# Annual Compound Net Rate – CNAR Definition

## What is the annual compound net rate – CNAR?

The compound annual net rate (CNAR) is the return on an investment after taking into account taxes. Although similar to the compound annual growth rate (CAGR), the CNAR is the net after tax. The compound annual net rate will be lower than the CAGR after taking taxes into account, but it is a better representation of an investor’s actual returns since most investments have tax implications.

## The formula for the annual net compound rate – CNAR is



CNAR

=

RR

Ã—

(

1

Tax rate

)

or:

RR

=

Annual rate of return

begin {aligned} & text {CNAR} = text {RR} times (1 – text {Tax Rate}) & textbf {where:} & text {RR} = text { Annual rate of return} end {aligned}

CNAR=RRÃ—(1Tax rate)or:RR=Annual rate of return

## How to calculate the annual compound net rate – CNAR

The compound annual net rate is calculated as the annual rate of return multiplied by 1 minus the tax rate.

## What does the CNAR tell you?

The Compound Annual Net Rate (CNAR) measures the return an investor earns over the course of a year for an investment after deducting taxes. Of course, this calculation only applies to taxable investments. Comparing the after-tax and pre-tax rate of return can help an investor assess the effect of tax liability on their investment.

The calculated effect of taxation on returns can be used for tax planning and long-term financial planning purposes. The majority of investments have tax implications, but the returns posted by banks and financial institutions only show pre-tax returns.

Key points to remember

• The return on an investment after taking into account taxes, such as capital gains, dividends and interest.
• Similar to the compound annual growth rate, but will generally always be lower given the tax implications.
• CNAR and CAGR will be the same when considering a tax-free investment, such as municipal bonds.

## Example of use of the annual net compound rate – CNAR

Let’s say an investor has held Microsoft stock (NASDAQ: MSFT) for the whole of 2018 and has a 20% tax rate. Their annual return on the market position would have been 18.7% for 2018. Including taxes, the compound annual net rate is 15%, or 18.7% times (1 – 20%).

## The difference between CNAR and compound annual growth rate – CAGR

The compound annual net rate pushes the CAGR one step further when factoring in taxes. If looking at a multi-year holding period for an investment, an investor will use the compound annual growth rate to determine the annual rate of return and then adjust it so that taxes flow to CNAR. CNAR and CAGR will be the same if the investment is tax exempt, as with municipal bonds.

## Limits on the use of the annual net compound rate – CNAR

The exact tax rate or implications may not always be known, or the rates may vary depending on the tax year, as is the case with tax reform. Calculating the CNAR using the wrong tax rate can have a significant impact on the final return. There are a variety of taxes to consider and need to be factored in, such as taxes on capital gains, dividends, and interest.