# Pro Rata: What It Means and Formula to Calculate It

> **Definition**
>
> Pro rata is a term that describes the distribution or allocation of assets in equal portions.

## What Is Pro Rata?

Pro rata is a Latin term that translates to "in proportion." Put simply, it is used to describe a proportionate allocation. It's a process in which an allocated asset is distributed in equal portions. An amount is assigned to one person according to their share of the whole if something is distributed to several people on a pro rata basis. A pro rata calculation is often used in business finance but can also determine the appropriate portions of any given whole.

### Key Takeaways

*   Pro rata typically means that everyone gets their fair share.
*   It means proportionally, such as dividends awarded to investors based on their investment.
*   The concept of pro rata is rooted in fractions because proration attempts to make two fractions equal, but with different denominators.
*   The practice of prorating can be applied to billing for services, paying out dividends, or allocating business partnership income.
*   Pro rata is calculated by dividing the instance of an item by the maximum quantity of that item. This ratio can then be applied to any related item to find the same proportion.

![Pro Rata](https://www.investopedia.com/thmb/ja2BZnb8e9zu-xSWAxTOj3JZL3M=/1500x0/filters:no_upscale():max_bytes(150000):strip_icc()/Pro-Rata-V2-969fcfa3cc5d4b8786806892e7d71f5f.jpg)

*— Investopedia / Matthew Collins*

## Understanding Pro Rata

Pro rata typically means that each party or person receives their fair share in proportion to the whole. Pro rata calculations can be used in many areas, including determining [dividend](https://www.investopedia.com/terms/d/dividend.asp) payments. These are cash payments by corporations made to shareholders.

Pro rata in the insurance industry is used to determine the amount of [premium](https://www.investopedia.com/terms/i/insurance-premium.asp) due for a policy that only covers a partial term. Allocating the appropriate portion of an annual interest rate to a shorter time frame can also be done on a pro rata basis.

Pro rata is also used to determine how much of a distribution from a qualified retirement account, such as an IRA, SEP, or [401(k)](https://www.investopedia.com/terms/1/401kplan.asp), is taxable when the account contains before and after-tax dollars. An account holder might have a 401(k) funded with 20% pre-tax dollars and 80% post-tax dollars. Withdrawals will consist of 20% taxable and 80% non-taxable money as a result.

## How to Calculate Pro Rata

Pro rata is calculated based on three factors:

1.  The number of items true, owned, or having been incurred.
2.  The total quantity of that item or the maximum quantity possible.
3.  The assigned quantity of a related item in the second factor above.

> Pro Rata Share = Number of "True" Items ÷ Maximum Quantity Possible

> Pro Rata Distribution = Pro Rata Share x Quantity of Related Item

Imagine an employee is set to receive a $10,000 [bonus](https://www.investopedia.com/terms/b/bonus.asp) this year. They'll receive a pro rata share of the bonus if they leave at any point. The employee leaves on March 20. The agreement awards the bonus based on the number of days worked, inclusive of the last day.

Divide the number of true items by the maximum quantity possible to calculate the pro rata share. The number of true items is the number of days worked. There are 79 days inclusive between January 1 and March 20, assuming it's not a leap year. The maximum number of days possible is 365.

> Pro rata share = 79 ÷ 365 = 21.64%

Multiply the pro rata share by the related item to calculate the pro rata portion. The item we want to prorate is the annual bonus, in this case.

> Pro rata distribution = 21.64% x $10,000 = $2,164

The employee will therefore receive a pro rata distribution of $2,164 by leaving on March 20, based on the prorated number of days worked for the year.  

> **Fast Fact**
>
> Pro rata can be communicated as a percentage, such as a shareholder who owns a 10% share of the company's stock. It can also be expressed as a quantity, such as the shareholder who owns 100,000 of the company's one million shares.

## Why Pro Rata Works

The mathematical concept of pro rata works because the proportion of one good is imposed on another. Pro rata entails taking a fraction of one item and conveying the same fraction on another base.

The root of pro rata is grounded in proportionally equal fractions with different denominators. The 79/365 fraction in our example is equal to the 2,164/10,000 fraction, ignoring rounding variances. Pro rata is, therefore, simply taking one fraction and finding its equal given a specific denominator. Pro rata attempts to solve for the numerator to make two fractions equal, given specific criteria.

Consider another example where you and a friend want to share four pieces of pizza proportionally. Each of you would receive 50% of the pizza if the slices were shared equally. This pro rata example is trying to determine which fraction with a denominator of four is equal to 1/2. Each of you gets two slices because 2/4 = 1/2.

## Examples of Pro Rata

### Pro Rata and Dividends Per Shareholder

Each investor is paid according to their holdings when a company pays dividends to its shareholders. The total amount of dividends paid would be $200 if a company has 100 [shares outstanding](https://www.investopedia.com/terms/o/outstandingshares.asp) and issues a dividend of $2 per share. The total dividend payments can't exceed this limit, no matter how many shareholders there are. The pro rata calculation must be used to determine the appropriate portion of that $200 whole due to each shareholder.

Assume there are only four shareholders. They hold 50, 25, 15, and 10 shares, respectively. The amount due to each shareholder is their pro rata share. This is calculated by dividing the ownership of each person by the total number of shares and then multiplying the resulting fraction by the total amount of the dividend payment.

The [majority shareholder's](https://www.investopedia.com/terms/p/principal-shareholder.asp) portion is therefore (50 ÷ 100) x $200 = $100. This makes sense because the shareholder owns half the shares and receives half the total dividends. The remaining shareholders get $50, $30, and $20, respectively.

> **Important**
>
> Be mindful of situations where weight isn't given to individuals. Every American citizen eligible to vote can cast a tally equal to every other citizen, regardless of their age, income, or any other factor. The pro rata value of the vote is equal to one divided by the total population that votes in this example.

### Pro Rata for Insurance Premiums

Another common use is to determine the amount due for a partial [insurance](https://www.investopedia.com/terms/i/insurance.asp) policy term. Most insurance policies are based on a 12-month term, so the insurance company must prorate the annual premium to determine the amount owed if a policy is needed for a shorter term. Divide the total premium by the number of days in a standard term and multiply by the number of days covered by the truncated policy to do this.

Assume an auto policy that typically covers a full year carries a premium of $1,000. The company must reduce the premium accordingly if the insured only requires the policy for 270 days. The pro rata premium due for this period is ($1,000 ÷ 365) x 270 = $739.73.

### Pro Rata for Interest Rates

Pro rata calculations are also used to determine the amount of interest that will be earned on an investment. The pro rata amount earned for a shorter period is calculated by dividing the total amount of interest by the number of months in a year and multiplying by the number of months in the truncated period if an investment earns an annual interest rate. The amount of interest earned in two months on an investment that yields 10% interest each year is (10% ÷ 12) x 2 = 1.67%.

Payment on [accrued interest](https://www.investopedia.com/terms/a/accruedinterest.asp) on bonds is calculated on a pro rata basis. Accrued interest is the total interest that has accumulated on a bond since its last coupon payment. The bondholder is still entitled to the interest that accrues up until the time the bond is sold if they sell the bond before the next coupon date. The bond buyer, not the issuer, is responsible for paying the bond seller the accrued interest, which is added to the market price of the bond.

The formula for accrued interest is as follows:

$\begin{aligned} &\text{AI} = \text{Face Value of Bond} \times \text{Coupon Rate} \times \text{Time Factor} \\ &\textbf{where:} \\ &\text{AI} = \text{Accrued Interest} \\ &\text{Coupon Rate} = \frac{ \text{Annual Coupon Rate} }{ \text{Number of Periods Per Year} } \\ &\text{Time Factor} = \frac{ \text{Days Lapsed Since Last Payment} }{ \text{Days in Payment Period} } \\ \end{aligned}$

The factor is calculated by dividing the length of time the bond was held after the last coupon payment by the time from one coupon payment to the next.

Consider a [bondholder](https://www.investopedia.com/terms/b/bondholder.asp) who sells their corporate bond on June 30. The bond has a face value of $1,000 and a 5% coupon rate that pays semiannually on March 1 and September 1. The buyer of the bond will pay the seller:

$\begin{aligned}&\$1,000 \times \frac { 5\% } { 2 } \times \frac { 122 }{ 184 } = \$16.58 \\\end{aligned}$

## What Is a Pro Rata Discount?

A pro rata discount is offered by a merchant to its customer. Companies offer [discounts](https://www.investopedia.com/terms/d/discount.asp) to attract new customers or to retain existing ones. The pro rata part of the discount depends on how the merchant structures the offer. For instance, a merchant may offer a new customer $20 off their first purchase if they spend $100 or more, which translates to a $5 discount if the customer buys four products.

A pro rata discount could also apply if a customer joins a monthly [subscription service](https://www.investopedia.com/ask/answers/042715/how-do-subscription-business-models-work.asp) on any day other than the first of the month. The merchant would apply a pro rata discount and only charge the customer for the number of days in the month they had the service, rather than the full subscription price for the month.

## Do Pro Rata and Prorated Mean the Same Thing?

Yes, pro rata and prorated mean the same thing. Both terms, which are often used interchangeably, indicate that a specific section of any given whole unit has a defined allocation for an underlying reason. Put simply, they mean to distribute something proportionally. For instance, a tenant's rent may be prorated if they move into their apartment in the middle of the month rather than on the first day.

## What Is a Pro-Rata Tranche?

A pro-rata tranche is part of a syndicated loan. There are two features to this product: revolving credit and an amortizing term loan. The revolving credit line matures on the same date as the term loan. This type of loan is found in the leveraged loan market and is commonly held by companies with high amounts of debt. Because it is a syndicated loan, the debt is spread out among lenders, which reduces the risk to each one involved.

## The Bottom Line

Pro rata translates to “in proportion” in Latin. Each entity or individual is entitled to a share of the whole that’s equal to their ownership percentage. It’s a common concept in business finance and investing. Dividends are awarded to investors based on the proportion of their investment to the whole.

A shareholder who owns 100,000 of a company’s 1 million outstanding shares owns 10% of the company’s outstanding stock and is therefore entitled to a pro rata portion commensurate with 10% of the dividends paid.

> **Article Sources**
>
> 1.  Internal Revenue Service. "[Rollovers of After-Tax Contributions in Retirement Plans](https://www.irs.gov/retirement-plans/rollovers-of-after-tax-contributions-in-retirement-plans)."