Question

3. Currently, BCA's bonds sell for $1,145. They pay a 8% semi-annual coupon, have a 14-year maturity, and a $1,000 par value, but they can be called in 5 years at $1,050. Assume that no costs other than the call premium would be incurred to call and refund the bonds, and also assume that the yield curve is horizontal, with rates expected to remain at current levels on into the future.

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3a. What is the yield to maturity for this bond?

3b. What is the yield to call for this bond?

Answer #1

YTM is the discount rate at which the price of the bond is calculated:

Price =

where C= coupon amount = (8/2)% of 1000 = 40 since it's semi annual coupon

n= number of periods= 14*2= 28

1145 =

this gives us approx 3.2%, hence annualized YTM= 2*3.2= 6.4%

It can also be calculated by the formula = (C+(F-P)/n)/((C+F)/2)= (40+(1000-1145)/28)/((1000+1145)/2) =~3.2%

Similarly, Yield to call (YTC) = (C+(F-CP)/n)/((F+CP)/2), F= Face value; CP= Call price

= (40+(1000-1050)/10)/((1000+1050)/2) = 3.4%

Hence annualized YTC = 2*3.4 = 6.8%

Please reach out in case of any doubts

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