An investor with a 1-year investment horizon purchases a 20-year 5% corporate bond. The prevailing price of the bond is Rs.82.3488 for a yield of 6.2%. Borrowed funds are not used for purchasing. The yield for all the maturities is same; therefore, the yield curve is flat. The yield for the on-the-run 30-year treasury issue is 5.5%. Therefore, the yield spread over the on-the-run treasury issue is 70 basis points.
The investor expects to reinvest the coupon rates at 5%; at the end of one year, the yield curve would shift down by 25 basis points. The yield for the 29-year treasury issue would be 5.25% and the yield spread to the 29-year treasury issue would be 80 basis points; therefore, the yield would be 6.05%, assuming that the price of the bond when discounted at a flat 6.05% is Rs.85.4376.
Calculation of total coupon payment and reinvestment income.
Annual reinvestment rate is given as 5%. Therefore for six months the reinvestment rate would be 2.5%. The coupon payment received at the end of six months is equal to Rs.2.50. This amount is reinvested at a reinvestment rate of 2.5% for six months. The total return using the future value of an annuity is as follows:
Semiannual Coupon payment reinvested for the six months
= Rs.2.5 (1.025) = Rs.2.56
Next semiannual payment (not reinvested) = Rs.2.5
Total = Rs.5.06
Price of the bond at the end of the 1-year investment horizon is Rs.85.4376
Total future returns = Rs.5.06 + Rs.85. 4376 = Rs.90.4976
Semiannual total return is:
(90.4976/85. 4376)1/2 - 1 = 2.92%
The total return on a bond-equivalent basis and on an effective rate basis are as follows:
2 x 2.92= 5.84 (Bond Equivalent Yield)
(1.0292)2 - 1 = 5.93 (Effective rate basis).