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Difficulty: HardDebt Securities and Bond Structure

An investor purchases a 1,000parvalue,61,000 par value, 6% corporate bond in the secondary market at a price of 108 ( 1,080). The bond matures in 10 years and is callable in 5 years at 103 ($1,030). Which of the following options correctly ranks the yields associated with this bond 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
    Current Yield > Nominal Yield > Yield to Maturity > Yield to Call
  4. D
    Nominal Yield > Yield to Call > Yield to Maturity > Current Yield

Answer

Nominal Yield > Current Yield > Yield to Maturity > Yield to Call
When a bond is purchased at a premium (above 1,000par),theinvestorreceivesannualinterestbasedonparvaluewhilepayingahighermarketprice.Consequently,NominalYield(statedcouponrate)isthehighestyield.CurrentYieldislowerthanNominalYieldbecauseannualincomeisdividedbyahigherpurchaseprice.YieldtoMaturityislowerthanCurrentYieldbecauseitincorporatesthelossofthepremiumovertheremaininglifeofthebond.YieldtoCallisthelowestyieldmeasurebecausethepremiumlossisamortizedoverashortertimeframe(5yearsinsteadof10)toacallprice(1,000 par), the investor receives annual interest based on par value while paying a higher market price. Consequently, Nominal Yield (stated coupon rate) is the highest yield. Current Yield is lower than Nominal Yield because annual income is divided by a higher purchase price. Yield to Maturity is lower than Current Yield because it incorporates the loss of the premium over the remaining life of the bond. Yield to Call is the lowest yield measure because the premium loss is amortized over a shorter timeframe (5 years instead of 10) to a call price ( 1,030) that is lower than the purchase price ($1,080).

Step-by-Step Solution

1
Determine the bond's pricing condition relative to par value.
The bond is trading at $1,080 (108% of par), which means it is selling at a premium.
Establishing premium vs. discount status dictates the relationship among yield measures.
2
Calculate Nominal Yield and Current Yield.
Nominal Yield is fixed at the stated coupon rate of 6.00%6.00\%. Current Yield is $60$1,080≈5.56%\frac{\$60}{\$1,080} \approx 5.56\%.
Current yield drops below nominal yield because the investor pays more than par for the same dollar coupon payments.
3
Analyze the impact of holding to maturity vs. early redemption (call).
Yield to Maturity (YTM) accounts for losing the 80premiumover10years.YieldtoCall(YTC)accountsforlosing80 premium over 10 years. Yield to Call (YTC) accounts for losing 50 premium (from 1,080downtothecallpriceof1,080 down to the call price of 1,030) over a shorter 5-year period.
Amortizing premium over a shorter duration (5 years to call) causes a greater annualized reduction in yield than amortizing over 10 years to maturity.
4
Establish the complete yield hierarchy.
Nominal Yield (6.00%6.00\%) > Current Yield (5.56%5.56\%) > Yield to Maturity > Yield to Call.
For premium bonds, YTC is always the lowest yield, while Nominal Yield is the highest.

Key Concept

Bond Yield Hierarchy for Premium Bonds
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Topics

Debt Securities and Bond Structure

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