2023 Cambridge IAL Accounting (9706) 模擬試題連答案詳解

1. **Identify original number of shares:**
$$\text{Original shares} = \frac{\$250,000}{\$0.50} = 500,000 \text{ shares}$$

2. **Calculate the rights issue:**
$$\text{New shares issued} = \frac{500,000}{5} = 100,000 \text{ shares}$$
$$\text{Nominal value of rights issue} = 100,000 \times \$0.50 = \$50,000$$
$$\text{Total proceeds of rights issue} = 100,000 \times \$1.20 = \$120,000$$
$$\text{Premium on rights issue} = \$120,000 - \$50,000 = \$70,000$$
$$\text{Share premium balance before bonus issue} = \$20,000\text{ (opening)} + \$70,000\text{ (rights)} = \$90,000$$

3. **Calculate the bonus issue:**
$$\text{Total shares before bonus issue} = 500,000 + 100,000 = 600,000 \text{ shares}$$
$$\text{Bonus shares issued} = \frac{600,000}{10} = 60,000 \text{ shares}$$
$$\text{Value of bonus shares (at nominal value of \$0.50)} = 60,000 \times \$0.50 = \$30,000$$

4. **Calculate final share premium balance:**
$$\text{Final share premium} = \$90,000 - \$30,000 = \$60,000$$

1 mark for the correct option B.
- Award 1 mark for correct calculation of final share premium balance of $60,000.
- Reject other options which result from incorrect treatment of share par value, wrong number of bonus shares, or omitting opening balances.

1. **Determine annual transfer from 2020 receipts:**
$$\text{Remaining balance on 1 Jan 2022} = \$8,000$$
$$\text{Remaining life} = 8 \text{ years}$$
$$\text{Annual transfer} = \frac{\$8,000}{8 \text{ years}} = \$1,000 \text{ per year}$$

2. **Determine annual transfer from 2021 receipts:**
$$\text{Remaining balance on 1 Jan 2022} = \$13,500$$
$$\text{Remaining life} = 9 \text{ years}$$
$$\text{Annual transfer} = \frac{\$13,500}{9 \text{ years}} = \$1,500 \text{ per year}$$

3. **Determine annual transfer from 2022 receipts:**
$$\text{New receipts in 2022} = \$10,000$$
$$\text{Amortization period} = 10 \text{ years}$$
$$\text{Annual transfer} = \frac{\$10,000}{10 \text{ years}} = \$1,000 \text{ per year}$$

4. **Total transfer for the year 2022:**
$$\text{Total transfer} = \$1,000 + \$1,500 + \$1,000 = \$3,500$$

1 mark for the correct option C.
- Award 1 mark for correct calculation of total transfer to Income and Expenditure account ($3,500).
- Reject incorrect options arising from simply applying 10% on the opening balance of $21,500 or ignoring the 2022 additions.

1. **Calculate the average investment:**
$$\text{Average investment} = \frac{\text{Initial investment} + \text{Scrap value}}{2} = \frac{\$180,000 + \$20,000}{2} = \$100,000$$

2. **Calculate total cash inflows:**
$$\text{Total cash inflows} = \$65,000 + \$75,000 + \$55,000 + \$45,000 = \$240,000$$

3. **Calculate total depreciation (loss in asset value):**
$$\text{Total depreciation} = \text{Initial investment} - \text{Scrap value} = \$180,000 - \$20,000 = \$160,000$$

4. **Calculate total accounting profit:**
$$\text{Total accounting profit} = \text{Total cash inflows} - \text{Total depreciation} = \$240,000 - \$160,000 = \$80,000$$

5. **Calculate average annual accounting profit:**
$$\text{Average annual profit} = \frac{\$80,000}{4 \text{ years}} = \$20,000$$

6. **Calculate ARR:**
$$\text{ARR} = \left( \frac{\text{Average annual profit}}{\text{Average investment}} \right) \times 100\% = \left( \frac{\$20,000}{\$100,000} \right) \times 100\% = 20\%$$

1 mark for the correct option D.
- Award 1 mark for correct calculation of average annual profit and average investment leading to 20%.
- Reject 60% (Option A) which uses average cash flows instead of profits.
- Reject 11.11% (Option B) which is based on initial investment.
- Reject 80% (Option C) which does not annualize the profit.

1. **Material Price Variance (calculated at purchase date):**
$$\text{Actual Price per kg} = \frac{\$21,000}{5,000 \text{ kg}} = \$4.20 \text{ per kg}$$
$$\text{Standard Price per kg} = \$4.00$$
$$\text{Price Variance} = (\text{Standard Price} - \text{Actual Price}) \times \text{Actual Quantity Purchased}$$
$$\text{Price Variance} = (\$4.00 - \$4.20) \times 5,000 \text{ kg} = \$1,000 \text{ (Adverse)}$$

2. **Material Usage Variance:**
$$\text{Standard Quantity for actual output} = 1,500 \text{ units} \times 3 \text{ kg/unit} = 4,500 \text{ kg}$$
$$\text{Actual Quantity Used} = 4,800 \text{ kg}$$
$$\text{Usage Variance} = (\text{Standard Quantity} - \text{Actual Quantity Used}) \times \text{Standard Price}$$
$$\text{Usage Variance} = (4,500 \text{ kg} - 4,800 \text{ kg}) \times \$4.00 = \$1,200 \text{ (Adverse)}$$

1 mark for the correct option A.
- Award 1 mark for calculating the correct price variance ($1,000 Adverse based on purchase quantity) and usage variance ($1,200 Adverse based on standard price).
- Reject options C and D because they calculate price variance on usage quantity ($960).

Using the indirect method under IAS 7:

1. **Adjustments to Profit Before Tax:**
$$\text{Profit before tax} = \$145,000$$
$$\text{Add: Depreciation} = +\$32,000$$
$$\text{Add: Loss on sale of equipment} = +\$4,500$$
$$\text{Add: Interest expense (finance cost)} = +\$8,000$$
$$\text{Operating profit before working capital changes} = \$189,500$$

2. **Adjustments for Working Capital:**
$$\text{Less: Increase in inventory} = -\$12,000$$
$$\text{Add: Decrease in trade receivables} = +\$7,000$$
$$\text{Less: Decrease in trade payables} = -\$9,500$$
$$\text{Cash generated from operations} = \$175,000$$

3. **Deduct Interest Paid:**
$$\text{Less: Interest paid} = -\$7,500$$
$$\text{Net cash from operating activities} = \$167,500$$

1 mark for the correct option A.
- Award 1 mark for correct treatment of non-cash items (+Depreciation, +Loss), adding finance costs, adjusting for working capital changes, and subtracting the actual interest paid ($7,500).
- Reject other options where interest paid is omitted or wrong adjustments are made to working capital.

1. **Revaluation surplus:**
The revaluation surplus of $20,000 belongs entirely to the old partners (A and B). It does not affect C's capital account.

2. **Goodwill adjustment (No goodwill account maintained):**
- Credit old partners in old ratio (3:2):
- A: $18,000
- B: $12,000
- Debit all partners in new ratio (5:3:2):
- A: $15,000
- B: $9,000
- C: $6,000
- Therefore, C's capital account is debited by $6,000 for his share of the written-off goodwill.

3. **Cash contribution by C:**
To achieve a final credit balance of $40,000 after being debited $6,000 for goodwill, C must introduce:
$$\text{Cash introduced} = \text{Required balance} + \text{Goodwill debit} = \$40,000 + \$6,000 = \$46,000$$

1 mark for the correct option C.
- Award 1 mark for correct calculation of C's share of goodwill debit of $6,000 and addition to the desired $40,000 capital balance.
- Reject $34,000 (Option A) which subtracts the goodwill share.
- Reject $40,000 (Option B) which ignores the goodwill adjustment.

1. **Determine the unit contribution for each product:**
$$\text{Contribution of X} = \$20 - \$12 = \$8$$
$$\text{Contribution of Y} = \$30 - \$18 = \$12$$

2. **Determine the contribution of a standard composite batch (3 units of X + 1 unit of Y = 4 units):**
$$\text{Batch contribution} = (3 \times \$8) + (1 \times \$12) = \$24 + \$12 = \$36 \text{ per batch}$$

3. **Calculate the break-even point in batches:**
$$\text{Break-even batches} = \frac{\text{Fixed costs}}{\text{Batch contribution}} = \frac{\$18,000}{\$36} = 500 \text{ batches}$$

4. **Calculate total units to break even:**
$$\text{Total units} = 500 \text{ batches} \times 4 \text{ units/batch} = 2,000 \text{ units}$$

1 mark for the correct option C.
- Award 1 mark for calculating correct batch contribution ($36), correct break-even batches (500), and converting to total units (2,000).
- Reject 500 units (Option A) which is just the number of batches.
- Reject 1,800 units (Option B) which uses a simple average contribution.

1. **Calculate the total purchase consideration:**
$$\text{Cash} = \$50,000$$
$$\text{Value of shares issued} = 100,000 \text{ shares} \times \$1.50 = \$150,000$$
$$\text{Total purchase consideration} = \$50,000 + \$150,000 = \$200,000$$

2. **Calculate the fair value of net assets acquired:**
$$\text{Non-current assets} = \$150,000$$
$$\text{Inventory} = \$25,000$$
$$\text{Trade receivables} = \$16,000$$
$$\text{Less: Trade payables} = (\$12,000)$$
$$\text{Fair value of net assets} = \$150,000 + \$25,000 + \$16,000 - \$12,000 = \$179,000$$

3. **Calculate goodwill:**
$$\text{Goodwill} = \text{Purchase consideration} - \text{Fair value of net assets}$$
$$\text{Goodwill} = \$200,000 - \$179,000 = \$21,000$$

1 mark for the correct option B.
- Award 1 mark for calculating correct purchase consideration ($200,000) and correct net asset fair value ($179,000) leading to $21,000.
- Reject $6,000 (Option A) which uses book values of assets and nominal value of shares.
- Reject $29,000 (Option C) which uses nominal value of shares instead of market value.
- Reject $44,000 (Option D) which uses book value of assets.

1. **Calculate the original number of ordinary shares:**
$$\text{Number of shares} = \frac{\$400,000}{\$0.50} = 800,000 \text{ shares}$$

2. **Calculate the number of bonus shares to be issued:**
$$\text{Bonus shares} = 800,000 \times \frac{1}{4} = 200,000 \text{ shares}$$

3. **Calculate the nominal value of the bonus issue:**
$$\text{Nominal value} = 200,000 \text{ shares} \times \$0.50 = \$100,000$$

4. **Apply the reserves optimization:**
To maintain reserves in their most flexible form, the non-distributable share premium reserve must be used first to fund the bonus issue, leaving the maximum possible balance in the distributable retained earnings.
$$\text{New Share Premium} = \$150,000 - \$100,000 = \$50,000$$

1 mark for the correct calculation:
- 1 mark for obtaining $50,000 (option A).
- Award 0 marks for options B, C, or D which represent incorrect handling of the bonus issue premium or share count.

Using a Subscriptions Account:

| Debit | $ | Credit | $
| :--- | :--- | :--- | :---
| Balance b/d (Arrears) | 1,500 | Balance b/d (Advance) | 900
| **Income & Expenditure (balancing figure)** | **32,400** | Bank (Receipts) | 32,000
| Balance c/d (Advance) | 1,200 | Irrecoverable Subscriptions | 400
| | | Balance c/d (Arrears) | 1,800
| **Total** | **35,100** | **Total** | **35,100**

Therefore, the subscription income to be credited to the Income and Expenditure Account is $32,400.

1 mark for the correct calculation:
- 1 mark for obtaining $32,400 (option C).
- 0 marks for standard mistakes such as omitting the write-off ($32,000, option B) or treating it as a debit adjustment.

We tabulate the discounted cash flows (DCF) for each year:

$$\begin{array}{|c|c|c|c|}
\hline
\text{Year} & \text{Net Cash Flow (\$)} & \text{Discount Factor at 10\%} & \text{Present Value (\$)} \\
\hline
0 & -80,000 \text{ (Machine)} - 10,000 \text{ (Working Cap)} = -90,000 & 1.000 & -90,000 \\
1 & 40,000 & 0.909 & +36,360 \\
2 & 35,000 & 0.826 & +28,910 \\
3 & 30,000 + 10,000 \text{ (Recovery)} = 40,000 & 0.751 & +30,040 \\
\hline
\text{NPV} & & & \mathbf{+5,310} \\
\hline
\end{array}$$

Hence, the Net Present Value is +$5,310.

1 mark for correct NPV calculation:
- 1 mark for +$5,310 (option B).
- 0 marks for omitting working capital recovery (-$2,200, option A), omitting working capital entirely (+$7,800, option C), or failing to record working capital outflow at Year 0 but keeping recovery (+$15,310, option D).

1. **Direct Labour Rate Variance:**
$$\text{Actual Rate paid} = \frac{\$24,780}{2,100 \text{ hours}} = \$11.80 \text{ per hour}$$
$$\text{Rate Variance} = (\text{Standard Rate} - \text{Actual Rate}) \times \text{Actual Hours Paid}$$
$$\text{Rate Variance} = (\$12.00 - \$11.80) \times 2,100 = \$0.20 \times 2,100 = \$420 \text{ Favourable (F)}$$

2. **Direct Labour Efficiency Variance:**
$$\text{Actual Hours Worked} = 2,100 \text{ paid} - 50 \text{ idle} = 2,050 \text{ hours}$$
$$\text{Standard Hours for actual production} = 500 \text{ units} \times 4 \text{ hours} = 2,000 \text{ hours}$$
$$\text{Efficiency Variance} = (\text{Standard Hours} - \text{Actual Hours Worked}) \times \text{Standard Rate}$$
$$\text{Efficiency Variance} = (2,000 - 2,050) \times \$12.00 = 50 \text{ hours (A)} \times \$12.00 = \$600 \text{ Adverse (A)}$$

1 mark for the correct pair of variances:
- 1 mark for Rate: $420 F; Efficiency: $600 A (option B).
- 0 marks for using worked hours to calculate the rate variance (option A), or using paid hours to calculate the efficiency variance (option C).

Let's perform the step-by-step adjustments to X's capital account:

1. **Opening Capital Balance:**
$$\text{Opening balance} = \$60,000$$

2. **Revaluation Surplus:**
The surplus is shared in the old profit-sharing ratio (3:2).
$$\text{X's share} = \$15,000 \times \frac{3}{5} = \$9,000 \text{ (Credit)}$$

3. **Goodwill Adjustments:**
* Goodwill credited to existing partners in the old ratio (3:2):
$$\text{X's share (Credit)} = \$20,000 \times \frac{3}{5} = \$12,000$$
* Goodwill debited to all partners in the new ratio (5:3:2):
$$\text{X's share (Debit)} = \$20,000 \times \frac{5}{10} = \$10,000$$
* Net Goodwill adjustment for X = $12,000 (Cr) - $10,000 (Dr) = $2,000 (Cr).

4. **Final Capital Account Balance of X:**
$$\text{Final Balance} = \$60,000 \text{ (opening)} + \$9,000 \text{ (revaluation)} + \$2,000 \text{ (goodwill)} = \$71,000$$

1 mark for the correct final capital balance:
- 1 mark for $71,000 (option C).
- 0 marks for options failing to record revaluation ($62,000, option A), sharing revaluation in the new ratio ($69,500, option B), or failing to write off goodwill ($81,000, option D).

1. **Calculate the Predetermined Overhead Absorption Rate (OAR):**
$$\text{OAR} = \frac{\text{Budgeted Overheads}}{\text{Budgeted Direct Labour Hours}} = \frac{\$180,000}{45,000 \text{ hours}} = \$4.00 \text{ per direct labour hour}$$

2. **Calculate the Overheads Absorbed:**
$$\text{Overheads Absorbed} = \text{OAR} \times \text{Actual Direct Labour Hours Worked}$$
$$\text{Overheads Absorbed} = \$4.00 \times 46,500 \text{ hours} = \$186,000$$

3. **Calculate the Under/Over-absorption:**
$$\text{Under/Over-absorption} = \text{Overheads Absorbed} - \text{Actual Overheads Incurred}$$
$$\text{Under/Over-absorption} = \$186,000 - \$192,000 = -\$6,000 \text{ (Under-absorbed)}$$

Since absorbed overheads are less than the actual overheads incurred, overheads are under-absorbed by $6,000.

1 mark for the correct value and direction:
- 1 mark for $6,000 under-absorbed (option B).
- 0 marks for $6,000 over-absorbed (option A) or comparing actual overheads directly to budgeted overheads ($12,000, options C and D).

1. **Determine the corrected cash book balance:**
$$\text{Original cash book balance (debit)} = \$8,450$$
$$\text{Less: Bank charges} = -\$120$$
$$\text{Less: Dishonoured cheque} = -\$450$$
$$\text{Corrected cash book balance (debit)} = \$8,450 - \$120 - \$450 = \$7,880$$

2. **Reconcile to find the bank statement balance ($X):**
$$\text{Bank Statement Balance} + \text{Uncredited deposits} - \text{Unpresented cheques} = \text{Corrected cash book balance}$$
$$X + \$2,100 - \$1,800 = \$7,880$$
$$X + \$300 = \$7,880 \implies X = \$7,580$$

1 mark for correct calculation of the bank statement balance:
- 1 mark for $7,580 (option A).
- 0 marks for failing to adjust the cash book before reconciliation ($8,150, option B), reversing the additions and subtractions of unpresented/uncredited items ($8,180, option C), or adding bank charges and dishonoured cheques to the cash book balance ($8,720, option D).

1. **Calculate the contribution margin per unit:**
$$\text{Contribution per unit} = \text{Selling Price} - \text{Variable Cost per unit}$$
$$\text{Contribution per unit} = \$25 - \$15 = \$10$$

2. **Calculate the required units for target profit:**
$$\text{Required sales (units)} = \frac{\text{Fixed Costs} + \text{Target Profit}}{\text{Contribution per unit}}$$
$$\text{Required sales (units)} = \frac{\$60,000 + \$30,000}{\$10} = \frac{\$90,000}{\$10} = 9,000 \text{ units}$$

1 mark for the correct number of units:
- 1 mark for 9,000 units (option C).
- 0 marks for dividing total costs by selling price (3,600 units, option A), calculating only break-even units (6,000 units, option B), or miscalculating the target contribution.

1. **Initial position:**
- Ordinary shares: 1,000,000 shares of $0.50 each.
- Share premium: $50,000.

2. **Rights Issue:**
- Ratio: 1 for 5.
- Number of rights shares issued: \(1,000,000 \times \frac{1}{5} = 200,000\) shares.
- Premium per share: \( \$0.80 - \$0.50 = \$0.30 \).
- Total share premium created: \( 200,000 \times \$0.30 = \$60,000 \).
- Share premium balance after rights issue: \( \$50,000 + \$60,000 = \$110,000 \).
- Total ordinary shares now in issue: \( 1,000,000 + 200,000 = 1,200,000 \) shares.

3. **Bonus Issue:**
- Ratio: 1 for 6.
- Number of bonus shares issued: \( 1,200,000 \times \frac{1}{6} = 200,000 \) shares.
- Nominal value of bonus shares: \( 200,000 \times \$0.50 = \$100,000 \).
- This is funded entirely from the share premium account.
- Remaining balance on share premium: \( \$110,000 - \$100,000 = \$10,000 \).

1 mark for correct calculation of final share premium balance.
- Share premium after rights issue = $110,000 (1 method mark)
- Value of bonus issue = $100,000 (1 method mark)
- Final balance = $10,000 (1 accuracy mark)

1. **Opening Life Membership Fund (1 Jan 2022):** $36,000.
2. **New receipts during the year:** \( 5 \times \$1,200 = \$6,000 \).
3. **Total fund before transfer:** \( \$36,000 + \$6,000 = \$42,000 \).
4. **Transfer to Income and Expenditure account (amortisation):** $5,100.
5. **Closing Life Membership Fund (31 Dec 2022):** \( \$42,000 - \$5,100 = \$36,900 \).

1 mark for correct final fund balance.
- Total fund before transfer = $42,000 (1 method mark)
- Transfer deduction = $5,100 (1 method mark)
- Final balance = $36,900 (1 accuracy mark)

Using the interpolation formula:
\( \text{IRR} = L + \left( \frac{NPV_L}{NPV_L - NPV_H} \right) \times (H - L) \)

Where:
- \( L = 15\% \)
- \( H = 22\% \)
- \( NPV_L = \$10,460 \)
- \( NPV_H = -\$4,240 \)

Substitute the values:
\( \text{IRR} = 15\% + \left( \frac{10,460}{10,460 - (-4,240)} \right) \times (22\% - 15\%) \)
\( \text{IRR} = 15\% + \left( \frac{10,460}{14,700} \right) \times 7\% \)
\( \text{IRR} = 15\% + (0.71156 \times 7\%) \)
\( \text{IRR} = 15\% + 4.98\% = 19.98\% \approx 20.0\% \).

1 mark for correct calculation of IRR using interpolation.
- Sum of NPVs = $14,700 (1 method mark)
- Interpolation fraction multiplied by difference = 4.98% (1 method mark)
- Final IRR = 20.0% (1 accuracy mark)

1. **Labour Rate Variance:**
- Standard Rate = $12.00
- Actual Rate = \( \frac{\$74,250}{5,500 \text{ hours}} = \$13.50 \)
- Rate difference = \( \s12.00 - \$13.50 = \$1.50 \text{ Adverse} \)
- Labour Rate Variance = \( 5,500 \text{ actual hours} \times \$1.50 = \s8,250 \text{ Adverse} \).

2. **Labour Efficiency Variance:**
- Standard hours for actual output = \( 1,500 \text{ units} \times 4 \text{ hours} = 6,000 \text{ hours} \)
- Actual hours worked = 5,500 hours
- Efficiency difference = \( 6,000 - 5,500 = 500 \text{ hours Favourable} \)
- Labour Efficiency Variance = \( 500 \text{ hours} \times \$12.00 \text{ standard rate} = \$6,000 \text{ Favourable} \).

1 mark for correct selection of rate and efficiency variances.
- Labour rate variance = $8,250 Adverse (1 method mark)
- Labour efficiency variance = $6,000 Favourable (1 method mark)
- Correct pair identified = Option A (1 accuracy mark)

According to IAS 7 (Statement of Cash Flows), the reconciliation from operating profit to cash generated from operations is:

- Operating profit: $185,000
- Add: Depreciation (non-cash expense): +$42,000
- Less: Gain on disposal (non-operating item): -$8,000
- Less: Increase in inventories (working capital outflow): -$12,000
- Add: Decrease in trade receivables (working capital inflow): +$7,000
- Less: Decrease in trade payables (working capital outflow): -$15,000

Calculation:
\( \$185,000 + \$42,000 - \$8,000 - \$12,000 + \$7,000 - \$15,000 = \$199,000 \).

1 mark for correct calculation of cash generated from operations.
- Non-cash adjustments (depreciation, gain) = +$34,000 (1 method mark)
- Working capital adjustments (inventory, receivables, payables) = -$20,000 (1 method mark)
- Cash generated from operations = $199,000 (1 accuracy mark)

1. **Update the Cash Book:**
- Original cash book balance: -$2,450 (credit balance / overdraft)
- Adjust bank charges: -$180
- Correct recording error of supplier cheque:
- Actual cheque = $620, recorded as $260.
- Additional credit (payment) needed = \( \$620 - \$260 = \$360 \).
- Adjust error: -$360.
- Corrected cash book balance: \( -\$2,450 - \$180 - \$360 = -\$2,990 \) (overdraft).

2. **Reconcile to Bank Statement:**
Let \( B \) be the bank statement balance.
\( \text{Corrected Cash Book Balance} = B + \text{Uncredited deposits} - \text{Unpresented cheques} \)
\( -\$2,990 = B + \$940 - \$1,150 \)
\( -\$2,990 = B - \$210 \)
\( B = -\$2,990 + \$210 = -\$2,780 \).

Thus, the bank statement balance is a $2,780 overdraft (debit balance).

1 mark for correct calculation of bank statement balance.
- Corrected cash book balance = -$2,990 (1 method mark)
- Reconciling items correctly signed = -$2,780 (1 method mark)
- Final answer identified as overdraft = $2,780 overdraft (1 accuracy mark)

1. **Original Breakeven Point:**
- Original contribution per unit = \( \$40 - \$24 = \$16 \).
- Original breakeven point = \( \frac{\$80,000}{\$16} = 5,000 \text{ units} \).

2. **New Required Sales for Target Profit:**
- New selling price = \( \$40 \times 0.9 = \$36 \).
- New contribution per unit = \( \$36 - \$24 = \$12 \).
- Required total contribution = \( \text{Fixed Costs} + \text{Target Profit} = \$80,000 + \$16,000 = \$96,000 \).
- Required sales in units = \( \frac{\$96,000}{\$12} = 8,000 \text{ units} \).

3. **Additional Units Required:**
- Additional units = \( 8,000 \text{ units} - 5,000 \text{ units} = 3,000 \text{ units} \).

1 mark for calculating correct additional units.
- Original breakeven = 5,000 units (1 method mark)
- New required sales = 8,000 units (1 method mark)
- Additional units = 3,000 units (1 accuracy mark)

1. **Revaluation Gain allocation (old ratio 3:2):**
- X: \( \$20,000 \times \frac{3}{5} = \$12,000 \)
- Y: \( \$20,000 \times \frac{2}{5} = \$8,000 \)

2. **Goodwill Adjustment:**
- Raise Goodwill (old ratio 3:2):
- X: \( +\$18,000 \)
- Y: \( +\$12,000 \)
- Write off Goodwill (new ratio 5:3:2):
- X: \( -\$15,000 \)
- Y: \( -\$9,000 \)
- Z: \( -\$6,000 \)
- Net Goodwill effect:
- X: \( +\$3,000 \)
- Y: \( +\$3,000 \)
- Z: \( -\$6,000 \)

3. **Capital Balances before Z's Cash introduction:**
- X: \( \$80,000 + \$12,000 + \$3,000 = \$95,000 \)
- Y: \( \$50,000 + \$8,000 + \$3,000 = \$61,000 \)
- Total X and Y Capital = \( \$95,000 + \$61,000 = \$156,000 \).

4. **Calculate Z's required Capital:**
- Z's profit share = 20% (2/10).
- X and Y combined capital ($156,000) represents 80% (8/10) of the total capital.
- Total Capital of new firm = \( \frac{\$156,000}{0.80} = \$195,000 \).
- Z's target capital balance = \( 20\% \times \$195,000 = \$39,000 \).

5. **Cash to be introduced by Z:**
- Z currently has a debit balance of -$6,000.
- Cash needed = \( \$39,000 - (-\$6,000) = \$45,000 \).

1 mark for correct calculation of cash introduced by Z.
- Combined capital of X and Y after adjustments = $156,000 (1 method mark)
- Total new capital and Z's target capital = $195,000 & $39,000 respectively (1 method mark)
- Cash introduced = $45,000 (1 accuracy mark)

To find the Net Present Value (NPV), we calculate the present values of all cash flows over the project's life, including the scrap value in Year 3:

1. **Year 0 Outflow**: \(-\$120,000 \times 1 = -\$120,000\)
2. **Year 1 Inflow**: \(\$50,000 \times 0.909 = \$45,450\)
3. **Year 2 Inflow**: \(\$60,000 \times 0.826 = \$49,560\)
4. **Year 3 Inflow** (Operating Inflow + Scrap Value): \((\$40,000 + \$20,000) \times 0.751 = \$60,000 \times 0.751 = \$45,060\)

**Total Present Value of Cash Inflows** = \(\$45,450 + \$49,560 + \$45,060 = \$140,070\)

**Net Present Value (NPV)** = \(\$140,070 - \$120,000 = \$20,070\).

1 mark for the correct answer of B ($20,070).
- Award 0 marks for A if scrap value is ignored in the NPV calculation ($5,050).
- Award 0 marks for C if scrap value is added directly without discounting ($25,050).

1. **Material Price Variance**:

- Standard Price (SP) = \(\$6.00\) per kg
- Actual Price (AP) = \(\$28,500 / 5,000\) kg = \(\$5.70\) per kg
- Formula: \((\text{SP} - \text{AP}) \times \text{Actual Quantity (AQ)}\)
- Calculation: \((\$6.00 - \$5.70) \times 5,000 = \$0.30 \times 5,000 = \$1,500\) Favourable

2. **Material Usage Variance**:

- Standard Quantity (SQ) for actual production = \(1,200 \text{ units} \times 4 \text{ kg/unit} = 4,800\) kg
- Formula: \((\text{SQ} - \text{AQ}) \times \text{SP}\)
- Calculation: \((4,800 \text{ kg} - 5,000 \text{ kg}) \times \$6.00 = -200 \times \$6.00 = \$1,200\) Adverse

1 mark for the correct answer A.
- Option B reverses the Favourable/Adverse tags.
- Option C uses standard quantity instead of actual quantity for the price variance calculation.
- Option D incorrectly uses actual price instead of standard price for the usage variance calculation.

We can reconstruct the Subscriptions Account (T-account) to find the transfer to the Income and Expenditure Account as the balancing figure:

**Debit side (Dr)**:
- Balance b/d (Arrears at start): \(\$1,800\)
- Balance c/d (Advance at end): \(\$600\)
- Income and Expenditure Account (balancing figure): \(X\)

**Credit side (Cr)**:
- Balance b/d (Advance at start): \(\$1,200\)
- Bank (Cash received): \(\$32,400\)
- Irrecoverable subscriptions (Written off): \(\$400\)
- Balance c/d (Arrears at end): \(\$1,500\)

Total Credit Side = \(\$1,200 + \$32,400 + \$400 + \$1,500 = \$35,500\)

Therefore, Total Debit Side must also be \(\$35,500\):

\(\$1,800 + \$600 + X = \$35,500\)

\(\$2,400 + X = \$35,500\)

\(X = \$33,100\).

1 mark for the correct answer C ($33,100).
- Award 0 marks for A if bad debts are incorrectly subtracted from credits ($32,300).
- Award 0 marks for B if the write-off of bad debts is ignored ($32,700).

1. **Revaluation adjustment** (allocated in the old profit-sharing ratio 3:2):
- Total gain = \(\$15,000\)
- X's share = \(3/5 \times \$15,000 = +\$9,000\)
- Y's share = \(2/5 \times \$15,000 = +\$6,000\)

2. **Goodwill adjustment** (no goodwill account retained):
- Credit old partners in old ratio (3:2):
- X: \(3/5 \times \$40,000 = +\$24,000\)
- Y: \(2/5 \times \$40,000 = +\$16,000\)
- Debit all partners in new ratio (5:3:2):
- X: \(5/10 \times \$40,000 = -\$20,000\)
- Y: \(3/10 \times \$40,000 = -\$12,000\)
- Net goodwill adjustment:
- X: \(+\$24,000 - \$20,000 = +\$4,000\)
- Y: \(+\$16,000 - \$12,000 = +\$4,000\)

3. **Final Capital Balances**:
- X: \(\$80,000 \text{ (opening)} + \$9,000 \text{ (revaluation)} + \$4,000 \text{ (goodwill)} = \$93,000\)
- Y: \(\$50,000 \text{ (opening)} + \$6,000 \text{ (revaluation)} + \$4,000 \text{ (goodwill)} = \$60,000\).

1 mark for the correct answer C.
- Option A is incorrect as it omits the asset revaluation entirely.
- Option B is incorrect as it applies the new ratio to the asset revaluation instead of the old ratio.
- Option D is incorrect as it raises goodwill but forgets to write it off.

1. **Calculate Purchase Consideration**:
- Share capital: \(100,000 \text{ shares} \times \$1 = \$100,000\)
- Share premium: \(100,000 \text{ shares} \times \$0.80 = \$80,000\)
- Cash paid: \(\$50,000\)
- Total Purchase Consideration = \(\$100,000 + \$80,000 + \$50,000 = \$230,000\)

2. **Calculate Fair Value of Net Assets**:
- Book value of net assets: \(\$180,000\)
- Revaluation of property: \(+\$40,000\)
- Inventory written down: \(-\$5,000\)
- Trade receivables written off: \(-\$3,000\)
- Total Fair Value of Net Assets = \(\$180,000 + \$40,000 - \$5,000 - \$3,000 = \$212,000\)

3. **Calculate Goodwill**:
- Goodwill = Purchase Consideration - Fair Value of Net Assets
- Goodwill = \(\$230,000 - \$212,000 = \$18,000\).

1 mark for the correct answer A ($18,000).
- Option B ($30,000) is incorrect because it treats the share premium as if it does not exist (valuing shares at par).
- Option C ($50,000) is incorrect because it compares the Purchase Consideration with the unadjusted book value of net assets ($180,000).
- Option D ($82,000) is incorrect because it subtracts property adjustments and adds inventory and receivable adjustments incorrectly.

1. **Identify the correct formula for ROCE**:

\(\text{ROCE} = \left( \frac{\text{Profit from operations}}{\text{Capital Employed}} \right) \times 100\%\)

2. **Calculate Capital Employed**:
Capital Employed includes total equity and non-current liabilities:

\(\text{Capital Employed} = \text{Ordinary Share Capital} + \text{Share Premium} + \text{Retained Earnings} + \text{Non-current liabilities}\)

\(\text{Capital Employed} = \$400,000 + \$50,000 + \$150,000 + \$200,000 = \$800,000\)

3. **Calculate ROCE**:
Using Profit from operations (before interest):

\(\text{ROCE} = \left( \frac{\$128,000}{\$800,000} \right) \times 100\% = 16.0\%\)

1 mark for the correct answer B (16.0%).
- Option A is incorrect because it uses profit after interest ($112,000) in the numerator.
- Option C is incorrect because it uses profit after interest and only equity ($600,000) as capital employed.
- Option D is incorrect because it uses profit before interest ($128,000) but only equity as capital employed.

**(a) Statement of Changes in Equity for Vanguard Retail Limited for the year ended 31 December 2023**

| Details | Ordinary Share Capital ($) | Share Premium ($) | Revaluation Reserve ($) | General Reserve ($) | Retained Earnings ($) | Total ($) |
|---|---|---|---|---|---|---|
| **Balances at 1 January 2023** | 300,000 | 80,000 | 50,000 | - | 115,000 | 545,000 |
| Final dividend (W1) | - | - | - | - | (30,000) | (30,000) |
| Rights issue (W2) | 75,000 | 45,000 | - | - | - | 120,000 |
| Interim dividend (W3) | - | - | - | - | (15,000) | (15,000) |
| Profit for the year | - | - | - | - | 95,000 | 95,000 |
| Revaluation of property | - | - | 40,000 | - | - | 40,000 |
| Transfer to General Reserve | - | - | - | 20,000 | (20,000) | - |
| **Balances at 31 December 2023** | **375,000** | **125,000** | **90,000** | **20,000** | **145,000** | **755,000** |

**Workings:**
* **W1: Final dividend:** Number of shares at 1 January 2023 = \( \frac{\$300,000}{\$0.50} = 600,000 \) shares. Final dividend = \( 600,000 \times \$0.05 = \$30,000 \).
* **W2: Rights issue:** Number of rights shares = \( 600,000 \times \frac{1}{4} = 150,000 \) shares. Ordinary share capital increase = \( 150,000 \times \$0.50 = \$75,000 \). Share premium increase = \( 150,000 \times (\$0.80 - \$0.50) = \$45,000 \). Total proceeds = \( \$120,000 \).
* **W3: Interim dividend:** Total shares in issue on 1 September 2023 = \( 600,000 + 150,000 = 750,000 \) shares. Interim dividend = \( 750,000 \times \$0.02 = \$15,000 \).

***

**(b) Liquidity Ratios**

**(i) Current Ratio:**
* **Formula:** \( \frac{\text{Current Assets}}{\text{Current Liabilities}} \)
* **2022:** \( \frac{\$45,000 + \$35,000 + \$10,000}{\$40,000 + \$10,000} = \frac{\$90,000}{\$50,000} = 1.80 : 1 \)
* **2023:** \( \frac{\$85,000 + \$55,000 + \$2,000}{\$88,000 + \$12,000} = \frac{\$142,000}{\$100,000} = 1.42 : 1 \)

**(ii) Liquid (Acid Test) Ratio:**
* **Formula:** \( \frac{\text{Current Assets} - \text{Inventory}}{\text{Current Liabilities}} \)
* **2022:** \( \frac{\$90,000 - \$45,000}{\$50,000} = \frac{\$45,000}{\$50,000} = 0.90 : 1 \)
* **2023:** \( \frac{\$142,000 - \$85,000}{\$100,000} = \frac{\$57,000}{\$100,000} = 0.57 : 1 \)

***

**(c) Liquidity Evaluation and Advice**

* **Analysis (max 3 marks):**
* Both liquidity ratios have deteriorated significantly over the year. The current ratio fell from 1.80:1 to 1.42:1, which is below the safe standard benchmark of 1.5:1 to 2.0:1.
* The liquid (acid test) ratio decreased severely from 0.90:1 to 0.57:1, showing that the company has only $0.57 of liquid assets to cover each $1 of immediate current liabilities. This presents a high risk of insolvency.
* Inventory levels have almost doubled from $45,000 to $85,000, locking up vital cash flow. Trade receivables have also expanded (from $35,000 to $55,000).
* This deterioration has led to the liquid cash balance of $10,000 turning into a bank overdraft of $12,000. Trade payables also increased significantly from $40,000 to $88,000, indicating that the company is delaying payment to suppliers to survive.

* **Recommendations (max 3 marks):**
1. Improve credit control and chase trade receivables faster (e.g., offer early settlement discounts).
2. Reduce stockholding levels by improving inventory management (e.g., Just-In-Time purchasing or running a promotional sale to turn inventory into cash).
3. Refinance short-term debt (like the overdraft) into a long-term loan to ease working capital pressure.

***

**(d) Capital vs. Revenue Reserves**
* **Capital Reserves:** These are created from non-trading activities (e.g., revaluing non-current assets or issuing shares above nominal value). They are not realized profits and cannot be used to pay cash dividends. *Example:* Share Premium account or Revaluation Reserve.
* **Revenue Reserves:** These are created out of realized trading profits (general business operations). They are available for distribution to shareholders as dividends. *Example:* Retained Earnings or General Reserve.

**(a) Statement of Changes in Equity [14 marks]**
* Opening balances row completely correct (1)
* Final dividend calculation showing \( (600,000 \times \$0.05) \) = $30,000 (1) correctly deducted from retained earnings (1)
* Rights issue: Share capital column increase by $75,000 (1), Share premium column increase by $45,000 (1), Total column increase by $120,000 (1)
* Interim dividend calculation showing \( (750,000 \times \$0.02) \) = $15,000 (1) correctly deducted from retained earnings (1)
* Profit for the year of $95,000 entered in Retained earnings and Total columns (1)
* Revaluation of property $40,000 entered in Revaluation reserve and Total columns (1)
* Transfer to General reserve: $20,000 added to General reserve (1) and deducted from Retained earnings (1)
* Closing balances row completely correct with column totals (1)

**(b) Ratio Calculations [6 marks]**
* (i) Current Ratio:
* 2022: 1.80:1 (1)
* 2023: 1.42:1 (1)
* (ii) Acid Test Ratio:
* 2022: Formula/working showing stock deduction (1) and final ratio 0.90:1 (1)
* 2023: Formula/working showing stock deduction (1) and final ratio 0.57:1 (1)

**(c) Evaluation and Recommendations [6 marks]**
* 1 mark for noting overall decline/deterioration in both ratios.
* 1 mark for analyzing inventory lock-up (inventory nearly doubled from $45,000 to $85,000).
* 1 mark for pointing out the shift from cash surplus to overdraft/payables delays.
* 3 marks for three distinct, practical recommendations to improve liquidity (1 mark per point; e.g., prompt debt recovery, JIT inventory system, refinancing overdraft to long-term loan).

**(d) Capital vs Revenue Reserves [4 marks]**
* Explanation of capital reserves (source/distribution constraint) (1)
* Suitable example of capital reserve (Share premium / Revaluation reserve) (1)
* Explanation of revenue reserves (distributable profits) (1)
* Suitable example of revenue reserve (Retained earnings / General reserve) (1)

(a) Sanjay - Updated Cash Book (Bank Column) at 30 April 2024

Debit Side:
- Balance b/d: $1,480
- Customer Receipt (Direct Transfer): $560
- Correction of error (G. Mills over-recording): $360
- Total Debit: $2,400

Credit Side:
- Bank charges: $45
- Standing order (Insurance): $120
- Dishonoured cheque (J. Carter): $310
- Balance c/d: $1,925
- Total Credit: $2,400

Balance b/d: $1,925 (Debit)


(b) Sanjay - Bank Reconciliation Statement at 30 April 2024

Balance per Bank Statement (Credit): $1,380
Add: Uncredited deposits: $1,080
Subtotal: $2,460

Less: Unpresented cheques:
- Cheque 400512: ($340)
- Cheque 400518: ($195)
Total unpresented cheques: ($535)

Balance per updated Cash Book (Debit): $1,925


(c) Three reasons for preparing a bank reconciliation statement regularly:
1. To detect and correct errors in the Cash Book (such as bank fees, standing orders, or transposition errors).
2. To identify any bank errors and notify the bank for correction.
3. To prevent and detect fraud, embezzlement, or unauthorized transactions.
4. To verify the accuracy of the double-entry records and ensure the true financial position is reported.

Part (a) [6 marks]:
- 1 mark for debiting direct transfer of $560.
- 1 mark for debiting the correction of the G. Mills payment error of $360 ($510 - $150).
- 1 mark for crediting bank charges of $45.
- 1 mark for crediting the standing order of $120.
- 1 mark for crediting the dishonoured cheque of $310.
- 1 mark for calculating the correct balance c/d and b/d of $1,925 (debit).

Part (b) [6 marks]:
- 1 mark for starting balance per bank statement of $1,380.
- 1 mark for adding uncredited deposits of $1,080.
- 1 mark for unpresented cheque 400512 of $340.
- 1 mark for unpresented cheque 400518 of $195.
- 1 mark for correct mathematical processing/subtotals.
- 1 mark for final reconciled balance of $1,925 (debit), matching the updated cash book balance.

Part (c) [3 marks]:
- 1 mark for each valid, distinct reason stated (up to a maximum of 3 marks).

**(a) Calculations of Total Sales and Total Purchases**

* **Total Sales:**
* Credit Sales = Closing Trade Receivables + Cash Received from Credit Customers - Opening Trade Receivables
* Credit Sales = \(13,800 + 84,500 - 11,200 = 87,100\)
* Total Sales = Credit Sales + Cash Sales
* Total Sales = \(87,100 + 12,000 = 99,100\)

* **Total Purchases:**
* Credit Purchases = Closing Trade Payables + Cash Paid to Trade Payables - Opening Trade Payables
* Credit Purchases = \(6,900 + 48,000 - 8,400 = 46,500\)
* (Note: Total purchases = $46,500, before deducting drawings of goods)

**(b) Charles - Income Statement for the year ended 31 December 2023**

* **Revenue (Sales):** $99,100
* **Cost of Sales:**
* Opening Inventory: $12,000
* Add: Purchases (\(46,500 - 1,500\) drawings): $45,000
* Less: Closing Inventory: ($14,500)
* Cost of Sales: ($42,500)
* **Gross Profit:** $56,600
* **Expenses:**
* Rent (\(9,600 + 800 - 1,200\)): $9,200
* Electricity (\(3,200 - 300 + 450\)): $3,350
* Depreciation on Equipment (\(20,000 \times 10\% + 8,000 \times 10\% \times 6/12\)): $2,400
* Total Expenses: ($14,950)
* **Profit for the year:** $41,650

**(c) Advantages of keeping full double-entry accounting records (Any three):**
1. It helps in verifying arithmetical accuracy through the preparation of a trial balance.
2. It reduces the risk of fraud and errors as every transaction has a dual effect.
3. It facilitates the easy preparation of financial statements (Income Statement and Statement of Financial Position) directly from ledger balances.
4. It provides reliable information to external users such as banks (for loans) and tax authorities.

**(a) 5 Marks total:**
* 1 mark for correct credit sales calculation formula/workings
* 1 mark for correct credit sales amount ($87,100)
* 1 mark for total sales ($99,100) (Own Figure - OF)
* 1 mark for correct credit purchases calculation formula/workings
* 1 mark for correct total credit purchases amount ($46,500)

**(b) 7 Marks total:**
* 1 mark for Revenue of $99,100 (OF from part a)
* 1 mark for Purchases adjusted for drawings ($45,000)
* 1 mark for Cost of Sales ($42,500) and Gross Profit ($56,600) (OF)
* 1 mark for Rent expense calculation ($9,200)
* 1 mark for Electricity expense calculation ($3,350)
* 1 mark for Depreciation calculation ($2,400)
* 1 mark for final Profit for the year ($41,650) (OF)

**(c) 3 Marks total:**
* 1 mark for each valid advantage stated, up to a maximum of 3 marks.

### **Part (a) differences**
1. **Inventory Valuation**: Under absorption costing, inventory is valued including a share of fixed production overheads. Under marginal costing, inventory is valued at variable (marginal) cost of production only.
2. **Treatment of Fixed Overheads**: Under absorption costing, fixed overheads are treated as product costs and are absorbed into product units. Under marginal costing, fixed overheads are treated as period costs and are written off in full against contribution in the period they are incurred.
3. **Profit Differences**: When production and sales volumes differ, profit under absorption costing differs from profit under marginal costing due to the timing of when fixed overheads are recognized as an expense.

### **Part (b)(i) Budgeted Overhead Absorption Rates (OAR)**

| Cost Item / Allocation | Basis | Total ($) | Machining ($) | Assembly ($) | Canteen ($) |
|---|---|---|---|---|---|
| **Indirect Materials** | Allocated | 24,000 | 12,000 | 8,000 | 4,000 |
| **Rent and rates** | Floor Space (3:2:1) | 24,000 | 12,000 | 8,000 | 4,000 |
| **Machinery Depreciation** | Machine Value (6:2:1) | 36,000 | 24,000 | 8,000 | 4,000 |
| **Power** | Power usage (8:5:2) | 15,000 | 8,000 | 5,000 | 2,000 |
| **Subtotals** | | 99,000 | 56,000 | 29,000 | 14,000 |
| **Reapportion Canteen** | Employees (15:25) | — | 5,250 | 8,750 | (14,000) |
| **Total Overheads** | | 99,000 | **61,250** | **37,750** | **0** |

* **Machining Department OAR**:
$$\text{OAR} = \frac{\text{Budgeted Overheads}}{\text{Budgeted Machine Hours}} = \frac{\$61,250}{5,000\text{ hours}} = \$12.25\text{ per machine hour}$$

* **Assembly Department OAR**:
$$\text{OAR} = \frac{\text{Budgeted Overheads}}{\text{Budgeted Direct Labor Hours}} = \frac{\$37,750}{5,000\text{ hours}} = \$7.55\text{ per direct labor hour}$$

### **Part (b)(ii) Under- or Over-absorption of Overheads**
* **Machining Department**:
$$\text{Overheads Absorbed} = 5,100\text{ actual hours} \times \$12.25 = \$62,475$$
$$\text{Actual Overheads} = \$63,000$$
$$\text{Under-absorption} = \$63,000 - \$62,475 = \$525\text{ (Under-absorbed)}$$

* **Assembly Department**:
$$\text{Overheads Absorbed} = 4,800\text{ actual hours} \times \$7.55 = \$36,240$$
$$\text{Actual Overheads} = \$36,800$$
$$\text{Under-absorption} = \$36,800 - \$36,240 = \$560\text{ (Under-absorbed)}$$

### **Part (c)(i) Profit under Absorption Costing**
* Standard cost per unit of Beta:
$$\text{Cost} = \text{Materials }(\$15) + \text{Labor }(\$10) + \text{Variable Overheads }(\$5) + \text{Fixed Overheads }(\$8) = \$38\text{ per unit}$$
* Sales Revenue: $$2,100\text{ units} \times \$50 = \$105,000$$
* Standard Cost of Sales: $$2,100\text{ units} \times \$38 = \$79,800$$
* Fixed Overhead Adjustment:
$$\text{Overheads Absorbed} = 2,400\text{ units produced} \times \$8 = \$19,200$$
$$\text{Actual Fixed Overheads} = \$16,000$$
$$\text{Over-absorbed Fixed Overheads} = \$19,200 - \$16,000 = \$3,200$$
* Adjusted Cost of Sales: $79,800 - $3,200 = $76,600
* **Profit under Absorption Costing**: $105,000 - $76,600 = **$28,400**

### **Part (c)(ii) Profit under Marginal Costing**
* Marginal Cost per unit: $15 + $10 + $5 = $30 per unit
* Contribution per unit: $50 - $30 = $20 per unit
* Total Contribution: $$2,100\text{ units} \times \$20 = \$42,000$$
* Less: Fixed Overheads incurred: $16,000
* **Profit under Marginal Costing**: $42,000 - $16,000 = **$26,000**

### **Part (c)(iii) Reconciliation**

| Item | Amount ($) |
|---|---|
| **Profit under Absorption Costing** | 28,400 |
| Less: Fixed overheads included in closing inventory ($$300\text{ units} \times \$8$$) | (2,400) |
| **Profit under Marginal Costing** | **26,000** |

### **Part (d) Special Order Evaluation**
**Financial Analysis**:
* Special export selling price: $34 per unit
* Incremental variable production cost: $30 per unit
* Incremental shipping cost: $2 per unit
* Total incremental cost: $32 per unit
* Incremental contribution per unit: $34 - $32 = +$2 per unit
* Total incremental profit: $$500\text{ units} \times \$2 = +\$1,000$$
* The order is financially viable as it increases total profit by $1,000.

**Non-Financial Analysis**:
* **Spare capacity**: Because Velo Ltd has spare capacity, accepting this order does not displace any normal, full-priced domestic sales.
* **Market separation**: Since this is an export market, there is less risk of domestic buyers discovering the lower price and demanding a discount.
* **Future opportunities**: Successful fulfillment could lead to recurring, larger orders in this international market.
* **Risk**: If regular customers learn about this low price, it could damage domestic brand reputation or lead to price wars.

**Recommendation**:
* Velo Ltd should accept the special export order because it makes a positive contribution of $1,000, covers all incremental costs, utilizes idle capacity, and has low risk of impacting domestic sales pricing.

**Part (a) (4 marks)**
* State and explain any two differences (2 marks per difference with clear comparison, max 4 marks).
* *Accept*: Inventory valuation difference (variable vs full costing) (2 marks).
* *Accept*: Fixed overhead treatment (period cost vs product cost) (2 marks).
* *Accept*: Profit difference when inventory levels change (2 marks).

**Part (b)(i) (8 marks)**
* Rent & rates allocation: Machining $12,000; Assembly $8,000; Canteen $4,000 (1 mark for all three correct).
* Machinery Depreciation: Machining $24,000; Assembly $8,000; Canteen $4,000 (1 mark for all three correct).
* Power: Machining $8,000; Assembly $5,000; Canteen $2,000 (1 mark for all three correct).
* Subtotals before reapportionment: Machining $56,000; Assembly $29,000; Canteen $14,000 (1 mark for all three correct).
* Canteen reapportionment to Machining: $5,250 (1 mark).
* Canteen reapportionment to Assembly: $8,750 (1 mark).
* OAR Machining: $12.25 per machine hour (1 mark, with units/basis).
* OAR Assembly: $7.55 per direct labor hour (1 mark, with units/basis).

**Part (b)(ii) (4 marks)**
* Machining absorbed overheads: 5,100 hours * $12.25 = $62,475 (1 mark).
* Machining under-absorption: $525 under-absorbed (1 mark) (allow OF from (b)(i)).
* Assembly absorbed overheads: 4,800 hours * $7.55 = $36,240 (1 mark).
* Assembly under-absorption: $560 under-absorbed (1 mark) (allow OF from (b)(i)).

**Part (c)(i) (3 marks)**
* Correct cost per unit of Beta: $38 (1 mark).
* Correct over-absorbed overhead calculation: $3,200 (1 mark).
* Correct final net profit: $28,400 (1 mark).

**Part (c)(ii) (3 marks)**
* Correct marginal cost per unit: $30 (1 mark).
* Correct total contribution: $42,000 (1 mark).
* Correct final profit under marginal costing: $26,000 (1 mark).

**Part (c)(iii) (2 marks)**
* Identify correct inventory volume difference: 300 units (1 mark).
* Reconciliation statement showing correct math to reconcile $28,400 to $26,000 (using 300 units * $8 = $2,400) (1 mark).

**Part (d) (6 marks)**
* Financial calculation of incremental unit contribution (+$2) or total contribution (+$1,000) (1 mark).
* Discussion of spare capacity and lack of domestic cannibalization (1 mark).
* Discussion of foreign market advantages (market separation) (1 mark).
* Discussion of risks (future price expectations, domestic awareness) (1 mark).
* Clear recommendation matching the analysis (1 mark).
* Quality of communication / structured evaluation (1 mark).
* *Maximum 6 marks.*

**(a) Calculation of the Accumulated Fund at 1 January 2023**

$$\begin{array}{lrr}
\text{\bf Assets:} & \text{(\$)} & \text{(\$)} \\
\text{Clubhouse and equipment (at valuation)} & 120,000 & \\
\text{Cafe inventory} & 2,400 & \\
\text{Subscriptions in arrears} & 800 & \\
\text{Cash at bank} & 4,700 & \\
\text{Total Assets} & & 127,900 \\
\text{\bf Liabilities:} & & \\
\text{Cafe trade payables} & 1,150 & \\
\text{Subscriptions in advance} & 400 & \\
\text{Wages accrued (Clubhouse staff)} & 350 & \\
\text{Total Liabilities} & & (1,900) \\
\hline
\text{\bf Accumulated Fund} & & \mathbf{126,000} \\
\hline
\end{array}$$

***

**(b) Cafe Trading Account for the year ended 31 December 2023**

$$\begin{array}{lrr}
& \text{(\$)} & \text{(\$)} \\
\text{Revenue (Cafe sales)} & & 14,200 \\
\text{\bf Less: Cost of Sales} & & \\
\text{Opening Inventory} & 2,400 & \\
\text{Purchases (W1)} & 7,850 & \\
\hline
\text{Goods available for sale} & 10,250 & \\
\text{Less: Closing Inventory} & (1,950) & \\
\hline
\text{Cost of Sales} & & (8,300) \\
\hline
\text{\bf Gross Profit} & & 5,900 \\
\text{Less: Cafe staff wages} & & (3,400) \\
\hline
\text{\bf Cafe Profit} & & \mathbf{2,500} \\
\hline
\end{array}$$

**Working 1 (W1): Cafe Purchases**
$$\text{Purchases} = \text{Cash paid to suppliers} + \text{Closing trade payables} - \text{Opening trade payables}$$
$$\text{Purchases} = 8,100 + 900 - 1,150 = \mathbf{7,850}$$

***

**(c) Income and Expenditure Account for the year ended 31 December 2023**

*Note: Two alternative methods for presenting subscription write-offs are acceptable and yield the same surplus.*

**Method A: Showing Subscriptions Income gross and Write-off as a separate expense**

$$\begin{array}{lrr}
\text{\bf Income} & \text{(\$)} & \text{(\$)} \\
\text{Subscriptions (W2)} & & 18,000 \\
\text{Cafe profit} & & 2,500 \\
\text{Competition surplus (W3)} & & 1,900 \\
\hline
\text{Total Income} & & 22,400 \\
\text{\bf Expenditure} & & \\
\text{Clubhouse wages (W4)} & 6,260 & \\
\text{General expenses} & 4,900 & \\
\text{Irrecoverable subscriptions written off} & 150 & \\
\text{Depreciation on clubhouse and equipment (W5)} & 11,000 & \\
\hline
\text{Total Expenditure} & & (22,310) \\
\hline
\text{\bf Surplus of income over expenditure} & & \mathbf{90} \\
\hline
\end{array}$$

**Method B: Showing Subscriptions Income net of write-off**

$$\begin{array}{lrr}
\text{\bf Income} & \text{(\$)} & \text{(\$)} \\
\text{Subscriptions (\$18,000 - \$150)} & & 17,850 \\
\text{Cafe profit} & & 2,500 \\
\text{Competition surplus (W3)} & & 1,900 \\
\hline
\text{Total Income} & & 22,250 \\
\text{\bf Expenditure} & & \\
\text{Clubhouse wages (W4)} & 6,260 & \\
\text{General expenses} & 4,900 & \\
\text{Depreciation on clubhouse and equipment (W5)} & 11,000 & \\
\hline
\text{Total Expenditure} & & (22,160) \\
\hline
\text{\bf Surplus of income over expenditure} & & \mathbf{90} \\
\hline
\end{array}$$

**Working 2 (W2): Subscriptions Account**
$$\begin{array}{lr|lr}
\text{\bf Dr} & \text{(\$)} & \text{\bf Cr} & \text{(\$)} \\
\hline
\text{Opening arrears} & 800 & \text{Opening advance} & 400 \\
\text{\bf Income & Expenditure (balancing figure)} & \mathbf{18,000} & \text{Bank (Receipts)} & 18,400 \\
\text{Closing advance} & 750 & \text{Irrecoverable subscriptions} & 150 \\
& & \text{Closing arrears} & 600 \\
\hline
& 19,550 & & 19,550 \\
\hline
\end{array}$$

**Working 3 (W3): Competition Surplus**
$$\text{Competition Entry Fees} - \text{Prizes} = 3,100 - 1,200 = \mathbf{1,900}$$

**Working 4 (W4): Clubhouse Wages**
$$\text{Wages} = \text{Paid} + \text{Closing accrued} - \text{Opening accrued} = 6,200 + 410 - 350 = \mathbf{6,260}$$

**Working 5 (W5): Depreciation**
$$\text{Depreciation} = \text{Opening value} + \text{Additions} - \text{Closing value} = 120,000 + 5,000 - 114,000 = \mathbf{11,000}$$

***

**(d) Discussion and Recommendation**

**Option 1: Increase subscription fee by 20%**
* **Pros:** Provides a regular, predictable, and recurring source of income. Assuming membership remains constant, it will generate an additional $3,600 per year ($18,000 \times 20\%$) to help build up reserves for future maintenance and equipment replacement.
* **Cons:** It does not solve the immediate cash flow requirement of $12,000 since it will take over three years to accumulate this sum. Furthermore, an aggressive increase may lead to a loss of members, causing total revenue to actually decrease.

**Option 2: Organise a fundraising gala dinner**
* **Pros:** If successful, it has the potential to raise the required $12,000 in a single event. It acts as a community-building exercise and raises the club's public profile.
* **Cons:** High planning risk and relies heavily on volunteer effort. Significant upfront costs (catering, entertainment) are involved, and if attendance or auction bids are low, it might yield a loss instead of a surplus.

**Recommendation:**
The committee should choose Option 2 for the immediate capital requirement of $12,000 since Option 1 cannot raise the funds in time. However, they may also consider a smaller, gradual subscription increase (e.g., 5%) to ensure long-term operational sustainability.

**(a) Accumulated Fund [Total 4 marks]**
* 1 mark for correct calculation of Total Assets ($127,900) containing correct components.
* 1 mark for correct calculation of Total Liabilities ($1,900) containing correct components.
* 1 mark for showing correct formula or logic (Assets - Liabilities).
* 1 mark for the final correct answer of $126,000.

**(b) Cafe Trading Account [Total 5 marks]**
* 1 mark for Cafe Sales ($14,200).
* 1 mark for correct Purchases figure of $7,850 (with working shown).
* 1 mark for correct Cost of Sales calculation ($8,300) [O/F allowed for Purchases].
* 1 mark for correct Gross Profit ($5,900) [O/F].
* 1 mark for correct Cafe Profit ($2,500) after deducting Cafe wages ($3,400).

**(c) Income and Expenditure Account [Total 11 marks]**
* 3 marks for Subscriptions income: 2 marks for adjustments (handling arrears, advances, and write-offs) and 1 mark for final correct value ($18,000 or $17,850).
* 1 mark for Cafe profit ($2,500) [O/F from (b)].
* 1 mark for Competition surplus ($1,900) with working.
* 2 marks for Clubhouse wages ($6,260) [1 mark for adjusting closing accrued, 1 mark for adjusting opening accrued].
* 1 mark for General expenses ($4,900).
* 2 marks for Depreciation ($11,000) [1 mark for including additions, 1 mark for final calculation].
* 1 mark for Surplus of income over expenditure ($90) [O/F]. Note: If Method A is used, 1 mark is also awarded for showing Irrecoverable Subscriptions of $150 as an expense.

**(d) Discussion and Recommendation [Total 5 marks]**
* Max 2 marks for discussion of Option 1 (advantages/disadvantages).
* Max 2 marks for discussion of Option 2 (advantages/disadvantages).
* 1 mark for a clear, reasoned recommendation based on the financial constraints (highlighting that Option 1 cannot raise $12,000 in the short term).

Part (a)
According to IAS 8 (Accounting Policies, Changes in Accounting Estimates and Errors):
- A prior period error must be corrected retrospectively (1).
- This requires restating the comparative amounts for the prior period(s) presented in which the error occurred (1).
- If the error occurred before the earliest prior period presented, the opening balances of assets, liabilities, and equity (usually retained earnings) for the earliest prior period presented must be restated (1).
- The correction is not recognized in the current year's profit or loss statement (1).

Part (b)(i)
Corrected Retained Earnings as at 1 January 2023:
Draft retained earnings as at 1 January 2023: $285,000
Add: Capitalisation of machinery (purchased 1 Jan 2022): +$60,000 (1)
Less: Depreciation on machinery for 2022 ($60,000 * 20%): -$12,000 (1)
Corrected Retained Earnings as at 1 January 2023: $333,000 (1)

Part (b)(ii)
Corrected Profit for the year ended 31 December 2023:
Draft profit for the year: $142,000
Less: Depreciation on the machinery for 2023 ($60,000 * 20%): -$12,000 (2)
Corrected Profit for the year ended 31 December 2023: $130,000 (1)

Part (c)
Vexton PLC
Statement of Cash Flows for the year ended 31 December 2023

Cash flows from operating activities:
Profit for the year: $130,000 [1 OF]
Adjustments for:
- Depreciation ($32,000 draft + $12,000 correction): $44,000 [2]
- Loss on disposal of machinery: $4,000 [1]
- Finance costs: $5,200 [1]
Operating profit before working capital changes: $183,200
- Increase in inventory ($41,500 - $35,000): -$6,500 [1]
- Decrease in trade receivables ($32,500 - $29,000): +$3,500 [1]
- Decrease in trade payables ($25,100 - $22,400): -$2,700 [1]
Cash generated from operations: $177,500
- Interest paid: -$5,200 [1]
Net cash from operating activities: $172,300 [1 OF]

Cash flows from investing activities:
- Purchase of machinery: -$98,000 [1] (Workings below)
- Proceeds from sale of machinery: $14,000 [1]
Net cash used in investing activities: -$84,000

Cash flows from financing activities:
- Proceeds from issue of ordinary shares ($100,000 + $25,000): $125,000 [1]
- Redemption of debentures ($80,000 - $50,000): -$30,000 [1]
- Dividends paid: -$40,000 [1]
Net cash from financing activities: $55,000

Net increase in cash and cash equivalents: $143,300 [1 OF]
Cash and cash equivalents at 1 January 2023: $12,000
Cash and cash equivalents at 31 December 2023: $155,300

Workings for Purchase of Machinery:
Corrected Opening Carrying Value (1 Jan 2023): $150,000 + $48,000 = $198,000
Corrected Closing Carrying Value (31 Dec 2023): $198,000 + $36,000 = $234,000
Machinery Carrying Value Account:
Debit: Opening Balance $198,000
Debit: Additions (Cash purchase) $98,000 (balancing figure)
Credit: Depreciation $44,000
Credit: Disposal (Carrying value) $18,000
Credit: Closing Balance $234,000

Part (d)
Advantages of preparing a statement of cash flows:
- It shows actual cash movements which are not affected by non-cash accounting policies or estimates (1).
- It assists stakeholders in evaluating the company's liquidity, solvency, and cash-generating ability (1).
- It facilitates comparison of profitability with cash generation (quality of profit) (1).
- It helps in budgeting and forecasting future cash requirements (1).
(Accept other valid points; maximum 3 marks).

Part (a) (Max 4 marks):
- Retrospectively corrected (1)
- Restating comparative amounts for prior period(s) presented (1)
- If before earliest period, adjust opening balances of assets, liabilities, and retained earnings of earliest period (1)
- Error correction is NOT included in current profit and loss (1)

Part (b)(i) (Max 3 marks):
- $285,000 draft (no mark)
- Add: $60,000 cost (1)
- Less: $12,000 depreciation (1)
- Corrected balance $333,000 (1)

Part (b)(ii) (Max 3 marks):
- $142,000 draft (no mark)
- Less: $12,000 depreciation (2) (1 mark for showing $60k * 20%)
- Corrected profit $130,000 (1)

Part (c) (Max 12 marks):
- Profit for the year: $130,000 (1 OF from b(ii))
- Depreciation: $44,000 (2) (1 mark for draft $32k + 1 mark for $12k correction)
- Loss on disposal: $4,000 (1)
- Finance costs adjustment: $5,200 (1)
- Change in Inventory: -$6,500 (1)
- Change in Receivables: +$3,500 (1)
- Change in Payables: -$2,700 (1)
- Interest paid: -$5,200 (1)
- Net operating cash: $172,300 (1 OF)
- Purchase of machinery: -$98,000 (1)
- Proceeds from sale: $14,000 (1)
- Share issue proceeds ($125,000) OR Debenture redemption (-$30,000) OR Dividends (-$40,000): (1) for any two, (2) for all three
- Net increase in cash & reconciliation: $155,300 (1 OF)

Part (d) (Max 3 marks):
- 1 mark for each valid advantage up to 3.

**(a) Calculation of Purchase Consideration**

- Premises: $150,000
- Equipment: $38,000
- Inventory: $16,500
- Trade Receivables ($14,000 \\times 0.95$): $13,300
- Goodwill: $30,000
- **Total assets acquired**: $247,800
- Less: Trade payables taken over: ($15,000)
- **Purchase Consideration**: **$232,800**

**(b) Partnership Realisation Account**

*Debits:*
- Premises (carrying value): $120,000
- Equipment (carrying value): $45,000
- Inventory (carrying value): $18,000
- Trade Receivables (carrying value): $14,000
- **Profit on Realisation**: $50,800
- Allocated to A (3/5): $30,480
- Allocated to B (2/5): $20,320
- *Total Debits*: $247,800

*Credits:*
- Trade Payables (taken over): $15,000
- Zeta plc (Purchase Consideration): $232,800
- *Total Credits*: $247,800

**(c) Partners' Capital Accounts**

*Debit side:*
- Shares in Zeta plc (allocated 3:2 of $140,000):
- A: $84,000
- B: $56,000
- Bank (final settlement):
- A: $56,480
- B: $44,320
- *Total Debits*: A: $140,480 | B: $100,320

*Credit side:*
- Balance b/f:
- A: $110,000
- B: $80,000
- Realisation Account (profit):
- A: $30,480
- B: $20,320
- *Total Credits*: A: $140,480 | B: $100,320

*(Note: Partnership Bank Account check: Opening balance $8,000 + Cash received from Zeta plc ($232,800 - $140,000 = $92,800) = $100,800. This is fully distributed to A ($56,480) and B ($44,320).)*

**(d) Discussion on accepting ordinary shares in Zeta plc**

*Advantages of accepting shares:*
- Capital Growth & Dividends: Partners can benefit from future capital appreciation and dividend distributions if Zeta plc performs well.
- Reduced Cash Drain: Zeta plc might not have been willing to pay 100% in cash, so accepting shares facilitated the deal.
- Diversified/Larger Entity: Being shareholders in a larger, limited company reduces personal liability and provides a more liquid asset (shares) than a partnership interest.

*Disadvantages of accepting shares:*
- Risk: The market value of Zeta plc's shares can fluctuate, and their investment could lose value.
- Loss of Control: As minority shareholders in a plc, A and B have virtually no control over business decisions, whereas they had full control as partners.
- Liquidity: If Zeta plc is unlisted, the shares might be difficult to sell.

*Conclusion / Recommendation:*
- The decision was reasonable if they wanted to exit active management while retaining an economic interest, but they should be aware of the investment risks involved.

**(a) Purchase Consideration [Total: 4 marks]**
- 1 mark for correct valuation of non-current assets (Premises $150,000 + Equipment $38,000)
- 1 mark for correct valuation of current assets (Inventory $16,500 + Receivables $13,300)
- 1 mark for Goodwill of $30,000
- 1 mark for deducting Trade payables of $15,000 to arrive at $232,800 (of)

**(b) Partnership Realisation Account [Total: 8 marks]**
- 1 mark for transferring Premises and Equipment at book values ($120,000 and $45,000)
- 1 mark for transferring Inventory and Trade receivables at book values ($18,000 and $14,000)
- 1 mark for transferring Trade payables ($15,000) on credit side
- 1 mark for recording Zeta plc purchase consideration ($232,800) on credit side (of)
- 2 marks for calculating correct total realisation profit of $50,800 (1 mark if arithmetic error but method correct)
- 2 marks for splitting profit between A ($30,480) and B ($20,320) (1 mark each) (of)

**(c) Partners' Capital Accounts [Total: 8 marks]**
- 1 mark for correct opening balances (A: $110,000, B: $80,000)
- 1 mark for transferring realisation profit correctly (A: $30,480, B: $20,320) (of)
- 2 marks for share distribution (A: $84,000, B: $56,000) (1 mark each) (of)
- 2 marks for bank balancing payments (A: $56,480, B: $44,320) (1 mark each) (of)
- 2 marks for format, correct entry directions, and balancing both sides

**(d) Discussion [Total: 5 marks]**
- Up to 2 marks for arguments in favour of accepting shares (e.g., dividend potential, capital growth, facilitation of sale).
- Up to 2 marks for arguments against/drawbacks of accepting shares (e.g., loss of management control, exposure to share price volatility, potential liquidity issues).
- 1 mark for a clear, reasoned concluding judgment.

### **(a) Calculation of Accounting Rate of Return (ARR)**

1. **Calculate total operating cash flows (before depreciation):**
* Year 1: \((30,000 \times \$5.00) - \$50,000 = \$100,000\)
* Year 2: \((40,000 \times \$5.50) - \$60,000 = \$160,000\)
* Year 3: \((50,000 \times \$6.00) - \$70,000 = \$230,000\)
* Year 4: \((25,000 \times \$5.00) - \$40,000 = \$85,000\)
* **Total Operating Cash Flows** = \(\$100,000 + \$160,000 + \$230,000 + \$85,000 = \$575,000\)

2. **Calculate total depreciation:**
* \(\text{Total Depreciation} = \text{Initial Cost} - \text{Scrap Value} = \$360,000 - \$40,000 = \$320,000\)

3. **Calculate total and average annual accounting profit:**
* \(\text{Total Profit} = \text{Total Operating Cash Flows} - \text{Total Depreciation} = \$575,000 - \$320,000 = \$255,000\)
* \(\text{Average Annual Profit} = \frac{\$255,000}{4 \text{ years}} = \$63,750\)

4. **Calculate average investment:**
* \(\text{Average Investment} = \frac{\$360,000 + \$40,000}{2} = \$200,000\)

5. **Calculate ARR:**
* \(\text{ARR} = \left( \frac{\$63,750}{\$200,000} \right) \times 100 = 31.875\%\) (or **31.88%**)

---

### **(b) Calculation of Net Present Value (NPV) at 10%**

| Year | Cash Flow Details | Net Cash Flow ($) | Discount Factor (10%) | Present Value ($) |
|---|---|---|---|---|
| 0 | Machine Cost + Working Capital | \((390,000)\) | 1.000 | \((390,000)\) |
| 1 | Operating Cash Flow | 100,000 | 0.909 | 90,900 |
| 2 | Operating Cash Flow | 160,000 | 0.826 | 132,160 |
| 3 | Operating Cash Flow | 230,000 | 0.751 | 172,730 |
| 4 | Operating Cash Flow + Scrap + WC Recovered | 155,000 | 0.683 | 105,865 |
| | **Net Present Value (NPV)** | | | **111,655** |

*Note on Year 4 Cash Flow:* \(\$85,000 \text{ (operating)} + \$40,000 \text{ (scrap)} + \$30,000 \text{ (working capital recovery)} = \$155,000\).

---

### **(c) Calculation of Internal Rate of Return (IRR)**

1. **Calculate NPV at 20%:**

| Year | Net Cash Flow ($) | Discount Factor (20%) | Present Value ($) |
|---|---|---|---|
| 0 | \((390,000)\) | 1.000 | \((390,000)\) |
| 1 | 100,000 | 0.833 | 83,300 |
| 2 | 160,000 | 0.694 | 111,040 |
| 3 | 230,000 | 0.579 | 133,170 |
| 4 | 155,000 | 0.482 | 74,710 |
| | **NPV at 20%** | | **12,220** |

2. **Apply IRR Interpolation Formula:**
$$\text{IRR} = L + \left[ \frac{\text{NPV}_L}{\text{NPV}_L - \text{NPV}_H} \right] \times (H - L)$$
* Where \(L = 10\%\), \(H = 20\%\), \(\text{NPV}_L = 111,655\), \(\text{NPV}_H = 12,220\)
$$\text{IRR} = 10\% + \left[ \frac{111,655}{111,655 - 12,220} \right] \times (20\% - 10\%)$$
$$\text{IRR} = 10\% + \left[ \frac{111,655}{99,435} \right] \times 10\% = 10\% + 11.23\% = 21.23\%$$

---

### **(d) Advice to the Directors**

* **Financial Factors:**
* The NPV is positive at $111,655, meaning the project will increase shareholder wealth.
* The IRR of 21.23% is significantly higher than the company's cost of capital (10%).
* The ARR of 31.88% shows strong profitability.
* **Non-financial / Other Factors:**
* **Estimation risk:** These are future estimates. Contribution levels or demand volumes might not be reached, especially if market competition changes.
* **Inflation & Cost changes:** Selling price/costs might rise, affecting contribution margins.
* **Working capital:** Is the $30,000 working capital sufficient to handle high-volume sales in Years 2 and 3?
* **Staffing/Resources:** Does the company have the necessary labor skills to run the new machine?

**Recommendation:** The directors should accept the project because it is financially highly viable with a strong positive NPV and an IRR well above the hurdle rate.

**(a) ARR Calculation [6 Marks]**
* Calculation of total operating profit/cash flows ($575,000) [1 mark]
* Calculation of total depreciation over 4 years ($320,000) [1 mark]
* Average annual accounting profit ($63,750) [1 mark]
* Average investment ($200,000) [1 mark]
* Correct application of the ARR formula [1 mark]
* Correct final ARR percentage of 31.88% (or 31.875%) [1 mark]

**(b) NPV Calculation [10 Marks]**
* Year 0 Net Outflow: -$390,000 [1 mark]
* Year 1 Operating Cash Flow: $100,000 [1 mark]
* Year 2 Operating Cash Flow: $160,000 [1 mark]
* Year 3 Operating Cash Flow: $230,000 [1 mark]
* Year 4 Operating Cash Flow: $85,000 [1 mark]
* Year 4 Scrap Value included: $40,000 [1 mark]
* Year 4 Working Capital Recovery included: $30,000 [1 mark]
* Correct application of 10% discount factors [1 mark]
* Sum of Present Values [1 mark]
* Correct final NPV of $111,655 [1 mark] (Accept $111,650 to $111,700 due to rounding)

**(c) IRR Calculation [4 Marks]**
* Calculation of Year 1 to 4 present values at 20% [1 mark]
* Correct calculation of NPV at 20% ($12,220) [1 mark]
* Proper application of the interpolation formula [1 mark]
* Correct final IRR of 21.23% (or 21.2%) [1 mark] (Or OF based on previous NPV)

**(d) Advice & Recommendations [5 Marks]**
* Analysis of financial indicators (NPV is positive, IRR is above cost of capital, strong ARR) [Max 2 marks]
* Discussion of non-financial factors/qualitative issues (reliability of forecasts, inflation risk, machinery life, staff skills) [Max 2 marks]
* Clear recommendation to proceed [1 mark]

**(a) Calculations of Variances**

1. **Sales Volume Profit Variance**:
\((\text{Actual Volume} - \text{Budgeted Volume}) \times \text{Standard Profit per Unit}\)
\((4,800 - 5,000) \times \$27 = \$5,400 \text{ (A)}\)

2. **Sales Price Variance**:
\((\text{Actual Selling Price} - \text{Standard Selling Price}) \times \text{Actual Quantity Sold}\)
Actual Selling Price = \(\$412,800 / 4,800 = \$86.00\) per unit
\((\$86.00 - \$85.00) \times 4,800 = \$4,800 \text{ (F)}\)

3. **Material Price Variance**:
\((\text{Standard Price} - \text{Actual Price}) \times \text{Actual Quantity Purchased}\)
Actual Material Price per kg = \(\$87,000 / 15,000 = \$5.80\)
\((\$6.00 - \$5.80) \times 15,000 = \$3,000 \text{ (F)}\)

4. **Material Usage Variance**:
\((\text{Standard Quantity for Actual Production} - \text{Actual Quantity Used}) \times \text{Standard Price}\)
Standard Quantity for Actual Production = \(4,800 \text{ units} \times 3 \text{ kg} = 14,400 \text{ kg}\)
\((14,400 - 15,000) \times \$6.00 = \$3,600 \text{ (A)}\)

5. **Labour Rate Variance**:
\((\text{Standard Rate} - \text{Actual Rate}) \times \text{Actual Hours Worked}\)
Actual Rate = \(\$141,450 / 11,500 = \$12.30\) per hour
\((\$12.00 - \$12.30) \times 11,500 = \$3,450 \text{ (A)}\)

6. **Labour Efficiency Variance**:
\((\text{Standard Hours for Actual Production} - \text{Actual Hours Worked}) \times \text{Standard Rate}\)
Standard Hours for Actual Production = \(4,800 \text{ units} \times 2.5 \text{ hours} = 12,000 \text{ hours}\)
\((12,000 - 11,500) \times \$12.00 = \$6,000 \text{ (F)}\)

**(b) Fixed Overhead Variances**

1. **Fixed Overhead Expenditure Variance**:
\(\text{Budgeted Fixed Overhead} - \text{Actual Fixed Overhead}\)
\(\$50,000 - \$48,500 = \$1,500 \text{ (F)}\)

2. **Fixed Overhead Volume Variance**:
\((\text{Actual Production} - \text{Budgeted Production}) \times \text{Standard Fixed Overhead Rate per Unit}\)
\((4,800 - 5,000) \times \$10.00 = \$2,000 \text{ (A)}\)
*(Alternatively: \((\text{Standard Hours for Actual Production} - \text{Budgeted Hours}) \times \text{Standard Rate per Hour} = (12,000 - 12,500) \times \$4.00 = \$2,000 \text{ (A)}\))*

**(c) Profit Reconciliation Statement for October**

| | \(\$\) | \(\$\) |
|---|---|---|
| **Budgeted Profit** \((5,000 \times \$27)\) | | 135,000 |
| Less: Sales Volume Profit Variance | | (5,400) |
| **Standard Profit on Actual Sales** | | **129,600** |
| | | |
| **Cost / Selling Price Variances** | **Favourable ($)** | **Adverse ($)** |
| Sales Price Variance | 4,800 | |
| Material Price Variance | 3,000 | |
| Material Usage Variance | | 3,600 |
| Labour Rate Variance | | 3,450 |
| Labour Efficiency Variance | 6,000 | |
| Fixed Overhead Expenditure Variance | 1,500 | |
| Fixed Overhead Volume Variance | | 2,000 |
| **Subtotals** | **15,300** | **9,050** |
| Net Variance | 6,250 (F) | |
| **Actual Profit** | | **135,850** |

*Direct Verification of Actual Profit:*
Revenue: \(\$412,800\)
Less Actual Costs:
Direct Materials: \(\$87,000\)
Direct Labour: \(\$141,450\)
Fixed Overheads: \(\$48,500\)
Total Actual Costs: \(\$276,950\)
Actual Profit = \(\$412,800 - \$276,950 = \$135,850\) (Verified)

**(d) Discussion and Explanations**

1. **Favourable Material Price & Adverse Material Usage**:
- The purchasing department may have bought cheaper, inferior-quality materials (giving a favourable price variance) (1 mark).
- This sub-standard material led to high wastage, defects, or scrap during the production process, resulting in more raw materials being consumed than standard (giving an adverse usage variance) (1 mark).

2. **Adverse Direct Labour Rate**:
- The company may have used higher-grade/skilled labor than planned, which commands a higher wage rate, or unexpected overtime premium rates had to be paid (1 mark).

**Part (a) [12 marks total]**
- Sales volume profit variance: 1 mark for \(\$5,400\), 1 mark for Adverse (A).
- Sales price variance: 1 mark for \(\$4,800\), 1 mark for Favourable (F).
- Material price variance: 1 mark for \(\$3,000\), 1 mark for Favourable (F).
- Material usage variance: 1 mark for \(\$3,600\), 1 mark for Adverse (A).
- Labour rate variance: 1 mark for \(\$3,450\), 1 mark for Adverse (A).
- Labour efficiency variance: 1 mark for \(\$6,000\), 1 mark for Favourable (F).

**Part (b) [4 marks total]**
- Fixed overhead expenditure variance: 1 mark for \(\$1,500\), 1 mark for Favourable (F).
- Fixed overhead volume variance: 1 mark for \(\$2,000\), 1 mark for Adverse (A).

**Part (c) [6 marks total]**
- Budgeted Profit of \(\$135,000\) (1 mark).
- Correct layout incorporating Sales Volume Profit Variance to reach Standard Profit on Actual Sales of \(\$129,600\) (1 mark).
- Correctly listing and subtotaling Favourable variances ($15,300) (1 mark).
- Correctly listing and subtotaling Adverse variances ($9,050) (1 mark).
- Calculating net variance of \(\$6,250\) Favourable (1 mark).
- Reconciled Actual Profit of \(\$135,850\) (1 mark).

**Part (d) [3 marks total]**
- d(1): 1 mark for identifying cheaper/lower-quality materials; 1 mark for linking this to higher waste/scrap/yield loss.
- d(2): 1 mark for identifying the use of higher-skilled labour (paid more) or payment of overtime premiums.