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Difficulty: Very hardDebt Securities and Bond Structure

An investor purchases a callable corporate bond with a par value of 1,000andastatedannualcouponrateof5.01,000 and a stated annual coupon rate of 5.0%. The bond matures in 10 years, is currently callable in 3 years at 1,010, and trades in the secondary market at a premium price of $1,060. Which of the following correctly lists the yields of this bond in order from highest to lowest?

  1. Nominal yield, current yield, yield to maturity, yield to callAnswer
  2. B
    Yield to call, yield to maturity, current yield, nominal yield
  3. C
    Nominal yield, current yield, yield to call, yield to maturity
  4. D
    Current yield, nominal yield, yield to maturity, yield to call

Answer

Nominal yield, current yield, yield to maturity, yield to call
When a bond is purchased at a premium above par value, the investor receives fixed coupon payments based on par (1,000),makingNominalYieldthehighestmetric.CurrentYieldislowerbecauseitdividesannualinterestbythehigherpurchaseprice(1,000), making Nominal Yield the highest metric. Current Yield is lower because it divides annual interest by the higher purchase price ( 1,060). Yield to Maturity (YTM) drops further because it factors in the loss of the premium over the remaining 10 years. Yield to Call (YTC) is the lowest yield metric (yielding the 'yield to worst') because the premium loss down to the $1,010 call price is accelerated over a shorter 3-year timeframe. Therefore, the yields ranked from highest to lowest are Nominal Yield, Current Yield, Yield to Maturity, and Yield to Call.

Step-by-Step Solution

1
Determine the bond's pricing status relative to par value
The purchase price of 1,060isabovethe1,060 is above the 1,000 par value, classifying the bond as trading at a premium.
Understanding whether a bond trades at a discount or premium dictates the directional relationship among its yield metrics.
2
Compare Nominal Yield and Current Yield for a premium bond
Nominal yield is fixed at 5.0%. Current yield (50annualcoupon/50 annual coupon / 1,060 price = 4.72%) is lower than nominal yield.
Because the investor pays more than par for the annual coupon cash flow, the effective yield on purchase price is lower than the face rate.
3
Evaluate Yield to Maturity (YTM) and Yield to Call (YTC)
YTM reduces yield further by amortizing the 60premiumover10years.YTCamortizesa60 premium over 10 years. YTC amortizes a 50 loss (1,060purchasepricedownto1,060 purchase price down to 1,010 call value) over just 3 years, causing the greatest annualized reduction.
Amortizing premium loss over a shorter call period reduces overall annualized yield more severely than spreading it across full maturity.
4
Construct the final yield hierarchy from highest to lowest
Nominal Yield > Current Yield > Yield to Maturity > Yield to Call
This complete sequence defines the standard yield hierarchy for any callable debt security trading at a premium.

Key Concept

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

Debt Securities and Bond Structure

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