1- You purchased a bond with the following characteristics: $1,000 par value 5.5
ID: 2724152 • Letter: 1
Question
1- You purchased 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 purchased 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
Step 1: Calculated the Current Price of the Bond
The current price of the bond can be calculated with the use of following formula:
Current Price = 27.50/(1+6%/2)^2 + 27.50/(1+6%/2)^4 + 27.50/(1+6%/2)^6 + 27.50/(1+6%/2)^8 + 27.50/(1+6%/2)^10 + 27.50/(1+6%/2)^12 + 27.50/(1+5.4%/2)^14 + 27.50/(1+5.4%/2)^16 + 27.50/(1+5.4%/2)^18 + 27.50/(1+5.4%/2)^20 + 27.50/(1+5.4%/2)^22 + 27.50/(1+5.4%/2)^24 + 27.50/(1+5.4%/2)^26 + 27.50/(1+5.4%/2)^28 + 27.50/(1+5.4%/2)^30 + 27.50/(1+5.4%/2)^32 + 27.50/(1+4.8%/2)^34 + 27.50/(1+4.8%/2)^36 + 27.50/(1+4.8%/2)^38 + 27.50/(1+4.8%/2)^40 + 27.50/(1+4%/2)^42 + 27.50/(1+4%/2)^44 + 27.50/(1+4%/2)^46 + 27.50/(1+4%/2)^48 + 27.50/(1+4%/2)^50 + 27.50/(1+4%/2)^52 + 27.50/(1+4%/2)^54 + 27.50/(1+4%/2)^56 + 27.50/(1+4%/2)^58 + 27.50/(1+4%/2)^60 + 27.50/(1+4%/2)^62 + 27.50/(1+4%/2)^64 + 27.50/(1+4%/2)^66 + 27.50/(1+4%/2)^68 + 27.50/(1+4%/2)^70 + (1,000 +27.50)/(1+4%/2)^72 = $716.42
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Step 2: Calculate Realized Yield on Bond
The realized yield can be calculated with the use of Rate function/formula of EXCEL/Financial Calculator. The function/formula for Rate is Rate(Nper,PMT-PV,FV) where Nper = Period, PMT = Coupon Payment, PV = Current Bond Price and FV = Face Value of Bonds
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Here, Nper = 18*2 = 36, PMT = 1,000*5.5%*1/2 = $27.50, PV = -$716.42 and FV = $1,000 [we use 2 since the bond is semi-annual]
Using these values in the above function/formula for Rate, we get,
Realized Yield = Rate(36,27.50-716.42,1000)*2 = 8.63% (answer)
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