1. The Bond Market The bond market is the market in which corporations and governments issue debt securities commonly called bonds to borrow long term funds from the general public. Bond investors are entitled to a stated fixed interest payment at regular intervals until maturity when the principal is finally paid. And the maturity periods range between 1 to more than 20 years. Bond characteristics Bonds are sold in unit prices at specified coupon (interest) rates often influenced by rating companies. Standard & Poor’s (S&P) and Moody’s are the two most popular international rating companies based in America. 1Prepared by Alhaj Nuhu Abdulrahman CHAPTER 5: BONDS MARKETS, BOND VALUATION AND INTEREST RATES

2. They rate bond issuers by assessing their creditworthiness, based on how likely they will default and the protection creditors have in the event of a default. Graded bonds are classified as investment grade bonds or junk grade bonds. Summary range ratings by the two companies Investment-Quality Bond Ratings Low-Quality or Junk Bond Ratings Standard & AAA ------------- BBB BB ---------------- D Poor’s Moody’s Aaa -------------- Baa Ba ---------------- C Common terminologies associated with bonds are: Coupon rate; Face value or par value; Maturity date; and indenture. The indenture: An indenture is a written agreement between the corporation (the borrower) and its lenders (the bond investors) 2Prepared by Alhaj Nuhu Abdulrahman

3. The basic provisions in a typical indenture include:  The terms of the bonds (i.e. Stated value and when interests will be paid)  The total amount of bonds issued  A description of property used as security  The repayment arrangements  The call provisions if any  Call premium if any  Deferred call if any  The details of the protective covenants. The Sinking Fund: The stated face value of a bond is usually repaid at maturity. They may as well be repaid in part or in full before maturity through a Sinking fund. A sinking fund is an account opened by the corporation usually at a bank for the purpose of repaying or early redemption of bonds. The company makes period deposits into the account for the purpose. 3Prepared by Alhaj Nuhu Abdulrahman Bond characteristics

4. Government or Treasury bonds – Issued by Central governments Municipal bonds- Issued by Local governments Agency bonds – Issued by State Utilities and State-owned enterprises Diaspora bonds – Issued by Central governments Zero coupon bonds – A type of corporate bond Floating rate bonds- Issued by both corporations and governments Convertible bonds - A type of corporate bond Income bonds - A type of corporate bond Put bonds - A type of corporate bond 4Prepared by Alhaj Nuhu Abdulrahman Other Types of Bonds

5. Bonds are issued at either discount, premium or par/face values. When interest rate rises, bond values tend to decline, but the values increase when the interest rate falls. To determine the value of a bond at a point in time, it is necessary to know the number of periods to maturity, face value, coupon rate, and prevailing market interest rate for bonds with similar features (referred to as required rate of return). The required interest rate is called yield to maturity (YTM), or just yield. Yield to maturity is defined as the discount rate that makes the present value of the bond’s payments equal to its price. Since coupon payments flow in the form of annuity a bond’s value can be computed first by computing the present value of the bond’s coupon payments, the present value of the principal amount and add the two values together. 5Prepared by Alhaj Nuhu Abdulrahman Bond Valuation and Yields

6. Thus, bond value = C x Illustration: Suppose a UPS Company issued bonds with 12% annual coupon rate, 10 year-maturity period and GH¢80 face value, while the prevailing market interest rate is 12%. What should be the market value of the bond? Coupon (C) = 12% x GH¢80 = GH¢9.6, r = 0.12, F = GH¢80, n = 10 payments Solution: Bond value = 9.6 x = 9.6 x = GH¢54.24 + GH¢25.76 = GH¢80 6Prepared by Alhaj Nuhu Abdulrahman Bond Valuation and Yields

7. The value of the bond is still GH¢80 as the par value because the coupon rate and the YTM are the same. When YTM is greater than coupon rate the bond value will be less than its par value. Conversely when YTM is less than coupon rate the value will be higher than the par value Exercise 1: What will be the value of the bond if (i) the market rate is instead 14% and (ii) the market rate is instead 10%? Exercise 2: How much should the bond sell (value) after two years of issue if (i) YTM is up to 14% and (ii) YTM is down to 10%? 7Prepared by Alhaj Nuhu Abdulrahman Bond Valuation and Yields

8. Semi-annual coupon payments In the previous illustrations coupon payments are assumed to be made once at the end of a year. In practice however, payments are made twice (semi-annually) in a year. Illustration: So from our previous illustration, if UPS Company’s coupon is to be paid on semi annual basis then C = 12%/2 = 6% x GH¢80 = GH¢4.8, r = 0.12/2 = 0.06, n = 10 x 2 = 20 payments Solution: Bond value = = = = = GH¢55.06 + GH¢24.94 = GH¢80 As a result of the semi-annual coupon payments, the effective annual rate is instead (1 + 0.06) 2 – 1 = 12.36% 8Prepared by Alhaj Nuhu Abdulrahman Bond Valuation and Yields

9. Semi-annual coupon payments Exercise 1: What will be the value of the bond if coupon is paid semi-annually under the following alternative market interest rates? (i) The market rate is 14% (ii) The market rate is 10% Exercise 2: How much should the bond sell (value) after two years of issue if (i) YTM is up to 14% and (ii) YTM is down to 10% (on semi-annual basis) 9Prepared by Alhaj Nuhu Abdulrahman Bond Valuation and Yields

10. The practice in investment activities is to consider the effect of inflation on interest rate, yield, and returns, which often leads to distinguishing between real and nominal rates. This enables investors know actual return earned on investment having recognized the effect of inflation. Nominal rates are rates of return that have not been adjusted for inflation. Real rates are rates of return that have been adjusted for inflation. Effect of inflation on rate of return: Suppose you invested GH¢100 today that pays 15.5% interest per annum. After a year the investment will be worth GH¢115.50. Suppose the prevailing inflation rate is 5%, what will be the effect of this on the 15.5% rate of return? Note: The 15.5% is the nominal rate but what will be real rate if inflation is accounted for? 10Prepared by Alhaj Nuhu Abdulrahman Interest rates and inflation

11. Solution: The GH¢115.50 future value of GH¢100 investment will be deflated by the inflation rate of 5%: Thus, PV = = = GH¢110 Thus real rate of return will be: The Fisher Effect The discussion above on nominal and real rates of return demonstrates their relationship often called the Fisher effect named after the great economist Irving Fisher. who first identified the relationship between nominal rates, real rates and inflation rates. That because investors know that inflation reduces the value of their investment they require compensation for decrease in value. Thus, the Fisher effect can be expressed as: 1 + R = (1 + r) x (1 + h). Where R is, r real rate, and h is for inflation rate. 11Prepared by Alhaj Nuhu Abdulrahman Interest rates and inflation

12. In the preceding illustration the nominal rate was 15.5% while inflation rate was 5%. What was the real rate? This can be done as follows: 1 + 0.1550 = (1 + r) x (1 + 0.05) 1 + r = 1.1550/1.05 = 1.10 1 + r = 1.10 r = 1.10 – 1 = 10% 12Prepared by Alhaj Nuhu Abdulrahman Interest rates and inflation

13. Loans of different maturity periods, often indicate different interest rates referred to as “term structure of interest rates”. The term-structure of interest rates tells us the time value of money lent for different lengths of time. Thus at any time, short-term and long-term interest rates will generally be different depending on future forecast on inflation. The yield (rate of return) of any debt security is therefore influenced by one or more of the following factors:  Inflation premium: Required extra compensation by lenders in the form of higher nominal rate for the expected erosion of the value of their returns by expected future inflation.  Interest rate risk premium: Required extra compensation for risk of loss on long- term bonds that may be caused by changes in interest rates. So interest rate risk premium increase with maturity. 13Prepared by Alhaj Nuhu Abdulrahman The Term Structure of Interest Rates

14.  Default risk (credit risk) premium: Required extra compensation in the form higher yields for possibility of default by a bond issuer.  Taxability premium: Required extra yields on taxable bonds as compensation for unfavourable tax regime.  Liquidity premium: Required extra compensation on bonds that might not be quickly sold and at a good price. Thus less liquid bonds will have higher yields than more liquid ones. Thus, determining the acceptable yield on a debt security requires careful analysis of each of these effects. 14Prepared by Alhaj Nuhu Abdulrahman The Term Structure of Interest Rates