Bond Valuation Masterclass

Theory
Q&A
Problems
Challenge

1. Bonds and Bond Valuation

A bond is typically an interest-only loan where the borrower pays fixed interest payments (coupons) periodically and repays the principal (face value or par value) at the end of the loan. The coupon rate is the annual coupon payment divided by the face value. The time to maturity is the number of years until the face value is paid.

Bond Values and Yields

The market interest rate required on a bond is its yield to maturity (YTM). Bond value is the present value of all future cash flows (coupon payments and face value) discounted at the YTM.

The General Bond Valuation Formula:

$$ \text{Bond Value} = C \times \left[ \frac{1 - 1/(1+r)^{t}}{r} \right] + \frac{F}{(1+r)^{t}} $$

Where $C$ is the coupon payment, $F$ is the face value, $r$ is the YTM per period, and $t$ is the number of periods to maturity.

Illustration: Xanth Co. Bond Cash Flows

A bond with an annual coupon of $80, a face value of $1,000, and 10 years to maturity has the following cash flows at an 8% YTM.

$$ \text{Bond Value} = \$80 \times \left[ \frac{1 - 1/(1.08)^{10}}{0.08} \right] + \frac{\$1,000}{(1.08)^{10}} = \$1,000 $$

Discount and Premium Bonds: When the YTM is higher than the coupon rate, the bond sells at a discount. When the YTM is lower than the coupon rate, the bond sells at a premium. When the YTM equals the coupon rate, the bond sells at par value.

Semiannual Coupons: In practice, most bonds pay coupons semiannually. The bond's quoted yield is an APR, so the periodic rate is half the quoted rate. The number of periods is twice the number of years.

Effective Annual Yield for Semiannual Bonds:

$$ \text{Effective annual rate} = (1 + r)^2 - 1 $$

Where $r$ is the semiannual rate.

Interest Rate Risk

Interest rate risk is the risk that a bond's price will fluctuate due to changes in interest rates. This risk depends on two factors: Time to Maturity (longer-term bonds have greater risk) and Coupon Rate (lower-coupon bonds have greater risk).

2. More about Bond Features

The core differences between **debt** and **equity** are that debt is not an ownership interest, its interest payments are tax-deductible for the firm, and unpaid debt can lead to legal claims on firm assets. The **indenture** is the legal document that details the bond agreement.

Key Bond Features:

  • Security: Debt can be secured by collateral or unsecured (e.g., a debenture).
  • Seniority: Indicates preference over other lenders.
  • Sinking Fund: An account to repay bonds over their life.
  • Call Provision: Allows the company to repurchase the bonds at a stated price.
  • Protective Covenants: Limit or specify certain actions the company can take.

3. Bond Ratings

Bond ratings assess the **creditworthiness** of the issuer, focusing on the likelihood of default. **Investment-grade bonds** are rated BBB/Baa or higher, while lower-rated bonds are considered junk bonds.

4. Different Types of Bonds

  • Government Bonds: U.S. Treasury issues are default-risk-free and tax-exempt at the state level. Municipal bonds are tax-exempt at the federal level.
  • Zero Coupon Bonds: Pay no coupons and are sold at a deep discount.
  • Floating-Rate Bonds: Have adjustable coupon payments tied to an interest rate index.
  • Put Bonds: Allow the holder to sell the bond back to the issuer.
  • Convertible Bonds: Can be swapped for a fixed number of shares of stock.

5. Inflation and Interest Rates

The Fisher effect describes the relationship between nominal rates (not adjusted for inflation) and real rates (adjusted for inflation).

The Fisher Effect:

$$ (1+R) = (1+r) \times (1+h) $$

Where $R$ is the nominal rate, $r$ is the real rate, and $h$ is the inflation rate. An approximation is $R \approx r + h$.

6. Determinants of Bond Yields

A bond's yield is composed of six key components:

  1. Real Rate of Interest
  2. Inflation Premium
  3. Interest Rate Risk Premium
  4. Default Risk Premium
  5. Taxability Premium
  6. Liquidity Premium