price.Rate of return investors earn if they buy the bond at P0 and hold it until maturity.

The YTM on a bond selling at par will always equal the coupon interest rate.


Basic Investment Rules

• If the value of an asset (it’s worth) is >= current market price, then you would buy it.– If the benefit >= cost, you would buy

• If the expected return of an investment is >= required return, you would buy it.– Remember: required return contains inflation and

RISK

Buy Return, Required Return Expected IfBuy Value,Market ValueIf


Valuation Example

• If the bond sells for $825, would you buy it?

• What is the yield to maturity? Bond Valuation


Valuation Example

• If the bond sells for $450, would you buy it?

• What is the yield to maturity?

Bond Valuation

Par Value $1,000.00 Bond Value $463.19Annual Coupon 0.00%Coupon per Period 0.00% Yield to Maturity 8.31%Required Return 8.00% if semi-annual, multiply by 2Time to Maturity 10 Yield to Call #NUM!Compounding Frequency 1Price 450.00$ Realized Yield to Maturity #NUM!Current Yield 0.00%



• Problem– Consider the following semi-annual bond:

• $1000 par value• 7 years until maturity• 9% coupon rate• Price is $1,080.55

– What is the bond’s yield to maturity?


6.2 Dynamic Behavior of Bond Prices

• Discount– A bond is selling at a discount if the price is less

than the face value.• Par

– A bond is selling at par if the price is equal to the face value.

• Premium– A bond is selling at a premium if the price is

greater than the face value.


Discounts and Premiums (cont'd)

Table 6.1 Bond Prices Immediately After a Coupon Payment


Time and Bond Prices

• Holding all other things constant, a bond’s yield to maturity will not change over time.

• Holding all other things constant, the price of discount or premium bond will move towards par value over time.

• If a bond’s yield to maturity has not changed, then the IRR of an investment in the bond equals its yield to maturity even if you sell the bond early.


Figure 6.1 The Effect of Time on Bond Prices

Copyright ©2014 Pearson Education, Inc. All rights reserved. 6-20 6-20

Bond valuation

1) c = 12% k = 10% n = 10 120(6.1446) + 1000(.3855) = 1122.89

2) c = 10% k = 10% n = 10 1000.00

3) c = 8% k = 10% n = 10 80(6.1446) + 1000(.3855) = 877.11

premium

discount


Price Converges on Par at Maturity

$1,000

$877

$1,122

time10 yrs

A) Go back to bond 3 on the previous slide. Put the value

in for the price. What is the YTM?

When you buy a bond what types of returns do you receive?

B) Go back to bond 1 on the previous slide. Put the value

in for the price. What is the YTM?


Interest Rate Changes and Bond Prices

• There is an inverse relationship between interest rates and bond prices.– As interest rates and bond yields rise, bond

prices fall.– As interest rates and bond yields fall, bond

prices rise.


Bond returns

• Yield to call– Refunding– Yield premium

• Realized YTM– Set a certain investment horizon– Predict price at end of the horizon


Bond Valuation

Par Value $1,000.00 Bond Value $914.86Annual Coupon 9.00%Coupon per Period 9.00% Yield to Maturity 10.19%Required Return 10.00% if semi-annual, multiply by 2Time to Maturity 20 Yield to Call 13.24%Compounding Frequency 1Price 900.00$ Realized Yield to Maturity 11.30%Current Yield 10.00%

Macaulay's Duration 9.6952Expected Future Price $1,098.00 Modified Duration 8.7987Years Until Sale 10 Convexity 121.9519

% Change in YTM 1.00%Call Premium $1,090.00 % Change in Value -8.80%Years to Call 5 New Price $820.81


Interest Rate Risk

• Price Risk– Change in price due 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.• 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 Changes and Bond Prices (cont'd)

• The sensitivity of a bond’s price to changes in interest rates is measured by the bond’s duration.– Bonds with high durations are highly sensitive to

interest rate changes.– Bonds with low durations are less sensitive to

interest rate changes.


6.4 Corporate Bonds

• The primary difference is the riskiness of the debt.

• Credit publishing companies primarily analyze the risk of default.


Corporate Bond Yields

• Investors pay less for bonds with credit risk than they would for an otherwise identical default-free bond.

• The yield of bonds with credit risk will be higher than that of otherwise identical default-free bonds.


Bond Ratings

• Investment Grade Bonds• Speculative Bonds

– Also known as Junk Bonds or High-Yield Bonds


Table 6.4 Bond Ratings


Table 6.4 Bond Ratings (cont’d)


Corporate Yield Curves

• Default Spread– Also known as Credit Spread– The difference between the yield on corporate

bonds and Treasury yields


Figure 6.3 Corporate Yield Curves for Various Ratings, June 2012

Source: Bloomberg


6.5 Sovereign Bonds

• Bonds issued by national governments– U.S. Treasury securities are generally considered

to be default free– All sovereign bonds are not default free

• e.g. Greece defaulted on its outstanding debt in 2012– Importance of inflation expectations

• Potential to “inflate away” the debt– European sovereign debt, the EMU, and the ECB


Discussion of Data Case Key Topic

Look at the Financial Industry Regulatory Authority’s website. What bond issues does Sirius Satellite Radio (ticker: SIRI) currently have outstanding? What are their yields? What are their ratings?

Source: www.finra.org

http://www.finra.org/

chapter 6 valuing bonds. copyright ©2014 pearson education, inc. all rights reserved.6-2 6.1 bond...

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