North North IncInc just issues a perpetual bonda perpetual bond that is callable

Question

North North IncInc just issues a perpetual bonda perpetual bond that is callable only at the end of year 2. The callprice is $1,000 (par value)plus an additional coupon payment.The current interest rate is interest rate is interest rate is interest rate is 6% per year.At the end of year 1 , interest rate either willeither increase to 7.4 % (40% probability) % (40% probability) or decrease to 4.9 % (60% probability)If in terest rate is 7 .4 % at the end of year 1, it will either increase to 9% (60% probability) or decrease 5% at the end of year 2. On other hand, If interest rate is (40% probability) at the end of year 2. On other hand, If interest rate is 4.9 % at the end of year 1, it will either increase to 7% (30% probability) or decrease 4% (70% probability) at the end of year 2.

a. What is the bond's value today if coupon i rate is set at is set at is set at 7%?

b. Suppose the bond is only callable at the end of year 1 and North will call the bond ifinterest rate decreases to 4.9% what coupon rate must it be so as to issue the bond at $950 ?

Explanation / Answer

(A) the bond value if coupon rate is set at 7%=1000+6×1000÷100+6÷10*(4.9÷100×(1000+1000×6÷100))+3÷10×(7÷100×(1060+4.9×1060÷100))=$1114.5

(B)rate at which bond is issued = (1000-950-0.6×0.049×1000)÷(1000÷100+0.6×0.049×1000÷100)=7.7%

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