A city has finance a local proars. Aject with a $600000 bond issue with a coupon

Question

A city has finance a local proars. Aject with a $600000 bond issue with a coupon rate of 6% compounded semi-annually. The bonds are redeemable in 13 years. At the same time, a sinkins fund earning interest at 5.3% compounded semi-annually is established to accumulate the full $600000 when the bonds mature in 13 years.

A) find the periodic cost of the debt

B) what is the book value of the debt in 7 years

C) construct a sinking fund schedule for the 9th year.

2. A $6000 bond paying interst at 9% compounded semi-annually is redeemable on july1, 2027. The bond is purchased on 0ctober 12 2014 to yield 7% compounded semi- annually. Calculte the purchase price.

Explanation / Answer

Solution :

A) the periodic cost of the debt would be the coupon interest rate paid every semi annually = $600000*6/2%

= $18000 every 6 months

B) the book value of debt would be $600000 because it is always recorded at par /Face value even after 7 years.

2) To compute the purchase price of the bond

YTM = Coupon interest +(Face value - Price )/n/(F.V + price )/2

will consider 4.5 % for 26 year and YTM = 7/2 = 3.5%. considering Face value = $100

.035 = 270 + (100- X)/26/(100+X)/2

.035 = 2*(7020 +100-X)/2600 + 26X

91+.91X = 14040 +100-2X

= 14049 = 2.91X

Hence X = 4827

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