Question

John Q is planning to buy a bond having a face value of $100,000 for $90,000. The bond is paying 8% per year payable semi-annually and is redeemable 6 years from now at its face value. What is the rate of return on this investment per six months and per year (nominal and effective)? (5 <= i* <= 6 % per six months)

Answer 1

Face value = 100000

Buy value = 90000

Coupon rate = 8% semiannual payment

Coupon payment = 8% * 100000 /2 = 4000

Maturity left = 6 years = 6*2 = 12 semiannual period

Let IRR be i% per semiannual period, then at i%, PW = 0

PW = -90000 + 4000*(P/A,i%,12) + 100000*(P/F,i%12) = 0

4000*(P/A,i%,12) + 100000*(P/F,i%12) = 90000

4*(P/A,i%,12) + 100*(P/F,i%12) = 90

using trail and error method

When i = 5%, 4*(P/A,i%,12) + 100*(P/F,i%12) = 91.1367

When i = 6%, 4*(P/A,i%,12) + 100*(P/F,i%12) = 83.2323

using interpolation

i = 5% + (91.1367-90)/(91.1367-83.2323) *(6-5)

i = 5% + 0.1438

i = 5.14% per semiannual period (Approx)

i = 5.14% * 2 = 10.28% per year (nominal)

effetive IRR per year = (1+0.0514)^2 - 1 = 0.10544 = 10.54%