Introduction to Investment Analysis Valuation of Bonds What are Bonds? • Bonds are a form of long-term debt (Will mature in one year or less) that usually is secured by property, usually with an original maturity of twenty to thirty years. Also could be for five years, such as Emirates Bonds. • Unsecured bonds are called debentures. Maturity refers to the length of time that the bond will be outstanding. • For coupon bonds, the issue promises to pay: – a fixed amount of interest periodically, annually or semi-annually if it is a coupon bond. – repay the principal on a specific date of maturity. • For zero-coupon bonds, the issuer promises to pay: – only the face value at maturity. – There are no periodic interest payments for zero-coupon bonds. Who issues bonds? • Bonds could issued by various levels of the government: At the Federal (no bonds in the UAE issued yet) and Emirate levels (Dubai 2003 will issue a AED 1.5 Billion bond), and by business corporations (e.g., Emirates Airlines) Characteristics of Bonds • The Par value, also known as the face value or maturity value, MV, of a bond or debenture and is a fixed amount (we will assume it to be AED 1,000 always). This is the amount of principal to be repaid at maturity for each bond. The Par value of Emirates Airlines is equal to AED 100,000. • The coupon interest rate, CR, is the stated annual rate of interest on the bond. A bond’s coupon rate never changes over the life of the bond, unless it is a floating rate bond such as that of Emirates Airlines. Characteristics of Bonds (Cont’d) • When the annual interest of a bond is stated in Dirham terms, it is called the coupon payment (CP). CP CR MV • For example, an offering of AED 400 million of 30-year debentures that carries a coupon interest rate of 12.25% has an annual coupon payment per bond as follows: 12.25 • CP 1000 AED122.5 100 Valuation of a bond • Because the cash flows of a bond are a contractual payment of a fixed amount of interest (CP) over a certain number of years, plus the maturity value (MV), the formula to value a bond is as follows: D CP ( PVIFA) MV ( PVIF ) 0 Kd ,n Kd ,n Where: D = current market price of the bond. 0 CP= Periodic coupon interest at the end of the period K = required rate of return on the debt instrument (bond) d n = number of periods remaining before the bond is redeemed MV= Principal or face value or maturity value of the bond Valuation Example • Page 29 of text. • If the required rate of return is less than the coupon rate (the rate offered by the issuing company), the bond sells for less than par value. • Bonds that sell at less than par value are said to be selling at a discount. • Bonds that sell for less than par value are said to be selling at a premium. Some relationships Relationship among required rates of return, Coupon rates, and Bond Prices If Then Bond Sells at a K Coupon Rate d discount Bond will sell at par K Coupon Rate d K Coupon Rate Bond will sell at a d premium Yield to Maturity • The yield to maturity of a bond is that discount rate that equates the present value of the bond’s cash flows to the market price. It is the same as the bond’s internal rate of return (IRR). • To illustrate, assume that a 10-year, AED 1,000 year par value bond has an annual coupon rate of 8%. If the bond’s current price is AED 935.80, what is the bond’s yield to maturity? YTM Calculation • From the valuation model: D CP ( PVIFA ) MV ( PVIF 0 Kd , n K d ,n AED 935.80 100( PVIFA ) 1000( PVIF ) K d ,10 K d ,10 • Because the price is less than the par value, the YTM must be more than 8%. • Use the IRR function in Excel to get a YTM = 9%. Valuation of Semi-annual Coupons • Up to this point, our examples of bond price calculations assumed that interest is paid annually, but many bonds pay interest semiannually. The procedure discussed above to value bonds can still be used but with three modifications: – Convert the annual coupon payment to semiannual payment, by dividing it by 2. – Convert the number of years to maturity, n, to the number of six- month periods to maturity, by multiplying n by 2. – Convert the required return from an annual rate,K d to a semiannual rate, by dividing it by 2. Valuation of Semi-annual Coupons • Substituting these changes into the equation yields: CP D ( PVIFA) MV ( PVIF ) kd 2 0 kd ,2n ,2n 2 2 Value of a 30-year bond paying a 4% semi-annual Coupon P a y m e n t N u m b Present value Present eSemi-annual of coupon value of Price of rrequired yield payments principal bond 0% 2400 1000 3400 2% 1390.435467 304.7823 1695.218 4% 904.939599 95.0604 1000 6% 646.4571082 30.31434 676.7714 8% 495.0620729 9.875854 504.9379 10% 398.6862919 3.28427 401.9706 12% 332.9619714 1.114086 334.0761 Relationship between Price and yield Relationship Between Price and Yield 4000 3500 3000 2500 Price 2000 Series1 1500 1000 500 0 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 Semiannual Required Yield Relationship between Price and yield • when the required rate of return rises (falls), the value of the bond falls (rises). • This inverse relationship is illustrated in the Graph above. Types of Bond Yields • There are five types of bond yields. 1. Coupon rate (also called the nominal yield), 2. Current yield, 3. Effective yield 4. Yield to maturity 5. Yield to call for callable bonds. Coupon Rate • The coupon rate is the interest rate used to calculate the periodic interest payment on the bond. It is set at the time the bond is issued and remains the same until the bond matures or is called back. It is calculated as follows: CP CR FV • CR = Coupon rate • CP = Annual coupon or interest payment • FV (MV) = Face value of the bond. Coupon rate Example • suppose the annual coupon payment is AED 100 and the face value is AED 1,000. The annual coupon rate would be: 100 CR 0.10 10% 1,000 Current Yield • The current yield is the ratio of the annual interest income to the current price of the bond. Unlike the coupon rate, the current yield varies with the price of the bond. Since it measures the interest per Dirham of investment of the bond, it is a better indicator of yield than the coupon rate. • The current yield is calculated as follows: CP CY Pr ice of bond Current Yield Example • Assume that the annual interest payment is AED 100 and the current price of the bond is AED 980. The current yield would be: 100 Current yield 0.1010 10.10% 990 Effective Yield • While the current yield is a better indicator of yield than the coupon rate, it is not an adequate measure of yield because it does not reflect capital gains or losses. • The effective yield reflects not only the interest income from the bond but also any capital gains or losses. CP ( P P ) • One year effective Yield: OEY 1 0 P 0 OEY = One-year effective yield CP = Coupon Payment P Price of the bond at the beginning of the year 0 P Price of the bond at the end of the year 1 Effective Yield Example • Assume the following data: P AED 970 0 Interest paid last year =AED 100 and P AED 990 1 • The One year effective yield is calculated as follows: • OEY= 100 (990 970) 0.1237 12.37% 970 • Also referred to as the Annual Holding Period Return Yield to maturity(Annual Coupon) • The yield to maturity is the true yield if the bond is held until maturity. • The true yield to maturity takes into consideration all the cash flows of the bond as well as the time value of money. • The true yield to maturity for an annual coupon bond is calculated using the following equation: where CP CP CP FV Pr ice ......... (1 YTM ) (1 YTM ) (1 YTM ) 1 2 3 (1 YTM ) n • YTM= Yield to maturity • N= number of years to maturity • FV = Face Value Yield to maturity(Semi-Annual Coupon) CP CP CP 2 2 2 FV Pr ice ............ YTM YTM YTM YTM 1 2 3 2n 1 1 1 1 2 2 2 2 • You need Excel or a financial calculator to solve for the Yield to maturity of a bond. The End Definitions • Long-term debt generally refers to debt that will mature in a year or more.
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