Perpetual Life corp, has issued consol bonds with coupon payments of $102. (Cons

Question

Perpetual Life corp, has issued consol bonds with coupon payments of $102. (Console pay interest forever and never mature. They are perpetuities) a. If the required of return on these bonds at the time they were issued was 10.2 % at what price were they sold to the public? Price sold to the public $ If the required return today is 15% at what price do the consoles sell? Current price $ you buy bond for $9-49 that has a coupon rate of 5.6% and a 8-year maturity. A year later, the bond price is $1.064. (Assume a face value of $1,000 and annual coupon payments) What is the new yields to maturity on the bond? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.) Yield to maturity % What is your rate of return over the year? (Do not round intermediate calculations. Enter your answer as a percent rounded to 2 decimal places.) Rate of return %

Explanation / Answer

A perpetual bond is a bond with no maturity date. Perpetual bonds are not redeemable but pay a steady stream of interest forever.In case of perpetual bond with no maturity date , price of the bond can be compted using the following formula.

Price of the bond =Interest payment/ required return

a) Prie sold to the public =$ 102/10.2% =$ 1000

b) if required rate of return is 15%, price of the bond =102/15%=$ 680

a) Yield to maturity (YTM) is the total return anticipated on a bond if the bond is held until the end of its lifetime
YTM formula ={Interest p.a +(Redeeption price- current bond price)/ No of years to maturity}/current bond price

={1000*5.6%+(1000-949)/8}/949

=0.0657 or 6.57%

b) Rate of return over the year =(Interest income +capital gain )/ Initial investment

=(56+115)/949

=18.02%

Capital gain =Market value at the end of the year -Initial investment =1064-949 =$ 115

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