Strategic Synchronization: Unraveling The Art Of Equalizing Investment Values

There are several ways to determine when two investments will have equal value. One way is to calculate the return on investment (ROI) for each investment. This can be done by comparing the current and initial values of the investments while accounting for dividends or interest earned. Another way is to use the Rule of 72, which is a simplified formula that measures the effect of compound interest on investment dollars. Additionally, the time-weighted returns (TWR) and money-weighted returns (MWR) are two standard methods for calculating investment returns and can be used to compare the performance of two investments.

Time-weighted returns (TWR)

TWR breaks up the return on an investment portfolio into separate intervals based on whether money was added or withdrawn from the fund. This allows investors to evaluate the performance of their investments based on the assets available for investment each day. It is calculated using the following formula:

TWR = [(1 + HP^1) x (1 + HP^2) x … x ( 1 + HP^n )] – 1

Where:

• TWR = Time-weighted return
• N = Number of Periods
• HP = (End Value – Initial Value + Cashflow)/(Initial Value + Cashflow)
• HP^n = Return for Period “n”

For example, let's say you invest $500,000 in Portfolio A on December 31. By June 1 of the next year, your portfolio has grown to $526,709. You then make an additional $50,000 deposit, bringing the total value to $576,709. At the end of the year, your portfolio has decreased to $537,908. To calculate the TWR for this scenario, you would first determine the rate of return for each sub-period:

First-period return = ($526,709 - $500,000) / $500,000 = 5.34%

Second-period return = [$537,908 – ($526,709 + $50,000)] / ($526,709 + $50,000) = -6.72%

Finally, to get the TWR, you would multiply the rates of return for each sub-period together and subtract 1:

TWR = [(1 + 5.34%) x (1 + -6.72%)] – 1 = -1.73%

This calculation allows investors to isolate the impact of market performance and investment selections from the distorting effects of cash flow.

Money-weighted returns (MWR)

MWR measures the rate of return on an account over a period of time, including investment decision-making and trading activity in the account (e.g. withdrawals, deposits, transfers). It shows personal investment experience and account performance, helping to clarify the impact that investment activity decisions are having on an account.

MWR is not an effective measure of a portfolio manager's performance and cannot be used to compare the performance of other funds. It is best used for measuring the performance of a personal account.

MWR is calculated using an intimidating-looking formula, which can be done manually or with the help of spreadsheet software like Microsoft Excel or Google Sheets. The formula for calculating MWR is:

$$\begin{equation*}

\text{MWR} = \frac{\text{Initial Investment} + \text{Deposits} - \text{Withdrawals}}{\text{Initial Investment}}

\end{equation*}$$

The goal of the calculation is to find the rate of return that results in the initial investment being equal to the present value of all cash flows.

To calculate MWR in a spreadsheet, create a column for dates and one for values. In the first row, enter the beginning date of the measurement period and the balance at the start. Then, create new rows for each inflow and outflow of cash, including the date and amount of cash flowing into or out of the portfolio, with withdrawals represented by negative numbers. Finally, enter the ending date of the measurement period and the ending value of the portfolio as a negative number.

MWR is a valuable tool for investors to understand their market timing and determine the success of any hired experts, such as financial advisors. However, it emphasises timing rather than asset performance, which can skew results.

Net present value (NPV)

NPV is the result of calculations that find the current value of a future stream of payments using the proper discount rate. The discount rate may reflect the cost of capital or the returns available on alternative investments of comparable risk. The discount rate is central to the NPV formula as it accounts for the fact that a dollar today is worth more than a dollar in the future due to inflation, interest rates, and opportunity costs.

The NPV formula is:

NPV = (1+i)^t x Cash flow – initial investment

Where:

• I = discount rate or required return
• T = number of time periods

NPV can be calculated using tables, spreadsheets (e.g. Excel), or financial calculators.

NPV is a useful tool for determining whether an investment will result in a net profit or loss. A positive NPV indicates that the projected earnings generated by an investment exceed the anticipated costs, representing a profitable venture. Conversely, a negative NPV suggests that the expected costs outweigh the earnings, signalling potential financial losses.

NPV is the most commonly used method for evaluating investment opportunities. However, it has some drawbacks, including its reliance on a long list of assumptions, sensitivity to small changes in assumptions, and the challenge of accurately adjusting for risk.

Internal rate of return (IRR)

The Internal Rate of Return (IRR) is a metric used in financial analysis to estimate the profitability of potential investments. It is the discount rate that makes the net present value (NPV) of all cash flows equal to zero in a discounted cash flow analysis. In other words, it is the expected compound annual rate of return that will be earned on a project or investment.

The IRR formula is as follows:

$$\begin{aligned}

&\text{0}=\text{NPV}=\sum_{t=1}^{T}\frac{C_t}{\left(1+IRR\right)^t}-C_0\\

&\textbf{where:}\\

&C_t=\text{Net cash inflow during period }t\\

&C_0=\text{Total initial investment costs}\\

&IRR=\text{The internal rate of return}\\

&t=\text{The number of time periods}

\end{aligned}$$

The IRR is used to determine whether a project or investment should be pursued. If the IRR is greater than the minimum required rate of return or the hurdle rate, then it is worth considering. The hurdle rate is typically a company's cost of capital, and if the IRR is greater than or equal to this, the company would likely accept the project as a good investment.

It is important to note that the IRR does not give the return on the initial investment in terms of real dollars. It also assumes that all positive cash flows will be reinvested at the same rate as the project, which may not be accurate. As such, it is important to consider other factors and metrics when making investment decisions.

Social return on investment (SROI)

SROI is a framework that quantifies the value of social, environmental, and economic outcomes generated by an organisation's activities. It provides a comprehensive view of the impact created per unit of investment, enabling stakeholders to assess projects' effectiveness and efficiency.

The process of calculating SROI involves several steps:

• Identifying Stakeholders: Understand who is affected by the investment, from investors to the local community and society at large.
• Mapping Outcomes: List the changes brought about by the investment, whether positive or negative, to see the full picture.
• Valuing Outcomes: Assign a monetary value to each identified change, using market prices or surveys.
• Calculating SROI: Add up the values of the outcomes and compare them to the investment's cost to get the SROI ratio.
• Communicating Results: Share the findings with everyone involved to ensure transparency.

SROI is particularly useful for corporations as it can improve program management through better planning and evaluation. It increases their understanding of their effect on the community and allows better communication of their work's value to internal and external stakeholders.

SROI can be calculated using the following formula:

SROI = (Social Impact Value - Initial Investment Amount) / (Initial Investment Amount x 100%)

Assigning a dollar value to social impact can be challenging, and various methodologies have been developed to help with this process, such as the Analytical Hierarchy Process (AHP).

While traditional cost-benefit analyses are used to compare different investments, SROI is used to evaluate the general progress of certain developments, showing the financial and social impact of a corporation's activities.

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