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Term: Pro-Rata

18 Oct 2017

### What is ‘Pro-Rata’

Pro rata is the term used to describe a proportionate allocation. It is a method of assigning an amount to a fraction according to its share of the whole. While a pro rata calculation can be used to determine the appropriate portions of any given whole, it is most commonly used in business finance.

### BREAKING DOWN ‘Pro-Rata’

Some of the most common uses for pro rata calculations are to determine dividend payments due to shareholders, to determine the amount of premium due for an insurance policy that only covered a partial term, or to allocate the appropriate portion of an annual interest rate to a shorter time frame.

### Dividends

When a company pays dividends to its shareholders, each investor is paid according to his holding. 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 holding 50, 25, 15 and 10 shares. The amount due to each shareholder is his pro rata share. This is calculated by simply 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 he owns half the shares and receives half the total dividends. The remaining shareholders get \$50, \$30 and \$20 respectively.

Another common use is to determine the amount due for a partial insurance policy term. Most insurance policies are based on a full 12-month year, so if a policy is needed for a shorter term, the insurance company must pro rate the annual premium to determine what is owed. To do this, simply 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.

### 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, he is 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: face value of bond x coupon rate x factor. 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 his 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 will of the bond will pay the seller \$1,000 x (5%/2) x (120/180) = \$16.67.