The total return on bond equivalent basis

by | Mar 3, 2023 | finance

 

Suppose that an investor has 8 years investment horizon. The investor is considering a 20-year semi-annual coupon bond selling at par and having a coupon rate of 10%. The investor expectations are as follows:
The first 6 semi-annual coupon payments can be reinvested from the time of receipt to the end of the investment horizon at an annual interest rate of 7%.
The remaining semi-annual coupon payments can be reinvested from the time of receipt to the end of the investment horizon at a 11% annual interest rate.
Investor believes that the required return on a 12-year bond of this quality at the end of the investment horizon will be 12%.
(a) Calculate the total return on bond equivalent basis?
(b) What is the total return on effective rate basis?

Sample Solution

Answer: (a) To calculate the total return on bond equivalent basis, we need to first determine the present value of all cash flows associated with this bond over the 8-year investment horizon. This includes coupon payments, principal repayment upon maturity date and any capital gains or losses due to changes in market interest rates.

Sample Solution

Answer: (a) To calculate the total return on bond equivalent basis, we need to first determine the present value of all cash flows associated with this bond over the 8-year investment horizon. This includes coupon payments, principal repayment upon maturity date and any capital gains or losses due to changes in market interest rates.

The coupon payments for the first 6 semi-annual periods can be discounted using an adjusted discount rate of 3.5% (=10%/2) while those after 6th period can be discounted at a rate of 5.5% (=11%/2). The present value of these two components will be $2412.77 and $2779.63 respectively, where each figure is calculated by multiplying 0 05125(=$1000 * 0 10 / 2 ) by appropriate power number depending on number payment periods left till 8 years ie 24 (6*2+6*2). Then finally ,the PV of principal repayment amount at 20th year which has an adjusted discount rate 11 %=(12%-1%) resulting value 2841 88 . Adding these three figures together gives us total PV investments as $8034 29.

Therefore total return on Bond Equivalent Basis (%) = [(8034 29 − 1000)/1000]*100 = 703 43 %.

(b) To calculate Total Return on Effective Rate basis, we use following formula : TRER (%)= ((Coupons + Principal Repayment )/(Price Paid))^(1/Years Till Maturity)-1 ;where Coupons = 5501 40(2412 77 + 2779 63 );Principal Repayment 2841 88 ;Price Paid 1000 ;Number Years Till Maturity 8 . Plugging these numbers into our equation yields TRER (%) = ((5501 40 + 2841 88)/1000)^0 125–1 = 9 41 %

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