Investment return consists of price change and dividends (or interest), but you also must consider the impact of inflation and taxes in determining your true return. In this post, I look at the impact of price change, dividends, inflation and taxes on an investment in the Vanguard Small-Cap Value Index fund over the 10 years ending 8/2/2010. In the remainder of this post, I’ll refer to the fund by its ticker symbol, VISVX.

The chart below shows the price history of VISVX for the 10 years ending 8/2/2010. If you want to see the chart more clearly, follow this link to the chart on Morningstar (the time period may be different).

The share price increased from $8.85 on 8/2/2000 to $14.15 on 8/2/2010. So the total **price change **for VISVX over 10 years was $5.30 per share, which is an increase of 60% ($5.30/$8.85 = 0.60 = 60%). (There are more calculations than usual in this post; if this makes your eyes glaze over, just skip over the math—hopefully you’ll still benefit from the concepts).

**Dividends**

A price history chart, like the one above, doesn’t show the impact of dividends on investment return.

Some companies distribute part of their earnings (profits) to shareholders in the form of dividends. A mutual fund that holds dividend paying stocks in its portfolio passes the dividends on to its shareholders. For example, in 2009 VISVX paid dividends that contributed 2.42% to its return. Some mutual fund shareholders choose to reinvest these dividends in more shares of the mutual fund.

A common way to show investment return, including the impact of reinvested dividends, is to use a chart showing the growth of $10,000 over the time period of interest. The chart below shows the growth of $10K invested in VISVX over the 10 years ending 8/2/2010 (with all dividends reinvested). To see the chart more clearly, use the link to the price chart (in the previous section), and change the chart type to *growth* using the drop-down menu near the top-left of the chart.

With all dividends reinvested, $10,000 grew to $21,090 over the 10 years ending 8/2/2010, for a total profit of $11,090. This is a total cumulative return of 111% ($11,090/$10,000 = 1.11 = 111%), which represents a compound annual return of 7.75%.^{1} Without considering dividends, $10,000 would have grown to about $16,000 (due to the 60% price increase), so the 10 year cumulative return was increased by more than $5,000 by reinvesting all dividends. The term *total return *is used to describe an investment return that includes reinvested dividends (and other distributions).^{2}

**Inflation**

Unfortunately, the actual spending power of our investment return is decreased by inflation. There’s nothing you can do to control the impact of inflation on a particular investment, but it’s important to remember the impact, and to consider it in evaluating investment returns.

Inflation in the US is most commonly measured by changes in the Consumer Price Index (CPI).^{3} As I write this, the CPI numbers are available through June 2010, so using the June 2000 value of 172.4 and the June 2010 value of 217.965 puts cumulative inflation at 26% (217.965/172.4 – 1 = 1.26 – 1 = 0.26 = 26%) for the 10 years ending June 2010. I’ll call 1.26 the *inflation factor*; it will be used in several calculations below. Roughly speaking, it costs about $1.26 in 2010 to buy what would have cost $1.00 in 2000. So, to convert 2010 dollars to 2000 dollars, we divide by the inflation factor of 1.26. Incidentally, this is a compound annual inflation rate of 2.34%.

The term *nominal return* describes the rate of return before adjusting for inflation, and the term *real return* describes the rate of return after adjusting for inflation. For small values of inflation, simply subtracting the inflation rate from the nominal return gives a reasonably accurate approximation of the real return, but for larger values, the exact formula should be used.^{4} For our example the formula is 2.11/1.26 - 1 = 1.67 – 1 = 0.67 = 67% (2.11 is the nominal, investment growth factor calculated as $21,090/$10,000, and 1.26 is the inflation factor derived in the previous paragraph). So the **real **10 year cumulative return on VISVX is 67%.

Here’s a summary of the 10 year cumulative returns, discussed so far, on an investment in VISVX:

**Price change**only: 60%- With reinvested
**dividends**: 111% - With reinvested dividends after
**inflation**: 67%

**Taxes**

Finally, federal and most state governments may take their cut of your investment returns in the form of income taxes. Between federal and state taxes, you may pay 25% or more of your investment gains to federal and state governments. On the other hand, if your taxable income is low enough, or your investments are held in a Roth IRA, you may pay little or no taxes on your gains. This is one area where there may be steps you can take to manage the impact on your investment returns. I won’t go into much detail, but here are a few points to consider.

If VISVX or any other mutual fund is held in a taxable account, taxes are paid on dividends each year, but no taxes are paid on gains due to price change until shares of the fund are sold. Currently, dividends and capital gains (gains due to price change) on investments held in taxable accounts are taxed at lower federal rates than ordinary income.

If held in a traditional IRA or 401(k), no taxes are paid until distributions are taken (normally in retirement), at which time distributions are taxed at ordinary income tax rates.

If held in a Roth IRA or Roth 401(k), no taxes are paid on investment returns. (However, this doesn’t necessarily mean that Roth accounts are superior to traditional tax privileged accounts; there are tradeoffs between the benefits of tax deferral in traditional tax privileged accounts and tax free returns in Roth accounts.)

For illustration purposes, let’s assume that VISVX had been held in a taxable account or a traditional IRA or 401(k), and that the effective tax rate on price change and dividends was 25%. Since taxes are paid on the return due to inflation (unfair as it may seem) as well as the real return, we use the nominal returns in our tax calculations.

Total profit from price change and reinvested dividends was $21,090 - $10,000 = $11,090. Levying our assumed 25% tax on the profit leaves us with 75% of $11,090, which is $8,318. Recalculating our after-tax return gives us a nominal, after-tax, cumulative return of 83% ($8,318/$10,000 = 0.83 = 83%) and a real (after inflation) after-tax cumulative return of 45% (1.83/1.26 – 1 = 1.45 – 1 = 0.45 = 45%). This represents a compound annual return of 3.79%—much less than the 7.75% calculated before considering inflation and taxes.

Reviewing the impact of the various return factors on the 10 year cumulative return of an investment in VISVX:

**Price change**only: 60%- With reinvested
**dividends**: 111% - With reinvested dividends, after
**inflation**: 67% - With reinvested dividends, after inflation and
**taxes**: 45%

Hopefully this illustrates the dramatic impact that dividends, inflation and taxes can have on real, after-tax investment returns. Whenever evaluating investment returns, be sure to keep these factors in mind.

**Notes**

1. **Compound Annual Return**: If you invest at a fixed annual rate of r, your investment will increase by a factor of 1+r after one year; for example, if you invest $1.00 at 5%, at the end of one year you will have (1+.05)*$1.00 = 1.05*$1.00 = $1.05. Assuming annual compounding, your investment also grows by a factor of 1+r in the second year, and after two years your original investment has grown by a factor of (1+r)*(1+r) = (1+r)^{2}. After n years, your original investment will increase by a factor of (1+r)^{n}; this equals the end value divided by the start value, so we have the following equation:

(1+r)^{n} = EndValue÷StartValue

To determine the compound annual return, r, given the start and end values, we solve the above equation for r by taking the n_{th} root of both sides of the equation and then subtracting 1 from both sides. Taking the n^{th} root of a number is the same as raising the number to the ^{1}⁄_{n} power, so the equation to determine r is:

r = (EndValue÷StartValue)^{1/n} - 1

So, to compute the compound annual return of an investment over a 10 year period, you divide the end value by the start value, raise it to the ^{1}⁄_{10} power, then subtract 1. Plugging in the numbers from our VISVX example for total nominal return gives us (21090/10000)^0.1 – 1 = 0.0775 = 7.75% (this version of the formula uses the spreadsheet symbol for exponentiation, ^, and uses the decimal form of ^{1}⁄_{10}) .

2. In addition to dividends, there may also be distributions of capital gains, due to the fund selling shares of stocks in its portfolio at a profit. The total return (growth) chart assumes that all distributions are reinvested, but to keep things simple, I refer only to dividends throughout this post.

3. CPI values are available at ftp://ftp.bls.gov/pub/special.requests/cpi/cpiai.txt.

4. The formula to calculate real return given nominal return is r = (1+R)/(1+i) - 1, where r = real rate of return, R = nominal rate of return, and i = inflation rate. Using the numbers in our example, R=1.11 and i = 0.26, so our calculation is (1+1.11)/(1+0.26) - 1 = 2.11/1.26 - 1 = 1.67 - 1 = 0.67 = 67%.

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