2025 Cambridge IAL Accounting (9706) 模擬試題連答案詳解

1. Identify the opening retained earnings: $120,000. 2. Add profit for the year: $115,000. 3. Calculate preference dividends: Cumulative preference shares require unpaid dividends from the prior year to be paid before ordinary dividends. 2021 dividend: 6% of $100,000 = $6,000; 2022 dividend: 6% of $100,000 = $6,000; Total preference dividends paid = $12,000. 4. Calculate ordinary dividends: Number of ordinary shares on 1 January 2022 = $400,000 / $0.50 = 800,000 shares. Rights issue: 1 for 4 = 800,000 / 4 = 200,000 shares. Total ordinary shares at 31 December 2022 = 1,000,000 shares. Ordinary dividend paid = 1,000,000 * $0.05 = $50,000. 5. Retained earnings on 31 December 2022 = $120,000 + $115,000 - $12,000 - $50,000 = $173,000.

1 mark for the correct answer A. Method: Award marks for calculating the cumulative preference dividend of $12,000, the ordinary dividend of $50,000, and the final net retained earnings of $173,000.

1. Number of existing ordinary shares = 500,000 / $1.00 = 500,000 shares. 2. Bonus issue size = 500,000 / 5 = 100,000 shares. 3. Nominal value of bonus issue = 100,000 * $1.00 = $100,000. 4. To preserve distributable reserves (Retained earnings) to the maximum extent, non-distributable capital reserves (like Share Premium) must be used first. 5. Share premium remaining = $150,000 - $100,000 = $50,000. 6. Retained earnings remains unchanged at $220,000.

1 mark for the correct answer A. Method: Award marks for calculating the bonus issue value ($100,000) and identifying that capital reserves should be utilized first to preserve distributable reserves.

1. Calculate the impact of revaluation: Only old partners P and Q share the $30,000 revaluation surplus, so R's capital is unaffected. 2. Calculate the impact of Goodwill write-off (not retained in the books): Goodwill is credited to old partners in their old ratio (3:2) and debited to all partners in their new ratio (2:2:1). R's share of the debit is $60,000 * 1/5 = $12,000. 3. Set up R's capital account equation: R's capital account starts with a debit of $12,000 for goodwill and is credited with cash C to yield a final balance of $50,000. Therefore, C - $12,000 = $50,000, which means C = $62,000.

1 mark for the correct answer D. Method: Award marks for identifying that R does not share in the revaluation, calculating R's goodwill write-off debit of $12,000, and solving for the cash contribution of $62,000.

1. Share the realization loss of $30,000 among partners in the profit-sharing ratio (2:2:1): X's share = $12,000; Y's share = $12,000; Z's share = $6,000. 2. Calculate capital balances after the realization loss: X = $48,000 (Credit); Y = $28,000 (Credit); Z = -$16,000 (Debit deficiency). 3. Under Garner v Murray, Z's deficiency of $16,000 is shared by solvent partners (X and Y) in the ratio of their last agreed capitals prior to dissolution ($60,000 : $40,000 = 3:2). X's share of the deficiency = $16,000 * 3/5 = $9,600. 4. Calculate the final payment to X: $48,000 - $9,600 = $38,400.

1 mark for the correct answer A. Method: Award marks for sharing the realization loss, calculating Z's final deficiency of $16,000, and distributing it between X and Y based on their opening capital ratio of 3:2.

1. Year 0 Cash Flow = -$120,000 (machine) - $15,000 (working capital) = -$135,000. 2. Present Value of inflows: Year 1: $50,000 * 0.909 = $45,450; Year 2: $60,000 * 0.826 = $49,560; Year 3: ($40,000 + $15,000 working capital recovery) * 0.751 = $55,000 * 0.751 = $41,305. Total PV of inflows = $136,315. 3. NPV = $136,315 - $135,000 = $1,315.

1 mark for the correct answer A. Method: Award marks for correctly setting up Year 0 cash flow of -$135,000, including Year 3 working capital recovery of $15,000, and discounting cash flows properly.

Using the linear interpolation formula: \( \text{IRR} = L + \left( \frac{\text{NPV}_L}{\text{NPV}_L - \text{NPV}_H} \right) \times (H - L) \). Lower rate \( L = 8\% \), Higher rate \( H = 14\% \), \( \text{NPV}_L = \$8,400 \), \( \text{NPV}_H = -\$3,600 \). Therefore, \( \text{IRR} = 8\% + \left( \frac{8,400}{8,400 - (-3,600)} \right) \times (14\% - 8\%) = 8\% + \left( \frac{8,400}{12,000} \right) \times 6\% = 8\% + 4.2\% = 12.2\% \).

1 mark for the correct answer C. Method: Award marks for correctly inputting the values into the linear interpolation equation and calculating 12.2%.

1. Direct Labour Rate Variance: Based on actual hours paid. Standard cost of actual hours paid = 3,400 hours * $12 = $40,800. Actual cost = $39,100. Rate Variance = $40,800 - $39,100 = $1,700 Favourable. 2. Direct Labour Efficiency Variance: Based on actual hours worked. Actual hours worked = 3,400 paid hours - 150 idle hours = 3,250 hours. Standard hours for actual production = 800 units * 4 hours = 3,200 hours. Variance in hours = 3,200 - 3,250 = 50 hours Adverse. Efficiency Variance = 50 hours * $12 standard rate = $600 Adverse.

1 mark for the correct answer A. Method: Award marks for using actual hours paid for the rate variance ($1,700 F) and adjusting actual hours paid to actual hours worked (3,250 hours) to calculate the efficiency variance ($600 A).

1. Direct Material Price Variance: Isolated at purchase. Standard cost of purchases = 4,000 kg * $8 = $32,000. Actual cost of purchases = $31,200. Price Variance = $32,000 - $31,200 = $800 Favourable. 2. Direct Material Usage Variance: Based on usage. Standard quantity for actual production = 1,200 units * 3 kg = 3,600 kg. Actual quantity used = 3,750 kg. Usage Variance in kg = 3,600 - 3,750 = 150 kg Adverse. Usage Variance in dollars = 150 kg * $8 standard price = $1,200 Adverse.

1 mark for the correct answer A. Method: Award marks for calculating the price variance based on purchased quantity of 4,000 kg ($800 F) and calculating the usage variance based on the actual quantity used of 3,750 kg ($1,200 A).

1. **Bonus Issue (1 March 2023):**
- The company has 800,000 shares in issue.
- Number of bonus shares = \(800,000 \times \frac{1}{4} = 200,000\) shares.
- Nominal value of bonus shares = \(200,000 \times \$0.50 = \$100,000\).
- This is funded from the share premium account, reducing its balance from \(\$150,000\) to \(\$50,000\).
- Total ordinary shares in issue becomes \(800,000 + 200,000 = 1,000,000\) shares.

2. **Rights Issue (1 July 2023):**
- Number of rights shares = \(1,000,000 \times \frac{1}{5} = 200,000\) shares.
- Issue price is \(\$0.80\) per share, which represents a premium of \(\$0.30\) per share (\(\$0.80 - \$0.50\)).
- Premium received on rights issue = \(200,000 \times \$0.30 = \$60,000\).

3. **Final Share Premium Balance:**
- \(\$50,000\) (after bonus issue) \(+\ \$60,000\) (from rights issue) = \(\$110,000\).

Award 1 mark for the correct answer. Method: Deduct \(\$100,000\) bonus from original \(\$150,000\) share premium, then add \(\$60,000\) premium from the rights issue to arrive at \(\$110,000\).

1. **Adjusted Distribution Costs:**
- \(\$120,000 - \$15,000 = \$105,000\)

2. **Adjusted Administrative Expenses:**
- Draft admin expenses: \(\$150,000\)
- Deduct 6 months of debenture interest paid: \(-\$6,000\) (calculated as \(\$200,000 \times 6\% \times \frac{6}{12}\))
- Add auditor's fees accrued: \(+\$8,000\)
- Add allowance for doubtful debts: \(+\$3,600\) (calculated as \(\$180,000 \times 2\%\))
- Adjusted administrative expenses = \(\$150,000 - \$6,000 + \$8,000 + \$3,600 = \$155,600\)

3. **Finance Costs:**
- The debentures were issued on 1 April 2023, so interest must be charged for 9 months.
- Total interest expense = \(\$200,000 \times 6\% \times \frac{9}{12} = \$9,000\)

4. **Profit for the Year:**
- Gross Profit: \(\$450,000\)
- Less Distribution Costs: \(-\$105,000\)
- Less Administrative Expenses: \(-\$155,600\)
- Profit from Operations: \(\$189,400\)
- Less Finance Costs: \(-\$9,000\)
- Profit for the Year: \(\$180,400\)

Award 1 mark for the correct answer. Method: Calculate adjusted admin expenses (\(\$155,600\)), adjusted distribution costs (\(\$105,000\)), and total 9-month finance costs (\(\$9,000\)) to find correct profit of \(\$180,400\).

1. **Revaluation adjustment:**
- Surplus of \(\$40,000\) is shared in the old ratio (5:3:2).
- Q's share of revaluation = \(\frac{3}{10} \times \$40,000 = \$12,000\).
- Q's capital after revaluation = \(\$90,000 + \$12,000 = \$102,000\).

2. **Goodwill adjustment (No goodwill account retained):**
- Goodwill is credited in old ratio (5:3:2) and debited in new ratio (3:2).
- Q's credit = \(\frac{3}{10} \times \$80,000 = \$24,000\).
- Q's debit = \(\frac{2}{5} \times \$80,000 = \$32,000\).
- Net goodwill adjustment for Q = \(\$24,000 - \$32,000 = -\$8,000\).

3. **Final Q Capital balance:**
- Q's final capital = \(\$102,000 - \$8,000 = \$94,000\).

Award 1 mark for the correct answer. Method: Apply old profit sharing ratio to revaluation (\(+\$12,000\)) and goodwill credit (\(+\$24,000\)), then deduct goodwill write-off in new ratio (\(-\$32,000\)) from Q's initial capital (\(\$90,000\)) to find \(\$94,000\).

1. **Loss on Realization:**
- Non-current assets loss: \(\$120,000 - \$98,000 = \$22,000\)
- Trade receivables loss: \(\$30,000 - \$26,000 = \$4,000\)
- Inventory loss: \(\$20,000 - \$15,000 = \$5,000\)
- Trade payables savings: \(\$10,000 - \$9,000 = -\$1,000\)
- Dissolution expenses: \(+\$3,000\)
- Total Loss on Realization = \(\$22,000 + \$4,000 + \$5,000 - \$1,000 + \$3,000 = \$33,000\).

2. **B's share of realization loss:**
- B's share (2/5) = \(\$33,000 \times 0.4 = \$13,200\).

3. **B's Capital account settlement:**
- Capital balance = \(\$60,000 - \$13,200 = \$46,800\).

4. **Total cash received by B:**
- Settlement of loan: \(\$15,000\)
- Settlement of capital: \(\$46,800\)
- Total cash received = \(\$15,000 + \$46,800 = \$61,800\).

Award 1 mark for the correct answer. Method: Determine total realization loss (\(\$33,000\)), B's share of loss (\(\$13,200\)), adjust capital balance (\(\$46,800\)), and add B's loan (\(\$15,000\)) to find total cash received (\(\$61,800\)).

1. **Cash Flow Schedule:**
- **Year 0:** Initial outflow = \(-\$150,000\) (machine) \(-\ \$20,000\) (working capital) = \(-\$170,000\).
- Present Value (PV) = \(-\$170,000 \times 1.000 = -\$170,000\).
- **Year 1:** Inflow = \(\$60,000\).
- PV = \(\$60,000 \times 0.909 = \$54,540\).
- **Year 2:** Inflow = \(\$70,000\).
- PV = \(\$70,000 \times 0.826 = \$57,820\).
- **Year 3:** Inflow = \(\$50,000\) (operating) \(+\ \$30,000\) (scrap) \(+\ \$20,000\) (working capital recovery) = \(\$100,000\).
- PV = \(\$100,000 \times 0.751 = \$75,100\).

2. **Net Present Value (NPV):**
- NPV = \(-\170,000 + 54,540 + 57,820 + 75,100 = \$17,460\).

Award 1 mark for the correct answer. Method: Correctly incorporate Year 0 working capital outflow, Year 3 recovery of working capital, and salvage value into annual cash flows to find NPV of \(\$17,460\).

Using the linear interpolation formula:
\[ \text{IRR} = L + \left( \frac{\text{NPV}_L}{\text{NPV}_L - \text{NPV}_H} \right) \times (H - L) \]
where:
- \( L = 8\% \)
- \( H = 12\% \)
- \( \text{NPV}_L = +\$2,800 \)
- \( \text{NPV}_H = -\$4,200 \)

\[ \text{IRR} = 8\% + \left( \frac{2,800}{2,800 - (-4,200)} \right) \times (12\% - 8\%) \]
\[ \text{IRR} = 8\% + \left( \frac{2,800}{7,000} \right) \times 4\% = 8\% + (0.4 \times 4\%) = 9.6\% \]

Award 1 mark for the correct answer. Method: Apply the IRR interpolation formula using the given discount rates and NPV values to find 9.6%.

1. **Direct Material Price Variance:**
- Actual price paid per kg = \(\frac{\$63,800}{22,000\text{ kg}} = \$2.90\) per kg.
- Price variance = \((\text{Standard Price} - \text{Actual Price}) \times \text{Quantity Purchased}\)
- Price variance = \((\$3.00 - \$2.90) \times 22,000\text{ kg} = \$2,200\) Favourable (F).

2. **Direct Material Usage Variance:**
- Standard quantity for actual production = \(5,000\text{ units} \times 4\text{ kg/unit} = 20,000\text{ kg}\).
- Actual quantity used in production = 20,800 kg.
- Usage variance = \((\text{Standard Quantity} - \text{Actual Quantity Used}) \times \text{Standard Price}\)
- Usage variance = \((20,000\text{ kg} - 20,800\text{ kg}) \times \$3.00 = \$2,400\) Adverse (A).

Award 1 mark for the correct answer. Method: Calculate price variance based on purchases (\(\$2,200\) F) and usage variance based on production usage (\(\$2,400\) A).

1. **Fixed Overhead Expenditure Variance:**
- Expenditure variance = \(\text{Budgeted Overheads} - \text{Actual Overheads}\)
- Expenditure variance = \(\$60,000 - \$62,500 = \$2,500\) Adverse (A).

2. **Fixed Overhead Volume Variance:**
- Standard fixed overhead rate per unit = \(2\text{ hours} \times \$5.00/\text{hour} = \$10.00\) per unit.
- Volume variance = \((\text{Actual Production} - \text{Budgeted Production}) \times \text{Standard Cost per unit}\)
- Volume variance = \((5,800\text{ units} - 6,000\text{ units}) \times \$10.00 = \$2,000\) Adverse (A).

(Note: Volume variance can also be calculated as: \((\text{Standard Hours for Actual Production} - \text{Budgeted Hours}) \times \text{Standard Hourly Rate} = (11,600\text{ hours} - 12,000\text{ hours}) \times \$5.00 = \$2,000\) Adverse).

Award 1 mark for the correct answer. Method: Calculate expenditure variance as \(\$2,500\) Adverse and volume variance as \(\$2,000\) Adverse based on the difference between budgeted and actual production.

1. Calculate average investment:
\(\text{Average Investment} = \frac{\text{Initial Outlay} + \text{Residual Value}}{2} = \frac{\$160,000 + \$20,000}{2} = \$90,000\)

2. Calculate average annual accounting profit:
\(\text{Average Annual Profit} = \frac{\$90,000}{5\text{ years}} = \$18,000\)

3. Calculate Accounting Rate of Return (ARR):
\(\text{ARR} = \frac{\$18,000}{\$90,000} \times 100\% = 20.00\%\)

1 mark for the correct option (B).
- Option A uses the initial investment of \(\$160,000\) instead of the average investment.
- Option C uses an incorrect profit or investment formula.
- Option D is the result of applying incorrect formulas.

1. Calculate standard quantity allowed for actual production:
\(2,500 \text{ units} \times 4 \text{ kg/unit} = 10,000 \text{ kg}\)

2. Compare with actual quantity used:
\(\text{Variance in quantity} = 10,400 \text{ kg} - 10,000 \text{ kg} = 400 \text{ kg (Adverse)}\)

3. Value at standard price:
\(\text{Material Usage Variance} = 400 \text{ kg} \times \$6.00 \text{ per kg} = \$2,400 \text{ (Adverse)}\)

1 mark for the correct calculation and classification (B).
- Option A incorrectly values the variance at the actual price of \(\$5.90\) instead of the standard price.
- Option C has the correct amount but the wrong variance direction (Favourable).
- Option D is incorrect.

1. Credit old partners with goodwill in their old profit-sharing ratio:
- A's share = \(\$60,000 \times \frac{3}{5} = \$36,000\) (Credit)

2. Debit new partners with goodwill in their new profit-sharing ratio:
- A's share = \(\$60,000 \times \frac{5}{10} = \$30,000\) (Debit)

3. Calculate net adjustment for A:
\(\$36,000 \text{ (Credit)} - \$30,000 \text{ (Debit)} = \$6,000 \text{ (Credit)}\)

1 mark for the correct answer (A).
- Option B reverses the adjustment.
- Option C uses A's new ratio share alone.
- Option D uses A's old ratio share alone.

1. Number of bonus shares issued = \(1,000,000 \times \frac{1}{5} = 200,000\) shares.
2. Nominal value of bonus shares = \(200,000 \times \$0.50 = \$100,000\).
3. Balance on the share premium account after funding the bonus issue = \(\$120,000 - \$100,000 = \$20,000\).

1 mark for the correct balance (A).
- Option B incorrectly assumes the par value of the shares is \(\$1.00\) each, resulting in a cost of \(\$200,000\) which exceeds the share premium balance.
- Option C is the total cost of the bonus issue.
- Option D is the original share premium balance before the bonus issue.

1. Year 0 cash flow for working capital = \(-\$30,000\) (Outflow)
2. Year 4 cash flow for working capital recovery = \(+\$30,000\) (Inflow)
3. Present Value of Year 4 recovery = \(\$30,000 \times 0.683 = \$20,490\)
4. Net Present Value of working capital = \(-\$30,000 + \$20,490 = -\$9,510\)

1 mark for the correct net present value of working capital (B).
- Option A incorrect, assuming recovery cancels out time value of money.
- Option C is only the discounted Year 4 cash flow as a negative.
- Option D is the discounted Year 4 cash flow as a positive.

1. **Direct Labour Rate Variance**:
\(\text{Standard Cost of Actual Hours} = 2,500 \text{ hours} \times \$12 = \$30,000\)
\(\text{Actual Cost} = \$28,750\)
\(\text{Rate Variance} = \$30,000 - \$28,750 = \$1,250 \text{ (Favourable)}\)

2. **Direct Labour Efficiency Variance**:
\(\text{Standard Hours for Actual Production} = 800 \text{ units} \times 3 \text{ hours/unit} = 2,400 \text{ hours}\)
\(\text{Actual Hours Worked} = 2,500 \text{ hours}\)
\(\text{Efficiency Variance in Hours} = 100 \text{ hours (Adverse)}\)
\(\text{Efficiency Variance} = 100 \text{ hours} \times \$12 \text{ per hour} = \$1,200 \text{ (Adverse)}\)

1 mark for the correct calculation and identification of both variances (A).
- Option B has the wrong Favourable/Adverse labels.
- Options C and D contain incorrect calculations or incorrect variance directions.

1. Calculate opening equity:
\(\text{Opening Equity} = \$500,000 + \$180,000 = \$680,000\)

2. Adjust for profit and dividends:
\(\text{Equity before rights issue} = \$680,000 + \$115,000 - \$40,000 = \$755,000\)

3. Calculate rights issue proceeds:
- Existing shares = \(\frac{\$500,000}{\$0.25} = 2,000,000\) shares.
- Rights shares issued = \(\frac{2,000,000}{4} = 500,000\) shares.
- Rights issue proceeds = \(500,000 \times \$0.40 = \$200,000\).

4. Calculate closing equity:
\(\text{Closing Equity} = \$755,000 + \$200,000 = \$955,000\)

1 mark for the correct total equity calculation (C).
- Option A misses the rights issue completely.
- Option B only increases the rights issue by nominal value (\(\$125,000\)) instead of total proceeds (\(\$200,000\)).
- Option D represents a calculation error.

1. Calculate total Interest on Drawings:
- X: \(\$20,000 \times 8\% = \$1,600\)
- Y: \(\$15,000 \times 8\% = \$1,200\)
- Total Interest on Drawings = \(\$2,800\)

2. Calculate total Interest on Capital:
- X: \(\$120,000 \times 5\% = \$6,000\)
- Y: \(\$80,000 \times 5\% = \$4,000\)
- Total Interest on Capital = \(\$10,000\)

3. Calculate Residual Profit:
\(\text{Residual Profit} = \text{Net Profit} + \text{Total Interest on Drawings} - \text{Total Salaries} - \text{Total Interest on Capital}\)
\(\text{Residual Profit} = \$95,000 + \$2,800 - \$25,000 - \$10,000 = \$62,800\)

4. Calculate X's share of residual profit:
\(\text{X's Share} = \$62,800 \times 60\% = \$37,680\)

1 mark for the correct share of residual profit (B).
- Option A ignores interest on drawings in the calculation.
- Option C subtracts interest on drawings instead of adding it.
- Option D is an incorrect option.

To find C's final loan account balance, we adjust his capital account for current account, revaluation surplus, and goodwill:

1. Transfer C's current account balance: $45,000 (Cr) - $3,000 (Dr) = $42,000.
2. Share of revaluation surplus: C's share is \( \frac{1}{6} \times \$24,000 = \$4,000 \). Capital balance becomes $42,000 + $4,000 = $46,000.
3. Goodwill adjustment: C's share of goodwill is \( \frac{1}{6} \times \$60,000 = \$10,000 \). Since goodwill is not maintained, it is written off among remaining partners A and B. Thus, C's capital is credited with $10,000, making the capital balance $46,000 + $10,000 = $56,000.
4. Less cash paid: $56,000 - $15,000 = $41,000.

The remaining balance of $41,000 is transferred to the loan account.

1 mark for the correct answer of C. Reject alternative options (A, B, D).

According to corporate accounting rules, the transfer to the Capital Redemption Reserve (CRR) is calculated as:

\( \text{CRR Transfer} = \text{Nominal Value of Shares Redeemed} - \text{Nominal Value of Fresh Issue of Shares} \)

\( \text{CRR Transfer} = (100,000 \times \$1) - (40,000 \times \$1) = \$100,000 - \$40,000 = \$60,000 \).

The premium on redemption is written off against reserves and does not affect the CRR.

1 mark for the correct answer of B. Reject alternative options (A, C, D).

1. Present Value of Cash Inflows:
- Year 1: $60,000 \times 0.909 = $54,540
- Year 2: $60,000 \times 0.826 = $49,560
- Total PV of Cash Inflows = $54,540 + $49,560 = $104,100.

2. Net Present Value (NPV):
\( \text{NPV} = \$104,100 - \$100,000 = \$4,100 \).

3. Sensitivity of the project to a change in the initial investment:
\( \text{Sensitivity} = \frac{\text{NPV}}{\text{Initial Investment}} \times 100\% = \frac{\$4,100}{\$100,000} \times 100\% = 4.10\% \).

1 mark for the correct answer of B. Reject alternative options (A, C, D).

The labor rate variance is calculated as:

\( \text{Labor Rate Variance} = (\text{Actual Hours} \times \text{Standard Rate}) - \text{Actual Cost} \)

\( \text{Labor Rate Variance} = (4,200 \times \$12) - \$49,560 \)

\( = \$50,400 - \$49,560 = \$840 \text{ Favorable} \).

Since the actual cost ($49,560) is lower than the standard cost allowed for actual hours worked ($50,400), the variance is favorable.

1 mark for the correct answer of B. Reject alternative options (A, C, D).

1. Since goodwill is not to be maintained in the books:
First, goodwill is credited to the old partners in their old profit-sharing ratio (3:2):
Y's share of goodwill = \( \frac{2}{5} \times \$75,000 = \$30,000 \text{ (Cr)} \).

Second, the total goodwill is written off among the partners in their new profit-sharing ratio. The new profit-sharing ratio is:
- Z = \( \frac{1}{5} \) (or \( \frac{5}{25} \))
- X = \( \frac{4}{5} \times \frac{3}{5} = \frac{12}{25} \)
- Y = \( \frac{4}{5} \times \frac{2}{5} = \frac{8}{25} \)

Y's share of goodwill written off = \( \frac{8}{25} \times \$75,000 = \$24,000 \text{ (Dr)} \).

2. Net adjustment on Y's capital account = \( \$30,000 \text{ (Cr)} - \$24,000 \text{ (Dr)} = \$6,000 \text{ (Cr)} \).

3. Y's final capital balance = \( \$50,000 \text{ (original)} + \$6,000 = \$56,000 \).

1 mark for the correct answer of B. Reject alternative options (A, C, D).

Using the linear interpolation formula for the Internal Rate of Return (IRR):

\( \text{IRR} = L + \left( \frac{N_L}{N_L - N_H} \right) \times (H - L) \)

Where:
- \( L = 10\% \)
- \( H = 20\% \)
- \( N_L = \$9,480 \)
- \( N_H = -\$5,760 \)

\( \text{IRR} = 10\% + \left( \frac{\$9,480}{\$9,480 - (-\$5,760)} \right) \times (20\% - 10\%) \)

\( = 10\% + \left( \frac{9,480}{15,240} \right) \times 10\% \)

\( = 10\% + 0.622 \times 10\% = 16.22\% \), which rounds to 16.2%.

1 mark for the correct answer of C. Reject alternative options (A, B, D).

Part (a)
Calculations:
1. Rights issue:
- Existing shares: \( \$600,000 / \$0.50 = 1,200,000 \) shares.
- Rights shares: \( 1,200,000 / 4 = 300,000 \) shares.
- Nominal value increase: \( 300,000 \times \$0.50 = \$150,000 \) (Ordinary Share Capital).
- Share premium increase: \( 300,000 \times (\$0.80 - \$0.50) = \$90,000 \).
- Total cash received: \( 300,000 \times \$0.80 = \$240,000 \).

2. Dividend:
- Shares in issue on 1 December 2022: \( 1,200,000 + 300,000 = 1,500,000 \) shares.
- Interim dividend paid: \( 1,500,000 \times \$0.02 = \$30,000 \).

3. Retained Earnings adjustments:
- Draft profit before tax: $145,000
- Less: Depreciation on machinery: \( \$220,000 \times 15\% = (\$33,000) \)
- Adjusted profit before tax: $112,000
- Less: Taxation: \( (\$22,000) \)
- Profit for the year: $90,000

Statement of Changes in Equity for the year ended 30 April 2023:
- Balances at 1 May 2022: Share Capital $600,000; Share Premium $150,000; Revaluation Reserve $80,000; General Reserve $0; Retained Earnings $340,000; Total $1,170,000.
- Rights Issue: Share Capital +$150,000; Share Premium +$90,000; Total +$240,000.
- Profit for the year: Retained Earnings +$90,000; Total +$90,000.
- Revaluation of Land: Revaluation Reserve +$50,000; Total +$50,000.
- Dividends Paid: Retained Earnings -$30,000; Total -$30,000.
- Transfer to General Reserve: General Reserve +$15,000; Retained Earnings -$15,000; Total $0.
- Balances at 30 April 2023: Share Capital $750,000; Share Premium $240,000; Revaluation Reserve $130,000; General Reserve $15,000; Retained Earnings $385,000; Total $1,520,000.

Part (b)
Reporting under IAS 7:
- Rights Issue: The cash receipt of $240,000 must be reported in the Financing Activities section of the Statement of Cash Flows as 'Proceeds from issue of ordinary shares'.
- Revaluation of Land: The upward revaluation of $50,000 is a non-cash transaction. No cash flows occurred, so it is excluded from the Statement of Cash Flows. It is instead disclosed in the notes to the financial statements and shown in the Statement of Comprehensive Income.

Part (c)
Rights Issue vs. Debentures:
- Rights Issue Advantages: No obligation to pay regular dividends (preserves cash flow); equity does not need to be repaid (no redemption pressure); improves the gearing ratio (financial risk is lowered).
- Rights Issue Disadvantages: EPS (earnings per share) may be diluted if the new funds do not generate proportional returns immediately; issuing costs can be high.
- 8% Debentures Advantages: Interest is tax-deductible, which lowers the effective cost of debt; does not dilute ownership or control of existing shareholders.
- 8% Debentures Disadvantages: Obligation to pay 8% interest annually regardless of profit levels; must be repaid at maturity; increases gearing and financial risk.
- Recommendation: If the company seeks to maintain a safe financial structure, the rights issue is recommended as it decreases gearing. However, if profit generation is expected to be high and rapid, debentures would prevent dilution of EPS.

Part (a) [Total: 12 marks]
- Opening balances correct: [1 mark]
- Rights issue: Ordinary Share Capital +$150,000 [2 marks], Share Premium +$90,000 [2 marks]
- Dividend paid: -$30,000 in Retained Earnings [2 marks]
- Land revaluation: +$50,000 in Revaluation Reserve [1 mark]
- Profit for the year calculation: ($145,000 - $33,000 - $22,000) = $90,000 [2 marks (including 1 mark for correct depreciation adjustment)]
- General reserve transfer: +$15,000 to General Reserve and -$15,000 from Retained Earnings [1 mark]
- Correct column totals and cross-cast totals: [1 mark]

Part (b) [Total: 4.5 marks]
- Explanation of rights issue as financing activity (+ $240,000): [2 marks]
- Explanation of land revaluation as a non-cash transaction with no cash flow effect (disclosed in notes): [2.5 marks]

Part (c) [Total: 6 marks]
- For discussing advantages/disadvantages of rights issue: [2 marks]
- For discussing advantages/disadvantages of 8% debentures: [2 marks]
- For clear supported recommendation: [2 marks]

Part (a)
Revaluation Account:
- Debit side:
- Equipment Write-down: \( \$90,000 - \$78,000 = \$12,000 \)
- Provision for Doubtful Debts: \( \$35,000 \times 4\% = \$1,400 \)
- Inventory Write-down: \( \$42,000 - \$38,500 = \$3,500 \)
- Credit side:
- Premises Revaluation: \( \$320,000 - \$250,000 = \$70,000 \)
- Net Profit on Revaluation: \( \$70,000 - (\$12,000 + \$1,400 + \$3,500) = \$53,100 \)
- Distributed to partners (old ratio 3:2:1):
- A: \( \$53,100 \times 3/6 = \$26,550 \)
- B: \( \$53,100 \times 2/6 = \$17,700 \)
- C: \( \$53,100 \times 1/6 = \$8,850 \)

Part (b)
Partners' Capital Accounts on 1 January 2023:

Debit Side:
- Current Account transfer (C): $12,000
- Goodwill Written Off (new ratio 3:2:1 among A, C, D):
- A: \( \$90,000 \times 3/6 = \$45,000 \)
- C: \( \$90,000 \times 2/6 = \$30,000 \)
- D: \( \$90,000 \times 1/6 = \$15,000 \)
- Settlement of B:
- 6% Loan: \( \$175,700 \times 50\% = \$87,850 \)
- Bank: \( \$175,700 \times 50\% = \$87,850 \)
- Balances c/d:
- A: $220,550
- C: $51,850
- D: $80,000

Credit Side:
- Balances b/f:
- A: $180,000
- B: $120,000
- C: $70,000
- Current Account transfer:
- A: $14,000
- B: $8,000
- Revaluation Profit:
- A: $26,550
- B: $17,700
- C: $8,850
- Goodwill Created (old ratio 3:2:1):
- A: $45,000
- B: $30,000
- C: $15,000
- Cash Introduced (D):
- D: \( \$80,000 \text{ (target)} + \$15,000 \text{ (goodwill write-off)} = \$95,000 \)

Verification of balances:
- B Capital: \( \$120,000 + \$8,000 + \$17,700 + \$30,000 = \$175,700 \) (fully settled, balance is nil).
- A Capital: \( \$180,000 + \$14,000 + \$26,550 + \$45,000 - \$45,000 = \$220,550 \).
- C Capital: \( \$70,000 - \$12,000 + \$8,850 + \$15,000 - \$30,000 = \$51,850 \).
- D Capital: \( \$95,000 \text{ (cash)} - \$15,000 \text{ (goodwill)} = \$80,000 \).

Part (c)
Difference between equity partnership and a partner loan:
- Profits and Losses: Equity partners share the profits and losses of the business according to the profit-sharing ratio. Loan providers do not share in profits or losses; they are external creditors.
- Return/Interest: Equity partners may receive interest on capital (if agreed in partnership deed) but only if profits are available. Loan providers receive a fixed rate of interest (e.g., 6%) which is an expense in the income statement and must be paid regardless of whether the partnership makes a profit or loss.
- Priority in Liquidation: In the event of dissolution, a loan provider is a creditor and is paid back before equity partners receive any return of capital.

Part (a) [Total: 4 marks]
- Premises gain: +$70,000 [1 mark]
- Equipment, Provision, and Inventory write-downs correct: [1 mark]
- Total Revaluation profit of $53,100 distributed in 3:2:1 ratio: [2 marks (all correct) / 1 mark (at least one correct)]

Part (b) [Total: 12.5 marks]
- Opening capital balances: [0.5 marks]
- Current account transfers to capital (A, B, C correct): [1.5 marks]
- Revaluation profits credited: [1.5 marks]
- Goodwill created (credited in old ratio): [1.5 marks]
- Goodwill written off (debited in new ratio to A, C, D): [1.5 marks]
- Cash paid to B ($87,850) and Loan account created ($87,850): [2 marks]
- Cash introduced by D ($95,000) calculated correctly: [2 marks]
- Correct closing balances for A ($220,550) and C ($51,850): [2 marks]

Part (c) [Total: 6 marks]
- Distinction regarding profit and loss sharing: [2 marks]
- Distinction regarding fixed interest vs. profit share: [2 marks]
- Distinction regarding priority of repayment upon dissolution: [2 marks]

Part (a)
NPV calculation at 10% cost of capital:
- Year 0 Outflow: \( (\$450,000) \times 1.000 = (\$450,000) \)
- Year 1 Cash Flow: \( \$120,000 \times 0.909 = \$109,080 \)
- Year 2 Cash Flow: \( \$150,000 \times 0.826 = \$123,900 \)
- Year 3 Cash Flow: \( \$160,000 \times 0.751 = \$120,160 \)
- Year 4 Cash Flow: \( \$140,000 \times 0.683 = \$95,620 \)
- Year 5 Cash Flow (Net Cash Inflow + Residual value = $110,000 + $50,000 = $160,000): \( \$160,000 \times 0.621 = \$99,360 \)
- Total PV of cash inflows: \( 109,080 + 123,900 + 120,160 + 95,620 + 99,360 = \$548,120 \)
- Net Present Value (NPV): \( \$548,120 - \$450,000 = \$98,120 \)

Part (b)
NPV calculation at 14%:
- Year 0: \( (\$450,000) \)
- Year 1: \( \$120,000 \times 0.877 = \$105,240 \)
- Year 2: \( \$150,000 \times 0.769 = \$115,350 \)
- Year 3: \( \$160,000 \times 0.675 = \$108,000 \)
- Year 4: \( \$140,000 \times 0.592 = \$82,880 \)
- Year 5: \( \$160,000 \times 0.519 = \$83,040 \)
- Total PV of cash inflows at 14%: \( 105,240 + 115,350 + 108,000 + 82,880 + 83,040 = \$494,510 \)
- NPV at 14%: \( \$494,510 - \$450,000 = \$44,510 \)

IRR formula:
\( IRR = L + \frac{NPV_L}{NPV_L - NPV_H} \times (H - L) \)
where \( L = 10\% \), \( H = 14\% \)
\( IRR = 10 + \frac{98,120}{98,120 - 44,510} \times (14 - 10) \)
\( IRR = 10 + \frac{98,120}{53,610} \times 4 = 10 + (1.83025 \times 4) = 10 + 7.32\% = 17.32\% \)

Part (c)
ARR (Average Investment Method):
- Total cash inflows (operating): \( 120,000 + 150,000 + 160,000 + 140,000 + 110,000 = \$680,000 \)
- Total depreciation over 5 years: \( \$450,000 - \$50,000 = \$400,000 \)
- Total profit over 5 years: \( \$680,000 - \$400,000 = \$280,000 \)
- Average annual profit: \( \$280,000 / 5 = \$56,000 \)
- Average investment: \( \frac{\text{Initial cost} + \text{Scrap value}}{2} = \frac{450,000 + 50,000}{2} = \$250,000 \)
- ARR = \( \frac{\$56,000}{\$250,000} \times 100\% = 22.4\% \)
- Note: if ARR is calculated using the initial investment method: \( \frac{\$56,000}{\$450,000} \times 100\% = 12.44\% \).

Part (d)
Advice & non-financial factors:
- Financial Advice: VeloTech Ltd should accept the project. The NPV is positive at $98,120, the IRR of 17.32% exceeds the hurdle cost of capital of 10%, and the ARR of 22.4% is highly attractive.
- Non-financial Factor 1: Staff retraining and morale. Installing automated assembly systems might cause redundancies or require intensive retraining of factory employees, leading to industrial friction.
- Non-financial Factor 2: Reliability and maintenance. Automated systems are subject to breakdowns. If the machine breaks down, the entire assembly line could halt, leading to lost sales and disappointed customers.

Part (a) [Total: 6 marks]
- Correct PV for Years 1-4: [2 marks]
- Correct PV for Year 5 (incorporating $50,000 scrap value, i.e. $160,000 x 0.621): [2 marks]
- Correct total PV of inflows and final NPV of $98,120: [2 marks]

Part (b) [Total: 6.5 marks]
- Correct PV calculations at 14% for Years 1-5: [2.5 marks]
- Correct NPV at 14% of $44,510: [1 mark]
- Correct insertion into IRR formula: [2 marks]
- Correct final IRR of 17.32%: [1 mark]

Part (c) [Total: 4 marks]
- Correct calculation of total and average profit ($56,000): [1.5 marks]
- Correct calculation of average investment ($250,000): [1 mark]
- Correct ARR of 22.4% (or 12.44% if using initial investment method): [1.5 marks]

Part (d) [Total: 6 marks]
- Clear financial recommendation based on calculations: [2 marks]
- First non-financial factor (e.g. staff impact, quality): [2 marks]
- Second non-financial factor (e.g. reliability, technological obsolescence): [2 marks]

Part (a)
1. Direct Material Price Variance:
- Formula: \( (\text{Standard Price} - \text{Actual Price}) \times \text{Actual Quantity} \)
- Actual Price = \( \$121,520 / 19,600 \text{ kg} = \$6.20 \text{ per kg} \).
- Variance = \( (\$6.00 - \$6.20) \times 19,600 = \$3,920 \text{ (Adverse)} \).

2. Direct Material Usage Variance:
- Formula: \( (\text{Standard Quantity for Actual Production} - \text{Actual Quantity}) \times \text{Standard Price} \)
- Standard Quantity for 4,800 units = \( 4,800 \times 4 \text{ kg} = 19,200 \text{ kg} \).
- Variance = \( (19,200 - 19,600) \times \$6.00 = 400 \text{ kg (A)} \times \$6.00 = \$2,400 \text{ (Adverse)} \).

3. Direct Labour Rate Variance:
- Formula: \( (\text{Standard Rate} - \text{Actual Rate}) \times \text{Actual Hours} \)
- Actual Rate = \( \$144,150 / 9,300 \text{ hours} = \$15.50 \text{ per hour} \).
- Variance = \( (\$15.00 - \$15.50) \times 9,300 = \$4,650 \text{ (Adverse)} \).

4. Direct Labour Efficiency Variance:
- Formula: \( (\text{Standard Hours for Actual Production} - \text{Actual Hours}) \times \text{Standard Rate} \)
- Standard Hours for 4,800 units = \( 4,800 \times 2 \text{ hours} = 9,600 \text{ hours} \).
- Variance = \( (9,600 - 9,300) \times \$15.00 = 300 \text{ hours (F)} \times \$15.00 = \$4,500 \text{ (Favourable)} \).

Part (b)
1. Fixed Overhead Expenditure Variance:
- Formula: \( \text{Budgeted Fixed Overheads} - \text{Actual Fixed Overheads} \)
- Variance = \( \$40,000 - \$42,500 = \$2,500 \text{ (Adverse)} \).

2. Fixed Overhead Capacity Variance:
- Formula: \( (\text{Actual Hours Worked} - \text{Budgeted Hours}) \times \text{Standard FOAR per hour} \)
- FOAR = \( \$40,000 / 10,000 \text{ hours} = \$4.00 \text{ per hour} \).
- Variance = \( (9,300 - 10,000) \times \$4.00 = 700 \text{ hours (A)} \times \$4.00 = \$2,800 \text{ (Adverse)} \).

3. Fixed Overhead Efficiency Variance:
- Formula: \( (\text{Standard Hours for Actual Production} - \text{Actual Hours Worked}) \times \text{Standard FOAR per hour} \)
- Variance = \( (9,600 - 9,300) \times \$4.00 = 300 \text{ hours (F)} \times \$4.00 = \$1,200 \text{ (Favourable)} \).

Part (c)
- Link between Efficiency Variances: Both variances are driven by the exact same productive efficiency metric. In March, the workers were efficient, saving 300 direct labour hours (standard 9,600 vs actual 9,300). This efficiency resulted in a Favourable direct labour efficiency variance of $4,500. Because fixed production overheads are absorbed based on direct labour hours, saving 300 labour hours automatically results in a Favourable fixed overhead efficiency variance of $1,200 (calculated as \( 300 \text{ hours} \times \$4.00 \)).
- Standard Costing for Performance Improvement: Management can use variance analysis to pinpoint specific areas of underperformance or efficiency. For example, the adverse material price and labor rate variances suggest cost control issues in purchasing and wages, while favorable labor efficiency suggests excellent factory floor productivity. This helps management implement 'management by exception' where corrective action is focused only on significant adverse variances.

Part (a) [Total: 8 marks]
- Direct Material Price Variance: $3,920 (A) [2 marks]
- Direct Material Usage Variance: $2,400 (A) [2 marks]
- Direct Labour Rate Variance: $4,650 (A) [2 marks]
- Direct Labour Efficiency Variance: $4,500 (F) [2 marks]

Part (b) [Total: 8.5 marks]
- Fixed Overhead Expenditure Variance: $2,500 (A) [2 marks]
- Fixed Overhead Capacity Variance: $2,800 (A) [3 marks (including 1 mark for calculating correct FOAR of $4.00 per hour)]
- Fixed Overhead Efficiency Variance: $1,200 (F) [3.5 marks]

Part (c) [Total: 6 marks]
- Identifying and explaining the link (both share the same 300 saved hours as base): [3 marks]
- Explaining how standard costing helps performance (e.g., feedback loop, accountability, control, cost reduction): [3 marks]

*(a) Realisation Account*

Debit:
- Premises: $120,000
- Equipment: $45,000
- Inventory: $28,000
- Trade receivables: $19,500
- Bank: $3,500
- Profit on Realisation: A (3/5) $30,000, B (2/5) $20,000
Total Debits = $266,000

Credit:
- Trade Payables: $16,000
- AB Ltd (Purchase consideration): $250,000
Total Credits = $266,000

*(b) Partners' Capital Accounts*

**A's Capital Account:**
Debit:
- Shares in AB Ltd (150,000 * $1.20 * 3/5): $108,000
- 8% Debentures in AB Ltd (Balancing): $41,000
Total = $149,000

Credit:
- Balance b/d: $110,000
- Current Account transfer: $9,000
- Realisation Profit: $30,000
Total = $149,000

**B's Capital Account:**
Debit:
- Shares in AB Ltd (150,000 * $1.20 * 2/5): $72,000
- 8% Debentures in AB Ltd (Balancing): $29,000
Total = $101,000

Credit:
- Balance b/d: $75,000
- Current Account transfer: $6,000
- Realisation Profit: $20,000
Total = $101,000

*(c) Advantages of Conversion (Three of the following):*
1. **Limited Liability:** Protection of partners' personal wealth as their liability is restricted to their investment.
2. **Separate Legal Entity:** The company can own property, sue, and be sued in its own name.
3. **Access to Capital:** Increased ability to raise finance through issuing shares or obtaining loans.
4. **Perpetual Succession:** The business continues to exist irrespective of changes in ownership.

*(d) Goodwill calculation:*
- Fair value of net assets acquired: Premises ($180,000) + Equipment ($38,000) + Inventory ($25,000) + Receivables ($18,525) + Bank ($3,500) - Payables ($16,000) = $249,025.
- Purchase consideration: $250,000.
- Goodwill = $250,000 - $249,025 = $975.
- **Treatment:** Goodwill is recognized as a non-current intangible asset. It is not amortised but tested annually for impairment.

*(a) Realisation Account (8 marks)*
- Transfer of assets to debit: 1 mark for all correct assets.
- Transfer of trade payables to credit: 1 mark.
- Credit entry for AB Ltd: 1 mark.
- Calculation of profit: 2 marks.
- Profit division (A: $30,000, B: $20,000): 3 marks (1.5 marks each).

*(b) Capital Accounts (8 marks)*
- Balance b/d and Current account transfers: 2 marks (1 mark per partner).
- Realisation profit credit: 2 marks (1 mark per partner).
- Share distribution debit: 2 marks (1 mark per partner).
- Debenture distribution debit (Balancing figure): 2 marks (1 mark per partner).

*(c) Advantages (6 marks)*
- 2 marks per advantage explained (up to 3 advantages).

*(d) Goodwill (3 marks)*
- 1 mark for correct calculation ($975).
- 1 mark for recognition as an intangible asset.
- 1 mark for testing for impairment annually instead of amortisation.

*(a)(i) NPV Calculation:*

**Machine X:**
- Year 0: ($150,000) * 1.000 = ($150,000)
- Year 1: $60,000 * 0.909 = $54,540
- Year 2: $55,000 * 0.826 = $45,430
- Year 3: $50,000 * 0.751 = $37,550
- Year 4: ($40,000 + $10,000 residual) * 0.683 = $34,150
**NPV of Machine X = $21,670**

**Machine Y:**
- Year 0: ($200,000) * 1.000 = ($200,000)
- Year 1: $80,000 * 0.909 = $72,720
- Year 2: $75,000 * 0.826 = $61,950
- Year 3: $70,000 * 0.751 = $52,570
- Year 4: ($60,000 + $20,000 residual) * 0.683 = $54,640
**NPV of Machine Y = $41,880**

*(a)(ii) ARR Calculation:*

**Machine X:**
- Average investment: ($150,000 + $10,000) / 2 = $80,000
- Total operating cash inflow: $205,000
- Less depreciation: $150,000 - $10,000 = $140,000
- Total profit over 4 years: $65,000
- Average annual profit: $65,000 / 4 = $16,250
- **ARR** = ($16,250 / $80,000) * 100% = **20.31%**

**Machine Y:**
- Average investment: ($200,000 + $20,000) / 2 = $110,000
- Total operating cash inflow: $285,000
- Less depreciation: $200,000 - $20,000 = $180,000
- Total profit over 4 years: $105,000
- Average annual profit: $105,000 / 4 = $26,250
- **ARR** = ($26,250 / $110,000) * 100% = **23.86%**

*(b) Recommendation:*
- V Ltd should purchase Machine Y. It has a higher NPV ($41,880 vs $21,670), meaning it creates greater shareholder wealth. It also has a higher ARR (23.86% vs 20.31%). The extra initial cost of $50,000 is justified by the returns.

*(c) Discussion:*
- **Advantages of NPV over ARR:** NPV considers the time value of money; NPV uses cash flows instead of accounting profits which can be manipulated; NPV has a clear rule of maximizing shareholder wealth.
- **Disadvantages of NPV / Advantages of ARR:** ARR is simpler to understand as a percentage; ARR is easier to calculate and does not require identifying a cost of capital rate; ARR aligns directly with accounting ROCE targets.

*(a)(i) NPV (8 marks)*
- Machine X correct flows & discounting: 3 marks, correct NPV: 1 mark.
- Machine Y correct flows & discounting (especially year 4 residual): 3 marks, correct NPV: 1 mark.

*(a)(ii) ARR (6 marks)*
- Machine X average investment (1 mark), average profit (1 mark), ARR (1 mark).
- Machine Y average investment (1 mark), average profit (1 mark), ARR (1 mark).

*(b) Recommendation (4 marks)*
- Clear decision for Y: 1 mark.
- Rationale pointing to higher NPV: 1 mark.
- Rationale pointing to higher ARR: 1 mark.
- Mention of risk/higher initial outlay of Y: 1 mark.

*(c) Discussion (7 marks)*
- Up to 4 marks for advantages of NPV (time value, objective cash flows, shareholder wealth focus).
- Up to 3 marks for advantages of ARR (simple percentage, no cost of capital required, familiar accounting metric).

*(a) Variance Calculations:*

**(i) Material Variances:**
- Actual price paid per kg = $106,920 / 19,800 kg = $5.40.
- **Material Price Variance** = (Standard Price - Actual Price) * Actual Quantity = ($5.50 - $5.40) * 19,800 = **$1,980 Favourable [F]**
- Standard Quantity for actual production = 4,800 units * 4 kg = 19,200 kg.
- **Material Usage Variance** = (Standard Quantity - Actual Quantity) * Standard Price = (19,200 - 19,800) * $5.50 = **$3,300 Adverse [A]**

**(ii) Labour Variances:**
- Actual hourly rate paid = $172,020 / 14,100 hours = $12.20.
- **Labour Rate Variance** = (Standard Rate - Actual Rate) * Actual Hours = ($12.00 - $12.20) * 14,100 = **$2,820 Adverse [A]**
- Standard Hours for actual production = 4,800 units * 3 hours = 14,400 hours.
- **Labour Efficiency Variance** = (Standard Hours - Actual Hours) * Standard Rate = (14,400 - 14,100) * $12.00 = **$3,600 Favourable [F]**

**(iii) Fixed Overhead Variances:**
- Budgeted Fixed Overheads = 5,000 units * $12.00 = $60,000.
- **Fixed Overhead Expenditure Variance** = Budgeted Fixed Overheads - Actual Fixed Overheads = $60,000 - $61,500 = **$1,500 Adverse [A]**
- **Fixed Overhead Volume Variance** = (Actual Units - Budgeted Units) * Standard Rate per unit = (4,800 - 5,000) * $12.00 = **$2,400 Adverse [A]**

**(iv) Fixed Overhead Sub-variances:**
- Budgeted Hours = 5,000 units * 3 hours = 15,000 hours.
- **Fixed Overhead Capacity Variance** = (Actual Hours - Budgeted Hours) * Standard Rate per hour = (14,100 - 15,000) * $4.00 = **$3,600 Adverse [A]**
- Standard hours for actual production = 14,400 hours.
- **Fixed Overhead Efficiency Variance** = (Standard Hours - Actual Hours) * Standard Rate per hour = (14,400 - 14,100) * $4.00 = **$1,200 Favourable [F]**

*(b) Reconciliation Statement:*

Standard Cost of Actual Production (4,800 * $70) = **$336,000**

*Add Favourable Variances:*
- Material Price Variance: $1,980
- Labour Efficiency Variance: $3,600
- Fixed Overhead Efficiency Variance: $1,200
Total Favourable = **$6,780**

*Less Adverse Variances:*
- Material Usage Variance: $3,300
- Labour Rate Variance: $2,820
- Fixed Overhead Expenditure Variance: $1,500
- Fixed Overhead Capacity Variance: $3,600
Total Adverse = **$11,220**

*Net Variance effect:* $11,220 - $6,780 = **$4,440 [A]**

Actual Cost of Production = **$340,440** (which matches direct materials $106,920 + direct labour $172,020 + fixed overheads $61,500).

*(c) Discussion on Labour Variances:*
1. **Usage of more highly skilled labour:** The company may have used senior, highly skilled workers instead of junior staff. This led to a higher actual wage rate than standard (Adverse Rate Variance) but their efficiency and speed reduced the total hours worked below the standard level (Favourable Efficiency Variance).
2. **Unplanned wage/bonus payments:** A wage increase or incentive scheme was introduced (Adverse Rate) which motivated the staff to work much faster than standard (Favourable Efficiency).

*(a)(i) Materials (4 marks)*
- 2 marks for Material Price Variance (1 mark for value, 1 mark for F).
- 2 marks for Material Usage Variance (1 mark for value, 1 mark for A).

*(a)(ii) Labour (4 marks)*
- 2 marks for Labour Rate Variance (1 mark for value, 1 mark for A).
- 2 marks for Labour Efficiency Variance (1 mark for value, 1 mark for F).

*(a)(iii) Fixed Overhead (4 marks)*
- 2 marks for Expenditure Variance (1 mark for value, 1 mark for A).
- 2 marks for Volume Variance (1 mark for value, 1 mark for A).

*(a)(iv) Fixed Overhead Sub-variances (4 marks)*
- 2 marks for Capacity Variance (1 mark for value, 1 mark for A).
- 2 marks for Efficiency Variance (1 mark for value, 1 mark for F).

*(b) Reconciliation Statement (5 marks)*
- 1 mark for correct Standard Cost start ($336,000).
- 1 mark for grouping and listing all favourable variances correctly.
- 1 mark for grouping and listing all adverse variances correctly.
- 1 mark for correct Net Variance calculated ($4,440 [A]).
- 1 mark for matching correct Actual Cost finish ($340,440).

*(c) Discussion (4 marks)*
- 2 marks per explained reason (1 mark for description, 1 mark for relating rate to efficiency effects).

### (a) Calculations for Project X

#### (i) Net Present Value (NPV) at 10% cost of capital
| Year | Cash Flow ($) | Discount Factor at 10% | Present Value ($) |
|---|---|---|---|
| 0 | (400,000) | 1.000 | (400,000) |
| 1 | 150,000 | 0.909 | 136,350 |
| 2 | 180,000 | 0.826 | 148,680 |
| 3 | 140,000 | 0.751 | 105,140 |
| 4 | 150,000* | 0.683 | 102,450 |
| **NPV** | | | **92,620** |

*Note: Year 4 cash flow includes the residual value of $40,000 ($110,000 + $40,000 = $150,000).

#### (ii) Net Present Value (NPV) at 15% cost of capital
| Year | Cash Flow ($) | Discount Factor at 15% | Present Value ($) |
|---|---|---|---|
| 0 | (400,000) | 1.000 | (400,000) |
| 1 | 150,000 | 0.870 | 130,500 |
| 2 | 180,000 | 0.756 | 136,080 |
| 3 | 140,000 | 0.658 | 92,120 |
| 4 | 150,000 | 0.572 | 85,800 |
| **NPV** | | | **44,500** |

#### (iii) Internal Rate of Return (IRR)
Using the interpolation formula:
\( \text{IRR} = L + \left( \frac{\text{NPV}_L}{\text{NPV}_L - \text{NPV}_H} \right) \times (H - L) \)
Where:
- \( L = 10\% \)
- \( H = 15\% \)
- \( \text{NPV}_L = 92,620 \)
- \( \text{NPV}_H = 44,500 \)

\( \text{IRR} = 10\% + \left( \frac{92,620}{92,620 - 44,500} \right) \times (15\% - 10\%) \)
\( \text{IRR} = 10\% + \left( \frac{92,620}{48,120} \right) \times 5\% \)
\( \text{IRR} = 10\% + 1.92477 \times 5\% = 19.62\% \)

#### (iv) Accounting Rate of Return (ARR)
- \( \text{Total Cash Inflows over 4 years} = 150,000 + 180,000 + 140,000 + 110,000 = \$580,000 \)
- \( \text{Total Depreciation} = \text{Initial Cost} - \text{Residual Value} = 400,000 - 40,000 = \$360,000 \)
- \( \text{Total Profit} = \text{Total Inflows} - \text{Total Depreciation} = 580,000 - 360,000 = \$220,000 \)
- \( \text{Average Annual Profit} = \frac{220,000}{4 \text{ years}} = \$55,000 \)
- \( \text{Average Investment} = \frac{\text{Initial Cost} + \text{Residual Value}}{2} = \frac{400,000 + 40,000}{2} = \$220,000 \)
- \( \text{ARR} = \frac{\text{Average Annual Profit}}{\text{Average Investment}} \times 100 = \frac{55,000}{220,000} \times 100 = 25.00\% \)
*(If initial investment is used instead: \( \text{ARR} = \frac{55,000}{400,000} \times 100 = 13.75\% \). both methods are acceptable, but standard is the average investment method.)*

---

### (b) Comparison of NPV and IRR

**Net Present Value (NPV):**
- *Advantages*:
- It represents the direct absolute addition to shareholder wealth, which is the primary financial objective of a listed company.
- It assumes reinvestment of cash flows at the company's cost of capital, which is a realistic and conservative assumption.
- It avoids the multiple rate of return problem that can occur with non-conventional cash flows.
- *Disadvantages*:
- It does not show the rate of return, making it harder for non-financial managers to conceptualize.
- It requires an upfront calculation of the cost of capital, which can be difficult to estimate accurately.

**Internal Rate of Return (IRR):**
- *Advantages*:
- It presents results as a percentage, which is easily understood by managers and can be directly compared against hurdle rates.
- It does not require the exact cost of capital to be calculated beforehand to make a decision (as long as it is known to be less than the IRR).
- *Disadvantages*:
- It can lead to incorrect project selection when comparing mutually exclusive projects of different scales (a small project with high IRR might be chosen over a large project with higher NPV).
- It assumes reinvestment of intermediate cash flows at the IRR itself, which is often unrealistic for highly profitable projects.

**(a)(i) NPV at 10% [5 marks total]**
- Correct cash flow for Year 4 of $150,000 (including residual value) [1 mark]
- Correct PV for Year 1 & 2 ($136,350 & $148,680) [1 mark]
- Correct PV for Year 3 & 4 ($105,140 & $102,450) [1 mark]
- Subtraction of initial investment ($400,000) [1 mark]
- Correct final NPV of $92,620 [1 mark]

**(a)(ii) NPV at 15% [5 marks total]**
- Correct cash flow of Year 4 ($150,000) [1 mark]
- Correct PV for Year 1 & 2 ($130,500 & $136,080) [1 mark]
- Correct PV for Year 3 & 4 ($92,120 & $85,800) [1 mark]
- Subtraction of initial investment ($400,000) [1 mark]
- Correct final NPV of $44,500 [1 mark]

**(a)(iii) IRR [3 marks total]**
- Use of correct interpolation formula [1 mark]
- Correct substitution of values [1 mark]
- Correct final answer of 19.62% (allow OF if calculation error in a(i) or a(ii)) [1 mark]

**(a)(iv) ARR [4 marks total]**
- Correct total accounting profit of $220,000 or average annual profit of $55,000 [1 mark]
- Correct average investment calculation of $220,000 (or initial investment of $400,000) [1 mark]
- Correct ARR formula application [1 mark]
- Correct final answer of 25.00% (or 13.75%) [1 mark]

**(b) Discussion of NPV vs IRR [8 marks total]**
- 1 mark for each valid advantage/disadvantage of NPV discussed (Max 4 marks)
- 1 mark for each valid advantage/disadvantage of IRR discussed (Max 4 marks)

### (a) Variance Calculations

#### (i) Direct Material Price Variance
- \( \text{Actual Price per kg} = \frac{\$50,840}{8,200 \text{ kg}} = \$6.20 \)
- \( \text{Standard Price} = \$6.00 \)
- \( \text{Variance} = (\text{Standard Price} - \text{Actual Price}) \times \text{Actual Quantity} \)
- \( \text{Variance} = (\$6.00 - \$6.20) \times 8,200 = \$1,640 \text{ Adverse (A)} \)

#### (ii) Direct Material Usage Variance
- \( \text{Standard Quantity allowed for actual production} = 2,100 \text{ units} \times 4 \text{ kg} = 8,400 \text{ kg} \)
- \( \text{Actual Quantity used} = 8,200 \text{ kg} \)
- \( \text{Variance} = (\text{Standard Quantity} - \text{Actual Quantity}) \times \text{Standard Price} \)
- \( \text{Variance} = (8,400 - 8,200) \times \$6.00 = \$1,200 \text{ Favourable (F)} \)

#### (iii) Direct Labour Rate Variance
- \( \text{Actual Rate per hour} = \frac{\$74,880}{6,400 \text{ hours}} = \$11.70 \)
- \( \text{Standard Rate} = \$12.00 \)
- \( \text{Variance} = (\text{Standard Rate} - \text{Actual Rate}) \times \text{Actual Hours} \)
- \( \text{Variance} = (\$12.00 - \$11.70) \times 6,400 = \$1,920 \text{ Favourable (F)} \)

#### (iv) Direct Labour Efficiency Variance
- \( \text{Standard Hours allowed for actual production} = 2,100 \text{ units} \times 3 \text{ hours} = 6,300 \text{ hours} \)
- \( \text{Actual Hours worked} = 6,400 \text{ hours} \)
- \( \text{Variance} = (\text{Standard Hours} - \text{Actual Hours}) \times \text{Standard Rate} \)
- \( \text{Variance} = (6,300 - 6,400) \times \$12.00 = \$1,200 \text{ Adverse (A)} \)

#### (v) Fixed Overhead Expenditure Variance
- \( \text{Budgeted Fixed Overhead} = 2,000 \text{ units} \times \$15 = \$30,000 \)
- \( \text{Actual Fixed Overhead} = \$31,500 \)
- \( \text{Variance} = \text{Budgeted Fixed Overhead} - \text{Actual Fixed Overhead} = \$30,000 - \$31,500 = \$1,500 \text{ Adverse (A)} \)

#### (vi) Fixed Overhead Volume Variance
- \( \text{Standard volume (budgeted)} = 2,000 \text{ units} \)
- \( \text{Actual volume} = 2,100 \text{ units} \)
- \( \text{Standard rate per unit} = \$15.00 \)
- \( \text{Variance} = (\text{Actual Production} - \text{Budgeted Production}) \times \text{Standard Rate per unit} \)
- \( \text{Variance} = (2,100 - 2,000) \times \$15.00 = \$1,500 \text{ Favourable (F)} \)

---

### (b) Reconciliation of Budgeted Profit to Actual Profit
- \( \text{Budgeted profit per unit} = \text{Selling Price (\$110)} - \text{Standard Cost (\$75)} = \$35 \)
- \( \text{Budgeted Profit} = 2,000 \text{ units} \times \$35 = \$70,000 \)
- \( \text{Sales Volume Variance (in profit terms)} = (2,100 - 2,000) \times \$35 = \$3,500 \text{ (F)} \)
- \( \text{Standard Profit on Actual Sales} = \$73,500 \)

| Item | $ | $ |
|---|---|---|
| **Budgeted Profit** | | **70,000** |
| Add: Sales Volume Variance (F) | | 3,500 |
| **Standard Profit on Actual Sales** | | **73,500** |
| **Variances:** | **Favourable ($)** | **Adverse ($)** |
| Direct Material Price | | 1,640 |
| Direct Material Usage | 1,200 | |
| Direct Labour Rate | 1,920 | |
| Direct Labour Efficiency | | 1,200 |
| Fixed Overhead Expenditure | | 1,500 |
| Fixed Overhead Volume | 1,500 | |
| **Subtotals** | **4,620** | **4,340** |
| **Net Favourable Variance** | | **280** |
| **Actual Profit** | | **73,780** |

*Check: Actual Revenue = $231,000. Actual Costs = $50,840 + $74,880 + $31,500 = $157,220. Actual Profit = $231,000 - $157,220 = $73,780. (Reconciliation is correct)*

---

### (c) Interaction of Labour Rate and Efficiency Variances
- A favourable labour rate variance indicates that the average actual wage rate paid to workers was lower than standard ($11.70 actual vs $12.00 standard).
- This saving is often achieved by hiring less experienced, lower-skilled, or temporary workers.
- However, because these workers are less skilled, they likely worked slower, required more supervision, and made more errors, resulting in the actual hours taken (6,400 hours) exceeding the standard hours allowed (6,300 hours).
- This reduction in productivity directly caused the adverse labor efficiency variance of $1,200.

**(a) Variance Calculations [16 marks total]**
- (i) Material Price Variance: $1,640 [1 mark] Adverse [1 mark] (with correct working [1 mark])
- (ii) Material Usage Variance: $1,200 [1 mark] Favourable [1 mark] (with correct working [1 mark])
- (iii) Labour Rate Variance: $1,920 [1 mark] Favourable [1 mark] (with correct working [1 mark])
- (iv) Labour Efficiency Variance: $1,200 [1 mark] Adverse [1 mark] (with correct working [1 mark])
- (v) Fixed Overhead Expenditure Variance: $1,500 [1 mark] Adverse [1 mark]
- (vi) Fixed Overhead Volume Variance: $1,500 [1 mark] Favourable [1 mark]

**(b) Reconciliation Statement [5 marks total]**
- Correct Budgeted Profit calculation ($70,000) [1 mark]
- Correct Sales Volume Variance in profit terms ($3,500 F) [1 mark]
- Correct listing and placement of cost variances (Favourable vs Adverse) [2 marks] (1 mark if minor error)
- Correct final reconciled Actual Profit ($73,780) [1 mark]

**(c) Discussion of variance relationships [4 marks total]**
- 1 mark for explaining that a lower wage rate indicates cheaper/lower-skilled labor.
- 1 mark for linking lower-skilled labor to lower productivity/working at a slower pace.
- 1 mark for stating this increases total hours worked above standard hours allowed.
- 1 mark for concluding that the wage saving was partially offset by inefficiency.