Table 18‐1 shows the duration calculation for a 5 percent, five‐year bond. The bond is priced at $974.17 because interest rates have risen so that the current Yield to Maturity (YTM) is 5.6 percent (semiannual yield, ytm, is 2.8 percent).

The cash flows, column 2, consist of ten $25 coupons (the annual coupon is $50) plus the return of principal at the end of the fifth year. Column 3 shows the present value of the cash flows using 2.8 percent as the discount rate. Column 4 shows the weights, or the present value of the cash flows as a percentage of the bond’s price, which in this example is $974.17. Notice that the final cash flow of $1,025 ($25 coupon plus $1,000 return of principal) accounts for 79.8 percent of the value of the bond on a weighted average basis. Column 5 is calculated by multiplying the weights in column 4 (which sum to 1.0) by the time periods in column 1 and summing these products. The end result, 4.48 years, is the present‐value weighted average number of years over which investors receive cash flows from the bond, which is the bond’s duration.

The duration of 4.48 years is approximately one‐half year less than the term to maturity of 5 years.

Table 18‐1

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TABLE 18-1 An Example of Calculating the Duration of a Bond with a 5 Percent Coupon, Five-Year Maturity, Currently Priced at $974.17 with aYTM of 5.6 Percent (1) Periods 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 (2) Cash Flow (CF) HHHHHHH25 1025 (3) PV of CFs 24.319 23.657 23.012 22.386 21.776 21.183 20.606 20.044 19.499 777.665 (4) Weighted PV of CFs (Weighted by Price) (3)/Price of the Bond 0.025 0.024 0.024 0.023 0.022 0.022 0.021 0.021 0.020 0.798 1.000 (5) Weighted Average of Time Periods (1) * (4) 0.012 0.024 0.035 0.046 0.056 0.065 0.074 0.082 0.090 3.991 4.477