# Should we always assume semi-annual periods with bonds, if no information is given?

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%.

BEY.

Bonds pay semiannually unless they specifically state otherwise.

Ok so you always assume semi-annual compounding. For you to use annual compounding they would explictly have to state “annual coupons”?

Yup.

I would always assume Bonds are semi, but what about corporate paper?

If it should ever come up, they’ll tell you.