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

Pro Rata

Investopedia / Matthew Collins

What Is Pro Rata?

Pro rata is a Latin term used to describe a proportionate allocation. It essentially translates to "in proportion," which means a process where whatever is being allocated will be distributed in equal portions.

If something is given out to people on a pro rata basis, it means assigning an amount to one person according to their share of the whole. While a pro rata calculation can be used to determine the appropriate portions of any given whole, it is often used in business finance.

Key Takeaways

  • If something is given out pro rata, it typically means everyone gets their fair share.
  • 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, as proration attempts to make two fractions equal to each other but with different denominators.
  • The practice of prorating can apply in many areas, 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.
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Pro-Rata

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, which are cash payments by corporations paid to shareholders.

In insurance, pro rata 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. For example, an account holder has a 401(k) funded with 20% pre-tax dollars and 80% post-tax dollars. As a result, withdrawals will consist of 20% taxable and 80% non-taxable money.

How to Calculate Pro Rata

Pro rata is calculated based on three items:

  1. The number of items true, owned, or having been incurred.
  2. The total quantity of that item (i.e. maximum quantity possible).
  3. The quantity of a related item that will be assigned in the second bullet above.

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

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

For example, imagine an employee set to receive a $10,000 bonus this year. If the employee leaves at any point, they will receive a pro rata share of the bonus. The employee leaves on March 20th. The agreement awards the bonus based on the number of days worked (inclusive of the last day).

To calculate the pro rata share, divide the number of true items by the maximum quantity possible. In this example, the number of true items is the number of days worked. Assuming a non-leap year, there are 79 days (inclusive) between January 1 and March 20. In addition, the maximum number of days possible is 365.

Pro rata share = 79 / 365 = 21.64%

To calculate the pro rata distribution, multiply the pro rata share by the related item. In this example, the item we want to pro rate is the annual bonus.

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

Therefore, in this example, by leaving on March 20th, the employee will receive a pro rata distribution of $2,164 based on the prorated number of days worked of the year.

Pro rata can be communicated as a percent (i.e. the shareholder owns 10% of the company's stock) or as a quantity (i.e. the shareholder owns 100,000 of the company's 1 million shares of stock.

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. In the example of above, the fraction 79/365 is equal to the fraction 2,164/10,000 (ignoring rounding variances). Therefore, pro rata is simply taking one fraction and finding its equal given a specific denominator. Stated another way, 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. If the slices are to shared equally, each of you would receive 50% of the pizza. Therefore, this pro rata example is trying to determine which fraction with a denominator of 4 is equal to 1/2. Since 2/4 = 1/2, each of you get two slices.

Examples of Pro Rata

Pro Rata and Dividends per Shareholder

When a company pays dividends to its shareholders, each investor is paid according to its holdings. If a company has 100 shares outstanding, for example, and issues a dividend of $2 per share, the total amount of dividends paid will be $200. No matter how many shareholders there are, the total dividend payments cannot exceed this limit. In this case, $200 is the whole, and the pro rata calculation must be used to determine the appropriate portion of that whole due to each shareholder.

Assume there are only four shareholders who 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, therefore, is (50 / 100) x $200 = $100. This makes sense because the shareholder owns half of the shares and receives half of the total dividends. The remaining shareholders get $50, $30, and $20, respectively.

Be mindful of situations where weight is not given to different individuals. For example, regardless of age, income, or any other factor, every American citizen eligible to vote can cast a tally equal to every other citizen. In this example, the pro rata value of the vote is equal to 1 divided by the total population that votes.

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 if a policy is needed for a shorter term, the insurance company must prorate the annual premium to determine what is owed. To do this, 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.

For example, assume an auto policy that typically covers a full year carries a premium of $1,000. If the insured only requires the policy for 270 days, then the company must reduce the premium accordingly. 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. If an investment earns an annual interest rate, then 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. The amount of interest earned in two months on an investment that yields 10% interest each year is (10% / 12) x 2 = 1.67%.

When it comes to bonds, payment on accrued interest is calculated on a pro rata basis. Accrued interest is the total interest that has accumulated on a bond since its last coupon payment. When the bondholder sells the bond before the next coupon date, they're still entitled to the interest that accrues up until the time the bond is sold. 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:

AI = Face Value of Bond × Coupon Rate × Time Factor where: AI = Accrued Interest Coupon Rate = Annual Coupon Rate Number of Periods Per Year Time Factor = Days Lapsed Since Last Payment Days in Payment Period \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} AI=Face Value of Bond×Coupon Rate×Time Factorwhere:AI=Accrued InterestCoupon Rate=Number of Periods Per YearAnnual Coupon RateTime Factor=Days in Payment PeriodDays Lapsed Since Last Payment

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.

For example, 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, which pays semiannually on March 1 and Sept. 1. The buyer of the bond will pay the seller:

$ 1 , 000 × 5 % 2 × 122 184 = $ 16.58 \begin{aligned}&\$1,000 \times \frac { 5\% } { 2 } \times \frac { 122 }{ 184 } = \$16.58 \\\end{aligned} $1,000×25%×184122=$16.58

What Does Pro Rata Mean?

Pro rata is a defined portion in relation to the entirety of an item. Instead of getting all of the items, someone can get a pro rata share, a proportional offering based on how much they are entitled to. For example, if I own 10% of a building, I may expect a pro rata share of 10% of the building's rental income.

What Is the Difference Between Prorated and Pro Rata?

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

How Do I Calculate Pro Rata?

Naturally, calculating the pro rata of different items varies since it calculates a proportion of a given whole. To calculate the prorated interest rate over six months, for instance, consider a company that charges 20% interest per year. Here, the prorated interest rate would be calculated as (20% / 12) x 6 = 10%. 

How Does Pro Rata Apply to Dividends Per Share?

When a company distributes dividends, typically it is executed on a pro rata basis. For example, consider a majority shareholder, such as a founder or key executive, who owns 50% of a company's total 1,000 shares and the company is issuing a $1 dividend. Of the $1,000 in dividends, the majority shareholder would receive $500 in value. 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 may offer a discount as an incentive to a new customer to try a product or service. They may offer a discount if the customer makes a purchase during a specific time period 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. For example, a merchant may offer a new customer $20 off their first purchase of products if they spend $100 or more. If the customer buys four products, each item would receive a $5 discount.

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. Rather than charging the customer the full subscription price for the month, the merchant would apply a pro rata discount and only charge the customer for the number of days in the month they actually had the service.

Article Sources
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  1. Internal Revenue Service. "Rollovers of After-Tax Contributions in Retirement Plans."