Question

E. Problem:

The current price of bond with $1,000 par value, 9.75% annual coupon, and 20 years to maturity is $1,318.

a. What is the Yield To Maturity (YTM)?

b. If the bond contains a call provision that allows the company to call the bond 7 years from now for $1,050. What is the Yield To Call (YTC)?

c. Based on the available information, is this bond likely to be called?

Answer 1

E.a. The face value or par value of the bond or FV is $1000 and the annual coupon rate is 9.75% or 0.0975. Therefore, the coupon payment or C=($1000*0.975)=$97.5. The price of the bond or P is given as $1318 and the years or time to maturity or n is 20 years.

We know, according to the mathematical formula to calculate Year to Maturity(YTM), YTM=C+{(FV-P)/n}/(FV+P)/2

Therefore, based on the mathematical formula to calculate YTM, we can state:-

YTM=C+{(FV-P)/n}/(FV+P)/2

YTM=$97.5+{($1000-$1318)/20}/($1000+$1318)/2

YTM=$97.5+(-$318/20)/$1418/2

YTM=($97.5-$15.9)/$709

YTM=$81.6/$709

YTM=0.1151 approximately

Hence, the YTM or year to maturity on the bond would be 0.1151 or 11.51% approximately.

b. The call price or CP of the bond is given as $1050 and the number of years to call or n, in this case, is 7 years. The coupon or interest payment on the bond or C has been derived as $97.5 and P is $1318. Therefore, based on the mathematical formula to calculate yield to call or YTC, YTC=C+{(CP-P)/n}/(CP+P)/2

Therefore, according to the mathematical formula to compute YTC, we can state:-

YTC=C+{(CP-P)/n}/(CP+P)/2

YTC=$97.5+{($1050-$1318)/7}/($1050+$1318)/2

YTC=$97.5+(-$268/7)/($2368/2)

YTC=$97.5-$38.29/$1184

YTC=$59.21/$1184

YTC=0.05 or 5% approximately

Therefore, the YTC on the bond would be 0.05 or 5% approximately.

c. In this particular instance, note that the YTC on the bond is actually less than its YTM implying that if the company calls the bond earlier than its subsequent maturity period, the overall or total return that it will obtain would be more than if its called off by the company earlier than its final expiration. Thus, the company is better off waiting until the bond is completely matured as opposed to calling it off earlier than its final maturity period, in this case.