Bond valuation for the beginners calculation with different types
- 2. LECTURE FRAMEWORK Key talking points 1. Introduction 2. Overview of a Fixed-Income Security 3. Legal, Regulatory and Tax Considerations 4. Structure of a Bond’s Cash Flows 5. Bonds with Contingency Provisions 6. Conclusion and Summary Fixed Income Securities
- 3. Introduction Fixed-income securities differ from equities in several ways: ❑ A fixed-income investor has no ownership rights in the business. ❑ The money borrowed (principal) is repaid at maturity. In addition, interest on the borrowed money is paid periodically. ❑ Fixed-income investors get paid before the common shareowners; hence the risk is lower. 1. There are two ways for an entity to raise capital: issuing equity and issuing fixed income securities. 2. Fixed-income is a commonly used method for governments and companies to borrow money from investors.
- 4. Overview of a Fixed Income Security Basic Features of a Bond ❑ Issuer of the bond ❑ Maturity of the bond ❑ Par value of the bond ❑ Coupon rate and frequency ❑ Currency denomination
- 5. Overview of a Fixed Income Security Maturity ❑ The maturity date is the date on which the last payment is made for a bond. ❑ Tenor, or time to maturity, is the time remaining until the maturity date. Based on maturity, bonds can be classified into the following: Money market securities: maturities of less than a year at issuance. Capital market securities: maturities longer than one year at issuance. Perpetual bonds: no stated maturity date. These bonds pay a periodic coupon on a certain par value indefinitely.
- 6. Overview of a Fixed Income Security Par Value ❑ Par value, principal amount, or principal is the amount an issuer agrees to pay the investor or bondholder on maturity date. It is also known as face value, redemption value, or nominal value. ❑ If a bond is selling above par value, it is trading at a premium. ❑ If a bond is selling below par value, it is trading at a discount. ❑ If a bond that is trading at face value, it is said to be trading at par.
- 7. Overview of a Fixed Income Security Credit risk ❑ It is the risk that interest and principal payments will not be made by the issuer as they come due. ❑ Credit rating agencies such as Moody’s and S&P assign a rating to issuers based on this risk. Bonds can be classified into two categories based on their creditworthiness: ❑ Investment grade ❑ Non-investment grade or high-yield or speculative bonds
- 8. Credit Ratings Investment grade Moody's Standard & Poor's Fitch Strongest Aaa AAA AAA Aa1 AA+ AA+ Aa2 AA AA Aa3 AA- AA- A1 A+ A+ A2 A A A3 A- A- Baa1 BBB+ BBB+ Baa2 BBB BBB Baa3 BBB- BBB- Non-investment-grade Moody's Standard & Poor's Fitch Ba1 BB+ BB+ Ba2 BB BB Ba3 BB- BB- B1 B+ B+ B2 B B B3 B- B- Caa1 CCC+ CCC+ Caa2 CCC CCC Caa3 CCC- CCC- Ca CC CC Weakest Moody's Standard & Poor's Fitch C C C D D
- 9. Overview of a Fixed Income Security Coupon Rate and Frequency Coupon rate, or nominal rate, is the interest rate paid on a bond every year by the issuer until its maturity date. It is calculated on the par value of the bond. Based on the frequency of coupon payments, we can classify bonds into the following: ❑ Plain vanilla bond ❑ Floating-rate bond or floating-rate notes or floaters ❑ Zero coupon bonds
- 10. Overview of a Fixed Income Security Bond Valuation 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. To value bonds and stocks we need to: ❑ Estimate future cash flows: ✔ Size (how much) and ✔ Timing (when) ❑ Discount future cash flows at an appropriate rate: The rate should be appropriate to the risk presented by the security.
- 11. WAYS TO EARN MONEY THROUGH BONDS Capital Gains Distributions Coupon Payments Current Yield.
- 12. Overview of a Fixed Income Security Coupon Effect and Maturity Effect For the same time-to-maturity, a lower-coupon bond has a greater percentage price change than a higher-coupon bond when their market discount rates change by the same amount. Generally, for the same coupon rate, a longer-term bond has a greater percentage price change than a shorter-term bond when their market discount rates change by the same amount.
- 14. Overview of a Fixed Income Security Yield to maturity the rate of interest would you earn on your investment if you bought a bond and held it to maturity The yield to maturity can be viewed as the bond’s promised rate of return, which is the return that investors will receive if all the promised payments are made. Three assumptions: ✔ Investor holds till maturity ✔ Issuer makes all payments ✔ Investor reinvests at YTM rate
- 15. Overview of a Fixed Income Security Structure of Fixed Income Securities The cash flows to investors can be divided into principal repayment and coupon payments. Principal can be repaid in three ways: ❑ Bullet bond ❑ Fully amortized ❑ Partially amortized
- 16. Case rd and coupon rate Bond will sell at: Calculation 1. Bond selling at price equal to par value. Going market rate of interest, rd, is equal to the coupon rate A fixed-rate bond will sell at its par value. Coupon rate = 10% Market Interest rate, rd = 10% Bond’s Value 1000 2. Bond selling for a price below its par value Going market rate of interest, rd, rises above the coupon rate A fixed-rate bond’s price will fall below its par value, and it is called a discount bond Coupon rate = 10% Market Interest rate, rd = 15% Bond’s Value=$707.63 3. Bond selling for a price above its par value Going interest rate, rd, falls below the coupon rate A fixed-rate bond’s price will rise above its par value, and it is called a premium bond Coupon rate = 10% Market Interest rate, rd = 5% Bond’s Value =$ 1518.98 5-3c Interest Rate Changes and Bond Prices
- 17. 5-3c Interest Rate Changes and Bond Prices Summary • The coupon rate remains fixed after the bond is issued, but interest rates in the market move up and down. • An increase in the market interest rate (rd) will cause the price of an outstanding bond to fall, whereas a decrease in rates will cause the bond’s price to rise.
- 18. Suppose market interest rate, rd, falls below the coupon rate, decreasing from 10% to 5%. Both the coupon interest payments and the maturity value remain constant, but now 5% would have to be used for rd The value of the bond at the end of the first year would be $1494.93 (n=14) Thus, if rd < the coupon rate, the bond would sell at a premium. If rd remained constant at 10 rd = 10% The value of the bond at the end of the first year would be $1000 (n=14) Thus, if rd = the coupon rate, the bond would sell at par Suppose market interest rate, rd, rise from10% to 15% during the first year rd = 15% The value of the bond at the end of the first year would be $713.78 (n=14) Thus, if rd > the coupon rate, the bond would sell at discount 5-4 Changes in Bond Values Over Time
- 19. 5-4 Changes in Bond Values Over Time • The arithmetic of the bond value increase should be clear, but what is the logic behind it? • Because rd has fallen to 5%, with $1,000 to invest you could buy new bonds like MicroDrive’s (every day some 10 to 12 companies sell new bonds), except that these new bonds would pay $50 of interest each year rather than $100 given by MircoDrive’s bond. • Naturally, you would prefer $100 to $50, so you would be willing to pay more than $1,000 for a MicroDrive bond to obtain its higher coupons. All investors would react similarly; as a result, the
- 21. 5-5 Bonds with Semiannual Coupons • To illustrate, assume now that MicroDrive’s bonds pay $45 interest every 6 months rather than $90 at the end of each year. • Each semiannual interest payment is only half as large, but there are twice as many of them. The nominal, or quoted, coupon rate is 9%, semiannual payments. • The Equation 5-1 would be modified as:
- 22. 5-6 Bond Yields • 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 three different yields are: – Yield to Maturity (YTM) – Yield to Call (YTC) – Current Yield (CY)
Editor's Notes
- #20: Figure 5-2 graphs the value of the bond over time, assuming that interest rates in the economy remain constant at 10%, fall to 5% and then remain constant at that level, or rise to 15% and remain constant at that level. Of course, if interest rates do not remain constant, then the price of the bond will fluctuate. However, regardless of what future interest rates do, the bond’s price will approach $1,000 as it nears the maturity date.