You bought a bond with the following characteristics: $1,000 par value 5.5% coup

Question

You bought a bond with the following characteristics: $1,000 par value 5.5% coupon Semiannual payments 18 years to maturity Bond was priced to yield 6%. For the first three years after you bought the bond interest rates remained constant at 6%. Then interest rates dropped to 5.4% and remained at that rate for five years. Then rates dropped further to 4.8% and remained at that rate for two more years. Rates dropped even lower to 4% and remained at that rate until the bond matured. Assume that all coupon interest payments were reinvested at the prevailing markets rate(s). Calculate the realized yield of this investment.

Explanation / Answer

Bond maturity value is $1,000 and with a coupon of 5.5%.

So, purchase price = 27.5 / 0.03 * (1-(1/1.03)^36) + 1000 / 1.03^36

= $945.42

The Future Value of all coupon rate = 27.5*1.03^35 + 27.5*1.03^34 + .. + 27.5*1.03^30 + 27.5*1.027^29 + 27.5*1.027^28 + ... + 27.5*1.027^20 + 27.5*1.024^19 + 27.5*1.024^18 + .. + 27.5*1.024^16 + 27.5*1.02^15 + .. + 27.5*1.02 + 27.5 + 1000

= 27.5 * [15.701 + 19.264 + 6.060 + 18.639] + 1000

= $2,640.768

Future Value of purchased price at realized yield will be equal to the the future value of all inflow.

945.42*(1+i)^36 = 2640.768

i = 2.89%

Therefore, Realized Yield of the investment is 2.89%.

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