Valuing Bonds Summary

Valuing Bonds Overview

• Bonds are debt securities issued by borrowers (corporations, governments).
• Investors receive periodic interest payments (coupons) and principal at maturity.

Key Components of Bonds

• Price: Current cost to buy the bond.
• Par Value (Face Value): Amount repaid at maturity.
• Maturity Date: End date when the issuer pays back the principal and final interest.
• Coupon Rate: Annual interest rate paid by the issuer.
• Coupon Payment: Calculated as $( ext{Coupon Rate} imes \frac{ ext{Par Value}}{ ext{Payments per Year}})$.
• Yield to Maturity (YTM): Discount rate reflecting total returns if held to maturity.
• Frequency (m): Number of coupon payments per year.

Types of Bonds

• Corporate vs. Government Bonds
• Coupon Schemes:
  • Zero Coupon: No periodic payments (e.g., T-bills).
  • Semi-annual: Payments twice a year.
  • Annual: Payments once a year.

Bond Pricing

• Bond price includes two cash flow components: an annuity (coupons) and a lump-sum (par value).
• Pricing formula: $P_B = PV( ext{Coupons}) + PV( ext{Par Value})$
  • $PV( ext{Coupons}) = ext{Coupon PMT} imes \frac{1 - (1 + r)^{-n}}{r}$
  • $PV( ext{Par Value}) = \frac{ ext{Par Value}}{(1 + r)^n}$

Relationship Between YTM and Coupon Rate

• Par Bond: Coupon Rate = YTM; Price = Par Value
• Premium Bond: Coupon Rate > YTM; Price > Par Value
• Discount Bond: Coupon Rate < YTM; Price < Par Value

Bond Rates

• Current Yield: $\frac{ ext{Annual Coupon}}{ ext{Current Price}}$
• Yield to Maturity: Expected return if held to maturity.

Bond Ratings

• Rated by agencies; above BBB is investment grade, below is speculative grade.
• Higher risk = higher yield due to risk premium.
  • Total risk = Issuer risk + Maturity risk.

Yield Curve

• Typically, yield increases with maturity; inversions signal potential recessions (e.g., 2-year vs. 10-year Treasury yields).