Total return of the bond on the assumption

by | Mar 3, 2023 | finance

 

An investor is considering buying a bond from Company HelloWorld. The bond pays 12% semi-annual coupon, it has 15 years to maturity and the current price of this bond is $1,150. This bond is callable at the end of year 5 (the first and only call date). The call price of the bond is $1,120. What is the RTC for this bond?
Suppose our investor’s investment horizon is only 7 years (a period extending beyond the first call date, but shorter than the maturity of the bond). Also
assume that this investor believes that she can invest all proceeds @ 9%.
(a) Compute the total return of the bond on the assumption that the bond is called in 5 years.
(b) Compute the total return of the bond on the assumption that the bond is not called and lives until maturity.

 

 

Sample Solution

(a) The total return for this bond if the bond is called in 5 years will be calculated using the reinvestment rate of 9% over the 7-year investment horizon. To calculate this, first we need to determine the present value at year 5 of all cash flows from year 6 to maturity (15 years). This is done by taking each coupon amount ((12/2)*1000=$600) and discounting it back to present value, then summing all discounted cash flows.
For example, PV of Cash Flow at Year 6 = $600/(1.09)^6 = $454.67
The total present value will be:
Total PV=($454.67+$454.67+…+$414.88)/(1-(1/ 1 .09 )^15 )=3860.99
Then we subtract this from the call price of $1120 to get our RTC or return on call : RTC=$1120 – 3860 .99=$2739 .01 or 2 .73 %

Sample Solution

(a) The total return for this bond if the bond is called in 5 years will be calculated using the reinvestment rate of 9% over the 7-year investment horizon. To calculate this, first we need to determine the present value at year 5 of all cash flows from year 6 to maturity (15 years). This is done by taking each coupon amount ((12/2)*1000=$600) and discounting it back to present value, then summing all discounted cash flows.
For example, PV of Cash Flow at Year 6 = $600/(1.09)^6 = $454.67
The total present value will be:
Total PV=($454.67+$454.67+…+$414.88)/(1-(1/ 1 .09 )^15 )=3860.99
Then we subtract this from the call price of $1120 to get our RTC or return on call : RTC=$1120 – 3860 .99=$2739 .01 or 2 .73 %

(b) If we assume that the bond does not get called and lives until maturity, then we can calculate its total return using a different equation that takes into account both principal repayment and coupon payments over 15 years with a reinvestment rate of 9%. This equation is as follows: Total Return=(PV+(Coupons x (1-(1/N))/r)/Price – 1 where N=number of cashflows per year (in this case semi-annual which equals 2), r=reinvestment rate (in this case 9%) and Price equals $1150.

Using these inputs, our total return calculation comes out as [(3860.99 + 5959-.6875)/ 1150]- 1 = 4 .87 %

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