Question

A $ 5,000 bond with a coupon rate of 5.8% paid semiannually has tenten years to maturity and a yield to maturity of 7%. If interest rates rise and the yield to maturity increases to 7.3%, what will happen to the price of the​ bond?

Answer 1

Step 1: Calculate Bond Price if YTM is 7%

The bond price can be calculated with the use of Present Value (PV) function/formula of EXCEL/Financial Calculator. The function/formula for PV is PV(Rate,Nper,PMT,FV) where Rate = Interest Rate (here, YTM), Nper = Period, PMT = Payment (here, Coupon Payment) and FV = Future Value (here, Face Value of Bonds).

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Here, Rate = 7%/2, Nper = 10*2 = 20, PMT = 5,000*5.8%*1/2 = $145 and FV = $5,000

Using these values in the above function/formula for PMT, we get,

Bond Price (PV) = PV(7%/2,20,145,5000) = $4573.63

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Step 2: Calculate Bond Price if YTM is 7.3%

Using the same Present Value function/formula as specified in Step 1, we can arrive at the bond price at a YTM of 7.3%.

Here, Rate = 7.3%/2, Nper = 10*2 = 20, PMT = 5,000*5.8%*1/2 = $145 and FV = $5,000

Using these valuesin PV function/formula, we get,

Bond Price (PV) = PV(7.3%/2,20,145,5000) = $4,474.20

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Step 3: Conclusion:

Based on the above calculations it can be concluded that the bond price will decrease from $4,573.63 to $4,474.20 as a result of an increase in YTM from 7% to 7.3%. This indicates that there is an inverse relationship between YTM and bond price.