Question

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The Black Hills Corporation issued a new series of bonds on January 1, 1990. The bonds...

The Black Hills Corporation issued a new series of bonds on January 1, 1990. The bonds were sold at par ($1,000), had a 12% coupon, and matured in 30 years on December 31, 2019. Coupon payments are made semiannually (on June 30 and December 31). (8 points)

a. What was the YTM on the date the bonds were issued?

b. What was the price of the bonds on January 1, 1995 (5 years later), assuming that interest rates had fallen to 10%.

c. Find the current yield, capital gains yield, and total yield on January 1, 1995, given the price as determined in part b.

d. On July 1, 2013 (6.5 years before maturity), Black Hills’ bonds sold for $916.42. What are the YTM, the current yield, and the capital gains yield for that date?

Expert Solution

Answer:

a.

The bond is sold at par which is $1,000. So, the YTM will be equal to the coupon rate of 12%. If the coupon rate and yield to maturity is same, then the bond price will be $1,000 or will trade at face value of bond.

Hence, the YTM of the bond is 12%.

b. Determination of price of bond:

Hence, the price of bond is $1,182.56.

c. Determination of current yield, capital gains yield and total yield:

Hence, the current yield is 10.15%, capital gains yield is -0.15% and total yield is 10%.

d. Determination of YTM, current yield, capital gains yield and total yield:

Hence, the YTM is 14%, current yield is 13.09%, capital gains yield is 0.91% and total yield is 14%.

jeff jeffy answered 2 years ago

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