On April 1, 2016. you consider the purchase of an outstanding bond that was issu

Question

On April 1, 2016. you consider the purchase of an outstanding bond that was issued on April 1. 2015 for 30 years. It has an 8% annual coupon. Thus, it matures April 1, 20451 It has five years of call protection when it was issued, which is until April 2020, at which time it can be called in with an 8% call premium. Interest rates have declined since it was issued a year ago, and it is now selling for 115.8757o of its par value of $1,000. What is the YTM? Show work What is the YTC? Show work If you decide to purchase the bond, which return would you expect to earn if the interest rates reiroin less than 8%, the YTM or YTC? Circle YTM or YTC Explain your answer.

Explanation / Answer

Approximate YTM = (Interest payment + (Face value - Price of Bond) / time to maturity) / (Face value + Price of Bond) / 2

= (80 + (1000 - 1158.75) / 29) / (1000+ 1158.75)/2

= 6.9%

We have to calculate a discount rate at which the PV of bond = Current price of the bond i.e $1158.75 and so we have to calculate it with trial and error method.

So, the YTM would be 6.74%

YTC

The equation for YTC is given below:

Bond price = Interest / 2 [1- (1+ YTC / 2)^-2 x Years to call) / YTC / 2] + Call Price / (1+ YTC / 2)^2x years to call)

1158.75 = 80 / 2 [1-(1+ YTC/2)^2x5 ) / YTC/ 2] + 1080 / (1+ YTC / 2)^2x5

Solving the equation with a financial calculator we get, YTC = 5.71%

If the interest rates remain less than 8%, then YTM should be chosen as this the maximum return that the bond will get over its life.

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