You bought a bond with the following characteristics: $1,000 par value 11% coupo

Question

You bought a bond with the following characteristics:

$1,000 par value                                                                       11% coupon

Semiannual payments                                                             36 years to maturity

Bond was priced to yield 12%.

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

The price on purchase of the bond is =pv(rate,nper,pmt,fv) wheree rate = 0.12/2, nper =36*2, pmt = 110/2 and FV =1000

So purchase price = pv(0.12/2,36*2,110/2, 1000) = 917.92

The Coupon received and reivested at 6% for the first three years = fv(rate,nper,pmt) =fv(0.06/2, 6,55) = 355. 76

Now this is invested for another 33 years. So the final FV is =fv(rate,nper,pmt,fv) =fv(0.0426,33,0,355.76) = 1409.43 ( the interest rate of 4.26 % is obtained by taking a geomteric mean of 5.4% for 5 years, 4.8% for 2 years and 4% for 26 years

The next coupon rate received and reinvesd at 5.4% for the next 5 years =fv(rate,nper,pmt) =fv(0.054/2,10,55) = 621.87

This is again invested for 28 years . 4.8% for 2 years and 4% for 26 years = 4.057%. =fv(0.0457,28,621.87) = 1,893.64

The next coupon rate received and reinvesd at 4.8% for the next 2 years = fv(0.048/2,4,55) = 228.05

This is again invested for 26 years at 4% = fv(0.04,26,228.05) = 632.25

The last investment is reinested the annuity at 4% for 26 years = fv(0.04/2,26*2,55) = 4950.90

At maturity pirncipal is received as $1000

So Total amount received in 36 years = 1000 + 4950.90 + 632.25 + 1893.64 + 1409.43 -917.92 = 8,968.30

So relaized yield = 8,968.30/917.92 * 100 = 977.024 % for 36 years

Hence annualized yield = 977.024^(1/36) -1 = 0.2107 = 21.07%

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