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

What Is Pro Rata?

Pro rata is a Latin term used to describe a proportionate allocation. It translates to "in proportion." It's a process in which an allocated asset will be 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 can be used to determine the appropriate portions of any given whole but it's often used in business finance.

Key Takeaways

It typically means that everyone gets their fair share if something is given out pro rata.
Pro rata means proportionally, such as dividends awarded to investors based on their proportion of investment.
The concept of pro rata is rooted in fractions because proration attempts to make two fractions equal to each other but with different denominators.
The practice of prorating can apply from billing for services to 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.

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 payments. These are cash payments by corporations made to shareholders.

Pro rata in the insurance industry is used to determine the amount of premium 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 via pro rata.

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) 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:

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

Pro Rata Share = (Number of "True" Items / Maximum Quantity Possible)

Pro Rata Distribution = Pro Rata Share * Quantity of Related Item

Imagine an employee is set to receive a $10,000 bonus this year. They'll receive a pro rata share of the bonus if they leave at any point. The employee leaves on March 20th. 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 pro rate is the annual bonus in this case.

Pro rata distribution = 21.64% * $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 of the year.

Pro rata can be communicated as a percent such as the shareholder owns 10% of the company's stock, or as a quantity such as the shareholder owns 100,000 of the company's 1 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 proportionally share four pieces of pizza. 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 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 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.

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 policy term. Most insurance policies are based on a 12-month period so the insurance company must prorate the annual premium to determine what's 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 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.

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 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 Sept. 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 Does Pro Rata Mean?

Pro rata is a defined portion relative to the entirety of an item. Someone can get a pro rata share or a proportional offering based on how much they are entitled to instead of receiving all the items. You may expect a pro rata share of 10% of the building's rental income if you own 10% of a building.

What Is the Difference Between Prorated and Pro Rata?

Pro rata and prorated are used interchangeably to define the same thing. Both signify that a specific section of any given whole unit has a defined allocation for an underlying reason.

How Do I Calculate Pro Rata?

Calculating the pro rata of items varies because it calculates a proportion of a given whole. Consider a company that charges 20% interest per year. The prorated interest rate would be calculated as (20% / 12) x 6 = 10% if you calculated it over six months.

How Does Pro Rata Apply to Dividends Per Share?

It's typically executed on a pro rata basis when a company distributes dividends. Consider a majority shareholder such as a founder or key executive who owns 50% of a company's total 1,000 shares. The company is issuing a $1 dividend. The majority shareholder would receive $500 in value of the $1,000 in dividends. The formula would be as follows: (50 / 100) x $1,000 = $500.

What Is a Pro Rata Discount?

A pro rata discount is a type of discount a merchant offers a customer. Companies offer customers discounts for a variety of reasons. They might offer one as an incentive to a new customer to try a product or service. They might offer a discount if the customer makes a purchase during a specific time or as a bonus to a returning customer.

The pro rata part of the discount varies depending on how the merchant has structured their offer. A merchant might offer a new customer $20 off their first purchase of products if they spend $100 or more. Each item would receive a $5 discount if the customer buys four products.

A pro rata discount could also apply if a customer joins a monthly subscription service 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 charging the full subscription price for the month.

The Bottom Line

Pro rata translates to “in proportion” in Latin. Each entity or individual is entitled to a share of a 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 dividends paid.