### Half payout time of the net present value

The dividend discount model (DDM) gives the net present value of all future dividends without preference on whether dividend is obtained 1 year or 100 years from now. This results in the mathematically correct but misleading result that the future return equals sum of dividend yield and dividend growth rate, r = Y + g. For a real investor, however, it is always preferable to buy stocks with high current yield as

1. the current yield is more certain than the speculative growth g and

2. the high yield results in substantial income now as apposed to 50 years from now.

The difference between high growth and high yield is illustrated in Figure 1 where the net present value of future dividends is plotted. The high dividend stock has initial dividend of \$5 and it grows by a modest 2% per year; however, the value of future dividends is discounted by r = 8% so the net present value is actually decreasing. The present value of dividends never quite go to zero but it decays exponentially. The math is identical to radioactive decay where the initial high radiation rate decays but never quite vanishes. Figure 1. The net present value of future dividends. While the dividends increase over time, their value discounted to today (net present value) actually decreases. Dollar today is more valuable than \$1.05 next year!

The high dividend stock has a lower starting dividend of \$2 but due to the higher growth rate, the net present value of future dividends decays more slowly. The DMM model gives identical valuation for the two stocks but clearly the high dividend stock is better with a ~30 year investment horizon.

The dividend half payout time is a useful measure to quantify the relative importance of growth vs. current yield. The half payout time is exactly what the name implies: it is the time in years in which the value of dividend payouts equal half of the total net present value NPV. Recall that the NPV is and the NPVN of the next N years of dividends equal Setting NPVnextN = 0.5 NPV and solving for N, we obtain the half payout time in years: The results from Equation (3) tabulated in the spread sheet below. As the spreadsheet shows, the half payout time for stock market as a whole (Y = 2%, g =5% as of 8/11/2011) is very long, close to 40 years. This is consistent with our analysis for the value of next N years of dividends. Contrast this with a dividend stock (for example T with Y = 6%, g =2% as of 8/11/2011) that gives half payout time of just 12 years which means that investor is likely to see the almost full value of investment in his/her lifetime (12 years will realize half value, another 12 years will realize half of the remaining value bringing total to 75% and so on). You can play with the numbers with the editable spreadsheet at https://docs.google.com/spreadsheet/ccc?key=0AlyBMfBlh5aodFNDS0huWVVHalhoZjdYUlZjM2J5Qmc&hl=en_US .

#### Half-payout time of NPV of future dividends

The half payout time analysis for H-model is more complicated but the following approximate formula is useful: Equation (4) is incorporated into the H-model spreadsheet found at the DDM-H page.