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Encyclopedia > Return on investment

In finance, the return on investment (ROI) or just return is a calculation used to determine whether a proposed investment is wise, and how well it will repay the investor. It is calculated as the ratio of the amount gained (taken as positive), or lost (taken as negative), relative to the basis. Finance studies and addresses the ways in which individuals, businesses and organizations raise, allocate and use monetary resources over time, taking into account the risks entailed in their projects. ...

The analysis of the return on investment is either done by static or dynamic formal methods, which may be distinguished by the role of time in the model chosen. Dynamic models take account of the fact that a later date of payment may be valued inferior in a model with interest rates. In other words, static approaches can be regarded as sufficient, if the distribution of payments in each period may be assumed as equal to others. All basic ROI-Models are deterministic, for instance the well-known Total Cost of Ownership Model by the Gartner Group. Deterministic models assume the security of prediction. Abandoning this leads into the wide sphere of risk-aware-models, that are inspired by the mathematics of insurances. Total cost of ownership (TCO) is a financial estimate designed to help consumers and enterprise managers assess direct and indirect costs related to the purchase of any capital investment, such as (but not limited to) computer software or hardware. ... Gartner, Inc. ...

In Marketing, the notion of "return on investment" is an increasingly important topic for Chief Marketing Officers (CMOs) who need to find ways to justify the high investments made across a broad range of marketing AND sales activities. When put together, these investments can represent between 15 and 40% of a given company's sales. Given the disparity of spend categories, and the inherent difficulty to assess the impact of several of them (e.g. the difficulty to be deterministic when assessing the impact of television on sales), companies have either been developing some intermediary/ surrogate metrics, or proceeded with more or less complex econometric modeling. The latter can however often suffer from (1) appearing as a "black box" to marketeers and (2) being limited to "known" media (and hence not being suited for new media (new per se or not regularly used by a given company or brand). New methods therefore present interesting potential for impact, namely leveraging "heuristics" and (controlled) experiments. This topic can be further expanded/ detailed. It has been suggested that Product marketing be merged into this article or section. ...

## Contents

There are two methods of calculating the basic ROI. Each has its own mathematical merits.

` Vi is the initial investment Vf is the final value s `

### Arithmetic return

In mathematical terms, the arithmetic return is defined as the following. $ROI_{Arith}=frac{V_f - V_i}{V_i} = frac{V_f}{V_i} - 1$

This return has the following characteristics:

• $ROI_{Arith}=+100%$ when the final value is twice the initial value
• ROIArith > 0 when the investment is profitable
• ROIArith < 0 when the investment is at a loss
• $ROI_{Arith}=-100%$ when investment can no longer be recovered

Interestingly, to compensate for a negative ROI, one needs a positive ROI that is higher in magnitude. For example, to recoup a 50% loss one needs to realize a 100% gain.

### Logarithmic return

The above definition is problematic in that a +10% return and a -10% return do not add up to 0%. For example, starting with \$100, a +10% return would result in \$110. A subsequent -10% return would result in \$99.

To correct this, academics use a natural log return called logarithmic return or geometric return. The natural logarithm is the logarithm to the base e, where e is approximately equal to 2. ... $ROI_{Log} = lnleft(frac{V_f}{V_i}right)$.

This return has similar characteristics:

• ROILog > 0 is profit
• ROILog < 0 is a loss
• Doubling occurs when $ROI_{Log}=ln(2)=69.3%$
• Total loss occurs when $ROI_{Log}to-infty$.

### Examples of high yielding investments

A tax lien is a lien imposed on property by law to secure payment of taxes. ... Angel Investors (or simply Angels) are affluent individuals who provide capital for business start-ups, usually in exchange for an equity stake. ... Private equity is a broad term that refers to any type of equity investment in an asset in which the equity is not freely tradable on a public stock market. ... A government bond is a bond issued by a national government denominated in the countrys own currency. ... A stock option is a specific type of option with a stock as the underlying instrument (the security that the value of the option is based on). ...

Compound annual growth rate (CAGR) is one method of assessing the average growth of a value over time. ... The expected gain (or expected return) is the weighted-average most likely outcome in gambling, probability theory, economics or finance. ... The internal rate of return (IRR) is defined as the discount rate that gives a net present value (NPV) of zero. ... Return on capital, also known as Return On Invested Capital (ROIC) is defined as NOPLAT / Invested Capital usually expressed as a percentage. ...

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