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FRM Part I · FRM Exam Part I · Corporate Bonds

A bond with a USD 100 million face value has a sinking fund that retires USD 10 million of par each year by lottery at par, starting in year 1, with the remainder due at maturity in year 10. The bonds trade at 104 and the coupon is 5%. A holder of USD 1 million face value is selected in the lottery. Which statement is correct?

The holder loses USD 40,000 relative to market value. The sinking fund redeems selected bonds at par, USD 1 million, while the bonds are worth 104, or USD 1.04 million, so redemption forfeits the premium.

  1. AThe holder suffers a loss of USD 40,000 versus market price on redemptionCorrect
  2. BThe holder gains USD 40,000 because redemption is at par
  3. CThe holder receives USD 1.04 million as the sinking fund pays market price
  4. DThe holder is unaffected because the sinking fund redeems at yield-to-maturity

Explanation

Redemption is at par: USD 1,000,000 versus market value of 1.04 x 1,000,000 = USD 1,040,000. The loss is USD 40,000. This is the sinking fund's disadvantage for holders when bonds trade above par. The gain option reverses the sign.

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