Here's an example for the 15 years from 1994 to 2009 (31 December). For UK equities, the opening yield (TRI) was 4.02 % (75,618.18) and the closing yield (TRI) was 3.20 % (218,740.17). Comparing the TRIs gives an MVR of 5.45 % but we need to “adjust” the TRIs in order to obtain the DVR. For this, I am discounting expected income over 15 years and capital after 15 years.

As a first guess, let us suppose that the DVR is 8.00 % and see what happens. For this example, we'll take growth at 50 %, leading to a net discount rate of 4.00 %. For 15 years, the capital and income factors are 0.5553 and 11.1184 at BOTH ends of the period.

Applying the actual yield gives opening and closing combined factors of 1.0022 and 0.9111. Applying those factors to the TRIs gives opening and closing values of 75,786.33 and 199,283.86. If the DVR were 8.00 %, then 75,786.33 rolled-up for 15 years at 8.00 % would give 199,283.86…but it doesn't. In fact, the correct result is 6.68 %.