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Difficulty: MediumDebt Securities and Bond Structure

A corporate bond with a 5%5\% coupon rate is currently trading in the secondary market at a discount price of $920\$920. Which of the following statements correctly describes the relationship between the bond's yields?

  1. The nominal yield is lower than the current yield, which is lower than the yield to maturity.Answer
  2. B
    The nominal yield is higher than the current yield, which is higher than the yield to maturity.
  3. C
    The current yield and yield to maturity are equal, and both are lower than the nominal yield.
  4. D
    The yield to maturity is lower than the current yield, but higher than the nominal yield.

Answer

The nominal yield is lower than the current yield, which is lower than the yield to maturity.
For any bond trading at a discount (below its $1,000\$1,000 par value), the current yield exceeds the nominal coupon rate because the annual interest payment is divided by a smaller market price denominator. Furthermore, the yield to maturity is higher than the current yield because YTM factors in the annualized capital gain realized as the bond matures back to par value. Therefore, the correct hierarchy for a discount bond is Nominal Yield < Current Yield < Yield to Maturity.

Step-by-Step Solution

1
Identify the purchase price relative to par value.
The bond is trading at $920\$920, which is below its $1,000\$1,000 par value, classifying it as a discount bond.
Determining whether a bond trades at a discount or premium establishes the directional relationship among its yields.
2
Compare nominal yield and current yield.
Current Yield ($50/$920=5.43%\$50 / \$920 = 5.43\%) is greater than Nominal Yield ($50/$1,000=5.00%\$50 / \$1,000 = 5.00\%).
Because the market price denominator is lower than par value, current yield exceeds the nominal coupon rate.
3
Determine the position of yield to maturity (YTM).
Yield to Maturity is higher than Current Yield because YTM includes the annualized $80\$80 price appreciation from $920\$920 up to $1,000\$1,000 par at maturity.
Discount bonds yield hierarchy follows: Nominal Yield < Current Yield < Yield to Maturity < Yield to Call.

Key Concept

Yield hierarchy for discount bonds
Estimated Time:1m 0s
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Topics

Debt Securities and Bond Structure

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