Question

Five years ago, you purchased an 8% coupon bond for 975$. Today you sold the bond for 1000$.Tax rate is 20%

.What is the rate of return if all the coupons were reinvested at 8.64%?

What is the rate of return if all coupons were reinvested at 4%?

Answer 1

Greetings,

We would have received coupon @8% on face value of 1000 = 80 for 5 years. After payment of taxes, coupon amount eligible for investment would have been 80 × (1-0.2) =64 for each year. Capital Gain = 1000-975 =25 Tax on CG =20% of 25 =5. Therefore post tax sale price =1000-5=995

Case 1 - Reinvestment rate is 8.64%. Post tax Reinvestment rate = 8.64×0.8=6.912%. Simply Find out the FV of coupons using following formula in excel -

+FV(rate =0.06912, n=5, PMT=64, PV =0, type=0) = 367.40

Add Post tax sale price 995

Total =367.40+995=1362.40.

Now equate inflow and outflow to get the IRR ie

975 = 1362.40/(1+R)^5

R = 6.92%

Case 2 - Reinvestment Rate is 4%. post tax Reinvestment rate is 4×0.8=3 2%.FV of the coupons using the same formula as above = 341.15 Add Sale price net of taxes =995

Total = 314.15+995 = 1336.15

975 = 1336.15/(1+R)^5

R = 6.505%