By definition, a partnership is a business with more than one owner. Literally, it is an association of two or more persons who put their money together in order to carry on a certain business. There are two types of partnerships by definition; namely Simple Partnership and Compound Partnership
In Simple Partnerships, the capitals of the persons involved are invested for the same period of time. On the other hand, in Compound Partnerships, the capitals of the partners are invested for different lengths of time, thus, Compound. In this article, we will be looking into the math involved in both Simple and Compound Partnerships and we will be seeing some mathematical examples.
Before we look into the math and examples, how is the partnership entity run? Well In general partnerships, every owner has control over the business. This also means that partners can be held personally liable for business debts and obligations. If a partnership cannot pay a debt, the creditor can obtain a judgment against any partner. If a partner signs a contract that the business cannot honor, the creditor can take action to seize that partner’s personal assets, such as their land, home, or car. Whatever risks are involved, partnership is the simplest and least expensive co-owned business structure to create and maintain.
Now that we have a basic concept about partnerships, let’s look into the math side:
1) If three partners X,Y & Z invest $1000, $1500 and $1800 respectively in a business, how would they share a profit of $2012?
To solve this kind of problem, we look into the time involved. Did the partners invest the money at the same time? Yes. Then the solution is simple as follows:
>> The profit is divided in the ratios of the capitals of X, Y & Z as $1000 : $1500 : $1800 or 10:15:18 by dropping the last two zeros of each amount.
>> Now we add the numbers as 10+15+18 = 43
>> Now X’s share will be (10/43)*2012 (total profit) = $467.907
>> Y’s share will be (15/43)*2012 = $701.860 and lastly
>> Z’s share will be (18/43) *2012 = $842.232
To see if our work is correct we have to add each partner’s profit share and get the total profit. In our case $467.907 + $701.860 + $842.232 = $2011.999
When a group of persons (say n number of persons) invested different amounts for different periods of time, then their profit ratio is as follows:
AT1 : BT2 : CT3 : ………. : XTn
Here the first person invested amount $A at period T1, second person invest amount $B at period T2, third person invested amount C at period T3 …… and so on. We will use this formula to solve our following problem (2).
2) X, Y and Z inter into partnership. X advances $1000 for 4 months, B advances $1500 for 8 months and Z advances $1800 for 10 months. If they gain a total profit of $2500 how would they share?
>> Here we have different times of period involved. Thus
>> Person X, in 4 months can earn as much profit as $1000*4 (or $4000 in one month)
>> person Y, in 8 months can earn as much profit as $1500*8 (or $12000 in one month) and
>> Person Z, in 10 months can earn as much profit as $1800*10 (or $18000 in one month)
Therefore, the profit should be divided in the ratio of 4000:12000:18000 or 4:12:18.
>> Now adding the ratios we get 4+12+18 = 34, so their shares will be as follows:
i) X’s share = (4/34)*2500 (total profit) = $ 294.118
ii) Y’s share = (12/34)*2500 = $ 882.353 and
iii) Z’s share = (18/34)*2500 = $ 1323.529
>> if we add up all the share each person got we get the $2499.9 which is approximately $2500
If you have these tips in hand, you can start partnership or inter partnership into someone. This writing is only intended to help the reader understand the maths involved in business partnerships.