A $1000 bond is redeemable at par in 20 years.The bond is callable at the end of 10 years at 1100.The price of the bond to yield j₂ = 5% is
• $1125.51 assuming the bond is held to maturity
• $1138.97 assuming the bond is called at 10 years
Which of the following statements is true?
(I) If you pay $1125.51 and bond is called after 10 years,the yield will exceed j₂ = 5%
(II) If you pay $1138.97 and bond is called after 10 years,the yield will be less than j₂ = 5%

Question

Quizplus · Accepted Answer

If the bond is held to maturity, the yield is simply the coupon rate of the bond, which is not given in the problem. To calculate the price of the bond to yield 5%, we can use the present value formula:

PV = (1000 / (1+0.05)^20) + (1100 / (1+0.05)^10)

PV = $552.54 + $683.97

PV = $1236.51

So, if the bond is held to maturity, the price of the bond would be $1125.51, which is less than the price if it is called ($1138.97). Therefore, if you pay $1125.51 and the bond is called after 10 years, your yield would be higher than 5%.

Thus, the statement (I) is true, but we cannot conclude anything about statement (II) as it is not clear what yield is being referred to.

A $1000 Bond Is Redeemable at Par in 20 Years