I just did exercise 27 of Schwes exams Vol 1, number 2 PM. We are supposed to calculate the annualized bond equivalent return of a 7-year, single-B rated, 9% coupon bond trading at par. The investor expects to hold the bond for two years, assumes a reinvestment rate of 8%, and believes the bond will be priced to yield 10% at the investment horizon.
In the solution everything is done based on semi annual periods. Any specific reason why we should assume semi annual periods?
Solution: The coupon interest on the bond is $90 per year or $45 per semiannual period. The facts assume that coupons received can be reinvested at 8% annually during the two-year investment horizon. The future value of an annuity of $45 per period for four periods at an assumed reinvestment rate of 4% per period is:
n = 4; i = 4; PMT = 45; solve for FV = $191.09.
At the investment horizon (in two years), the bond is expected to be a 5-year, 9% coupon bond, priced to yield 10% (5% per period). The price of the bond at the investment horizon is, therefore, expected to be $961.39. This future bond price and the expected return are calculated as follows:
n = 10; i = 5; PMT = 45; FV = 1,000; solve for PV = −961.39
Total future value = $191.09 + $961.39 = $1,152.48
Using financial calculator, solve for semiannual return:
n = 4; FV = 1,152.48; PV = -1,000; PMT = 0; solve for i = 3.61
Annualized total return = 2 × 3.61% = 7.22%.