# Profit Sharing Ratio

By profit sharing ratio in a partnership firm, we mean the ratio in which the profits and losses of the firm are to be distributed amongst the partners.

The basis for arriving at the ratio is the agreement between the partners. If there is a partnership deed, the ratio should be ascertained from the provisions in the partnership deed. In the absence of a partnership deed and where there is no indication as to the agreement between the partners in this aspect, it should be considered as equal share for all partners.

The ratio may be specified in terms of absolute values or it may be expressed as the ratio of their Capital account balances or it may be based on anything else as agreed upon by the partners. Deriving this ratio (if it is not given) would be one important requirement in problem solving.

# Different Ratios for Profit Sharing and Loss Sharing

If the partners so agree, the Profit Sharing Ratio and the Loss Sharing Ratio may be different. There may be a partner who has a share in profits only but not a partner who has a share in losses only.

# Expressing the Profit Sharing Ratio

The profit sharing ratio may be expressed in a number of different forms. Whatever may be the form in which the ratio is expressed it can always be converted to a form convenient to us for being used in problem solving.

# Simple Ratio [Natural Numbers represent shares]

May, Day and Way are partners sharing profits in the in the ratio 1 : 3 : 4.

Rewriting the ratio as below would aid your calculations

 May : Day : Way = 1 : 3 : 4 = =

Expressing the shares as ratios with a common denominator would be useful in calculations.

# Simple Ratio [Fractions represent shares]

Where the shares are represented by fractional numbers, one should always check to see if the sum of the fractional parts representing shares add up to 1.

# Like Fractions representing shares

Fractions with the same denominator are like fractions.

Ramu, Damu and Mamu share profits in the ratio $\frac{2}{9}:\frac{3}{9}:\frac{4}{9}$

## verification

Sum of like fractions =
 Sum of numerators common denominator

Common denominator is 9.

 $\frac{2}{9}+\frac{3}{9}+\frac{4}{9}$ = $\frac{2+3+4}{9}$ = $\frac{9}{9}$ = 1

# Unlike Fractions represent shares

Fractions with different denominators are unlike fractions

Goon, Doon and Moon share profits in the ratio $\frac{1}{2}:\frac{1}{3}:\frac{1}{4}$

## verification

Sum of unlike fractions =
 Sum of (Product of the fraction and LCM of the denominators) Common denominator

LCM of denominators i.e. 2, 3, 4 is 12.

 $\frac{1}{2}+\frac{1}{3}+\frac{1}{4}$ = $\frac{\left(\frac{1}{2}×12\right)+\left(\frac{1}{3}×12\right)+\left(\frac{1}{4}×12\right)}{12}$ = $\frac{13}{12}$ ≠ 1

## Remedy

If you find that the fractions representing shares of partners are not adding up to 1, you have to derive the actual ratio using the given fractions.

Multiply each fraction with the LCM of the denominators to obtain a ratio in natural numbers which when expressed as fractions would add up to 1.

### Principle

Multiplying all the terms of the ratio with the same number will not change the ratio.
 Goon : Doon : Moon = $\frac{1}{2}:\frac{1}{3}:\frac{1}{4}$ = $\frac{1}{2}×12:\frac{1}{3}×12:\frac{1}{4}×12$ = $6:4:3$ = $\frac{6}{13}:\frac{4}{13}:\frac{3}{13}〈6+4+3=13〉$

This represents the ratio of profit sharing between partners and is in a form suitable for calculations.

# Trivia

A father left his property to be shared by his three sons as follows : $\frac{1}{2}$ to the youngest, ${\frac{1}{3}}^{rd}$ to the middle and ${\frac{1}{6}}^{th}$ to the eldest son. They were struck up with the problem of sharing the 17 horses in their stable. They approached their fathers best friend and asked him to help them out. He thought about it and asked them to take one of his horses, include it in the horses to be shared and then share the horses (along with the one he gave). The sons did so and finally were left with 1 horse which they returned to its rightful owner. How did this happen?

# Interest on Capital

Interest on Capital is to be paid
• # Only when agreed upon

Interest on Capital is to be paid to partners only if it is specifically agreed upon. If there is no mention regarding this, in the partnership agreement (deed), then no interest need be paid.
• # Only out of profits

Interest is to be paid only out of profits. Where there is a loss, no interest should be paid on capital, even if the partnership agreement provides for the same.
• # @ 6% if rate is not mentioned

Where the partnership deed provides for payment of interest on capital and it does not mention the rate of interest to be paid, it is a convention to pay interest @ 6% p.a.

# On What Balance is Interest calculated

Interest is paid on capital for the reason that it has been used for the purpose of the partnership business.

The balance in Capital account unless where it is maintained under Fixed Capital Method, keeps fluctuating on account of a number of reasons, thus making it difficult to assess the amount of capital employed in the business. There would be a change on account of appropriations made at the end of the accounting period like salary to partners, commission to partners, etc. Even during the course of the accounting period, the balances may change on account of additional capital introduced, capital withdrawn, etc.,

In the absence of appropriate information, it is a convention that interest is paid on the opening balances in Capital Accounts on the assumption that it has been employed for the full length of the accounting period and all other changes to the capital account have been done towards the end of the accounting period.

In problem solving we will come across these situations.

• ## Opening Balance known

Where Capital a/c balances at the beginning of the accounting period are known and there is no change in the balance through out the period, interest is calculated on the opening balance.
• ## Closing Balance and Appropriations at the end known

Where Capital a/c balances at the end are known and the changes at the end of the accounting period that have affected the account are also known, the opening balance in capital accounts is ascertained using the information relating to the changes and interest is calculated thereon.
• ## Closing balance and all transactions known

Where the Capital a/c balances at the end are known and the changes over the accounting period as well as those at the end of the accounting period are known, the capital account balances at various points of time (when changes take place) and the period for which the capital has been utilised is ascertained and interest is calculated thereon.
• ## Closing balance known

Where the Capital a/c balances at the end are known and no other information is available, or where the information relating to transactions affecting the capital account are known without the information relating to the date/period of occurrence, we calculate the interest based on the closing balance.

# Interest on Drawings

Interest on Drawings is to be charged
• # Only when agreed upon

Interest on Drawings is to be charged to partners only if it is specifically agreed upon. If there is no mention in the partnership agreement regarding this, no interest need be charged.
• # @ 6% if rate is not mentioned

Where the partnership deed provides for charging interest on drawings and it does not mention the rate of interest to be charged, it is a convention to charge interest @ 6% p.a.

# Calculating Interest on Drawings

Interest is charged on drawings for the reason that the amount has been withdrawn by the partners without allowing it for being used for the purpose of the business.

In the absence of appropriate information, it is a convention that the interest on drawings is calculated on the "Drawings a/c" balance at the end.

In problem solving we will come across these variations.

• ## Closing Balance known

Where the Drawings a/c balances at the end of the accounting period are known and there is no information relating to the time of drawing, interest is calculated on the closing balance.
• ## Amount and dates of Drawings are known

Where drawings made during the period and the dates on which the drawings have been made are known, interest is calculated based on the amount drawn and the period of use, since the period for which the withdrawn amounts are used can be ascertained.
• ## Drawings made at regular intervals

Where the Drawings are made at regular intervals, all the drawings are converted to an equivalent of drawings for a specified period and interest is calculated thereon.

The information available is the same as the information available in the case of amount and dates of drawing known. However, since the drawings are made at regular intervals, converting them to an equivalent amount would make it easier to calculate interest.

# Salary to Partners

Salary is to be paid to partners only if it is specifically agreed upon.

If there is no mention in the partnership agreement then no salary need be paid.

# Commission to Partners

Commission is to be paid to partners only if it is specifically agreed upon.

If there is no mention in the partnership agreement then no commission need be paid.

# Expressing Commission

Commission payable to partners may be expressed in a number of different ways. It may be
• Specified amount
• Per unit of sales relatable to the partner
• Per days of activity of the partner
• As a % of Sales, NetProfit, Purchases or any other value.
What method is employed for expressing and calculating commission is dependent on the reason for which the commission is being offered and the agreement between the partners.

There are two ways commission as a % of a value can be expressed. How it is expressed decides how the commission is calculated mathematically.

Consider Commission being calculated as a % of Net Profit as an example.

• # Before charging such commission

Where there is no specific mention we assume that the commission is being expressed as a % of value before charging such commission. Calculation is straight forward.

Commission = Value × % of Commission.

Eg : Net Profit is 1,25,000 and commission is 8% of net profits.

 Commission = 8% of Net Profit = Net profit before charging such commission × 8% = 1,25,000 × 8% = 10,000
• # After charging such commission

Under this method, commission is expressed as a % of value after charging such commission.

The commission should work out to 8% of the value remaining after charging or deducting commission.

# Formula

Let
• V = Value before charging such commission
• C = Commission
• R = Rate of Commission (in %)
Commission
= Value after charging such commission × Rate of Commission
= (Value before charging such commission − Commission) × Rate of Commission

⇒ 100C = VR − CR
⇒ 100C + CR = VR
⇒ C(100 + R) = VR
$⇒C=V×\frac{R}{\left(100+R\right)}$

Eg : Net Profit is 1,25,000 and commission is 8% of net profits after charging such commission.

 Commission = 8% of Net Profit after charging such commission = Net profit after charging such commission × 8% = Net profit before charging such commission × $\frac{8}{\left(100+8\right)}$ = $1,25,000×\frac{8}{108}$ = 9,259.26

## Verify

Net Profit after charging such commission
= Net profit before charging such commission − Commission
= 1,25,000 − 9,259.26
= 1,15,740.74

Commission
= Net profit after charging such commission × 8%
= 1,15,740.74 × 8%
= 9,259.26