6 - 1 CHAPTER 6 Bonds and Their Valuation Key features of bonds Bond valuation Measuring yield Assessing risk

6 - 2 The value of any financial asset (a stock, a bond, a lease) or even a physical asset such as an apartment building or a piece of machinery is simply the present value of the cash flows the asset is expected to produce. Financial Asset Valuation

6 - 3 Financial Asset Valuation  PV= CF 1+r r 1n r n n r CF 1 CF n CF 2 Value...

6 - 4 Bond Valuation r d the bond’s market rate of interest N the number of years before the bond matures INT dollars of interest paid each year M the par, or maturity, value of the bond

6 - 5 What’s the value of a 10-year, 10% coupon bond if r d = 10%?  V.10 B  $1, % ,000 V = ? = $ = $1,000.  r d  1 N + V B M +

6 - 6 The bond consists of a 10-year, 10% annuity of $100/year plus a $1,000 lump sum at r = 10%: $ $1, PV annuity PV maturity value Value of bond ====== d

6 - 7 If r remained constant at 10 percent, what would the value of the bond be one year after it was issued? d  V.10 B  $1, = $ = $1,000.  r d  1 N + V B M +

6 - 8 Changes in Bond Values over Time At the time a coupon bond is issued, the coupon is generally set at a level that will cause the market price of the bond to equal its par value. A bond that has just been issued is known as a new issue (Month from the issue date). Once the bond has been on the market for a while, it is classified as an outstanding bond. Newly issued bonds generally sell very close to par, but the prices of outstanding bonds vary widely from par. IF r d changed, a bond with a $100 coupon that sold at $1000 par when it was issued will sell for more or less than $1,000 thereafter.

6 - 9 When r d rises, above the coupon rate, the bond’s value falls below par, so it sells at a discount. What would happen if expected inflation rose by 3%, causing r = 13%?  V.13 B  $1, = $ = $837.  r d  1 N + V B M + d

What would happen after one year if r d remains 13%?

What would happen if expected inflation rose by 5%, causing r = 15%?

What would happen if inflation fell, and r d declined to 7% ? If coupon rate > r d, price rises above par, and bond sells at a premium. -  V.07 B  $1, = $ = $1,  r d  1 N + V B M +

What would happen after one year if r d remains 7%?

What would happen if inflation fell, and r d declined to 5% ?

M Bond Value ($) Years remaining to Maturity 1,211 1, r d = 7%. r d = 13%. r d = 10%.

A par bond stays at $1,000 if r d remains constant. At maturity, the value of any bond must equal its par value. Interest rates do change over time, but the coupon rate remains fixed after the bond has been issued. Whenever the going rate of interest rises above the coupon rate, the price of bond will fall below its par value. Such a bond is called a discount bond. Discount = Price-Par value = $837 - $1,000 = 163 Whenever the going rate of interest falls below the coupon rate, the price of bond will rise above its par value. Such a bond is called a premium bond. premium = Price-Par value = $ $1,000 = 211

Callaghan Motors’ bonds have 10 years remaining to maturity. Interest is paid annually, the bonds have a $1,000 par value, and the coupon interest rate is 8 percent. The bonds have a yield to maturity (market rate) of 9 percent. What is the current market price of these bonds? Problem 1 (Bond Value)

Bond Yields If you examine the any bond market table (e.g The Wall Street Journal) you will typically see information regarding each bond’s maturity date, price, and coupon interest rate. You will also see the Bond’s reported yield. Bond’s reported yield. Unlike the coupon interest rate, which is fixed, the bond’s yield varies from day to day depending on current market conditions. Moreover, the yield can be calculated in three different ways, and three “answers” can be obtained. These different yields are described in the following sections. Yield to Maturity Yield to Call Current Yield

What’s “yield to maturity”? YTM is the rate of return earned on a bond held to maturity. Also called “promised yield.” The interest rate generally discussed by investors when they talk about rates of return. The yield to maturity is generally the same as the market rate of interest, r, and to find it, all you need to do is solve the Equation. d

What’s the YTM on a 10-year, 9% annual coupon, $1,000 par value bond that sells for $887? r d =? 1,000 PV 1. PV 10 PV M 887 Find r d that “works”!...

 r  $1,  r d  1 N + V B M d That’s need spreadsheet, financial calculator or You could substitute values for r until you find a value that “works”. d Find r d that “works”! NI/YR PV PMTFV INPUTS OUTPUT

If coupon rate < r d, bond sells at a discount. If coupon rate = r d, bond sells at its par value. If coupon rate > r d, bond sells at a premium. If r d rises, price falls. Price = par at maturity.

Find YTM if price were $1, NI/YR PV PMTFV 7.08 Sells at a premium. Because coupon = 9% > r d = 7.08%, bond’s value > par. INPUTS OUTPUT

current yield If you examine brokerage house reports on bonds, you will often see reference to a bond’s current yield. The current yield is the annual interest payment divided by the bond’s current price. Current yield= For example, if MicroDrive’s bonds with a 10 percent coupon were currently selling at $985, the bond’s current yield would be 12 percent ($100/$837). Annual coupon pmt Current price

Capital gains yield Change in price Beginning price Capital gains yield =