The Application of the Present Value Concept Chapter 6 Valuing Bond The Application of the Present Value Concept 1

Topics Covered Bond Characteristics Interest Rates and Bond Prices Current Yield and Yield to Maturity Bond Rates of Return The Yield Curve Corporate Bonds and the Risk of Default 2

Bond Characteristics Bond - Security that obligates the issuer to make specified payments to the bondholder. Coupon - The interest payments made to the bondholder. Face Value - (Par Value, Principal or Maturity Value) - Payment at the maturity of the bond. Coupon Rate - Annual interest payment as a percentage of face value.

Bond Characteristics A bond also has (legal) rights attached to it: If the borrower doesn’t make the required payments, bondholders can force bankruptcy proceedings In the event of bankruptcy, bond holders get paid before equity holders

An Example of A Bond Example A coupon bond that pays coupon of 5% annually, with a face value of $1000, has a discount rate of 2.15% and matures in three years. The coupon payment is $50 annually In the third year, the bondholder is supposed to get $50 coupon payment plus the face value of $1000. The discount rate is different from the coupon rate.

Bond Cash Flows

Coupon Rate vs. Discount Rate WARNING The coupon rate IS NOT the discount rate used in the Present Value calculations. The coupon rate merely tells us what cash flow the bond will produce. Since the coupon rate is listed as a %, this misconception is quite common.

Bond Pricing – Zero Coupon Bonds Example How much is a 10-yr zero coupon bond worth today if the face value is $1,000 and the effective annual rate is 8% ? P0=1000/1.0810=$463.2 present value of the face value paid at the maturity Zero coupon bonds are also called zeros or stripped bonds.

Bond Pricing – Coupon Bonds The price of a coupon bond is the Present Value of all cash flows generated by the bond (i.e. coupons and face value) discounted at the required rate of return.

Bond Pricing Example What is the price of a 5 % annual coupon bond, with a $1,000 face value, which matures in 3 years? Assume a required return of 2.15%.

Bond Pricing Another way to think of bond pricing PV = PV (coupons) + PV (face value) PV of An Annuity Financial calculator: n=3, i=2.15, PMT=50, FV= 1,000  PV=(-)1,081.95

Bond Pricing Example What is the price of the 5% coupon bond if the required rate of return is 2.15% AND the coupons are paid semi-annually?

Bond Pricing Example What is the price of the 5% coupon bond if the required rate of return is 2.15% AND the coupons are paid semi-annually? Financial calculator: n=6, i=1.075, PMT=25, FV= 1,000  PV=(-)1,082.37 13 13

Interest Rates and Bond Prices Example What is the price of the 5% annual coupon bond if the required rate of return is 5 %? Financial calculator: n=3, i=5, PMT=50, FV= 1,000  PV=(-)1,000

Interest Rates and Bond Prices Example (continued) What is the price of the bond if the required rate of return is 15 %? Financial calculator: n=3, i=15, PMT=50, FV= 1,000  PV=(-)771.68

Interest Rates and Bond Prices Example (continued) Q: How do bond prices vary with interest rates? Market interest rate > Coupon rate Bond price < Face value : discount bond Market interest rate < Coupon rate Bond price > Face value: premium bond

Bond Prices Over Time

Interest Rates and Bond Prices

Interest Rate Risk

Bond Yields Current Yield - Annual coupon payments divided by bond price. The current yield does not measure the bond’s total rate of return. It overstates the return of premium bonds It understates the return of discount bonds

Bond Yields Yield To Maturity (YTM) - Interest rate for which the present value of the bond’s payments equal the price.

Bond Yields Calculating Yield to Maturity (YTM=r) If you are given the price of a bond (PV) and the coupon rate, the yield to maturity can be found by solving for r.

Bond Yields Example What is the YTM of a 5% annual coupon bond, with a $1,000 face value, which matures in 3 years? The market price of the bond is $1,081.95. Financial calculator: n=3, PV=(-)1,081.95, PMT=50, FV= 1,000  i=2.15

Bond Yields WARNING Calculating YTM by hand can be very tedious. It is highly recommended that you learn to use the “IRR” or “YTM” or “i” functions on a financial calculator.

Bond Yields Example In the previous example, what is the YTM if the coupons are paid semiannually? Financial calculator: n=6, PV=(-)1,081.95, PMT=25, FV=1,000  i=1.082

Bond Yields Example A 4-year maturity bond with a 14 percent coupon rate can be bought for $1,200. What is the YTM if the coupon is paid annually? What if it is paid semiannually? If coupon is paid annually If coupon is paid semiannually Financial calculator: n=4, PV=(-)1,200, PMT=140, FV= 1,000  i=7.97 Financial calculator: n=8, PV=(-)1,200, PMT=70, FV= 1,000  i=4.026 per 6 month. It would be reported in the financial press as 8.05 percent annual yield (yield to maturity).

Bond Rates of Return Rate of Return – Total income per period per dollar invested.

Bond Rates of Return Rate of Return versus Yield to Maturity The yield to maturity defined as the discount rate that equates the bond’s price to the present value of all its promised cash flows. a measure of the average rate of return you will earn over the bond’s life if you hold it to maturity. The rate of return can be calculated for any particular holding period based on the actual income and the capital gain or loss on the bond over that period.

Bond Rates of Return Example Our 5.5 percent annual coupon bond currently has 3 years left until maturity and sells today for $1,056.03. Its yield to maturity is 3.5 percent. Suppose that by the end of the year (Note: at this time, the bond will have only 2 years to maturity), interest rates have fallen and the bond’s yield to maturity is now only 2.0 percent. What will be the bond’s rate of return?

Bond Rates of Return Example (Continued) Suppose that the bond’s yield to maturity had risen to 5 percent during the year. What will be the bond’s rate of return?

The Yield Curve Term Structure of Interest Rates - A listing of bond maturity dates and the interest rates that correspond with each date. Yield Curve - Graph of the term structure. 26

The term structure of interest rates (Yield curve)

YTM for corporate and government bonds The YTM of corporate bonds is larger than the YTM of government bonds Why does this occur?

Default Risk Default (or credit) risk Default premium The risk that a bond issuer may default on its bonds. Default premium The additional yield on a bond investors require for bearing credit risk. Investment grade bonds Bonds rated Baa or above by Moody’s or BBB or above by S&P’s. Junk bonds Bonds with a rating below Baa or BBB

Default Risk

Default Risk

Corporate Bonds Zero coupons Floating rate bonds Convertible bonds Callable bonds