Valuation and

Valuation and

Characteristics of Bonds

Principles Used

Principle 1: The Risk-Return Trade-off – We Won’t Take on Additional Risk Unless We Expect to Be Compensated with Additional Return.

Principle 2: The Time Value of Money – A Dollar Received Today is Worth More Than a Dollar Received in the Future

Principle 3: Cash-Not Profits-Is King.

BOND VALUATION

Type of debt or long-term promissory note, issued by a borrower, promising to its holder a predetermined and fixed amount of interest on specific dates and principal upon maturity.

BOND CHARACTERISTICS Par Value Coupon Rate Maturity Date Call Provision

Convertible Bonds Income Bonds. Indexed bond

BOND CHARACTERISTICS

Par Value: Face value of the bond, returned to the

bondholder at maturity

Maturity Date: The length of time until the bond issuer

returns the par value to the bondholder and terminates or redeems the bond.

BOND CHARACTERISTICS Coupon Rate:

Rate of interest paid as a percentage of the par value.

Fixed Rate Vs Floating Rate Zero Coupon Bonds – Issued at a deep

discount and do not pay interest.

Interest Payment:= Coupon rate X Par Value

BOND CHARACTERISTICS Call Provision – The borrower may

redeem the bond early. Usually includes a call premium.

Sinking Fund Provision – Requires borrower to regularly retire a portion of the bond by either calling it or buying it on the open market.

BOND CHARACTERISTICS Convertible Bonds:

Bonds may be converted into common stock at a fixed price.

Income Bonds: Only pays interest if the company

makes a profit. Indexed bond:

Interest based on an inflation index.

TYPES OF BONDS US Government Bonds Municipal Bonds Corporate Bonds EuroBonds Junk Bonds

U.S. Government Bonds

Treasury Bills No coupons (zero coupon security) Face value paid at maturity Maturities up to one year

Treasury Notes Coupons paid semiannually Face value paid at maturity Maturities from 2-10 years

U.S. Government Bonds Treasury Bonds

Coupons paid semiannually Face value paid at maturity Maturities over 10 years The 30-year bond is called the long

bond. Treasury Strips

Zero-coupon bond Created by “stripping” the coupons and

principal from Treasury bonds and notes.

CORPORATE BONDS

Mortgage Bonds – Bonds secured with real property.

Debentures – Unsecured bonds.

Eurobonds Securities (bonds) issued in a country

different from the one in whose currency the bond is denominated

Example: a U.S. dollar-denominated bond issued by a

non-U.S. entity outside the U.S. A eurodollar bond that is denominated in

U.S. dollars and issued in Japan by an Australian company would be an example of a eurobond. The Australian company in this example could issue the eurodollar bond in any country other than the U.S.

Junk Bonds (High-Yield Bonds)

Junk Bond is a bond that is rated below investment grade at the time of purchase.

High risk debt with ratings of BB or below by Moody’s and Standard & Poor’s

High yield — typically pay 3%-5% more than AAA grade long-term bonds

These bonds have a higher risk of default or other adverse credit events, but typically pay higher yields than better quality bonds in order to make them attractive to investors.

BOND RATINGS Bonds are rated as to their riskiness

by several firms. (Moody’s Investment Service and Standard & Poor’s) Bonds with the highest rating are rated

AAA. As bonds become riskier their ratings

drop. Riskiness is the chance of default. Investment grade bonds must be rated at

least BBB.

Bond RatingsMoody’s S&P Quality of Issue

Aaa AAA Highest quality. Very small risk of default.

Aa AA High quality. Small risk of default.

A A High-Medium quality. Strong attributes, but potentiallyvulnerable.

Baa BBB Medium quality. Currently adequate, but potentiallyunreliable.

Ba BB Some speculative element. Long-run prospectsquestionable.

B B Able to pay currently, but at risk of default in thefuture.

Caa CCC Poor quality. Clear danger of default .

Ca CC High specullative quality. May be in default.

C C Lowest rated. Poor prospects of repayment.

D - In default.

Bond Valuation

The value of a bond is a combination of: The amount and timing of the cash

flows to be received by investors maturity The investor’s required rate of return

BOND VALUATION

VB = Present Value of the Interest Payments plus the Present Value of the Maturity Value (Par Value).

BOND VALUATION

BOND VALUE

Interest Paymen

t ($) Par Value

Number of

Periods

Interest Rate

BOND VALUATI0N A company issues a 3 year bond with a par

value of $1,000 and a coupon rate of 10%. The required rate of return on the bond is also 10%. What is the value of the bond? Par Value = 1,000 Interest Rate (r) = 10% Interest Payment = 10% x 1,000 = $100 No. of periods = 3 years

BOND VALUATION

Present Value of the Interest Payments Interest Payment $100

10% ~ .10

Bond Valuation

$91

$83

$75

0 1 2 3r=10%

$100 $100 $100100

(1 + .10)1

100

(1 + .10)2

100

(1 + .10)3

$249

Present Value of the Interest Payments

Bond Valuation

Present Value of the Maturity Value

$1,000

3 yrs10% ~ .10

Bond Valuation

$751

0 1 2 3r=10%

$1,000

$1,000

(1 + .10)3

Present Value of the Maturity Value

Bond Valuation

$91

$83

$75

0 1 2 3

$100 $100 $100100

(1 + .10)1

100

(1 + .10)2

100

(1 + .10)3

$249

Present Value of the Interest Payments plus the Present Value of the Maturity Value

$751

$1,000

$1,000

(1 + .10)3

$1,000 = Vb When the coupon rate and i are equal the value of the bond will always be the par value.

Review QuestionsIn your groups calculate the value of

the bonds. A company issues a 3 year bond

with a par value of $1,000 and a coupon rate of 10%. The required rate of return on the bond is also 5%. What is the value of the bond?

A company issues a 3 year bond with a par value of $1,000 and a coupon rate of 5%. The required rate of return on the bond is also 10%. What is the value of the bond?

TAKE TEN MINUTES


value of $1,000 and a coupon rate of 10%. The required rate of return on the bond is also 5%. What is the value of the bond? Par Value = 1,000 Interest Rate (r) = 5% Interest Payment = 10% x 1,000 = $100 No. of periods = 3 years

Bond Valuation

$95

$91

$86

0 1 2 3

$100 $100 $100100

(1 + .05)1

100

(1 + .05)2

100

(1 + .05)3

$272


$864

$1,000

$1,000

(1 + .05)3

$1,136 = Vb Whenever interest rates fall, bond prices go up. Sell at a premium.

BOND VALUATI0N A company issues a 3 year bond with a

par value of $1,000 and a coupon rate of 5%. The required rate of return on the bond is also 10%. What is the value of the bond? Par Value = 1,000 Interest Rate (r) = 10% Interest Payment = 5% x 1,000 = $50 No. of periods = 3 years

Bond Valuation

$45

$41

$38

0 1 2 3

$50 $50 $5050

(1 + .10)1

50

(1 + .10)2

50

(1 + .10)3

$124


$751

$1,000

$1,000

(1 + .10)3

$876 = Vb Whenever interest rates go up bond values fall.Sells at a discount.

BOND VALUATION

Interest rates change over time, so a bond’s value will fluctuate over time.

BOND VALUATI0N (EXCEL)A company issues a 30 year bond with a par

value of $1,000 and a coupon rate of 10%. The required rate of return on the bond is also 10%. What is the value of the bond?

Using PV formulanper = 30, rate = .10, Pmt = 100, FV = 1,000

PV = 1,000

When the coupon rate and i are equal the value of the bond will always be the par value.

SEMI-ANNUAL COUPONS

Most bonds have semiannual coupons.

When valuing a bond with semiannual coupons divide the Pmt by 2; multiply n by 2.


value of $1,000 and a coupon rate of 10%. The required rate of return on the bond is also 10%. What is the value of the bond, if interest payments are paid semi-annually? Par Value = 1,000 Interest Rate (r) = 10% per yr / 2 = 5% Interest Payment = (10%/2) x 1,000 = 50 No. of periods = 3 X 2 = 6

BOND VALUATION

nper = 6 rate = .05 Pmt = 50 FV = 1,000 PV = ???

BOND VALUATION

nper = 6 rate = .05 Pmt = 50 FV = 1,000 PV = 1,000

Calculate the value of a bond with the following features, assuming that interest is paid semi-annually and that the face value of the bond is $1,000:

Problem

Coupon rate

Yield to maturity

Years to maturity

Bond value

a 8% 10% 3

b 4% 6% 1.5

c 6% 4% 2

d 6.25% 6% 2

e 4% 8% 2.5

BOND YIELDS

Yield to maturity – the yield you will receive if you hold the bond until it matures.

YIELD TO MATURITY

Let’s use the same example: we issue a bond with a 10% coupon. The price is $1,000 (the par value). What is the yield to maturity?

nper = 30, Pmt = 100, FV = 1,000, PV = -1,000

The FV and Pmt are amounts we will receive; the PV is an amount we pay so it is a minus.

YIELD TO MATURITY

Let’s use the same example: we issue a bond with a 10% coupon. The price is $1,000 (the par value). What is the yield to maturity?

nper = 30, Pmt = 100, FV = 1,000, PV = -1,000 rate = 10% The same as the Coupon rate; if FV and PV

are equal the interest rate will equal the coupon rate.

YIELD TO MATURITY

Now let’s assume that 5 years go by and we pay $1,225.08 for our bond. What is the yield to maturity?

nper = 25, Pmt = 100, FV = 1,000, PV = -1,225.08

YIELD TO MATURITY

Now let’s assume that 5 years go by and we pay $1,225.08 for our bond. What is the yield to maturity?

nper = 25, Pmt = 100, FV = 1,000, PV = -1,225.08

rate = 7.91

Review QuestionsIn your groups calculate the YTM

The $1,000 face value EFG bond has a coupon of 10% (paid semi-annually), matures in 4 years, and has current price of $1,140. What is the EFG bond's yield to maturity?

The NOP bond has an 8% coupon rate (semi-annual interest), a maturity value of $1,000, matures in 5 years, and a current price of $1,200. What is the NOP's yield-to-maturity?

YIELD TO CALL

Company’s can call bonds early. Company’s will generally call

bonds when interest rates have fallen and new bonds can be issued with a lower coupon rate.

YIELD TO CALL

Let’s assume the bond in our example is callable 10 years after issue.

Again, five years have gone by, so the bond can be called in five years.

All other information remains the same.

YIELD TO CALL

nper = 5 (years until bond can be called)

Pmt = 100FV = 1,000PV = -1,225.08Rate = ????

YIELD TO CALL

nper = 5 (years until bond can be called)

Pmt = 100FV = 1,000PV = -1,225.08Rate = 4.83

The yield to call is less than the yield to maturity because we will receive fewer $100 payments.

CURRENT YIELD

The ratio of the interest payment to the bond’s current market price. The interest payment divided by the

current price of the bond.

In our example: Current Yield = 100/1,225.08 =

8.16%

Review QuestionsIn your groups calculate the following:

• The $1,000 face value ABC bond has a coupon rate of 6%, with interest paid semi-annually, and matures in 5 years. If the bond is priced to yield 8%, what is the bond's value today?

• The KLM bond has a 8% coupon rate,with interest paid semi-annually, a maturity value of $1,000, and matures in 5 years. If the bond is priced to yield 6%, what is the bond's current price?

• The HIJ bond has a current price of $800, a maturity value of $1,000, and matures in 5 years. If interest is paid semi-annually and the bond is priced to yield 8%, what is the bond's annual coupon rate?

Documents

Valuation and