Question

You are called in as a financial and asus to appraise the bonds of orseln's clothing store. The $1000 per value bond have a "d annual interest rate of 10% which is paid semi annually. The yield to maturity on the bond as 10% annual interests there are 10 years to maturity.

a. compute the price of the bond based on semiannual analysis

b. with 5 years to maturity, if yield to maturity goes down substantially to 10%, what will be the new price of bonds?

Answer 1

a) Given in the question:

Face value of the bond (F): $1000

Annual Interest rate: 10% but paid semi annually; hence interest rate (c): 10/2: 5%

Similarly, semiannual YTM on the Bond (r): 10/2: 5%

Number of Years: 10; since paid semiannually; hence, number of years (t): 10*2: 20

Method 1:

Since, interest rate = YTM; hence it's a Par Bond and so, the Price of the Bond will be equal to its Face value i.e. $1000.

Method 2:

Hence; Price of Bond: 0.05*1000*((1-(1+0.05)^(-20))/0.05) + 1000/((1+0.05)^20)

: $1000

b)

Since, the value of YTM is still same i.e. 10% annually : 5% semiannually

and coupon rate (c): 5% semiannually

Hence, there would be no difference to the Price of the Bond with passage of time.

Still, the Price of the Bond would be $1000.