Looks as if you are misunderstanding... if you receive dividends, these are positive cash flows that contribute to the IRR calculation. If you reinvest these dividends, then in addition to the income component on IRR, so too will be the change in value of the reinvestment. The formula used for IRR is below, an it is accurate and correct. We also further geometrically link IRR for sub period returns and closer GIPS compliance. Please contact our tech support team directly if you have add'l questions: email@example.com
Internal Rate of Return (Modified IRR Method)
The internal rate of return calculates return for the period taking into effect the exact timing of each cash flow. The model properly weights the timing of cash flows (additions/ withdrawals) for a portfolio or an individual asset, for a selected date range, to provide the return calculation. Internal rate of return can be equated to the compounded effective interest rate that a savings account would have had to earn in order to reach the portfolios' current present value including all investment flows (purchases, sales, income, interest, reinvestment, etc.), while adjusted for timing of the specific flows.
Key variables in the model include: Beginning Market Value, Ending Market Value, Income, Reinvestments, Sum of all Cash Flows within the period (additions/withdrawals), and Weight Factor (# of total days in the period that the cash flow "F" has been in, or out of, the portfolio). The return derived here can then be stored to be used in 'linking' returns.
The calculation is:
MVE = Summate Fi(1+R)^Wi
(^ denotes raised to the power of)
MVE = the market value at the end of the period (includes any interest or dividends earned but not withdrawn, i.e. reinvestments, etc.).
MVB = the market value at the beginning of the period, (includes any interest or dividends earned but not withdrawn, i.e. reinvestments, etc.).
Summate F = the sum of the cash flows within the period (contributions to the portfolio are positive flows, and withdrawals or distributions are negative flows). The market value at the start of the period is also treated as a cash flow at the beginning of the period, i.e. MVB = F0.
R = the internal rate of return.
Wi = is the proportion of the total number of days in the period that the cash flow Fi has been in (or out of) the portfolio. The formula for Wi is:
Wi = [CD-Di] / [CD] (this is the weighting component)
CD = the total number of days in the period.
Di = the number of days since the beginning of the period in which cashflow Fi occurred.
IRR is derived by selecting values for R and solving the equation until the result equals MVE. For example, if there were a total of three cash flows for the period (including the beginning market value treated as F0) - there will be three terms in the computational formula:
MVE = F0(1+R)^W0 + F1(1+R)^W1 + F2(1+R)^W2 .
The first term deals with the first cash flow, F0, which is the value of the portfolio at the beginning of the period (MVB). Wi is the proportion of the period that the cash flow Fi was in (or out) of the portfolio. Because F0 is in for the whole period, W0 = 1. The larger the value of Fi in the term, the more it will contribute to the total. But the smaller the exponent (i.e., the value of Wi), the less the term will contribute to the sum. This usually means that the first term, with a large F0 and W0 = 1, will contribute far more than the other terms.
Source: Global Investment Performance Standards Second Edition (2006), Charlottesville, VA 22903, pg 87-88.