Bond Discount

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Bond Discount: What It Is, Why It Happens, and How to Calculate It

What is a bond discount?

A bond discount occurs when a bond’s market price is below its face (par) value. For typical bonds the par value is $1,000. Investors who buy at a discount receive the full par value at maturity, producing capital appreciation in addition to any coupon payments.

Key takeaways

  • A bond trades at a discount when its market price is less than par—often because prevailing market interest rates exceed the bond’s coupon rate.
  • Buying a discounted bond yields potential capital gain at maturity (par value received).
  • Bonds can also trade at a premium when their coupon rate is above current market rates.
  • Other drivers of discounts include deteriorating credit quality, oversupply, or higher perceived default risk.

How a discount affects investors

  • Coupon payments remain fixed for a given bond. If market interest rates rise, newer bonds offer higher yields, making older bonds with lower coupons less attractive; their prices fall to provide comparable yields.
  • An investor buying at a discount benefits from both coupon income and the difference between purchase price and par at maturity.
  • Investment return should be measured by yield to maturity (which factors in coupon payments and capital gain or loss), not just the coupon rate.

Discount vs. premium (brief)

  • Discount: market price < par. Occurs when coupon rate < market rate.
  • Par: market price = par. Coupon rate = market rate.
  • Premium: market price > par. Occurs when coupon rate > market rate.

Example: calculating a bond discount

Assume:
* Par value = $1,000
* Coupon rate = 3.5% (paid semiannually)
* Market annual rate = 5% (paid/compounded semiannually)
* Time to maturity = 3 years

Steps:
1. Periods = 3 years × 2 = 6
Periodic market rate = 5% / 2 = 2.5%
Periodic coupon rate = 3.5% / 2 = 1.75%
Coupon payment per period = 1.75% × $1,000 = $17.50

  1. Present value of principal:
    PV_principal = 1000 / (1.025^6) = $862.30

  2. Present value of coupons (sum of discounted $17.50 payments):
    PV_coupons = 17.50/(1.025) + 17.50/(1.025^2) + … + 17.50/(1.025^6) = $96.39

  3. Market price = PV_principal + PV_coupons = $862.30 + $96.39 = $958.69

  4. Discount amount = Par − Market price = $1,000 − $958.69 = $41.31
    Discount rate = 41.31 / 1,000 = 4.13%

Because the market price ($958.69) is below par, the bond is trading at a discount.

Common reasons bonds trade at a discount

  • Rising market interest rates (reduces the value of existing lower-coupon bonds)
  • Worsening credit rating or increased default risk
  • Excess supply relative to demand in the secondary market
  • Zero-coupon bonds and some short-term issues are issued at a discount because they pay no periodic coupons

Conclusion

A bond discount signals that current market yields exceed the bond’s coupon rate or that risk has increased. Buying at a discount can enhance total return through capital appreciation at maturity, but investors should evaluate yield to maturity, credit risk, and interest-rate risk before purchasing. Understanding how and why discounts form helps investors compare bonds and make informed fixed-income decisions.