Chapter 4 — Goodwill in Partnership Accounts: Exercise Solutions Guide
How to Use This Page
Goodwill is a high-weightage chapter in the board exam. Practise every method thoroughly — average profit, super profit, capitalisation of average profit, capitalisation of super profit, and annuity. For numerical problems, always write the formula first, then substitute values, then calculate. Show every step. Examiners award marks for the method, not just the final answer. Pay special attention to adjustments like abnormal gains, non-recurring expenses, and changes in profit trends.
Key Concepts (Quick Recap)
- Goodwill: An intangible asset that represents the reputation, customer base, and earning capacity of a firm beyond normal returns. It arises from factors like location, brand, efficiency, and customer loyalty.
- Types of Goodwill: (i) Purchased goodwill — acquired by paying a price; (ii) Self-generated goodwill — built over time, not purchased.
- Average Profit Method:
Goodwill = Average Profit × Number of years of purchase - Super Profit Method:
Goodwill = Super Profit × Number of years of purchase where Super Profit = Average Profit − Normal Profit - Normal Profit:
Normal Profit = Capital Employed × Normal Rate of Return / 100 - Capitalisation of Average Profit Method:
Goodwill = Capitalised Value of Average Profit − Capital Employed where Capitalised Value = Average Profit × 100 / Normal Rate - Capitalisation of Super Profit Method:
Goodwill = Super Profit × 100 / Normal Rate - Annuity Method:
Goodwill = Super Profit × Annuity Factor (annuity factor is obtained from present value tables for the given rate and number of years) - Factors Affecting Goodwill: Location, reputation, management efficiency, profitability, market share, patents, trademarks, customer loyalty, risk factor.
- Need for Goodwill Valuation: On admission, retirement, death of a partner, change in profit-sharing ratio, dissolution of partnership, and sale of business.
I. Choose the Best Answer (MCQs)
1. Goodwill is a: (a) Tangible asset (b) Intangible asset ✓ (c) Fictitious asset (d) Current asset
ExplanationGoodwil is an intangible asset because it has no physical form but has value due to the firm's reputation and earning capacity.
2. Under the average profit method, goodwill is calculated as: (a) Average Profit × Capital Employed (b) Average Profit × Number of years of purchase ✓ (c) Super Profit × Number of years of purchase (d) Average Profit / Normal Rate
ExplanationThe average profit method multiplies the average profit by the number of years of purchase to arrive at goodwill.
3. Super profit is: (a) Average profit minus normal profit ✓ (b) Total profit minus average profit (c) Capital employed times normal rate (d) Average profit times normal rate
ExplanationSuper profit is the excess of average profit over normal profit (the minimum expected return on capital employed).
4. Under the capitalisation of super profit method, goodwill = Super Profit × 100 / Normal Rate. If super profit is ₹20,000 and normal rate is 10%, goodwill is: (a) ₹2,00,000 ✓ (b) ₹1,00,000 (c) ₹20,000 (d) ₹2,000
ExplanationGoodwill = 20,000 × 100 / 10 = ₹2,00,000.
5. Normal profit is calculated as: (a) Capital Employed × Average Rate (b) Capital Employed × Normal Rate of Return / 100 ✓ (c) Average Profit × Normal Rate / 100 (d) Super Profit × 100 / Normal Rate
ExplanationNormal profit represents the minimum expected return on the capital employed at the normal rate of return.
6. Which of the following does NOT affect the value of goodwill? (a) Location of the business (b) Reputation of the firm (c) Book value of machinery ✓ (d) Management efficiency
ExplanationThe book value of machinery is a tangible asset value and does not directly affect the intangible value of goodwill.
7. When goodwill is raised in the books at the time of admission, it is debited to: (a) Goodwill Account ✓ (b) Incoming Partner's Capital Account (c) All Partners' Capital Accounts (d) Revaluation Account
ExplanationThe Goodwill Account is debited when goodwill is raised (created) in the books.
8. The annuity method of goodwill valuation uses: (a) Average profit only (b) Super profit and annuity factor ✓ (c) Capital employed and normal profit (d) Total profit and purchase years
ExplanationUnder the annuity method, Goodwill = Super Profit × Annuity Factor, where the annuity factor is the present value of ₹1 per year for the given number of years at the given discount rate.
9. If profits for the last 5 years are ₹10,000, ₹12,000, ₹8,000, ₹15,000, and ₹20,000, the average profit is: (a) ₹13,000 ✓ (b) ₹12,000 (c) ₹15,000 (d) ₹10,000
ExplanationAverage Profit = (10,000 + 12,000 + 8,000 + 15,000 + 20,000) / 5 = 65,000 / 5 = ₹13,000.
10. Goodwill is raised and written off when: (a) A new partner is admitted and does not bring his share of goodwill (b) A partner retires (c) There is a change in profit-sharing ratio (d) All of the above ✓
ExplanationGoodwill needs to be valued and adjusted whenever there is a change in the profit-sharing arrangement — admission, retirement, death, or change in ratio.
II. Fill in the Blanks
1. Goodwill is an intangible asset. 2. Under the average profit method, Goodwill = Average Profit × Number of years of purchase. 3. Super Profit = Average Profit − Normal Profit. 4. Normal Profit = Capital Employed × Normal Rate of Return / 100. 5. Under the capitalisation of super profit method, Goodwill = Super Profit × 100 / Normal Rate. 6. Goodwill arises only when the firm earns super profit (profit above normal returns). 7. The annuity method uses the present value factor to calculate goodwill. 8. Goodwill is valued at the time of admission, retirement, death, or change in profit-sharing ratio. 9. Self-generated goodwill is not recorded in the books of accounts under AS 26. 10. The weighted average method gives more weight to recent years' profits.
III. True or False
1. Goodwill is a tangible asset. ✗ False — Goodwill is an intangible asset with no physical existence.
2. Super profit is the excess of average profit over normal profit. ✓ True — Super profit = Average profit − Normal profit. It represents the extra earning capacity.
3. Under the capitalisation method, goodwill can be negative. ✓ True — If capital employed exceeds the capitalised value of average profit, goodwill is negative (negative goodwill or "badwill").
4. Purchased goodwill is recorded in the books of accounts. ✓ True — Only purchased goodwill (where a price is paid) can be recorded in the books. Self-generated goodwill cannot be shown as per AS 26.
5. The average profit method is the same as the super profit method. ✗ False — The average profit method uses average profit directly. The super profit method uses only the excess over normal profit.
6. Goodwill has no value when the firm earns only normal profit. ✓ True — If average profit equals normal profit, super profit is zero, and goodwill under the super profit method has no value.
7. Goodwill is valued only at the time of admission of a partner. ✗ False — Goodwill is valued on admission, retirement, death, change in ratio, and dissolution.
IV. Match the Following
| Column A | Column B |
|---|
| 1. Average Profit Method | (d) Average Profit × No. of years purchase |
| 2. Super Profit Method | (e) Super Profit × No. of years purchase |
| 3. Capitalisation of Average Profit | (a) Capitalised value − Capital employed |
| 4. Capitalisation of Super Profit | (b) Super Profit × 100 / Normal Rate |
| 5. Annuity Method | (c) Super Profit × Annuity Factor |
V. Answer Briefly
1. What is goodwill? What are its characteristics?
Answer
Goodwill is an intangible asset that represents the value of a firm's reputation, customer relationships, brand value, and earning capacity over and above its normal returns on investment. Characteristics: (i) It is an intangible asset — has no physical form. (ii) It is attached to the business — cannot be sold separately. (iii) Its value fluctuates — depends on profitability and reputation. (iv) It can be purchased or self-generated. (v) It is valued at the time of admission, retirement, death, or change in profit-sharing ratio. (vi) Self-generated goodwill cannot be shown in the books as per AS 26.
2. Distinguish between purchased goodwill and self-generated goodwill.
Answer
| Basis | Purchased Goodwill | Self-generated Goodwill | |---|---|---| | Meaning | Acquired by paying a price for it | Built over time by the firm itself | | Recording | Can be recorded in the books | Cannot be recorded in the books (AS 26) | | Valuation | Equal to the price paid | Valued only when needed (admission, etc.) | | Payment | Money or consideration is paid | No consideration is paid | | Appearance | Shown on the assets side of Balance Sheet | Not shown in Balance Sheet |
3. What factors affect the value of goodwill?
Answer
The value of goodwill depends on: (i) Location — A prime location attracts more customers. (ii) Reputation — Good reputation brings more business. (iii) Management efficiency — Efficient management increases profitability. (iv) Market conditions — Favourable market conditions increase value. (v) Profitability — Higher profits mean higher goodwill. (vi) Risk — Lower risk means higher goodwill. (vii) Patents and trademarks — Exclusive rights add value. (viii) Customer relationships — Loyal customers increase goodwill. (ix) Capital employed — Less capital for same profit means higher return rate and goodwill.
4. State the formula for goodwill under each method.
Answer
1. Average Profit Method: Goodwill = Average Profit × Number of years of purchase Average Profit = Total Profit / Number of years 2. Weighted Average Profit Method: Goodwill = Weighted Average Profit × Number of years of purchase Each year's profit is multiplied by a weight (higher weights for recent years). 3. Super Profit Method: Goodwill = Super Profit × Number of years of purchase Super Profit = Average Profit − Normal Profit Normal Profit = Capital Employed × Normal Rate / 100 4. Capitalisation of Average Profit Method: Capitalised Value = Average Profit × 100 / Normal Rate Goodwill = Capitalised Value − Capital Employed 5. Capitalisation of Super Profit Method: Goodwill = Super Profit × 100 / Normal Rate 6. Annuity Method: Goodwill = Super Profit × Annuity Factor Annuity Factor = Present value of ₹1 per year for n years at the given rate.
5. When is goodwill valued in a partnership firm?
Answer
Goodwill is valued in the following situations: (i) On admission of a new partner — the new partner must compensate for their share of goodwill. (ii) On retirement or death of a partner — the outgoing partner is entitled to their share of goodwill. (iii) On change in profit-sharing ratio — when partners agree to change their ratio. (iv) On dissolution or sale of the firm — to determine the purchase consideration. (v) On amalgamation of firms — to calculate the value of each firm.
6. How is average profit calculated when there are adjustments?
Answer
When past profits have abnormal or non-recurring items, the following adjustments are made: Add back (to profit): - Abnormal losses (fire, theft) — these reduce profit but are not recurring - Non-operating losses - Overvaluation of closing stock (deducted from profit, so add back) Deduct (from profit): - Abnormal gains (lottery, speculation) — these increase profit but are not recurring - Non-operating income - Undervaluation of closing stock - Income from non-business assets Also adjust: - Management remuneration (if not already deducted) - Depreciation (if not already provided) Adjusted Average Profit = Total of adjusted profits / Number of years
7. What is the weighted average profit method? When is it used?
Answer
Under the weighted average profit method, each year's profit is assigned a weight — higher weights for more recent years. This method is used when there is a clear trend of increasing or decreasing profits, and recent profits are more representative of future earning capacity. Formula: Weighted Average Profit = Sum of (Profit × Weight) / Sum of Weights Goodwill = Weighted Average Profit × Number of years of purchase Example: If profits for 3 years are ₹10,000, ₹15,000, ₹20,000, weights 1, 2, 3: Weighted Average = (10,000×1 + 15,000×2 + 20,000×3) / (1+2+3) = (10,000 + 30,000 + 60,000) / 6 = 1,00,000 / 6 = ₹16,667
VI. Answer in Detail
1. Calculate goodwill under the Average Profit Method with adjustments.
Answer
Problem: The profits of a firm for the last 5 years are: ₹40,000, ₹50,000, ₹35,000, ₹60,000, and ₹55,000. Goodwill is valued at 3 years' purchase of average profit. However, the following adjustments are needed: - Year 2 includes a speculative gain of ₹5,000 - Year 3 includes a loss by fire of ₹8,000 (not insured) - Year 5 includes a non-operating income of ₹3,000 - Management remuneration of ₹10,000 per year has not been deducted from any year's profit Step 1: Adjust each year's profit | Year | Profit (₹) | Adjustments | Adjusted Profit (₹) | |---|---|---|---| | 1 | 40,000 | −10,000 (remuneration) | 30,000 | | 2 | 50,000 | −5,000 (speculative gain) −10,000 (remuneration) | 35,000 | | 3 | 35,000 | +8,000 (abnormal loss) −10,000 (remuneration) | 33,000 | | 4 | 60,000 | −10,000 (remuneration) | 50,000 | | 5 | 55,000 | −3,000 (non-operating income) −10,000 (remuneration) | 42,000 | | Total | | | 1,90,000 | Step 2: Calculate Average Profit `` Average Profit = 1,90,000 / 5 = ₹38,000 ` Step 3: Calculate Goodwill ` Goodwill = Average Profit × Number of years of purchase = 38,000 × 3 = ₹1,14,000 ``
2. Calculate goodwill under the Super Profit Method.
Answer
Problem: A firm has earned an average profit of ₹75,000 per year. The capital employed in the firm is ₹4,00,000 and the normal rate of return is 12%. Goodwill is valued at 4 years' purchase of super profit. Step 1: Calculate Normal Profit `` Normal Profit = Capital Employed × Normal Rate / 100 = 4,00,000 × 12 / 100 = ₹48,000 ` Step 2: Calculate Super Profit ` Super Profit = Average Profit − Normal Profit = 75,000 − 48,000 = ₹27,000 ` Step 3: Calculate Goodwill ` Goodwill = Super Profit × Number of years of purchase = 27,000 × 4 = ₹1,08,000 ``
3. Calculate goodwill under the Capitalisation of Average Profit Method and Capitalisation of Super Profit Method.
Answer
Problem: A firm's average profit is ₹1,20,000. Capital employed is ₹8,00,000. Normal rate of return is 15%. Method A: Capitalisation of Average Profit Method Step 1: Capitalised Value of Average Profit `` Capitalised Value = Average Profit × 100 / Normal Rate = 1,20,000 × 100 / 15 = ₹8,00,000 ` Step 2: Calculate Goodwill ` Goodwill = Capitalised Value − Capital Employed = 8,00,000 − 8,00,000 = ₹0 ` In this case, since average profit equals normal return, goodwill is zero. The firm earns exactly the normal rate of return. Now with a different example: Average profit ₹1,50,000, capital employed ₹8,00,000, normal rate 15%. ` Capitalised Value = 1,50,000 × 100 / 15 = ₹10,00,000 Goodwill = 10,00,000 − 8,00,000 = ₹2,00,000 ` Method B: Capitalisation of Super Profit Method Using the second example (Average profit ₹1,50,000, capital ₹8,00,000, normal rate 15%): Step 1: Calculate Normal Profit ` Normal Profit = 8,00,000 × 15 / 100 = ₹1,20,000 ` Step 2: Calculate Super Profit ` Super Profit = 1,50,000 − 1,20,000 = ₹30,000 ` Step 3: Calculate Goodwill ` Goodwill = Super Profit × 100 / Normal Rate = 30,000 × 100 / 15 = ₹2,00,000 `` Note: Both methods give the same result. This confirms the calculation is correct.
4. Calculate goodwill under the Weighted Average Profit Method.
Answer
Problem: A firm's profits for the last 5 years are: - 2021-22: ₹30,000 - 2022-23: ₹40,000 - 2023-24: ₹55,000 - 2024-25: ₹65,000 - 2025-26: ₹85,000 There is a clear increasing trend, so use weights 1, 2, 3, 4, 5. Goodwill is valued at 3 years' purchase. Step 1: Calculate Weighted Average | Year | Profit (₹) | Weight | Product (₹) | |---|---|---|---| | 2021-22 | 30,000 | 1 | 30,000 | | 2022-23 | 40,000 | 2 | 80,000 | | 2023-24 | 55,000 | 3 | 1,65,000 | | 2024-25 | 65,000 | 4 | 2,60,000 | | 2025-26 | 85,000 | 5 | 4,25,000 | | Total | | 15 | 9,60,000 | `` Weighted Average Profit = 9,60,000 / 15 = ₹64,000 ` Step 2: Calculate Goodwill ` Goodwill = Weighted Average Profit × Number of years of purchase = 64,000 × 3 = ₹1,92,000 `` For comparison, the simple average would be (30,000 + 40,000 + 55,000 + 65,000 + 85,000) / 5 = 2,75,000 / 5 = ₹55,000, giving goodwill of ₹1,65,000. The weighted method gives a higher value because it gives more importance to recent, higher profits.
5. Calculate goodwill under the Annuity Method.
Answer
Problem: A firm earns a super profit of ₹50,000 per year. Goodwill is valued at 4 years' purchase. The present value of ₹1 per year at 10% for 4 years (annuity factor) is 3.170. Calculate goodwill under the annuity method. Calculation: `` Goodwill = Super Profit × Annuity Factor = 50,000 × 3.170 = ₹1,58,500 ` The annuity method takes into account the time value of money. It gives a lower value than the simple super profit method (which would give 50,000 × 4 = ₹2,00,000) because future super profits are discounted to present value. Comprehensive Example (combining multiple concepts): A firm's profits for the last 4 years are: ₹80,000, ₹1,00,000, ₹90,000, and ₹1,10,000. Capital employed is ₹5,00,000. Normal rate of return is 12%. Calculate goodwill at 3 years' purchase under: (a) Average Profit Method (b) Super Profit Method (c) Capitalisation of Average Profit Method (d) Capitalisation of Super Profit Method (a) Average Profit Method: ` Average Profit = (80,000 + 1,00,000 + 90,000 + 1,10,000) / 4 = 3,80,000 / 4 = ₹95,000 Goodwill = 95,000 × 3 = ₹2,85,000 ` (b) Super Profit Method: ` Normal Profit = 5,00,000 × 12% = ₹60,000 Super Profit = 95,000 − 60,000 = ₹35,000 Goodwill = 35,000 × 3 = ₹1,05,000 ` (c) Capitalisation of Average Profit Method: ` Capitalised Value = 95,000 × 100 / 12 = ₹7,91,667 (approx.) Goodwill = 7,91,667 − 5,00,000 = ₹2,91,667 ` (d) Capitalisation of Super Profit Method: ` Goodwill = 35,000 × 100 / 12 = ₹2,91,667 `` Note: Methods (c) and (d) give the same result, confirming consistency.
6. A and B are partners sharing profits 3:2. They admit C for 1/5 share. Goodwill is valued at ₹2,00,000. C brings ₹40,000 as his share of goodwill. Pass the necessary journal entries.
Answer
Calculations: - C's share = 1/5 - C's share of goodwill = 2,00,000 × 1/5 = ₹40,000 - Sacrificing ratio = Old ratio = 3:2 (since only C is admitted and no new ratio is given) - A's sacrifice = 1/5 × 3/5 = 3/25 - B's sacrifice = 1/5 × 2/5 = 2/25 Journal Entries: Case 1: When goodwill is raised in the books (at full value) `` Goodwill A/c Dr. 2,00,000 To A's Capital A/c 1,20,000 To B's Capital A/c 80,000 (Goodwill raised at full value in old ratio 3:2) Cash/Bank A/c Dr. 40,000 To C's Capital A/c 40,000 (C brings his share of goodwill) A's Capital A/c Dr. 1,20,000 B's Capital A/c Dr. 80,000 To Goodwill A/c 2,00,000 (Goodwill written off in new ratio — assuming new ratio 3:2 unchanged) ` Note: If goodwill is not to appear in the books, the raising entry is reversed after the premium is distributed. Case 2: When goodwill is not raised in the books (premium method) ` Cash/Bank A/c Dr. 40,000 To Premium for Goodwill A/c 40,000 (C brings his share of goodwill) Premium for Goodwill A/c Dr. 40,000 To A's Capital A/c 24,000 To B's Capital A/c 16,000 (Premium distributed in sacrificing ratio 3:2) `` A's share = 40,000 × 3/5 = ₹24,000 B's share = 40,000 × 2/5 = ₹16,000
Common Mistakes to Avoid
1. Using total profit instead of average profit — Always divide the total profit by the number of years before multiplying by the purchase years. 2. Forgetting to adjust profits for abnormal items — Speculative gains, fire losses, non-operating income must be adjusted before calculating average profit. 3. Confusing super profit with average profit — Super profit = Average profit − Normal profit. Don't skip the normal profit step. 4. Calculating normal profit incorrectly — Normal profit = Capital Employed × Normal Rate / 100. Use the capital employed, not the average profit. 5. Mixing up the capitalisation formulas — Capitalisation of average profit: Goodwill = Capitalised Value − Capital Employed. Capitalisation of super profit: Goodwill = Super Profit × 100 / Normal Rate. These give the same result but the formulas are different. 6. Not considering weighted average when there is a trend — When profits are steadily increasing or decreasing, use the weighted average method to give more importance to recent years.
Exam Checklist
- [ ] I can calculate goodwill under the Average Profit Method (with adjustments)
- [ ] I can calculate goodwill under the Super Profit Method
- [ ] I can calculate goodwill under both Capitalisation Methods
- [ ] I can use the Weighted Average Profit Method when there is a profit trend
- [ ] I can apply the Annuity Method with the given annuity factor
- [ ] I can adjust profits for abnormal items, non-recurring income, and management remuneration
- [ ] I can pass journal entries for goodwill on admission of a partner
- [ ] I can distinguish between purchased and self-generated goodwill
- [ ] I can calculate sacrificing ratio and distribute goodwill accordingly
- [ ] I know when goodwill is valued (admission, retirement, death, change in ratio)
