Question

Suppose that the market interest rate is 4% and then drops overnight to 2%. Calculate the present values of the 1.25%, 3-year bond and of the 1.25%, 30-year bond both before and after this change in interest rates. Assume annual coupon payments. Confirm that your answers correspond with Figure 6.5. Use your financial calculator or a spreadsheet. You can find a box on bond pricing using Excel later in this chapter.

Answer 1

(A) The present value of 1.25%, 3 year bond before the change in interest rates =PV(rate,nper,pmt,fv) in excel where rate = 0.04, nper = 3, pmt =1.25%*1000 = 12.5 and fv =1000.

The present value of 1.25%, 3 year bond before the change in interest rates =PV(0.04,3,12.5,1000) = $923.68

(B) The present value of 1.25%, 30 year bond before the change in interest rates =PV(rate,nper,pmt,fv) in excel where rate = 0.04, nper = 30, pmt =1.25%*1000 = 12.5 and fv =1000.

The present value of 1.25%, 30 year bond before the change in interest rates =PV(0.04,30,12.5,1000) = $524.47

(C) The present value of 1.25%, 3 year bond after the change in interest rates =PV(rate,nper,pmt,fv) in excel where rate = 0.02, nper = 3, pmt =1.25%*1000 = 12.5 and fv =1000.

The present value of 1.25%, 3 year bond after the change in interest rates =PV(0.02,3,12.5,1000) = $978.37

(D) The present value of 1.25%, 30 year bond after the change in interest rates =PV(rate,nper,pmt,fv) in excel where rate = 0.02, nper = 30, pmt =1.25%*1000 = 12.5 and fv =1000.

The present value of 1.25%, 30 year bond after the change in interest rates =PV(0.02,30,12.5,1000) = $832.03

Yes, the answers obtained do correspond with the figure 6.5