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Difficulty: MediumDebt Securities and Bond Structure

An investor purchases a 1,000parvaluecorporatebondwitha1,000 par value corporate bond with a 4\%couponrateforasecondarymarketpriceof coupon rate for a secondary market price of 920. Which of the following statements accurately describes the relationship among the bond's yields?

  1. The yield to maturity is greater than the current yield, which is greater than the nominal yield.Answer
  2. B
    The nominal yield is greater than the current yield, which is greater than the yield to maturity.
  3. C
    The nominal yield and current yield are equal, but both are less than the yield to maturity.
  4. D
    The yield to maturity is lower than the nominal yield because of the discounted purchase price.

Answer

The yield to maturity is greater than the current yield, which is greater than the nominal yield.
For any debt security selling at a discount to par value, the yield to maturity is the highest yield, followed by the current yield, with the nominal yield (coupon rate) being the lowest. This occurs because the investor receives the stated coupon payments plus the gain realized when the bond reaches full par value at maturity.

Step-by-Step Solution

1
Determine whether the bond is trading at a discount, par, or premium.
The purchase price of 920islessthantheparvalueof920 is less than the par value of 1,000, establishing that the bond is trading at a discount.
Identifying price relative to par is required to establish the yield hierarchy.
2
Compare Nominal Yield and Current Yield.
Nominal yield is fixed at 4.0%4.0\%. Current yield is 40/920=4.35%40 / 920 = 4.35\%. Thus, Current Yield > Nominal Yield.
Paying less than par increases the annual return percentage relative to the fixed coupon.
3
Factor in principal appreciation at maturity for Yield to Maturity (YTM).
YTM includes annual interest plus the gain realized as the bond matures at $1,000, making YTM > Current Yield.
YTM reflects total annualized return over the remaining life of the bond.

Key Concept

Discount Bond Yield Hierarchy (YTM > CY > NY)
Estimated Time:1m 15s
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Topics

Debt Securities and Bond Structure

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