Duration

On the average, the present value of the cash flows of a two year, 8% Treasury note, valued at par, take 1.8875 years to reach the owner. Thus, a risk free lump sum payment due in two years should have a discount rate that is equivalent to a Treasury note of slightly more than two years.

Table 5-1 shows the duration of Treasury bonds and other semi-annual coupon bonds by yield. Note that the higher the yield to maturity, the shorter the duration. This is because the later payments, including the principal repayment, are discounted at a higher rate, lowering their effect in the weighted average.

Table 5-1 can be used to help estimate a reasonable discount rate. Let us assume that Treasury yields of intermediate to long term bonds are in the 8% range and that you have a lump sum retirement payment coming to you in 10 years. Since this retirement payment is a lump sum, it has a duration of 10 years. Looking at the 8% column of Table 5-1 we find that 19 year Treasury bonds have a duration of 10.07 years. Therefore, we look at the yield on 19 year Treasury bonds to determine an appropriate risk-free discount rate. As we saw in Chapter 4, yield curves tend to flatten out when maturities are more than about 10 years because of the uncertainty.

Table 5-2 shows that the duration of an annuity is longer than that of a bond of equal maturity. If, for example, you have an annuity of 10 years with a present value of $1,000 and interest rates are in the 8% range, that annuity will have a duration of 8.39 years. Table 5-1 then shows us that this corresponds to a Treasury bond of about 13 years and this can be used to estimate an appropriate discount rate.