Bond Valuation

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Bond Valuation

Bond valuation determines the present value of a bond’s future cash flows: the periodic coupon payments and the principal (face) value repaid at maturity. It helps investors compare a bond’s expected return with other investment opportunities.

Key points

  • Bonds pay periodic coupons and return face (par) value at maturity.
  • Fair value = present value of future coupon payments + present value of face value.
  • The discount rate is typically the yield to maturity (YTM).
  • Bond prices move inversely to market interest rates.
  • Some bonds (e.g., municipals) have tax features that affect their attractiveness.

How bond valuation works

Value is found by discounting each future cash flow to today using an appropriate discount rate (usually the bond’s YTM). Conceptually:

Value = Present value of coupons + Present value of face value

In formula form (plain text):
Value = sum for t=1 to T of [C / (1 + r)^t] + F / (1 + r)^T

where:
* C = coupon payment per period
F = face (par) value repaid at maturity
 r = discount rate per period (YTM adjusted for period length)
* T = total number of periods

Coupon bond example (semiannual)

A corporate bond: face value F = $1,000, annual coupon = 5% (paid semiannually), maturity = 2 years, YTM = 3% (annual).

Convert to semiannual periods:
* Semiannual coupon rate = 5% / 2 = 2.5% → C = $25 per period
Number of periods T = 2 years × 2 = 4
 Periodic discount rate r = 3% / 2 = 1.5% = 0.015

Compute present values:
* PV of coupons = 25/(1.015)^1 + 25/(1.015)^2 + 25/(1.015)^3 + 25/(1.015)^4 ≈ $96.36
* PV of face value = 1000/(1.015)^4 ≈ $942.18

Bond value ≈ $96.36 + $942.18 = $1,038.54

Zero-coupon bond valuation

Zero-coupon bonds make no periodic payments; they are issued at a discount and pay face value at maturity. Value is just the present value of the face value:

Value = F / (1 + r)^T

Example: F = $1,000, YTM = 3% annual, T = 2 years:
Value = 1000 / (1.03)^2 ≈ $942.59

Intuitive summary (simple)

A bond is a loan to the issuer: you receive interest payments over time and the principal back at the end. Bond valuation converts those future payments into today’s dollars to decide whether the bond’s return is worth its price.

Common questions answered

  • Why does market price differ from face value?
    Market price reflects current interest rates, issuer credit risk, time to maturity, and any embedded options. The bond always repays face value at maturity, but market price can be above (premium) or below (discount) face value.

  • Why do bond prices move inversely to interest rates?
    If market rates rise, existing bonds with lower coupons become less attractive and their prices fall to yield the market rate; if rates fall, existing higher-coupon bonds become more attractive and trade at premiums.

  • What is duration?
    Duration measures a bond’s price sensitivity to changes in interest rates (approximate percentage price change for a 1% change in rates). Longer maturities and lower coupons generally increase duration.

  • How are convertible bonds valued?
    Convertible bonds are priced as a straight bond plus the value of the option to convert into equity. Valuation considers the bond’s cash flows, stock volatility, conversion ratio, and interest rates.

Practical considerations

  • Use the appropriate period convention (annual vs. semiannual) for coupons and YTM.
  • Taxes and credit risk materially affect real returns—e.g., municipal bonds may be attractive to investors in high tax brackets because of federal tax exemption.
  • Reinvestment risk (assumption that coupon payments can be reinvested at the YTM) is embedded in the YTM concept.

Bottom line

Bond valuation is a discounted cash flow exercise: determine the present value of coupons and principal using an appropriate discount rate. It informs whether a bond’s market price offers an acceptable return relative to alternatives and risk.