Question

You purchase a bond issued by XYZ Ltd, which is a 8% semi-annual coupon bond with a term to maturity of 10 years, and currently trading at par. Four years later, immediately after receiving the eighth coupon payment, you sell the bond to your best friend. You best friend’s nominal yield to maturity is 7% per annum. Write down an equation that can be solved to find your total realised return over the 4-year holding period.

Answer 1

The amount of income received during 4 years = 8%/2 * 1000 * 8 semi-annual payments = $320

Now we have to find the amount at which you sold the bond to your best friend. For your friend the remaining time = 10 - 4 = 6 years and so he will get 6*2 = 12 coupon payments of 8%/2*1000 = $40 each

His yield to maturity = 7% and so effective yield for a half year period = 7%/2 = 3.5%

Thus the price = $40 * PVIFA (3.5%, 12) + 1,000* PVIF (3.5%, 12)

= $1,048.32

Now holding period return = ((income + (end of period value - original value))/original value * 100

= ((320+($40 * PVIFA (3.5%, 12) + 1,000* PVIF (3.5%, 12) - 1,000))/1,000 * 100

This equation can be solved and we will get a return of: ((320+(1048.32-1000)/1000)*100

= 36.83%