Interest Rates and Bond Valuation

FEATURES OF BONDS
A bond is a long-term debt instrument that pays the bondholder a specified amount of periodic interest rate over a specified period of time
The bond’s principal is the amount borrowed by the company and the amount owed to the bond holder on the maturity date
The bond’s maturity date is the time at which a bond becomes due and the principal must be repaid
The bond’s coupon rate is the specified interest rate (or $ amount) that must be periodically paid

COUPON PAYMENT
A bond has a 7% coupon and pays interest semi-annually.
What is the amount of each interest payment if the face value of a bond is $1,000?

BONDS WITH MATURITY DATES
For example, find the price of a 10% coupon bond with three years to maturity if market interest rates are currently 10%.
B0 = $100 + $100 + ($100 + $1,000)
(1+.10)1 (1+.10)2 (1+.10)3

BOND PRICING
A bond has a 9% coupon rate, matures in 12 years and pays interest semi-annually. The face value is $1,000.
What is the current price of this bond if the market rate of return is 8.3%?
Enter 12×2 8.3/2 90/2 1,000
N I/Y PV PMT FV
Solve for ±1,052.55

TIME TO MATURITY
A bond is currently selling at a price of $977.03. The face value is $1,000 and the coupon rate is 8%. Interest is paid semi-annually.
How many years is it until this bond matures if the market rate of return is 8.4%?
Enter 8.4/2 ±977.03 80/2 1,000
N I/Y PV PMT FV
Solve for 16
There are 16 semi-annual periods, or 8 years, until the bond maturity date.

FEATURES OF BOND
The bond’s current yield is the annual interest (income) divided by the current price of the security
The bond’s yield-to-maturity is the yield (expressed as a compound rate of return) earned on a bond from the time it is acquired until the maturity date of the bond
A yield curve graphically shows the relationship between the time to maturity and yields for debt in a given risk class

CURRENT YIELD
The Current Yield measures the annual return to an investor based on the current price
Current = Annual Coupon Interest
Yield Current Market Price
For example, a 10% coupon bond which is currently selling at $1,150 would have a current yield of:
Current = $100 = 8.7%
Yield $1,150

CURRENT YIELD
Annual income (interest or dividends) divided by the current price of the security.
This measure looks at the current price of a bond instead of its face value and represents the return an investor would expect if he or she purchased the bond and held it for a year.
This measure is not an accurate reflection of the actual return that an investor will receive in all cases because bond and stock prices are constantly changing due to market factors.

CURRENT YIELD
An 8%, semi-annual coupon bond has a $1,000 face value and matures in 8 years.
What is the current yield on this bond if the yield to maturity is 7.8%?

CURRENT YIELD
Enter 8×2 7.8/2 80/2 1,000
N I/Y PV PMT FV
Solve for ±1,011.74

YIELD TO MATURITY (YTM)
The yield to maturity measures the compound annual return to an investor and considers all bond cash flows. It is essentially the bond’s IRR based on the current price.
PV = I1 + I2 + … + (In + Mn)
(1+k)1 (1+k)2 (1+k)n
Notice that this is the same equation we saw earlier when we solved for price. The only difference then is that we are solving for a different unknown. In this case, we know the market price but are solving for return.

YIELD TO MATURITY
A 6% bond pays interest annually and matures in 14 years. The face value is $1,000 and the current market price is $896.30.
What is the yield to maturity?
Enter 14 ±896.30 60 1,000
N I/Y PV PMT FV
Solve for 7.2

YIELD CURVE

HOLDING PERIOD YIELD
You bought a bond exactly one year ago for $1,004.50. Today, you sold the bond at a price of $987.40. The bond paid interest semi-annually at a coupon rate of 6%.
What is your holding period yield on this bond?
Enter 1×2 /2 ±1,004.50 60/2 987.40
N I/Y PV PMT FV
Solve for 4.29

INTEREST RATE RISK
You own two bonds. Both bonds have a 6% coupon and pay interest semi-annually. Both have a face value of $1,000. Bond A matures in two years while bond B matures in 10 years.
What is the price of each bond at a market rate of 6%? What happens if the rate increases to 7%.
Bond A:
Enter 2×2 6/2 60/2 1,000
N I/Y PV PMT FV
Solve for ±1,000
Bond B:
Enter 10×2 6/2 60/2 1,000
N I/Y PV PMT FV
Solve for ±1,000

INTEREST RATE RISK
Bond A:
Enter 2×2 7/2 60/2 1,000
N I/Y PV PMT FV
Solve for ±981.63
Bond B:
Enter 10×2 7/2 60/2 1,000
N I/Y PV PMT FV
Solve for ±928.94
The amount of bond price volatility depends on three basic factors:
length of time to maturity
risk
amount of coupon interest paid by the bond

BONDS WITH MATURITY DATES

PRICE CONVERGES ON PAR AT MATURITY
It is also important to note that a bond’s price will approach par value as it approaches the maturity date, regardless of the interest rate and regardless of the coupon rate

YIELD TO MATURITY
The yield to maturity measures the compound annual return to an investor and considers all bond cash flows. It is essentially the bond’s IRR based on the current price
Note that the yield to maturity will only be equal if the bond is selling for its face value ($1,000)
And that rate will be the same as the bond’s coupon rate
For premium bonds, the current yield > YTM
For discount bonds, the current yield < YTM

ZERO COUPON BOND
You are considering purchasing a 10-year, zero coupon bond with a face value of $1,000.
How much are you willing to pay for this bond if you want to earn a 12% rate of return? Assume annual compounding.
Enter 10 12 1,000
N I/Y PV PMT FV
Solve for ±321.97

ZERO COUPON BOND
Winslow, Inc. issues 20-year zero coupon bonds at a price of $224.73. The face value is $1,000.
What is the amount of the implicit interest for the first year of this bond’s life?

CORPORATE BOND QUOTE

CORPORATE BOND QUOTE
The closing price of a bond is quoted in the newspaper as 101.366.
What is the market price if the face value is $1,000?

TYPES OF BONDS

NOMINAL OR ACTUAL RATE OF INTEREST (RETURN)
The nominal rate of interest is the actual rate of interest charged by the supplier of funds and paid by the demander
The nominal rate differs from the real rate of interest, k* as a result of two factors:
Inflationary expectations reflected in an inflation premium (IP), and
Issuer and issue characteristics such as default risks and contractual provisions as reflected in a risk premium (RP)

NOMINAL OR ACTUAL RATE OF INTEREST
Using this notation, the nominal rate of interest for security 1, k1 is given in equation 6.1, and is further defined in equations 6.2 and 6.3.

FISHER EFFECT
Last year, you earned 14.59% on your investments. The inflation rate was 4.30% for the year.
What was your real rate of return for the year?