Topic: Discounted cash flow techniques

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AFM – Nov 2016 – L3 – Q3b – Discounted cash flow techniques

Calculate the Net Present Value (NPV) of a new product investment project considering real terms and inflation adjustments.

A company plans to invest GH¢7 million in a new product. Net contribution over the next five years is expected to be GH¢4.2 million per annum in real terms. Marketing expenditure of GH¢1.4 million per annum will also be needed. Expenditure of GH¢1.3 million per annum will be required to replace existing assets, and additional investment in working capital, equivalent to 10% of contribution, will be needed at the start of each year. Working capital will be released at the end of the project. The following inflation forecasts are made for the next five years:

  • Contribution: 8%
  • Marketing: 3%
  • Assets: 4%
  • General prices: 4.70%

The real cost of capital is 6%. All cash flows are in real terms. Ignore tax.

Required:
Calculate the Net Present Value (NPV) of the project and appraise whether it is a worthwhile project.

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AFM – May 2017 – L3 – Q2a – Discounted cash flow techniques

Use Macaulay duration method to choose the best bond option for ABE based on recovery period.

ABE has surplus cash which can be invested for at least five years. The company has consulted you to help them choose an investment that gives the shortest recovery period. The company presented the information on two types of bonds as follows:

Bond Redemption Nominal Value (GH¢) Redemption Value Coupon Rate (%) Price (GH¢)
A 5 years 1,000 At par 7.00 950
B 6 years 1,000 5% premium 7.50 1,010

Required:
Use the Macaulay Duration method to advise ABE on the best bond option to select for their investment. (12 marks)

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AFM – May 2019 – L3 – Q2a – Discounted cash flow techniques

Compare leasing and buying options for a machine and recommend the most viable choice based on net present value analysis.

Rahim Ltd requires a machine for 5 years. There are two alternatives, either to take it on lease or buy basis. The company is reluctant to invest an initial amount for the project and approaches their bankers. The bankers are ready to finance 100% of its initial required amount at a 15% rate of interest for any of the alternatives.

Under lease option, an upfront security deposit of GH¢5,000,000 is payable to the lessor, which is equal to the cost of the machine. Out of which, 40% shall be adjusted equally against annual lease rent. At the end of life of the machine, the expected scrap value will be at book value after providing depreciation at 20% on written down value basis.

Under the buying option, loan repayment is in equal annual installments of the principal amount, which is equal to annual lease rent charges. However, in the case of bank finance for the lease option, repayment of principal amount equal to lease rent is adjusted every year, and the balance at the end of 5th year.

Assume income tax rate is 30%, interest is payable at the end of every year, and discount rate at 15% p.a. The following discounting factors are given:

Year Factor
1 0.8696
2 0.7562
3 0.6576
4 0.5718
5 0.4972

Required:
Recommend the most viable option on the basis of net present values.

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AFM – Nov 2015 – L3 – Q2 – Discounted Cash Flow Techniques | Sources of Finance and Cost of Capital

Evaluate the financial viability of a proposed air conditioner manufacturing project using APV.

ABC Manufacturing Ltd (ABC) is an indigenous Ghanaian company that manufactures components used in air conditioners. The company now wants to manufacture air conditioners for sale in Ghana. Though the manufacture of air conditioners will be a completely new business, directors of ABC plan to integrate it into the company’s core business.

ABC has premises it considers suitable for the project. This premises was acquired two years ago at the cost of GHS50,000. ABC will acquire and install the needed machinery immediately, so production and sales can commence during the first year. The directors of ABC intend to develop the project for five years and then sell it to a suitable investor for an after-tax consideration of GHS20 million.

The following data are available for the project:

  1. The cost of acquiring and installing plant and machinery needed for the project will be GHS5 million at the start of the first year. Tax-allowable depreciation is available on the plant and machinery at the rate of 30% on reducing balance basis.
  2. Working capital requirement for each year is equal to 10% of the year’s anticipated sales. ABC has to make working capital available at the beginning of the respective year. It is expected that 40% of working capital will be redeployed to other projects at the end of the fifth year when the project is sold.
  3. It is expected that 2,000 units will be manufactured and sold in the first year. Unit sales will grow by 5% each year thereafter.
  4. Unit sales price is estimated at GHS2,200 in the first year. Thereafter, the unit sales price is expected to be increased by 10% each year.
  5. Unit variable cost will be GHS1,100 per unit in the first year. Unit variable cost is expected to increase by 8% each year after the first year.
  6. Fixed overhead costs are estimated at GHS1.5 million in total in each year of production/sale. One-half of the total fixed overhead costs are head office allocated overheads. After the first year of production/sales, fixed overhead costs are expected to increase by 5% per year.

ABC Ltd pays tax at 25% on taxable profits. Tax is payable in the same year the profit is earned. ABC Ltd uses 25% as its discount rate for new projects but the directors feel that this rate may not be appropriate for this new venture.

Currently, ABC can borrow at 500 basis points above the five-year Treasury note yield rate. Ghana’s government is enthused by the venture and has offered ABC a subsidized loan of up to 60% of the investment funds required at an interest rate of 200 basis points above the five-year Treasury note yield rate. ABC plans to use debt capital to finance the project by taking advantage of the government’s subsidized loan and raising the balance through a fresh issue of 5-year debentures. Issues costs, which can be assumed to be tax-deductible expenses, will be 5% of the gross proceeds from the debenture offer. The financing strategy for the project is not expected to affect the company’s borrowing capacity in any way.

ABC Ltd will be the first indigenous Ghanaian company to manufacture air conditioners in Ghana. However, it will be competing with XYZ Ltd, a listed company with majority shares held by foreign investors. The cost of equity of XYZ Ltd is estimated to be 20% and it pays tax at 22%. XYZ has 10 million shares in issue that are trading at GHS5.5 each, and bonds with total market value of GHS40 million.

The five-year Treasury note yield rate is currently 10% and the return on the market portfolio is 18%.

Required:
Evaluate, on financial grounds, whether ABC should implement the project or not. (20 marks)

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AFM – Nov 2018 – L3 – Q1a – Discounted cash flow techniques

Evaluating an irrigation project using the Adjusted Present Value (APV) method, incorporating debt financing, government subsidy, and project cash flows.

One-Village Water Resources Ltd (One-Village) is considering a damming and irrigation project that will supply water to tomato farms around the Oti River. One-Village plans to commence the construction and installation phase of the project immediately and complete it in three years. One-Village will invest GH¢3 million in new plants and equipment now. Mobilisation to the project site will cost GH¢0.5 million now. Development costs are expected to be GH¢3 million in the first year, GH¢4 million in the second year, and GH¢2 million in the third year.

The commercial phase of the project will commence in the fourth year and run indefinitely. The project will generate after-tax net cash flows of GH¢6 million in the fourth year and GH¢8 million in the fifth year. Beyond the fifth year, cash flows will grow by 5% every year to perpetuity.

One-Village has 10 million shares outstanding, which are currently trading at GH¢3.5 each. The total value of its debt stock is GH¢20 million. One-Village plans to finance the investment requirements of the construction and installation phase of the project with new debt. Its borrowing cost is 20%, while its cost of equity is 25%. The Government of Ghana is promoting large-scale farming and is willing to give a subsidised loan of up to GH¢10 million at 15% annual interest. One-Village plans to take the maximum subsidised loan from the Government of Ghana and finance the balance with a bank loan. Issue costs, which are tax-deductible, are expected to be GH¢0.6 million. Both loans will be repaid in five years. One-Village falls into the 22% corporate income tax category. The risk-free interest rate is 14%, and the return on the market portfolio is 18%.

Required:
Evaluate the project using the adjusted present value (APV) technique and recommend whether it should be implemented or not. (12 marks)

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AFM – May 2018 – L3 – Q2 – Discounted cash flow techniques | Valuation and the use of free cash flows

Evaluating investment options using NPV and IRR to advise a company on which projects should be undertaken.

The Board of Peartek Ltd is considering the company’s capital investment options for the coming year, and is evaluating the following potential investments:

Investment A:

  • Investment of GH¢60,000, including GH¢40,000 for capital equipment and GH¢20,000 for increases in working capital.
  • Expected sales of 10,000 units next year with a sales price of GH¢10 and variable costs of GH¢6 per unit.
  • Sales price is expected to decline by 20% per annum due to competition, sales volume to fall by 10%, and variable costs to decline by 20%.
  • Overheads of GH¢15,000 annually, including a GH¢4,000 depreciation charge.
  • The project will be wound up in year three, with working capital recovered and capital equipment sold off for 25% of its cost.

Investment B:

  • Immediate outlay of GH¢90,000, financed by borrowing at 6%.
  • Expected net profits of GH¢12,000 next year, rising by 3% per annum indefinitely.

Investment C:

  • Outlay of GH¢25,000 financed by retained profits.
  • Expected annual net cash profits:
    • Years 1 to 4: GH¢3,000
    • Years 5 to 7: GH¢5,000
    • From year 8 onwards: GH¢7,000 in perpetuity.

The company discounts projects lasting 10 years or less at 10%, and others at 13%. Ignore taxation.

Required:

a) As a financial management analyst, you have been asked to advise the board of Peartek Ltd (in the form of a briefing report) which investment should be undertaken. Use the NPV method in your analysis. (15 marks)

b) Minority of board members feel that the Internal Rate of Return (IRR) should also be used as either an alternative or a complementary method of investment appraisal. Calculate the IRR of investments A and B and comment accordingly. (5 marks)

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AFM – May 2016 – L3 – Q2a – Discounted cash flow techniques, Valuation and use of free cash flows, Theories of capital structure

Compute NPV for two investment projects using WACC and CAPM, and provide recommendations based on risk analysis.

a) Joebel Limited is a diversified company operating in different industries on the African Continent. The shares of the company are widely traded on the stock exchange and currently have a market price of GH¢3.20 per share. The company’s dividend payment over the last five years is as follows:

Year Dividend Per Share (DPS) (GH¢)
2015 0.35
2014 0.32
2013 0.30
2012 0.29
2011 0.28

The Board of Directors of Joebel Limited is considering two main investment opportunities: one in the Oil and Gas sector and the other in the Hotel and Tourism sector. Both projects have short lives and their associated cash flows are as follows:

Year Oil & Gas (GH¢’000) Hotel & Tourism (GH¢’000)
1 85 180
2 175 195
3 160 150

The investment in Oil and Gas would cost GH¢400,000, while the investment in Hotel and Tourism would cost GH¢405,000. The Management of the Company has identified the industry beta for Oil and Gas as 1.2 and for Hotel and Tourism as 1.6. However, Joebel Limited’s company beta is 1.5. The average return on companies listed on the stock exchange is 25%, and the yield on Treasury bills is 20%.

Required:
i) Compute the Net Present Values (NPV) of both projects using the company’s weighted average cost of capital as the discount rate. (5 marks)
ii) Compute the NPV using a discount rate that takes into account the risk associated with the individual projects. (5 marks)
iii) Advise Management regarding the suitability and acceptability of the projects. (1 mark)

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AFM – May 2016 – L3 – Q1a – Discounted cash flow techniques, Sources of finance and cost of capital

Calculate the average rate of return for two stocks and analyze portfolio return using different methods.

a) Crown Limited has a mixture of investment portfolios, stock A and Stock B. The historical performance return on the stocks are as follows:

Year Stock A Return (%) Stock B Return (%)
2010 -10 -3
2011 18 21
2012 39 44
2013 14 4
2014 33 28

Required:
i) Calculate the average rate of return for each stock during the period of 2010 to 2014. (3 marks)
ii) Calculate the average return on the portfolio during the period if Crown Limited held 50% each of stock A and stock B. (3 marks)
iii) Calculate the return of the portfolio using the standard deviation approach. (4 marks)

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AFM – Nov 2016 – L3 – Q3b – Discounted cash flow techniques

Calculate the Net Present Value (NPV) of a new product investment project considering real terms and inflation adjustments.

A company plans to invest GH¢7 million in a new product. Net contribution over the next five years is expected to be GH¢4.2 million per annum in real terms. Marketing expenditure of GH¢1.4 million per annum will also be needed. Expenditure of GH¢1.3 million per annum will be required to replace existing assets, and additional investment in working capital, equivalent to 10% of contribution, will be needed at the start of each year. Working capital will be released at the end of the project. The following inflation forecasts are made for the next five years:

  • Contribution: 8%
  • Marketing: 3%
  • Assets: 4%
  • General prices: 4.70%

The real cost of capital is 6%. All cash flows are in real terms. Ignore tax.

Required:
Calculate the Net Present Value (NPV) of the project and appraise whether it is a worthwhile project.

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AFM – May 2017 – L3 – Q2a – Discounted cash flow techniques

Use Macaulay duration method to choose the best bond option for ABE based on recovery period.

ABE has surplus cash which can be invested for at least five years. The company has consulted you to help them choose an investment that gives the shortest recovery period. The company presented the information on two types of bonds as follows:

Bond Redemption Nominal Value (GH¢) Redemption Value Coupon Rate (%) Price (GH¢)
A 5 years 1,000 At par 7.00 950
B 6 years 1,000 5% premium 7.50 1,010

Required:
Use the Macaulay Duration method to advise ABE on the best bond option to select for their investment. (12 marks)

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AFM – May 2019 – L3 – Q2a – Discounted cash flow techniques

Compare leasing and buying options for a machine and recommend the most viable choice based on net present value analysis.

Rahim Ltd requires a machine for 5 years. There are two alternatives, either to take it on lease or buy basis. The company is reluctant to invest an initial amount for the project and approaches their bankers. The bankers are ready to finance 100% of its initial required amount at a 15% rate of interest for any of the alternatives.

Under lease option, an upfront security deposit of GH¢5,000,000 is payable to the lessor, which is equal to the cost of the machine. Out of which, 40% shall be adjusted equally against annual lease rent. At the end of life of the machine, the expected scrap value will be at book value after providing depreciation at 20% on written down value basis.

Under the buying option, loan repayment is in equal annual installments of the principal amount, which is equal to annual lease rent charges. However, in the case of bank finance for the lease option, repayment of principal amount equal to lease rent is adjusted every year, and the balance at the end of 5th year.

Assume income tax rate is 30%, interest is payable at the end of every year, and discount rate at 15% p.a. The following discounting factors are given:

Year Factor
1 0.8696
2 0.7562
3 0.6576
4 0.5718
5 0.4972

Required:
Recommend the most viable option on the basis of net present values.

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AFM – Nov 2015 – L3 – Q2 – Discounted Cash Flow Techniques | Sources of Finance and Cost of Capital

Evaluate the financial viability of a proposed air conditioner manufacturing project using APV.

ABC Manufacturing Ltd (ABC) is an indigenous Ghanaian company that manufactures components used in air conditioners. The company now wants to manufacture air conditioners for sale in Ghana. Though the manufacture of air conditioners will be a completely new business, directors of ABC plan to integrate it into the company’s core business.

ABC has premises it considers suitable for the project. This premises was acquired two years ago at the cost of GHS50,000. ABC will acquire and install the needed machinery immediately, so production and sales can commence during the first year. The directors of ABC intend to develop the project for five years and then sell it to a suitable investor for an after-tax consideration of GHS20 million.

The following data are available for the project:

  1. The cost of acquiring and installing plant and machinery needed for the project will be GHS5 million at the start of the first year. Tax-allowable depreciation is available on the plant and machinery at the rate of 30% on reducing balance basis.
  2. Working capital requirement for each year is equal to 10% of the year’s anticipated sales. ABC has to make working capital available at the beginning of the respective year. It is expected that 40% of working capital will be redeployed to other projects at the end of the fifth year when the project is sold.
  3. It is expected that 2,000 units will be manufactured and sold in the first year. Unit sales will grow by 5% each year thereafter.
  4. Unit sales price is estimated at GHS2,200 in the first year. Thereafter, the unit sales price is expected to be increased by 10% each year.
  5. Unit variable cost will be GHS1,100 per unit in the first year. Unit variable cost is expected to increase by 8% each year after the first year.
  6. Fixed overhead costs are estimated at GHS1.5 million in total in each year of production/sale. One-half of the total fixed overhead costs are head office allocated overheads. After the first year of production/sales, fixed overhead costs are expected to increase by 5% per year.

ABC Ltd pays tax at 25% on taxable profits. Tax is payable in the same year the profit is earned. ABC Ltd uses 25% as its discount rate for new projects but the directors feel that this rate may not be appropriate for this new venture.

Currently, ABC can borrow at 500 basis points above the five-year Treasury note yield rate. Ghana’s government is enthused by the venture and has offered ABC a subsidized loan of up to 60% of the investment funds required at an interest rate of 200 basis points above the five-year Treasury note yield rate. ABC plans to use debt capital to finance the project by taking advantage of the government’s subsidized loan and raising the balance through a fresh issue of 5-year debentures. Issues costs, which can be assumed to be tax-deductible expenses, will be 5% of the gross proceeds from the debenture offer. The financing strategy for the project is not expected to affect the company’s borrowing capacity in any way.

ABC Ltd will be the first indigenous Ghanaian company to manufacture air conditioners in Ghana. However, it will be competing with XYZ Ltd, a listed company with majority shares held by foreign investors. The cost of equity of XYZ Ltd is estimated to be 20% and it pays tax at 22%. XYZ has 10 million shares in issue that are trading at GHS5.5 each, and bonds with total market value of GHS40 million.

The five-year Treasury note yield rate is currently 10% and the return on the market portfolio is 18%.

Required:
Evaluate, on financial grounds, whether ABC should implement the project or not. (20 marks)

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AFM – Nov 2018 – L3 – Q1a – Discounted cash flow techniques

Evaluating an irrigation project using the Adjusted Present Value (APV) method, incorporating debt financing, government subsidy, and project cash flows.

One-Village Water Resources Ltd (One-Village) is considering a damming and irrigation project that will supply water to tomato farms around the Oti River. One-Village plans to commence the construction and installation phase of the project immediately and complete it in three years. One-Village will invest GH¢3 million in new plants and equipment now. Mobilisation to the project site will cost GH¢0.5 million now. Development costs are expected to be GH¢3 million in the first year, GH¢4 million in the second year, and GH¢2 million in the third year.

The commercial phase of the project will commence in the fourth year and run indefinitely. The project will generate after-tax net cash flows of GH¢6 million in the fourth year and GH¢8 million in the fifth year. Beyond the fifth year, cash flows will grow by 5% every year to perpetuity.

One-Village has 10 million shares outstanding, which are currently trading at GH¢3.5 each. The total value of its debt stock is GH¢20 million. One-Village plans to finance the investment requirements of the construction and installation phase of the project with new debt. Its borrowing cost is 20%, while its cost of equity is 25%. The Government of Ghana is promoting large-scale farming and is willing to give a subsidised loan of up to GH¢10 million at 15% annual interest. One-Village plans to take the maximum subsidised loan from the Government of Ghana and finance the balance with a bank loan. Issue costs, which are tax-deductible, are expected to be GH¢0.6 million. Both loans will be repaid in five years. One-Village falls into the 22% corporate income tax category. The risk-free interest rate is 14%, and the return on the market portfolio is 18%.

Required:
Evaluate the project using the adjusted present value (APV) technique and recommend whether it should be implemented or not. (12 marks)

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AFM – May 2018 – L3 – Q2 – Discounted cash flow techniques | Valuation and the use of free cash flows

Evaluating investment options using NPV and IRR to advise a company on which projects should be undertaken.

The Board of Peartek Ltd is considering the company’s capital investment options for the coming year, and is evaluating the following potential investments:

Investment A:

  • Investment of GH¢60,000, including GH¢40,000 for capital equipment and GH¢20,000 for increases in working capital.
  • Expected sales of 10,000 units next year with a sales price of GH¢10 and variable costs of GH¢6 per unit.
  • Sales price is expected to decline by 20% per annum due to competition, sales volume to fall by 10%, and variable costs to decline by 20%.
  • Overheads of GH¢15,000 annually, including a GH¢4,000 depreciation charge.
  • The project will be wound up in year three, with working capital recovered and capital equipment sold off for 25% of its cost.

Investment B:

  • Immediate outlay of GH¢90,000, financed by borrowing at 6%.
  • Expected net profits of GH¢12,000 next year, rising by 3% per annum indefinitely.

Investment C:

  • Outlay of GH¢25,000 financed by retained profits.
  • Expected annual net cash profits:
    • Years 1 to 4: GH¢3,000
    • Years 5 to 7: GH¢5,000
    • From year 8 onwards: GH¢7,000 in perpetuity.

The company discounts projects lasting 10 years or less at 10%, and others at 13%. Ignore taxation.

Required:

a) As a financial management analyst, you have been asked to advise the board of Peartek Ltd (in the form of a briefing report) which investment should be undertaken. Use the NPV method in your analysis. (15 marks)

b) Minority of board members feel that the Internal Rate of Return (IRR) should also be used as either an alternative or a complementary method of investment appraisal. Calculate the IRR of investments A and B and comment accordingly. (5 marks)

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AFM – May 2016 – L3 – Q2a – Discounted cash flow techniques, Valuation and use of free cash flows, Theories of capital structure

Compute NPV for two investment projects using WACC and CAPM, and provide recommendations based on risk analysis.

a) Joebel Limited is a diversified company operating in different industries on the African Continent. The shares of the company are widely traded on the stock exchange and currently have a market price of GH¢3.20 per share. The company’s dividend payment over the last five years is as follows:

Year Dividend Per Share (DPS) (GH¢)
2015 0.35
2014 0.32
2013 0.30
2012 0.29
2011 0.28

The Board of Directors of Joebel Limited is considering two main investment opportunities: one in the Oil and Gas sector and the other in the Hotel and Tourism sector. Both projects have short lives and their associated cash flows are as follows:

Year Oil & Gas (GH¢’000) Hotel & Tourism (GH¢’000)
1 85 180
2 175 195
3 160 150

The investment in Oil and Gas would cost GH¢400,000, while the investment in Hotel and Tourism would cost GH¢405,000. The Management of the Company has identified the industry beta for Oil and Gas as 1.2 and for Hotel and Tourism as 1.6. However, Joebel Limited’s company beta is 1.5. The average return on companies listed on the stock exchange is 25%, and the yield on Treasury bills is 20%.

Required:
i) Compute the Net Present Values (NPV) of both projects using the company’s weighted average cost of capital as the discount rate. (5 marks)
ii) Compute the NPV using a discount rate that takes into account the risk associated with the individual projects. (5 marks)
iii) Advise Management regarding the suitability and acceptability of the projects. (1 mark)

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AFM – May 2016 – L3 – Q1a – Discounted cash flow techniques, Sources of finance and cost of capital

Calculate the average rate of return for two stocks and analyze portfolio return using different methods.

a) Crown Limited has a mixture of investment portfolios, stock A and Stock B. The historical performance return on the stocks are as follows:

Year Stock A Return (%) Stock B Return (%)
2010 -10 -3
2011 18 21
2012 39 44
2013 14 4
2014 33 28

Required:
i) Calculate the average rate of return for each stock during the period of 2010 to 2014. (3 marks)
ii) Calculate the average return on the portfolio during the period if Crown Limited held 50% each of stock A and stock B. (3 marks)
iii) Calculate the return of the portfolio using the standard deviation approach. (4 marks)

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