PREPARED BY:  BUH DESMOND  NKESI KEVIN KONGNYU (18CMBA18) ROME BUSINESS SCHOOL, CAMEROON BOND VALUATION

OUTLINE Definition Key Bond Characteristics What is Bond Valuation? Types of bonds Bond Terminology Factors that affect the value of a bond Bond Valuation Worked Examples Approaches to Bond Valuation References

What is a Bond? A bond is a debt instrument that provides a periodic stream of interest payments to investors while repaying the principal sum on a specified maturity date. A bond’s terms and conditions are contained in a legal contract between the buyer and the seller, known as the indenture. Different types of bonds offer investors different options. For example, there are bonds that can be redeemed prior to their specified maturity date, and bonds that can be exchanged for shares of a company. Key Bond Characteristics Each bond can be characterized by several factors. These include: Face Value Coupon Rate Coupon Maturity Call Provisions Put Provisions Sinking Fund Provisions

TYPES OF BONDS Corporate Bonds – Issued by Corporations to expand or finance a project, usually taxable and offer higher returns. Government Bonds – Treasury bonds carry the lowest degree of risk and are the benchmark against which all other types of bonds are measured. Although their market values fluctuate, they are considered the safest. Municipal Bonds – Issued by the local government usually to finance specific projects. Other terminologies – Agency bonds, Collateralized bonds, Commercial papers, Convertible bonds, Covenant bonds, Credit Rating, Debentures What is Bond Valuation? Bond valuation includes calculating the present value of the bond's future interest payments, also known as its cash flow, and the bond's value upon maturity, also known as its face value or par value. Because a bond's par value and interest payments are fixed, an investor uses bond valuation to determine what rate of return is required for a bond investment to be worthwhile.

a) Face/Par Value The face value (also known as the par value) of a bond is the price at which the bond is sold to investors when first issued; it is also the price at which the bond is redeemed at maturity. In the U.S., the face value is usually $1,000 or a multiple of $1,000. b) Coupon Rate The periodic interest payments promised to bond holders are computed as a fixed percentage of the bond’s face value; this percentage is known as the coupon rate. c) Coupon A bond’s coupon is the dollar value of the periodic interest payment promised to bondholders; this equals the coupon rate times the face value of the bond. For example, if a bond issuer promises to pay an annual coupon rate of 5% to bond holders and the face value of the bond is $1,000, the bond holders are being promised a coupon payment of (0.05)($1,000) = $50 per year. d) Maturity A bond’s maturity is the length of time until the principal is scheduled to be repaid. Occasionally a bond is issued with a much longer maturity. There have also been a few instances of bonds with an infinite maturity; these bonds are known as consols. With a consol, interest is paid forever, but the principal is never repaid. BOND TERMINOLOGIES

e) Call Provisions Many bonds contain a provision that enables the issuer to buy the bond back from the bondholder at a pre-specified price prior to maturity. This price is known as the call price. A bond containing a call provision is said to be callable. f) Put Provisions Some bonds contain a provision that enables the buyer to sell the bond back to the issuer at a pre-specified price prior to maturity. This price is known as the put price. A bond containing such a provision is said to be putable. g) Sinking Fund Provisions Some bonds are issued with a provision that requires the issuer to repurchase a fixed percentage of the outstanding bonds each year, regardless of the level of interest rates. A sinking fund reduces the possibility of default; default occurs when a bond issuer is unable to make promised payments in a timely manner. Since a sinking fund reduces credit risk to bond holders, these bonds can be offered with a lower yield than an otherwise identical bond with no sinking fund. h) zero-coupon bonds A zero-coupon bond is a bond that makes no periodic interest payments and is sold at a deep discount from face value. The buyer of the bond receives a return by the gradual appreciation of the security, which is redeemed at face value on a specified maturity date. I) Current Price Depending on the level of interest rate in the environment, the investor may purchase a bond at par, below par, or above par. For example, if interest rates increase, the value of a bond will decrease since the coupon rate will be lower than the interest rate in the economy.

j) The yield This is the discount rate of the cash flows. Therefore, a bond's price reflects the value of the yield left within the bond. The higher the coupon total remaining, the higher the price. A bond with a yield of 2% likely has a lower price than a bond yielding 5%. The term of the bond further influences these effects. BOND TERMINOLOGIES Factors That Affect The Price Of A Bond 1. Interest rates In general, when interest rates rise, bond prices fall. When interest rates fall, bond prices rise. 2. Inflation In general, when inflation is on the rise, bond prices fall. When inflation is decreasing, bond prices rise. That’s because rising inflation erodes the purchasing power of what you’ll earn on your investment. 3. Credit ratings Credit rating agencies assign credit ratings to bond issuers and to specific bonds. A credit rating can provide information about an issuer’s ability to make interest payments and repay the principal on a bond. In general, the higher the credit rating, the more likely an issuer is to meet its payment obligations – at least in the opinion of the rating agency. If the issuer’s credit rating goes up, the price of its bonds will rise. If the rating goes down, it will drive their bond prices lower.

Bonds are issued by borrowers to raise funds for long-term investments; the main issuers of bonds in the are: Government, Corporations, Municipalities and Foreign Entities A)Government A government bond is a debt security issued by a government to support government spending. They include; savings bonds, Treasury bonds and Treasury Inflation Protected Security (TIPS). Before investing in government bonds, investors need to assess several risks associated with the country, such as country risk, political risk, inflation risk and interest rate risk, although the government usually has low credit risk. B) Corporations A corporate bond is a bond issued by a corporation in order to raise financing for a variety of reasons such as to ongoing operations, M&A, or to expand business. The term is usually applied to longer term debt instrument, with maturity of at least one year. Corporate debt instruments with maturity shorter than one year are referred to as commercial paper. C) Municipalities A municipal bond is issued by a state or local government; as a result, they carry little or no default risk. Municipal bonds offer an extremely favorable tax treatment to investors. They are not taxed by federal, state or local governments as long as the bond holder lives in the municipality in which the bonds were issued. As a result, municipal bonds can be issued with very low yields. D) Foreign Entities Foreign bonds are issued by foreign governments and corporations and are denominated in dollars. BOND USERS

Bond Valuation in Practice Like a stock, the value of a bond determines whether it is a suitable investment for a portfolio and hence, is an integral step in bond investing. Bond valuation, in effect, is calculating the present value of a bond’s expected future payment(s). The theoretical fair value of a bond is calculated by discounting the present value of its coupon payments by an appropriate discount rate.

A bond’s price equals the present value of its expected future cash flows. The rate of interest used to discount the bond’s cash flows is known as the yield to maturity (YTM.) Valuating A Bond a) Pricing Coupon Bonds A coupon-bearing bond may be priced with the following formula: where: C = the periodic coupon payment y = the yield to maturity (YTM) F = the bond’s par or face value t = time T = the number of periods until the bond’s maturity date Example: Suppose that a bond has a face value of $1,000, a coupon rate of 4% and a maturity of four years. The bond makes annual coupon payments. If the yield to maturity is 5%, the bond’s price is determined as follows:

Valuating A Bond b) Pricing Zero Coupon Bonds A zero-coupon bond does not make any coupon payments; instead, it is sold to investors at a discount from face value. The difference between the price paid for the bond and the face value, known as a capital gain, is the return to the investor. The pricing formula for a zero coupon bond is: Example: Suppose that a one-year zero-coupon bond is issued with a face value of $1,000. The discount rate for this bond is 8%. What is the market price of this bond? Tips In order to be consistent with coupon-bearing bonds, where coupons are typically made on a semi-annual basis, the yield will be divided by 2, and the number of periods will be multiplied by 2: Solution

Other Approaches to Bond Valuation: Relative Price Approach – Its an extension of the Present value approach. The yield to maturity on the bond is determined based on the bond's Credit rating relative to a government security with similar maturity or duration. The better the quality of the bond, the smaller the spread between its required return and the YTM of the benchmark. Arbitrage-free pricing approach - Here, each cash flow is separately discounted at the same rate as a zero-coupon bond corresponding to the coupon date. Stochastic calculus approach – This embeds the fact that future interest rates are not certain and therefore adjust the present value calculations accordingly.