Admitting a New Partner

Imagine you and a friend have spent the last five years building a highly successful bakery. You’ve worked late nights, built a loyal customer base, and finally started making serious profits. Now, you want to expand and open a second branch, but you need more capital and an extra pair of hands. You decide to bring in a third friend as a new partner.

When this new person walks through the door, they aren't just bringing cash. They are stepping into a business that is already successful—a success you built. Because of this, you can't just add their name to the deed and carry on. The old partnership agreement legally ends, and a new one begins.

In the previous chapter, we learned how to revalue assets and liabilities so the old partners get the benefit of the property's appreciation before the new partner joins. Now, we are going to look at the entire accounting process of admitting that new partner.

There is a strict, logical sequence to follow when a new partner is admitted. If you understand the why behind each step, you will never need to memorize the journal entries.

Let’s walk through these steps one by one.

Step 1: Calculating the Ratios

The moment a new partner joins, the profit pie has to be sliced into more pieces. If the new partner gets a slice, the old partners must give up a portion of theirs. This brings us to two crucial calculations: the New Profit-Sharing Ratio and the Sacrificing Ratio.

The exam loves to test your ability to calculate these ratios under different scenarios. Let's look at the three most common cases.

Case 1: Only the new partner's share is given

This is the simplest and most common scenario. The problem tells you the old ratio and the new partner's share, but says nothing about how the new partner acquired it.

The Rule: We assume the old partners sacrifice their shares in their old profit-sharing ratio.

Worked Example: A and B are partners sharing profits in the ratio of 3:2. They admit C for a 1/5th share in the profits. Calculate the new ratio and sacrificing ratio.

1. 1Let the total profit of the firm be 1.
2. 2C's share = 1/5.
3. 3Remaining profit for A and B = 1 - 1/5 = 4/5.
4. 4A and B will share this remaining 4/5th in their old ratio (3:2).
5. 5A's new share = 3/5 of 4/5 = 12/25.
6. 6B's new share = 2/5 of 4/5 = 8/25.
7. 7C's share = 1/5, which we multiply by 5/5 to get a common denominator = 5/25.
8. 8New Ratio: 12:8:5.
9. 9Sacrificing Ratio: Since nothing else was stated, it remains their old ratio: 3:2. (You can verify this using Old - New: A's sacrifice is 3/5 - 12/25 = 3/25. B's is 2/5 - 8/25 = 2/25. Ratio is 3:2).

Case 2: The new partner acquires their share in a specific ratio

Here, the new partner dictates exactly how much they are taking from each old partner.

Worked Example: X and Y share profits at 5:3. Z joins for a 1/4th share, which he acquires equally from X and Y.

1. 1Z's total share = 1/4.
2. 2Z takes half of this from X: 1/4 × 1/2 = 1/8. (This is X's actual sacrifice).
3. 3Z takes half of this from Y: 1/4 × 1/2 = 1/8. (This is Y's actual sacrifice).
4. 4X's new share = Old Share - Sacrifice = 5/8 - 1/8 = 4/8.
5. 5Y's new share = Old Share - Sacrifice = 3/8 - 1/8 = 2/8.
6. 6Z's share = 1/4, which is 2/8.
7. 7New Ratio: 4:2:2, which simplifies to 2:1:1.
8. 8Sacrificing Ratio: 1:1 (since Z acquired it equally).

Case 3: Old partners surrender a specific fraction of their own share

Read the wording carefully here. "Surrenders 1/4th of his share" is very different from "surrenders 1/4th from his share".

Worked Example: P and Q share profits at 2:1. P surrenders 1/4th of his share, and Q surrenders 1/3rd of his share in favor of R.

1. 1P's sacrifice = 1/4 of 2/3 = 2/12.
2. 2Q's sacrifice = 1/3 of 1/3 = 1/9.
3. 3P's new share = 2/3 - 2/12 = 8/12 - 2/12 = 6/12 (or 1/2).
4. 4Q's new share = 1/3 - 1/9 = 3/9 - 1/9 = 2/9.
5. 5R's share = P's sacrifice + Q's sacrifice = 2/12 + 1/9. (Common denominator 36: 6/36 + 4/36 = 10/36).
6. 6Convert all to denominator 36: P = 18/36, Q = 8/36, R = 10/36.
7. 7New Ratio: 18:8:10, which simplifies to 9:4:5.

Step 2: Treatment of Goodwill (Premium for Goodwill)

When a new partner joins, they are stepping into a ready-made business. If the firm makes ₹1,00,000 in profit the very next day, the new partner gets a cut of it, even though they didn't do the years of hard work to build the firm's reputation.

To make things fair, the new partner must pay a bonus to the old partners. This bonus is called the Premium for Goodwill.

There are a few different ways the new partner can bring in this goodwill. Let's look at the accounting treatment for each.

Scenario A: Paid Privately

The new partner hands the cash directly to the old partners outside the business (e.g., at a coffee shop).

• Accounting Entry: None. Because the transaction happened outside the firm, no entry is passed in the firm's books.

Scenario B: Brought in cash and retained in the business

The new partner brings their share of goodwill in cash, and the money stays in the firm's bank account to help the business grow.

Entry 1: Receiving the cash

• Debit: Cash/Bank A/c (with the goodwill amount)
• Credit: Premium for Goodwill A/c

Entry 2: Distributing it to the sacrificing partners

• Debit: Premium for Goodwill A/c
• Credit: Old Partners' Capital A/cs (in their Sacrificing Ratio)

Scenario C: Brought in cash and withdrawn by old partners

The new partner brings the cash, it is credited to the old partners, but the old partners immediately withdraw that cash to take home.

• Pass Entry 1 and Entry 2 exactly as shown in Scenario B.
• Entry 3: Withdrawing the cash
• Debit: Old Partners' Capital A/cs (with the amount they withdraw)
• Credit: Cash/Bank A/c

Scenario D: The new partner cannot bring goodwill in cash

Sometimes, the new partner has enough money for their capital contribution, but not enough liquid cash to pay the premium for goodwill right now. The firm doesn't let them off the hook. Instead, the firm deducts the goodwill amount from the new partner's Current Account.

• Debit: New Partner's Current A/c (with their share of goodwill)
• Credit: Old Partners' Capital A/cs (in their Sacrificing Ratio)

Scenario E: Hidden Goodwill

This is a favorite trick in advanced exam questions. The problem won't mention the word "goodwill" at all. Instead, you have to deduce that it exists based on the capital the new partner brings.

How to spot and calculate it: Suppose A and B have a combined adjusted capital of ₹60,000. They admit C for a 1/4th share, and C brings in ₹40,000 as capital.

1. 1If C pays ₹40,000 for a 1/4th share, the total capital of the firm should be ₹40,000 × 4 = ₹1,60,000.
2. 2But what is the actual total capital? It's A and B's capital (₹60,000) + C's capital (₹40,000) = ₹1,00,000.
3. 3The difference between what the firm should be worth (₹1,60,000) and what it is actually worth on paper (₹1,00,000) is the Hidden Goodwill.
4. 4Hidden Goodwill = ₹60,000.
5. 5C's share of this goodwill is 1/4th of ₹60,000 = ₹15,000. You would then pass the entry for Scenario D (debiting C's Current A/c for ₹15,000).

Step 3: Revaluation of Assets and Liabilities

We covered this extensively in the previous chapter, so we won't repeat the mechanics here. Just remember the sequence: before you finalize the new partner's admission, you must prepare a Revaluation Account. Any profit or loss from revaluing the assets and liabilities belongs entirely to the old partners, and is transferred to their Capital Accounts in their Old Profit-Sharing Ratio.

Step 4: Accumulated Profits, Reserves, and Losses

Look at the firm's old Balance Sheet on the date of admission. You might see items like "General Reserve," "Profit & Loss A/c (Credit Balance)," or "Workmen Compensation Reserve" on the liabilities side. On the assets side, you might see "Profit & Loss A/c (Debit Balance - a loss)" or "Deferred Revenue Expenditure."

These are past earnings (or past losses) that were never distributed. Because they were generated before the new partner arrived, the new partner has zero right to them.

Before the new partner's account is opened, you must sweep the Balance Sheet clean of these items.

For Accumulated Profits and Reserves:

• Debit: General Reserve A/c, P&L A/c
• Credit: Old Partners' Capital A/cs (in their Old Ratio)

For Accumulated Losses:

• Debit: Old Partners' Capital A/cs (in their Old Ratio)
• Credit: P&L A/c (Debit balance), Deferred Revenue Expenditure A/c

Step 5: Adjustment of Capital Accounts

Sometimes, the partners decide that in the newly reconstituted firm, everyone's capital should perfectly match their new profit-sharing ratio. If someone has too much capital, they will withdraw the excess. If someone has too little, they will bring in more cash.

There are two main ways this is tested.

Method 1: Adjusting Old Partners' Capital based on the New Partner's Capital

Here, the new partner's capital is the anchor. We use it to calculate what the total firm's capital should be, and then force the old partners' accounts to match.

Worked Example: A and B are partners sharing profits at 2:1. Their capitals, after all adjustments for goodwill, reserves, and revaluation, are ₹80,000 and ₹40,000 respectively. They admit C for a 1/4th share. C brings in ₹50,000 as capital. They decide to adjust their capitals according to the new profit-sharing ratio.

Step A: Find the new profit-sharing ratio.

• Remaining share = 1 - 1/4 = 3/4.
• A's new share = 2/3 of 3/4 = 2/4.
• B's new share = 1/3 of 3/4 = 1/4.
• C's share = 1/4.
• New Ratio = 2:1:1.

Step B: Calculate the total capital of the new firm.

• If C brings ₹50,000 for a 1/4th share, the total capital = ₹50,000 × 4/1 = ₹2,00,000.

Step C: Determine the required capital for A and B.

• A's required capital = 2/4 of ₹2,00,000 = ₹1,00,000.
• B's required capital = 1/4 of ₹2,00,000 = ₹50,000.

Step D: Compare required capital with actual adjusted capital to find the difference.

• Partner A: Needs ₹1,00,000. Currently has ₹80,000.
• Action: A must bring in ₹20,000 cash. (Debit Cash, Credit A's Capital).
• Partner B: Needs ₹50,000. Currently has ₹40,000.
• Action: B must bring in ₹10,000 cash. (Debit Cash, Credit B's Capital).

Method 2: Calculating the New Partner's Capital based on the Old Partners' Capital

Sometimes, the new partner says, "I will bring in capital proportionate to my share," but the exact rupee amount isn't given. You have to calculate it based on the old partners.

Worked Example: X and Y share profits at 3:2. After all adjustments (goodwill, revaluation, reserves), X's capital is ₹90,000 and Y's capital is ₹60,000. They admit Z for a 1/4th share. Z is to bring in proportionate capital. How much should Z bring?

Step A: Find the combined capital of the old partners.

• X's Capital + Y's Capital = ₹90,000 + ₹60,000 = ₹1,50,000.

Step B: Determine what share of the firm this combined capital represents.

• If Z takes a 1/4th share, the remaining share for X and Y combined is 3/4th.
• Therefore, ₹1,50,000 represents 3/4th of the total firm's capital.

Step C: Calculate the total capital of the firm.

• Total Capital = ₹1,50,000 × (4/3) = ₹2,00,000.

Step D: Calculate Z's required capital.

• Z's share is 1/4th of the total capital.
• Z's Capital = ₹2,00,000 × 1/4 = ₹50,000.
• Z must bring in ₹50,000 in cash.

Quick Revision

• Reconstitution: Admitting a new partner dissolves the old partnership agreement and creates a new one, though the business continues.
• Sacrificing Ratio: Calculated as Old Share minus New Share. It represents what the old partners gave up.
• Default Sacrifice: If the problem only gives the new partner's share, assume the old partners sacrifice in their old profit-sharing ratio.
• Goodwill Distribution: The Premium for Goodwill brought by the new partner is ALWAYS credited to the old partners in their Sacrificing Ratio.
• No Cash for Goodwill: If the new partner cannot bring goodwill in cash, debit their Current Account (not Capital Account) and credit the old partners' Capital Accounts.
• Hidden Goodwill: Calculated when the total implied capital of the firm (based on the new partner's contribution) is higher than the actual combined capital of all partners.
• Reserves and Past Profits: General reserves and accumulated P&L balances belong to the old partners and are distributed in the Old Ratio.
• Capital Adjustments: When adjusting capitals to match the new ratio, any shortfall is brought in as cash by the partner, and any excess is withdrawn as cash (or transferred to their Current Accounts, depending on what the deed specifies).