Admission of a Partner: Valuation, Goodwill, Capital Adjustments

What is Partnership?

A partnership is a business owned by two or more people who share profits and losses. Partners contribute capital, skills, or labor to run the business.

Key Features of Partnership:

• Agreement: Partners must have a written or oral agreement (Partnership Deed).
• Unlimited Liability: Partners are personally responsible for business debts.
• Mutual Agency: Each partner can act on behalf of the firm.
• Profit Sharing: Profits and losses are shared as per the agreement.

Why Admit a New Partner?

Partners may admit a new partner for:

• More Capital: To expand the business.
• Special Skills: To improve efficiency.
• Retirement/Death: To continue the business smoothly.

Steps for Admission of a Partner

When a new partner joins, the following steps are followed:

1. Valuation of Goodwill

Goodwill is the reputation or good name of the business. It is calculated when a new partner joins or leaves.

Methods of Goodwill Valuation:

Example: Average Profit Method

Given:

• Profits for 3 years: Rs. 50,000, Rs. 60,000, Rs. 70,000
• Goodwill is to be valued at 2 years' purchase.

Solution:

1. Calculate average profit: $$\text{Average Profit}=\frac{50,000+60,000+70,000}{3}=\frac{180,000}{3}=60,000$$
2. Calculate goodwill: $$\text{Goodwill}=60,000\times 2=120,000$$

2. Sacrificing Ratio

When a new partner joins, the existing partners may sacrifice some of their profit-sharing ratio to accommodate the new partner.

Example:

• Old profit-sharing ratio: A:B = 3:2
• New partner C joins with a 1/5 share.
• Remaining share for A and B: 4/5 (since 1/5 is for C).
• New ratio for A and B: 3:2 (but total is now 4/5).
• Adjust old ratio to 4/5: $$\text{New ratio for A}=\frac{3}{5}\times \frac{4}{5}=\frac{12}{25}$$ $$\text{New ratio for B}=\frac{2}{5}\times \frac{4}{5}=\frac{8}{25}$$
• New ratio: A:B:C = 12:8:5

3. Adjustment of Capital Accounts

The new partner’s capital is adjusted to match the old partners’ capital ratio.

Example:

• Old partners’ capital: A = Rs. 100,000, B = Rs. 80,000 (ratio 5:4).
• New partner C brings Rs. 60,000 as capital.
• Total capital after admission: Rs. 240,000.
• New capital ratio: A:B:C = 5:4:3 (assuming equal sacrifice).
• Calculate new capital amounts: $$\text{Total parts}=5+4+3=12$$ $$\text{A’s new capital}=\frac{5}{12}\times 240,000=100,000$$ $$\text{B’s new capital}=\frac{4}{12}\times 240,000=80,000$$ $$\text{C’s new capital}=\frac{3}{12}\times 240,000=60,000$$
• No adjustment needed in this case because C’s capital matches the ratio.

4. Journal Entries for Admission

The following journal entries are passed when a new partner is admitted:

1. For Goodwill (if brought in cash):

   Cash A/c Dr. 120,000
   To Goodwill A/c 120,000
   

2. For Goodwill (if not brought in cash, credited to old partners):

   Goodwill A/c Dr. 120,000
   To A’s Capital A/c 72,000 (3/5 share)
   To B’s Capital A/c 48,000 (2/5 share)
   

3. For New Partner’s Capital:

   Cash A/c Dr. 60,000
   To C’s Capital A/c 60,000
   

4. For Revaluation of Assets/Liabilities (if any):

   Asset A/c Dr. (Increase)
   Liability A/c Dr. (Decrease)
   To Asset A/c (Decrease)
   To Liability A/c (Increase)
   To Revaluation A/c (Balance)
   

5. For Transfer of Revaluation Profit/Loss:

   Revaluation A/c Dr. (Profit)
   To A’s Capital A/c (Old ratio)
   To B’s Capital A/c (Old ratio)
   

   Or,

   A’s Capital A/c Dr. (Loss)
   B’s Capital A/c Dr. (Loss)
   To Revaluation A/c (Loss)
   

Solved Example: Admission of a Partner

Given:

• A and B are partners with capitals of Rs. 50,000 and Rs. 30,000, respectively (ratio 2:1).
• C is admitted with a 1/4 share in profits.
• C brings Rs. 40,000 as capital and Rs. 20,000 for goodwill.
• Profits for the last 3 years: Rs. 20,000, Rs. 25,000, Rs. 30,000.
• Goodwill is valued at 2 years' purchase of average profit.

Solution:

Step 1: Calculate Goodwill

$$\text{Average Profit}=\frac{20,000+25,000+30,000}{3}=25,000$$ $$\text{Goodwill}=25,000\times 2=50,000$$ But C brings only Rs. 20,000 for goodwill. The remaining Rs. 30,000 is credited to A and B in their old ratio (2:1).

Step 2: Calculate New Profit-Sharing Ratio

• Old ratio: A:B = 2:1
• C’s share: 1/4
• Remaining share: 3/4 (for A and B).
• New ratio for A and B: 2:1 (but total is 3/4).
• Adjust old ratio to 3/4: $$\text{A’s new share}=\frac{2}{3}\times \frac{3}{4}=\frac{6}{12}=\frac{1}{2}$$ $$\text{B’s new share}=\frac{1}{3}\times \frac{3}{4}=\frac{3}{12}=\frac{1}{4}$$
• New ratio: A:B:C = 1/2 : 1/4 : 1/4 = 2:1:1

Step 3: Journal Entries

1. For Goodwill:

   Cash A/c Dr. 20,000
   Goodwill A/c Dr. 30,000
   To A’s Capital A/c 20,000 (2/3 share)
   To B’s Capital A/c 10,000 (1/3 share)
   

2. For C’s Capital:

   Cash A/c Dr. 40,000
   To C’s Capital A/c 40,000
   

3. For Adjustment of Capital (if needed):

   • Total capital after admission: Rs. 50,000 (A) + Rs. 30,000 (B) + Rs. 40,000 (C) + Rs. 20,000 (goodwill) = Rs. 140,000.
   • New capital ratio: A:B:C = 2:1:1 (total parts = 4).
   • A’s new capital: (2/4) × 140,000 = Rs. 70,000 (increase by Rs. 20,000).
   • B’s new capital: (1/4) × 140,000 = Rs. 35,000 (increase by Rs. 5,000).
   • C’s capital remains Rs. 40,000 (no change).
   • Journal entry for adjustment:

     A’s Capital A/c Dr. 20,000
     B’s Capital A/c Dr. 5,000
     To Cash A/c 25,000
     

Comparison Table: Old vs. New Partnership

Advantages and Disadvantages of Admitting a Partner

Advantages:

• More Capital: Helps in business expansion.
• Special Skills: New partner may bring expertise.
• Continuity: Business continues smoothly after retirement/death.

Disadvantages:

• Loss of Control: Existing partners may lose decision-making power.
• Conflicts: Disagreements may arise over profit-sharing.
• Unlimited Liability: New partner is also liable for business debts.

NEB Board-Style Questions

Short Answer Questions:

1. What is goodwill? Explain any two methods of goodwill valuation.
2. What is a sacrificing ratio? How is it calculated?
3. Why is the capital of existing partners adjusted when a new partner is admitted?

Long Answer Questions:

1. A and B are partners with capitals of Rs. 100,000 and Rs. 80,000, respectively. C is admitted with a 1/3 share in profits. C brings Rs. 60,000 as capital and Rs. 30,000 for goodwill. The profits for the last 3 years are Rs. 40,000, Rs. 50,000, and Rs. 60,000. Goodwill is valued at 2 years' purchase of average profit. Show the journal entries for C’s admission.
2. Explain the steps involved in the admission of a new partner in a partnership firm. Also, discuss the treatment of goodwill and revaluation of assets and liabilities.

Exam Tip

• Understand the Concepts: Know the difference between goodwill brought in cash and goodwill credited to old partners.
• Calculate Carefully: Always double-check calculations for goodwill, new ratios, and capital adjustments.
• Journal Entries: Practice writing journal entries for different scenarios (e.g., when goodwill is not brought in cash, when assets are revalued).
• NEB Focus: The board often asks for journal entries and explanations of sacrificing ratio and goodwill valuation. Be prepared to show all steps clearly.

flowchart TD
    A["Old Partners<br/>(A and B)"] -->|"Admit New Partner<br/>(C)"| B["New Partner<br/>(C Joins)"]
    B --> C["Calculate Goodwill"]
    B --> D["Determine Sacrificing Ratio"]
    B --> E["Adjust Capital Accounts"]
    B --> F["Pass Journal Entries"]
    C --> G["Average Profit Method<br/>Super Profit Method"]
    D --> H["Old Ratio<br/>New Ratio"]
    E --> I["Equal Capital<br/>Adjusted Capital"]
    F --> J["Goodwill Entry<br/>Capital Entry<br/>Revaluation Entry"]