Question

New Business Ventures, Inc., has an outstanding perpetual bond with a coupon rate of 9 percent that can be called in one year. The bond makes annual coupon payments. The call premium is set at $130 over par value. There is a 60 percent chance that the interest rate in one year will be 11 percent, and a 40 percent chance that the interest rate will be 6 percent. If the current interest rate is 9 percent, what is the current market price of the bond? Assume a par value of $1,000. (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

Perpetual Bond price formula (if not called) = Coupon amount/Interest rate

Coupon amount = Par Value * Interest rate

1000*9%= 90

if Interest rate in 1 year is 11%, Bond will not be called. as coupon interest rate is less than market rate. In this case, price of Bond at year 1 = 90/11% =

818.1818182

Probability of this is 60%

If interest rate is 6% in one year, Bond will be called as in this case coupon rate will be more than market rate.

So redemption price or price at year 1 is $1000+130 call premium= $1130

Probability is 40%

Today interest rate (i) for Calculation of price today is 9%

Bond price formula = Coupon amount for year 1/(1+ i)^n + Price at year 1/(1+i)^n

If not called, probability is 60%. Price =

90/(1+9%)^1 + 818.18182/(1+9%)

=833.1943303

If called, Probability is 40%, price is

°90/(1+9%)^1 + 1130/(1+9%)=

=1119.266055

Current market price or Expected price = (Price 1*Probability)+(Price 2*Probability)

(833.1943303*60%)+(1119.266055*40%)

947.6230202

So, Current market price of bond is $947.62