slide 1 valuation and characteristics of bonds characteristics of bonds valuation bond valuation...

Valuation and Characteristics of Bonds Characteristics of Bonds Valuation Bond Valuation Bond Quotes Duration

Characteristics of BondsBonds pay fixed coupon (interest) payments at fixed intervals (usually

every 6 months) and pay the par value at maturity

Par value = $1000 Coupon = 6.5% of par value per year

= $65 per year ($32.50 every 6 months) Maturity = 28 years (matures in 2029) Issued by AT&T

0 6m 1 2 … 28

$32.50 $32.50 $32.50 $32.50 $32.50 $32.50+$1000

Types of Bonds Debentures – unsecured bonds Subordinated debentures – unsecured “junior”

debt Mortgage bonds – secured bonds Zeros – bonds that pay only par value at maturity;

no coupons Junk bonds – speculative or below-investment

grade bonds; rated BB and below. High-yield bonds

Types of Bonds (Continued) Eurobonds – bonds denominated in one currency

and sold in another country. (Borrowing overseas)

example – suppose Disney decides to sell $1,000 bonds in France. These are U.S. $ denominated bonds trading in a foreign country. Why do this? If borrowing rates are lower in France To avoid SEC regulations

Bond Indenture The bond contract between the firm and the

trustee representing the bondholders Lists all of the bond’s features: coupon, par value,

maturity, etc Lists restrictive provisions which are designed to

protect bondholders Describes repayment provisions

Value Book Value: value of an asset as shown on a

firm’s balance sheet; historical cost Liquidation value: amount that could be received

if an asset were sold individually Market value: observed value of an asset in the

marketplace; determined by supply and demand Intrinsic value: economic or fair value of an

asset; the present value of the asset’s expected future cash flows

Security Valuation In general, the intrinsic value of an asset = the present

value of the stream of expected cash flows discounted at an appropriate required rate of return

Can the intrinsic value of an asset differ from its market value?

Ct = cash flow to be received at time t k = the investor’s required rate of return V = the intrinsic value of the asset

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Bond Valuation Discount the bond’s cash flows at the investor’s required

rate of return the coupon payment stream (an annuity) the par value payment (a single sum)

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Bond Example Suppose our firm decides to issue 20-year bonds

with a par value of $1,000 and annual coupon payments. The return on other corporate bonds of similar risk is currently 12% (required return), so we decide to offer a 12% coupon interest rate

What would be a fair price for these bonds?

Note: If the coupon rate = required return, the bond will sell for par value

N I/Y P/Y PV PMT FV MODE

20 12 1 -1000 120 1000

Bond Example (Continued)

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Bond Example (Continued) Suppose interest rates fall immediately after we

issue the bonds. The required return on bonds of similar risk drops to 10%


Note: If the coupon rate > required return, the bond will sell for a premium


20 10 1 -1,170.27 120 1000

Bond Example (Continued) Suppose interest rates rise immediately after we

issue the bonds. The required return on bonds of similar risk rises to 14%


Note: If the coupon rate < required return, the bond will sell for a discount


20 14 1 -867.54 120 1000

Bond Example (Continued) For the last bond example assume that the interest

paid semi-annually What would be a fair price for these bonds?


40 14 2 -866.68 60 1000

Bond Example (Continued)

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Yield-To-Maturity The expected rate of return on a bond The rate of return investors earn on a bond if they

hold it to maturity Suppose we paid $898.90 for a $1,000 par 10%

coupon bond with 8 years to maturity and semi-annual coupon payments

What is our yield-to-maturity?N I/Y P/Y PV PMT FV MODE

16 12 2 -898.90 50 1000

Zero Bond Example Suppose you pay $508 for a zero coupon bond

that has 10 years left to maturity What is your yield-to-maturity?


10 7 1 -508.00 0 1000

The Financial Pages: Corporate BondsCur Net

Yld Vol Close Chg

Polaroid 11 1/2 Mat. 19.3 395 59 3/4 ...

What is the yield-to-maturity?


10 (Assumed) 26.48 2 -597.50 57.50 1000

Cur Net

Yld Vol Close Chg

HewlPkd Mat. ... 20 51 1/2 +1

What is the yield-to-maturity?

The Financial Pages: Corporate Bonds


16 (Assumed) 4.24 1 -515.00 0 1000

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

Makes getting up-to-date prices difficult, particularly on small company or municipal issues

Treasury securities are an exception Bond yield information is available online. One good site is

Bonds Online http://www.bondsonline.com/ Follow the “bond search,” “search/quote center,” “corporate/agency

bonds,” and “composite bond yields” links Observe the yields for various bond types, and the shape of the yield curve.

Corporate Bond Price Reporting

Coupon rate: 8.375% Coupon payment per year = $83.75 = 0.08375 X 1,000

Bond matures on July 15, 2033 Trading volume = $763,528,000 (Face value of bonds traded) Quoted price: 100.641% of face value, so if face value is 1,000, the price is

$1,006.41. Bond prices are quoted as a percent of par, just as the coupon is quoted as a

percent of par. The bond’s yield (8.316%) is 362 basis points (3.62%) above the comparable

maturity Treasury bond yield (30-year Treasury bond yield). 100 basis points = 1%

Current yield = 8.322% Computed as annual coupon divided by current price ($83.75 / $1,006.41 =

8.32%)

Corporate Bond Price Reporting – Continued

How can we determine the yield on GM bond? To do that we use another TI BA II PLUS worksheet – BOND Date entry: mm.ddyy

2ND BOND 2ND CLR WORK 01.1305 ENTER (Settlement date.) 8.375 ENTER (Annual coupon interest rate in percent form.) 07.1533 ENTER (Maturity date.) 100 ENTER (Face value entered as 100. If the bond has a call price it can be set to

that.) ACT (“ACT” is actual day count. Can be changed to “360” by using 2ND SET) 2/Y (Coupon payment per year. Can be changed to “1/Y” by using 2ND SET) Since we are computing yield (YLD) 100.641 ENTER (Non-negative price of the bond as a % of face value.) CPT (Go back to “YLD” to compute.) AI (“AI” is Accrued Interest as dollar amount per face value amount.) DUR (“DUR” is Duration of the bond – average time it takes to recover the market

price.)

Clean and Dirty Price of a Bond How much do you think you will pay for the previous bond per $100 par

value? Price a buyer would pay will include “Accrued Interest” (AI) if a bond is

purchased after the last coupon but before the next coupon payment This is because a seller is entitled to receive some of the next coupon

payment based on the fraction of six month period she owned it. A quotation excluding AI is called “Clean Price” What you pay for the bond is called “Dirty Price” Dirty Price = Clean Price + Accrued Interest Dirty Price = $100.641 + $4.142 = $104.783

AI is quite close to 8.375 / 2 = 4.1875 since we are short by two days to make it a full six month period (1/13/05 vs. 1/15/05)

4.1875 × 178/180 = 4.141 You pay Dirty Price (Clean Price + AI) to the seller and get the next coupon in

two days in full

More on Clean and Dirty Price of a Bond

Why do dealers quote clean price then? Clean prices excludes price drops of bonds due

to a coupon payment. This drop can also be observed for stock when

there is a dividend payment. Clean prices change not because of a coupon

payment but rather because of a change in general direction of interest rates or a change in the credit quality of borrower

Maturity Ask

Rate Mo/Yr Bid Asked Chg Yld

9 Nov 18 139:14 139:20 -34 5.46 What is the yield-to-maturity using ASK price with 35

periods? PV = (139 + 20/32)% of 1,000 = 1,396.25

The Financial Pages: Treasury Bonds


35 5.457 2 -1,396.25 45.00 1000

Treasury Bond Price Reporting

Coupon rate = 9% Matures in November 2018 Bid price (Dealer’s Bid – dealer is willing to pay) is 145 and 25/32 percent of

par value. 145:25 = (145+25/32)% of par value = 145.78125% of par value If you want to sell $100,000 par value T-bonds, the dealer is willing to pay

1.4578125(100,000) = $145,781.25 Ask price (Dealer’s Ask – dealer is willing to receive) is 145 and 26/32 percent

of par value. 145:26 = (145+26/32)% of par value = 145.8125% of par value If you want to buy $100,000 par value T-bonds, the dealer is willing to sell them for

1.458125(100,000) = $145,812.50 The difference between the bid and ask prices is called the bid-ask spread and it

is how the dealer makes money. Note that Ask Price is higher than Bid Price. Why is that?

The price changed by 22/32 percent or $687.50 for a $100,000 worth of T-bonds (22/32)% of par.

(22/32)% = 0.6875% and 0.6875% X $100,000 = $687.50. The yield based on the ask price is 4.51%

Treasury Bond Price Reporting – Continued If the date of quotation is January 14, 2005 and exact maturity date is

11/15/2018 what is the yield based on ask price? 2ND BOND 2ND CLR WORK 01.1405 ENTER (Settlement date.) 9.000 ENTER (Annual coupon interest rate in percent form.) 11.1518 ENTER (Maturity date.) 100 ENTER (Face value entered as 100. If the bond has a call price it can be

set to that.) ACT (“ACT” is actual day count. Can be changed to “360” by using 2ND SET) 2/Y (Coupon payment per year. Can be changed to “1/Y” by using 2ND SET) Since we are computing yield (YLD) 145.8125 ENTER (Non-negative price of the bond as a % of face value.) CPT (Go back to “YLD” to compute.

Bond Pricing Theorems The following statements about bond pricing are always true.

Bond prices and market interest rates move in opposite directions

When a bond’s coupon rate is (greater than / equal to / less than) the market’s required return, the bond’s market value will be (greater than / equal to / less than) its par value

Given two bonds identical but for maturity, the price of the longer-term bond will change more than that of the shorter-term bond, for a given change in market interest rates

Given two bonds identical but for coupon, the price of the lower-coupon bond will change more than that of the higher-coupon bond, for a given change in market interest rates

Last two have implications for bond price volatility

Factors Affecting Bond Price Volatility The longer the maturity, The lower the coupon rate, The lower the initial required yield,

===> the larger is the effect of a change in the required yield on the price of a bond.

Bond Price Volatility and Duration The Duration of a bond is a linear approximation

of the percentage change in its price given a 100 basis point (one percent) change in required yield Measures a bond’s percentage price volatility For example, a bond with a duration of 7 will gain

about 7% in price if required yield falls 1%

Bond Duration

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Duration Example Calculating the duration of a 4-year bond with an

8 percent coupon rate (annual payments). The required return of this bond is 9%, and the maturity value is $1,000

Duration Example (Continued)

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