Equations For Investment: Strategies And Math For Success

There are several equations that can be used to calculate the profitability of an investment. One of the most popular is the return on investment (ROI) formula, which is used to evaluate the efficiency of an investment or compare the efficiency of several investments. ROI is calculated by subtracting the initial cost of the investment from its final value, then dividing this new number by the cost of the investment, and finally multiplying it by 100.

Other equations that can be used to calculate investment returns include the Gordon equation, which assumes stocks get their ultimate value from being able to one day return earnings to investors, and the time-weighted rate of return (TWR) formula, which measures the rate of return of a portfolio by eliminating the distorting effects of changes in cash flows.

Formula investing is a method that rigidly follows a prescribed theory or formula to determine investment policy. It can be related to how an investor handles asset allocation, the types of securities they invest in, or how much and how frequently they invest.

Return on Investment (ROI)

ROI is a popular metric due to its versatility and simplicity. It can be used to evaluate the performance of a wide range of investments, including stocks, business ventures, and real estate transactions. It is also useful for comparing the efficiency of different investments and ranking them accordingly.

However, ROI has some limitations. Firstly, it does not take into account the holding period of an investment, which can be an issue when comparing investment alternatives. Secondly, ROI does not adjust for risk, which is an important factor in investment returns. Additionally, ROI calculations can be manipulated by omitting certain costs, and they may not always reflect the true profitability of an investment due to the factor of time.

To address the issue of time, an annualized ROI calculation can be performed. This calculation accounts for the length of time an investment is held and provides a more accurate comparison between investments.

> ROI = (Net Income / Cost of Investment) x 100%

And here is an example of how to calculate ROI:

> An investor purchases a property valued at $500,000 and sells it two years later for $1,000,000.

> ROI = ($1,000,000 - $500,000) / $500,000 x 100% = 100%

Compound interest

The formula for calculating compound interest is:

=[P (1 + i)n] – P

= P [(1 + i)n – 1]

Where:

• I = annual interest rate
• N = number of compounding periods
• P = principal amount

For example, if you have a 3-year loan of $10,000 at an interest rate of 5%, compounded annually, the amount of interest would be:

$10,000 [(1 + 0.05)3 – 1] = $10,000 [1.157625 – 1] = $1,576.25

The power of compound interest is that it always results in a value greater than or equal to other methods, like simple interest. For example, an amount of $1,000 invested over a period of time at a 10% rate would give a simple interest of $100 for each successive time period of 1 year, but would give a compound interest of $100, $210, $331, $464.10, and so on.

The more often compounding occurs, the higher the interest accrued. This can have a significant effect on the final balance, especially in the long term. Compounding may occur on different frequencies, such as daily, monthly, quarterly, or annually. The most simple compounding frequency is yearly, but in reality, compounding can happen much more frequently, even reaching continuous compounding, which is the theoretical limit of the process.

The Rule of 72 is a quick way to estimate how long it will take for your money to double when the amount is compounded annually. You can find out how long it will take by dividing 72 by your rate of return. For example, if you have a rate of return of 4%, your money will double in 72 / 4 = 18 years.

Simple interest

The formula for simple interest is:

SI = (P x R x T)/100

Where:

• SI = simple interest
• P = principal (the initial amount)
• R = rate of interest in % per annum (written as R/100, so 100 in the formula)
• T = time (usually calculated as the number of years)

For example, if you borrow $1,000 at a rate of 5% for 1 year, the simple interest will be:

SI = (1000 x 5 x 1)/100 = $50

So you will need to repay $1,050 in total.

The formula can also be written as SI = PRT, where R is given as a decimal (so 0.05 in the example above).

Net present value (NPV)

NPV is the result of calculations that determine the current value of a future stream of payments using the proper discount rate. Projects with a positive NPV are generally worth undertaking, while those with a negative NPV are not. A positive NPV indicates that the projected earnings generated by an investment exceed the anticipated costs, while a negative NPV indicates that the expected costs outweigh the earnings.

The formula for NPV is:

NPV = (Cash inflow – Cash outflow) / (1 + i)^t – Initial investment

Where:

• I = Required return or discount rate
• T = Number of time periods

NPV analysis is used extensively in finance and accounting to determine the value of a business, investment security, capital project, or new venture. It is considered an all-encompassing metric as it takes into account all revenues, expenses, and capital costs associated with an investment. It also considers the timing of each cash flow, which can significantly impact the present value of an investment.

NPV is often used by corporate finance professionals, such as investment bankers and accountants, to determine which investments, projects, or mergers are worth pursuing. Business owners can also benefit from understanding NPV to make budgeting decisions and assess their business's future value.

NPV has some drawbacks, including the need to make a long list of assumptions and the challenge of accurately adjusting for risk. Additionally, NPV does not capture the full range of benefits and impacts of an investment, as it is driven by quantitative inputs and does not consider non-financial metrics.

Annualised ROI

The annualised rate of return is calculated by averaging returns into a year-long time frame. It accounts for all the losses and gains over time and provides a measure of performance that equalises all investments over the same time period. This is useful for investments with volatile returns or variable interest rates, as it can be difficult to accurately assess how these investments are performing.

The formula for calculating the annualised rate of return is:

Where:

N = number of years the investment is held

For example, assume an individual placed $100,000 into a high-interest savings account with a variable interest rate. With no additional contributions, six years later, the account balance amounts to $115,900. Using the formula, the annualised rate of return for this investment is 2.50%.

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