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hug-sch committed Jul 22, 2024
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Expand Up @@ -3518,7 +3518,7 @@ <h1 id="the-money-weighted-rate-of-return">The money-weighted rate of return</h1
<p>where <em>n</em> = the number of cash flows in the reporting period, CF<sub>t</sub> = the cash flow at time <em>t</em>, and RD<sub>t</sub> = the number of remaining days within the period after CF<sub>t</sub>. For MVB, RD equals the entire period, represented in days. To annualize the return rate, you need to divide the remaining days by 365. To calculate the periodic return rate for the entire period such as 2 years, divide by the number of days of the entire period; e.g. 730 days.</p>
<p>Equation 1 closely resembles the calculation of Future Value. In Figure 1, assuming a 10% interest on your investments, the initial 1000 EUR capital will grow to a future value of 1331 EUR in three years. Additional cashflows of 500 EUR and 1000 EUR in the following years will result in 605 EUR and 1100 EUR respectively. The total Future Value of the investment will then be 3036 EUR in three years.</p>
<p><figure class="pp-figure" id="_figure-1"><figcaption>Figure 1. Visualisation of Future Value calculation.</figcaption><img alt="" src="../images/info-irr-future-value.svg"> </figure></p>
<p>Calculating IRR is in fact the inverse of calculating the future value (FV) of an investment. You don't know the interest rate or IRR, but you do know the MVB, the MVE, and the intermittent cashflows. According to Equation:</p>
<p>Calculating IRR is the inverse of calculating the future value (FV) of an investment. You don't know the interest rate or IRR, but you do know the MVB, the MVE, and the intermittent cashflows. According to Equation:</p>
<p><code>1000 * (1 + IRR)^(3x365/365) + 500 * (1 + IRR)^(2x365/365) + 1000 * (1 + IRR)^(365/365) = 3036</code></p>
<p>From this point forward, equations will be presented in a spreadsheet-like style, utilizing the asterisk (*) for multiplication and the caret (^) for power. This approach results in more concise equations that can be easily copied and pasted directly into a spreadsheet for verification.</p>
<p><code>500 * (1 + IRR)^(2x365/365)</code> is thus the expected future value of a cash flow of 500 EUR at time 2025-01-01 by the end of the period (after 2*365 days) with an annual interest rate = IRR. Please note that in the absence of any cash flows, Equation 1 resembles the (annualized) simple return formula <a href="../">MVE = MVB x (1 + r)</a>.</p>
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