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Difficulty: HardDebt Securities and Bond Structure

An investor acquires a 10-year corporate bond in the secondary market at a discount price of 910.Thebondpaysa5910. The bond pays a 5% annual coupon and is callable in 5 years at its par value of 1,000. If market interest rates decline and the issuer calls the bond at the 5-year call date, which of the following statements correctly describes the yield relationship experienced by the investor?

  1. The Yield to Call (YTC) is higher than the Yield to Maturity (YTM), which is higher than the Current Yield (CY).Answer
  2. B
    The Yield to Call (YTC) is lower than the Yield to Maturity (YTM), because early redemption reduces the total number of coupon payments collected.
  3. C
    The Current Yield (CY) equals the Yield to Call (YTC), because the redemption price at the call date equals the par value.
  4. D
    The Nominal Yield (NY) represents the highest return rate the investor will earn over the 5-year holding period.

Answer

The Yield to Call (YTC) is higher than the Yield to Maturity (YTM), which is higher than the Current Yield (CY).
For any bond purchased at a discount, the yield relationship from lowest to highest is Nominal Yield < Current Yield < Yield to Maturity < Yield to Call (when called at par or higher). Because the investor purchased the bond at 910andreceivesthefull910 and receives the full 1,000 par value after only 5 years rather than waiting the full 10 years to maturity, the annualized return from the discount gain is accelerated. Thus, Yield to Call (YTC) is the highest yield, followed by Yield to Maturity (YTM), Current Yield (CY), and Nominal Yield (NY).

Step-by-Step Solution

1
Determine the bond pricing status
The bond is purchased at 910,whichisbelowparvalue(910, which is below par value ( 1,000), making it a discount bond.
Discount bonds have market prices lower than their principal par value.
2
Establish the baseline discount yield hierarchy
Nominal Yield (NY) < Current Yield (CY) < Yield to Maturity (YTM).
For discount bonds, Current Yield exceeds Nominal Yield because the price paid is less than par, and YTM further accounts for the capital gain at maturity.
3
Evaluate the effect of early call at par on a discount bond
Accelerating the $90 discount gain over 5 years instead of 10 years increases the annualized rate of return, so YTC > YTM.
Earning the full par redemption value sooner compresses the timeframe for the capital gain, maximizing the annualized yield to call.

Key Concept

Yield Hierarchy for Discount and Callable Debt Securities
Estimated Time:1m 30s
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Topics

Debt Securities and Bond Structure

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