KIC plans to issue $4m of bonds, coupon rate 7% and 30 yrs to maturity. Current

Question

KIC plans to issue $4m of bonds, coupon rate 7% and 30 yrs to maturity. Current market interest 8%. In one year, interest rate on the bonds will be either 8% or 6% with equal probability. If bonds are noncallable what is price of bonds today? Assume par $1000 and Semi-Annual payments. KIC plans to issue $4m of bonds, coupon rate 7% and 30 yrs to maturity. Current market interest 8%. In one year, interest rate on the bonds will be either 8% or 6% with equal probability. If bonds are noncallable what is price of bonds today? Assume par $1000 and Semi-Annual payments.

Explanation / Answer

Suppose the bond is paying annual coupon

Price of the bond could be calculated using below formula.

P = C* [{1 - (1 + YTM) ^ -n}/ (YTM)] + [F/ (1 + YTM) ^ -n]

Where,

                Face value = $1000

                Coupon rate = 0.0725

                YTM or Required rate = 0.08

                Time to maturity (n) = 30 years

                Annual coupon C = $72.5

Let's put all the values in the formula to find the bond current value

P = 72.5* [{1 - (1 + 0.08) ^ -30}/ (0.08)] + [1000/ (1 + 0.08) ^30]

P = 72.5* [{1 - (1.08) ^ -30}/ (0.08)] + [1000/ (1.08) ^30]

P = 72.5* [{1 - 0.09938}/ 0.08] + [1000/ 10.06266]

P = 72.5* [0.90062/ 0.08] + [99.3773]

P = 72.5* 11.25775 + 99.3773

P = 816.186875 + 99.3773

P = 915.564175

So price of the bond is $915.56

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