Question

There are 10 bonds, each one with par value of $100, 4% semiannual coupons and redemption value of $120. The bonds are purchased for $106 each. One bond will mature in 11 years, the second in 12 years, and so on, with 10th bond maturing in 20 years. How many of the bonds will earn a nominal yield rate of at least 4.5% per annum compounded semiannually?

Answer 1

From the problem we get the following information

Effective interest rate per annum = ((1+(4%/2))^2)-1 = 4.04%

So, Interest from the bond per year = $100 * 4.04% = $4.04

       Initial Cash Outflow = $106

       Per Year Cash Inflow = $4.04

       Last Year Cash Inflow = $4.04 + $120 = $124.04

       Nominal Yield rate per annum

                     = IRR per annum

                     = IRR (Cash flow year 1, Cash flow year 2, ..............., Cash flow year n)

       Nominal yield rate per annum compounded semiannually

                      = (Sqrt(1+IRR per annum) - 1) * 2

       Interest rate calulation for the 10 bonds are given in the table below.

      Calulations are done based on the above mentioned formulas.

Hence, from the above table and calculation we can derive that only 3 bonds (Bond-1, Bond-2 & Bond-3) will earn a nominal yield rate of at least 4.5% per annum compounded semiannually.