Bonds and Fixed Income Securities W8 — A bond is a fixed income security that represents a loan made by an investor to a borrower. It typically includes: • A fixed interest payment (coupon). • A specified repayment date (maturity date). • The amount borrowed (face value or principal ). — Key Terms in Bonds 1. Face Value (Par Value): The amount the bondholder will receive at maturity. Typically $1,000 per bond. 2. Coupon Rate: The annual interest rate paid on the face value, expressed as a percentage. 3. Coupon Payment: The periodic interest payment made to bondholders: Coupon Payment = Face Value · Coupon Rate 4. Maturity Date: The date on which the bond issuer repays the principal. 5. Yield: The rate of return an investor earns on a bond, which depends on the purchase price and interest payments. 6. Market Price: The current trading price of the bond, which can differ from the face value. 1 — Types of Bonds Bonds can be categorized into several types based on the issuer, structure, and purpose: • Government Bonds: Issued by national governments to finance public projects or debt. • Municipal Bonds: Issued by local or regional governments, often tax-exempt. • Corporate Bonds: Issued by companies to raise capital for expansion or operations. • Zero-Coupon Bonds: Sold at a discount and pay no periodic interest. Instead, the investor receives the face value at maturity. • Convertible Bonds: Allow bondholders to convert bonds into a predetermined number of shares of the issuing company. — Bond Pricing Formula The price of a bond is the present value of its future cash flows, which include periodic coupon payments and the repayment of the principal. The formula is: P = n X t=1 F C + t (1 + r) (1 + r)n where: • P : Price of the bond. • C: Coupon payment per period. • F : Face value of the bond. • r: Discount rate (or yield per period). • n: Number of periods until maturity. — Example: Calculating the Price of a Bond A bond has the following characteristics: 2 • Face value: $1,000. • Coupon rate: 6% (annual payments). • Time to maturity: 5 years. • Market yield: 5%. Calculate the price of the bond. Solution: 1. Calculate the annual coupon payment: C = Face Value · Coupon Rate = 1, 000 · 0.06 = 60 2. Use the bond pricing formula: P = 5 X t=1 60 1, 000 + t (1 + 0.05) (1 + 0.05)5 3. Break it into components: • Present value of coupon payments: 5 X t=1 60 60 60 60 60 60 = + + + + t 2 3 4 (1.05) 1.05 (1.05) (1.05) (1.05) (1.05)5 Numerical calculations: 60 ≈ 57.14, 1.05 60 ≈ 54.42, (1.05)2 60 ≈ 51.83 (1.05)3 60 60 ≈ 49.36, ≈ 47.01 4 (1.05) (1.05)5 Sum: 57.14 + 54.42 + 51.83 + 49.36 + 47.01 = 259.76 • Present value of the face value: 1, 000 ≈ 783.53 (1.05)5 4. Add the components: P = 259.76 + 783.53 = 1, 043.29 Answer: The price of the bond is approximately $1,043.29. — 3