541 growth of an estate. Spending tends to be inflexible. Declining markets will reduce the value of an estate, and therefore if spending remains unchanged it will consume a larger percentage of the individual's assets. Spending requirements will tend to rise with inflation. This can intensify the adverse impact of inflation. Markets often react badly to a surge in the rate of inflation. Declining nominal market returns, declining real asset values, and increased spending requirements would obviously be a difficult combination, possibly leading to accelerating sales of assets at depressed prices.

The feasibility of a spending policy must be considered in combination with the impact of taxation and inflation. Preservation of an estate's real value requires that investment returns are at least equal to the sum of taxation, inflation, and spending. If we assume that income and capital gains taxes will take about 30 percent of investment returns, then spending should not exceed (70% X Pretax investment return) - Inflation. If we plug in some numbers that seem reasonable based on historic averages, an 8.0 percent pretax investment return and 3.0 percent inflation would allow for spending 2.6 percent of a portfolio's value. This calculation does not allow for spending increases linked to inflation. Based on horizon and expected inflation, the sustainable spending rate is something less than 2.6 percent.

When considering sustainable spending policies, investors should consider the range of possible outcomes rather than simply the mean expected return. In an environment of low or negative portfolio returns, fixed real spending requirements will consume an increasing portion of the portfolio's value. This can lead to an accelerating downward spiral. At the end of Chapter 30 we will show that even modest spending requirements can cause significant deterioration in worst-case forecasts.

CALCULATING AFTER-TAX RETURNS

Investment decisions should be based on expected after-tax returns. Investment horizon, the method by which an asset is disposed of, and the tax characteristics of the entity that holds an asset all affect the calculation of expected after-tax return. Let us use an equity index fund to illustrate. We will expect a 2 percent dividend yield and 8 percent annual appreciation. Dividends will be paid at the end of the year, they will be subject to income tax, and the net dividend will be reinvested. All appreciation will be unrealized until the fund is sold.

Horizon

The investor expects to sell after one year. Taxes will be 40% X 2% + 20% X 8% = 2.4%.

The expected after-tax return is 7.6%.

We define the effective tax rate as 1 - (After-tax return/Pretax return).

In this case, the effective tax rate is 24%.

Let us now change the assumption to a five-year holding period. This will allow appreciation to compound on a pretax basis. Table 29.2 shows the expected growth in value and cost basis.

The sale will produce gross proceeds of $155.28 and will require a capital