Calculate the accumulated amount if GH¢2500.00 were invested at 18% compound interest for a period of six years.
a) Kofy Addo invested GH¢4,000 into his bank account at the beginning of every year for four years. The bank paid interest at 8% compounded annually for the first four years. Thereafter, the interest rate changed to 8.35%, but Kofy Addo did not make any more deposits. At the end of the sixth year, he withdrew GH¢5000.
Required:
i) Calculate the size of the investment at the end of the sixth year, before the withdrawal.
ii) Calculate the size of the investment after the withdrawal in the sixth year.
iii) Calculate the balance in the account after the eighth year.
b) Kofy Addo decided to start saving money for his future. At the end of each month, he deposited GH¢500 into an account at Trust Bank, which earned an interest rate of 9% per annum compounded monthly.
Required:
i) Determine the balance of Kofy Addo’s account after 20 years. (4 marks)
ii) Calculate the amount deposited into the account over the 20-year period. (2 marks)
iii) Calculate how much interest he earned over the 20-year period. (2 marks)
iv) Calculate the effective annual rate of interest. (2 marks)
a)
= GH¢22,8530.01
ii)
Size of investment after withdrawal = 22,853.01 – 5,000
= GH¢17,853.01
iii)
Balance after the 8th year = 
= GH¢20,958.94
ii)
Amount deposited = 500 x (12 x 20) = GH¢120,000
iii)
Interest earned = GH¢333,943.44 – GH¢120,000 = GH¢213,943.44
iv)
Kwabena was able to recover GH¢150,000 out of GH¢200,000 invested in the Savings and Loans Company. How much money should he invest at a return of 6% per annum so as to earn an annual income of GH¢15,000 for a period of 10 years? (10 marks)
= 15000(7.36) = GHS 110,400.00
The following statement of financial position relates to Sankofa and Kaakyire as at 31 October 2020.
| Statement of Financial Position | Sankofa (GH¢’000) | Kaakyire (GH¢’000) |
|---|---|---|
| Non-current assets | ||
| Property, Plant and Equipment | 37,000 | 30,000 |
| Investment Property | 5,000 | – |
| Investments | 24,000 | – |
| Total Non-current assets | 66,000 | 30,000 |
| Current assets | ||
| Inventory | 9,000 | 8,000 |
| Other current assets | 21,000 | 14,000 |
| Total Current assets | 30,000 | 22,000 |
| Total assets | 96,000 | 52,000 |
| Equity and liabilities | ||
| Ordinary shares (issued @ GH¢2.50) | 20,000 | 8,000 |
| Retained earnings | 26,000 | 16,000 |
| Total Equity | 46,000 | 24,000 |
| Non-current liabilities | ||
| 10% debentures | 11,900 | 12,000 |
| Current liabilities | ||
| Payables | 38,100 | 16,000 |
| Total Equity and liabilities | 96,000 | 52,000 |
Additional information:
i) On 1 November 2018, Sankofa purchased 2.4 million of the ordinary shares of Kaakyire when Kaakyire’s retained earnings balance stood at GH¢11 million. There have been no movements in share capital since the acquisition. As part of the consideration given for the shares acquired, the shareholders of Kaakyire accepted 1 million shares worth GH¢7 million in Sankofa at acquisition. The remaining consideration was agreed to be paid on 31 October 2020 for GH¢12.1 million. The present values of GH¢1 receivable based on 10% (considered to be an appropriate discount rate for Sankofa) are as follows:
| Present Value of GH¢1 receivable |
|---|
| In one year’s time: |
| In two years’ time: |
Entries have been correctly passed for the effects of all of the above, including any unwound discounts, except for the final payment made on 31 October 2020.
ii) At acquisition, the fair values of Kaakyire’s assets, liabilities, and contingencies were equal to their carrying amounts, with the exception of the following assets:
| Carrying amount (GH¢’000) | Fair value (GH¢’000) |
|---|---|
| Trade receivables | 1,250 |
| Inventory | 1,500 |
| Properties | 14,000 |
The properties had a remaining useful life of 10 years. No items of property were sold during the two years to 31 October 2020. The inventory and the receivable were realised during the post-acquisition period.
iii) On 1 November 2019, Kaakyire sold an item of plant to Sankofa for GH¢5 million. Kaakyire originally bought the plant from Gyidie for GH¢6 million, and Kaakyire had provided accumulated depreciation of GH¢2.2 million up to the date of sale. Kaakyire considered the plant to have a remaining useful life of 5 years at the date of transfer.
iv) The Investment Property in the books of Sankofa represents an office facility that was completed on 1 November 2018 at the cost of GH¢3.5 million. The useful economic life of the facility was estimated at 20 years. Immediately after the acquisition of Kaakyire, Sankofa began to rent this property out to Kaakyire under a lease agreement. Sankofa Group values its investment properties using the fair value model under IAS 40 Investment Properties and its owner-occupied properties using the cost model under IAS 16 Property, Plant and Equipment.
v) On 1 November 2019, Sankofa acquired 30% of the ordinary shares of Kaboom at the cost of GH¢6 million. During the year ended 31 October 2020, Kaboom reported a profit after tax of GH¢2 million. No dividends were paid or declared by Kaboom during the period. At year-end, Kaboom’s inventory included GH¢1.2 million worth of goods bought from Sankofa during the year to October 2020. Sankofa charges a 25% margin on all sales.
On 31 October 2019, Goodwill acquired in Kaakyire was attributed with an impairment loss of GH¢0.5 million. The group’s policy is to measure non-controlling interest at the proportion of the fair value of the subsidiary’s net assets.
Required:
Prepare the Consolidated Statement of Financial Position for the Sankofa Group as at 31 October 2020.
Calculate the geometric mean of the following rates of return for an investment on the Ghana Stock Exchange:
0.50, 0.30, -0.50, -0.25
The geometric mean of the rates of return is -7.52%.
KuKu invested GHS 2000.00 into a Deluxe Equity Fund.
Required:
(i) Determine how long it will take for the GHS 2000.00 investment to accumulate GHS 800.00 interest at 10% compounded quarterly, if the interest is allowed for the fractional part of a conversion period (1 month = 30 days).
(ii) Determine how long it will take the GHS 2000.00 investment to triple in value if it doubled in value in 6 years at a certain rate of interest compounded monthly (1 month = 30 days).
(iii) Determine the interest rate in (ii).
(i) Time to accumulate GHS 800 interest at 10% compounded quarterly:
To calculate how long it will take for the GHS 2000 investment to accumulate GHS 800 interest at 10% compounded quarterly, we use the compound interest formula:
Where:
Taking logarithms:
Therefore, it will take approximately 3 years, 4 months, and 11 days for the investment to accumulate GHS 800 interest.
(ii) Time to triple in value if it doubles in 6 years:
If the GHS 2000 investment doubled in value in 6 years, it means the new value after 6 years is GHS 4000. To determine how long it will take for the investment to triple (GHS 6000), we use the same compound interest formula.
Let the time it takes to double be t=6t = 6 years and let the time to triple be t3t_3. We know the investment doubles in 6 years, so the interest rate is compounded monthly. Let rr be the interest rate.
Using the formula for doubling:
We now solve for r and use it to determine how long it will take to triple.
n= 9 years 6 months and 4 days
(iii) Interest rate for doubling in 6 years:
From the logarithmic equation, we have:
Therefore, the interest rate is 0.96 percent
Calculate the sum of the infinite geometric progressions:
(i) 
(ii) 
(i) The given geometric progression is 
The sum to infinity of a geometric progression is given by: 
(ii) The geometric progression is 
The sum to infinity is 
Obiya Ltd assembles computer equipment from bought-in components and distributes them to various wholesalers and retailers. It has recently subscribed to an inter-firm comparison service. Members submit accounting ratios as specified by the operator of the service, and in return, members receive the average figures for each of the specified ratios taken from all of the companies in the same sector that subscribe to the service. The specified ratios and the average figures for Obiya’s sector are shown below:
Ratios of sector companies for the period to 30 September 2017
| Ratio | Sector Average |
|---|---|
| Return on capital employed | 22.1% |
| Net asset turnover | 1.8 times |
| Gross profit margin | 30% |
| Net profit (before tax) margin | 12.50% |
| Current ratio | 1.6:1 |
| Quick ratio | 0.9:1 |
| Inventory holding period | 46 days |
| Accounts receivable collection period | 45 days |
| Accounts payable payment period | 55 days |
| Debt to equity | 40% |
| Dividend yield | 6% |
| Dividend cover | 3 times |
Obiya Ltd’s financial statements for the year to 30 September 2017 are set out below:
Statement of profit or loss for the year ended 30 September 2017
| Description | GH¢’000 |
|---|---|
| Revenue | 2,425 |
| Cost of sales | (1,870) |
| Gross profit | 555 |
| Other operating expenses | (215) |
| Operating profit | 340 |
| Finance costs | (34) |
| Exceptional item (note ii) | (120) |
| Profit before tax | 186 |
| Income tax | (90) |
| Profit for the period | 96 |
Statement of changes in equity (extract)
For the year ended 30 September 2017
| Description | GH¢’000 |
|---|---|
| Retained earnings – 1 October 2016 | 179 |
| Net profit for the period | 96 |
| Dividends paid (Interim GH¢60,000; final GH¢30,000) | (90) |
| Retained earnings – 30 September 2017 | 185 |
Statement of financial position as at 30 September 2017
| Description | GH¢’000 |
|---|---|
| Non-current assets | |
| Property, plant, equipment | 540 |
| Current assets | |
| Inventory | 275 |
| Accounts receivable | 320 |
| Bank | – |
| Total current assets | 595 |
| Total assets | 1,135 |
| Equity | |
| Ordinary shares (25 pesewas each) | 150 |
| Retained earnings | 185 |
| Total equity | 335 |
| Non-current liabilities | |
| 8% loan notes | 300 |
| Current liabilities | |
| Bank overdraft | 65 |
| Trade accounts payable | 350 |
| Taxation | 85 |
| Total current liabilities | 500 |
| Total equity and liabilities | 1,135 |
Notes:
i) The details of the non-current assets are:
| Description | Cost (GH¢’000) | Accumulated depreciation (GH¢’000) | Net book value (GH¢’000) |
|---|---|---|---|
| At 30 September 2017 | 3,600 | 3,060 | 540 |
ii) The exceptional item relates to losses on the sale of a batch of computers that had become worthless due to improvements in microchip design.
iii) The market price of Obiya’s shares throughout the year averaged GH¢6.00 each.
Required:
a) Calculate the ratios for Obiya equivalent to those provided by the inter-firm comparison service.
(5 marks)
b) Write a report analyzing the operational performance, gearing, investment, and liquidity of Obiya Ltd based on a comparison with the sector averages. (10 marks)
Ratios for Obiya Ltd for the period to 30 September 2017:
| Description | Obiya Ltd |
|---|---|
| Return on capital employed (186 + 34 loan interest ÷ (335 + 300)) | 34.6% |
| Net asset turnover (2,425 ÷ (335 + 300)) | 3.8 times |
| Gross profit margin (555 ÷ 2,425 × 100) | 22.9% |
| Net profit margin (186 ÷ 2,425 × 100) | 7.7% |
| Current ratio (595 ÷ 500) | 1.19:1 |
| Quick ratio (320 ÷ 500) | 0.64:1 |
| Inventory holding period (275 ÷ 1,870 × 365) | 54 days |
| Accounts receivable collection period (320 ÷ 2,425 × 365) | 48 days |
| Accounts payable payment period (350 ÷ 1,870 × 365) | 68 days |
| Debt to equity (300 ÷ 335 × 100) | 90% |
| Dividend yield (15p ÷ GH¢6 × 100) | 2.5% |
| Dividend cover (96 ÷ 90) | 1.07 times |
(5 marks evenly spread)
b)
Report on Financial Performance of Obiya Ltd
To: Management of Obiya Ltd
From: Financial Analyst
Subject: Analysis of Financial Performance, Gearing, Investment, and Liquidity Compared to Sector Averages
While Obiya Ltd demonstrates strong operational efficiency in terms of asset turnover, its profitability margins are weaker compared to the sector, and it faces significant liquidity and gearing challenges. Additionally, its investment return for shareholders is below sector expectations, and the company’s dividend policy appears unsustainable. Immediate attention should be given to improving liquidity, addressing high debt levels, and managing inventory more effectively to avoid future losses.
(10 marks evenly spread)
Fortune acquired shares in Obolo Company Ltd, a manufacturing company situated in Nsawam, and the following transactions took place:
i) He acquired 100,000 ordinary shares for GH¢115,600 on 14 March, 2020. He also acquired another 220,000 shares on 26 November, 2020 at a price of GH¢1.2 per share.
ii) On 24 December, 2020, he sold 235,000 shares for GH¢305,500 which attracted a sales commission of 1.5% of the sales value to the brokerage firm.
Required:
Compute the capital gains tax.
Computation of Cost of Shares Sold:
Jacobs Limited and Idowu Company Limited both manufacture and sell auto parts. The summarised profit and loss accounts of the two companies for 2014 are as follows:
| Jacobs Ltd (GH¢’000) | Idowu Co Ltd (GH¢’000) | |
|---|---|---|
| Sale Revenue | 1,500 | 800 |
| Operating Expenses | (800) | (620) |
| Profit | 700 | 180 |
Each company has earned a constant level of profit for a number of years, and both are expected to continue to do so. The policy of both companies is to distribute all profits as dividends to ordinary shareholders as they are earned. Neither company has any fixed interest capital. Details of the ordinary share capital of the two companies are as follows:
| Jacobs Ltd (GH¢’000) | Idowu Co Ltd (GH¢’000) | |
|---|---|---|
| Authorised Ordinary Shares | 2,500 | 2,000 |
| Issued Ordinary Shares | 2,000 | 1,000 |
| Market Value per Share (Ex Div) | 3.50 | 1.50 |
The directors of Jacobs Limited are considering submitting a bid for the entire share capital of Idowu Co Limited. They believe that, if the bid succeeds, the combined sales revenue of the two companies will increase by GH¢60,000 per annum, and savings in operating expenses, amounting to GH¢50,000 per annum, will be possible. Part of the machinery at present owned by Idowu Co Limited would no longer be required and could be sold for GH¢100,000. Furthermore, the directors of Jacobs Limited believe that the takeover would result in a reduction to 9% in the annual return required by the ordinary shareholders of Idowu Co Limited.
Required:
i) On the basis of the above information, calculate the maximum price that Jacobs Ltd should be willing to pay for the entire share capital of Idowu Co Limited. (6 marks)
ii) Calculate the minimum price that the ordinary shareholders in Idowu Co Ltd should be willing to accept for their shares. (4 marks)
Assume that the takeover price is agreed at the figure calculated in part (ii) above, and that the purchase consideration will be settled by an exchange of ordinary shares in Idowu Co Ltd for the ordinary shares of Jacobs Ltd. Show how the entire benefit from the takeover will accrue to all the present shareholders of Jacobs Ltd. (6 marks)
The sale of the unused machinery would generate GH¢100,000, so the total value after the acquisition is:
TotalValue=GH¢9,900,000+GH¢100,000=GH¢10,000,000Total Value = GH¢9,900,000 + GH¢100,000 = GH¢10,000,000
Step 5: Calculate the maximum price
The maximum price Jacobs Ltd should pay is the difference between the value after the acquisition and its current value before the acquisition.
ii) Minimum price Idowu Co Ltd shareholders should accept
The minimum price that the ordinary shareholders in Idowu Co Ltd should accept is the current market value of their shares.
Thus, the minimum price the ordinary shareholders in Idowu Co Ltd should accept is GH¢1,500,000.
(Total: 10 marks)
b)
The agreed takeover price for Idowu Co Ltd was GH¢1,500,000, based on the minimum acceptable price for Idowu’s shareholders as calculated in part 3(a)(ii).
We need to determine how the entire benefit from the acquisition will accrue to the shareholders of Jacobs Ltd using a share exchange mechanism.
Let x represent the number of new shares to be issued to Idowu Co Ltd’s shareholders. The total number of shares in issue after the acquisition will be 2,000,000 shares (since Jacobs Ltd originally has 2,000,000 issued shares).
The total value of Jacobs Ltd after the acquisition is GH¢10,000,000 (as calculated in 3(a)(i)).
For the benefit of the acquisition to accrue fully to Jacobs Ltd’s shareholders, the value of the shares issued to Idowu Co Ltd’s shareholders should equal the agreed takeover price of GH¢1,500,000. This gives us the following equation:
The market value per share after the acquisition will be:
Before the acquisition, the market value of Jacobs Ltd’s shares was GH¢3.50 per share. After the acquisition, the value of each share increases to GH¢4.25, representing a gain of GH¢0.75 per share.
For Jacobs Ltd’s original 2,000,000 shares:
2,000,000×0.75=GH¢1,500,000
Thus, the shareholders of Jacobs Ltd will receive the entire benefit from the acquisition, which is GH¢1,500,000, the same as the agreed takeover price.
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