Pro Rata (Proportionate Allocation)

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.

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. Pro rata is also used to determine the amount of premium due for an insurance 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 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.

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 30th. The bond has a face value of $1,000 and a 5% coupon rate, which pays semi-annually on March 1st and September 1st. The buyer of the bond will pay the seller:

$ 1 , 000 × 5 % 2 × 120 180 = $ 16.67 \begin{aligned} &\$1,000 \times \frac{ 5\% }{ 2 } \times \frac{ 120 }{ 180 } = \$16.67 \end{aligned} $1,000×25%×180120=$16.67

What Is Pro Rata?

In business financing, pro rata refers to conducting a payment on a proportional basis. For instance, in a partial insurance policy, the insurance company may calculate the premium pro rata, or proportional to the shorter term. If the annual term was $100 for instance, the pro rata premium for 120 days would cost roughly a third of this total. Along with insurance premiums, pro rata is used in dividend payouts, interest payments, or income allocation. 

How Does Pro Rata Work?

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 the following company with a 20% interest in a 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, that 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: (500 /1,000) x $1 = $500.