Question

You are considering the purchase of a 15 year bond with annual coupon of 9.5%. The bond has a face value of $1000 and makes annual interest payments. If you require an 11% yield on this investment:

What is the max price you are willing to pay for the bond?

Your total wealth at the end of 15 years if you purchased this bond will be? And how much did you earn in additional interest if you reinvested each coupon payment of $95 at 11% for the entire 15 years? Show work in the space below.

Verify that your realized yield at the end of 15 years is the same as the bond’s yield to maturity of 11%. What are the key risks in bond investments?

Answer 1

Bond coupon = $1000*9.5% = $95

Max price of the bond= 95/1.11 + 95/1.11^2+.... + 95/1.11^15+ 1000/1.11^15

= 95/0.11*(1-1/1.11^15) +1000/1.11^15

=$892.14

Total wealth at the end of 15 years = coupon amount +face value = 95*15+1000 = $2425

Amount earned if $95 coupon was reinvested at 11%

= 95*1.11^14+95*1.11^13+.....+95

=95/0.11*(1.11^15-1)

=$3268.51

So, additonal amount earned as interest on coupon amount = $3268.51 - $95*15 = $1843.51

Total wealth at end of 15 years = $2425+$1843.51= $4268.51

As the total amount invested was $892.14, rate of interest earned for 15 years (r) is given by

892.14*(1+r)^15= 4268.51

r = 0.11 or 11%

So, the overall rate of return earned was 11% (Same as required rate)

The key risk are the interest rate risk and reinvestment risk. If the bond is not held till maturity , the price is dependent on and is inversely related to interest rates prevailing at the time of selling, so there is interest rate risk. Further, if the reinvestment rate on bonds is less than the required rate, overall realised rate of return is also less. So, this is the reinvestment risk