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  • 15 Marks

FM – May 2017 – L3 – Q7 – Investment Appraisal Techniques

Provide background on the Capital Asset Pricing Model (CAPM) and its use in project evaluation.

ou were recently appointed by a major manufacturing company as the senior accountant at one of the divisions of the company, which is located in Makurdi. You have received the following memorandum from the divisional manager:

“I tried to see you today, but you were busy with the auditors.
I have to go to a meeting at the head office on Friday about the new project. We sent to the head office its projected cash flow figures before you arrived. Apparently, one of the head office finance people has discounted our figures, using a rate which was calculated from the Capital Asset Pricing Model. I do not know why they are discounting the figures, because inflation is predicted to be negligible over the next few years. I think that this is all a ploy to stop us from going ahead with the project and let another division have the cash.
I looked up Capital Asset Pricing Model in a finance book which was lying in your office, but I could not make a head or tail of it, and anyway it all seemed to be about buying shares and nothing about our project.
We always use payback for the smaller projects which we do not have to refer to head office. I am going to argue for it now because the project has a payback of less than five years, which is our normal yardstick.
I am very keen to go ahead with the project because I feel that it will secure the medium-term future of our division.
I will be tied up all day tomorrow, so again I will not be able to see you. Could you please make a few notes for me which I can read on the way on Friday morning? I want to know how the Capital Asset Pricing Model is supposed to work, plus any other things which you feel I ought to know for the meeting. I do not want to look like a fool or lose the project because they blind me with science.
As you have probably discovered, I do not know much about finance, so please do not use any technical jargon or complicated maths.”

Required:
Prepare notes for the divisional manager which provide helpful background for the meeting.

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  • 20 Marks

FM – Nov 2023 – L3 – SB – Q3 – Investment Appraisal Techniques

Calculate and compare NPV for two proposals involving equipment purchase vs. existing machinery for contract fulfillment.

Niko Plc, a large equity-financed company, has a year-end of December 31. It must fulfill a contract in Abuja and has two proposals to choose from: Proposal A (purchasing new machinery) and Proposal B (using existing machinery).

Proposal A:

  • Outlay of N312,500,000 on December 31, 2023, for new plant and machinery.
  • Projected net cash inflows (before tax, in nominal terms):
    • 2024: N200,000,000
    • 2025: N275,000,000
    • 2026: N350,000,000
  • Scrap value: N25,000,000 at end of 2026.

Proposal B:

  • Uses a machine with a net realizable value of N250 million, with an alternative sale value of N300 million on January 1, 2025, if unused.
  • Cash inflows (in nominal terms):
    • 2024: N350,000,000
    • 2025: N350,000,000
  • Labour costs:
    • 2024: N100 million (replacement staff cost of N110 million)
    • 2025: N108 million (replacement staff cost of N118.8 million)
  • Machine residual value: N0 at project end in 2025.

Additional Details:

  • Working capital: 10% of year-end cash inflows, released upon project completion.
  • Expected annual inflation rates: 2024 – 10%, 2025 – 8%, 2026 – 6%, 2027 – 5%.
  • Real cost of capital: 10%.
  • Income tax: 40%, payable one year after the accounting period.
  • Capital allowances: 20% reducing balance for Proposal A’s plant and machinery.

Required:

  • a. Calculate the NPV at December 31, 2023, for each proposal. (17 Marks)
  • b. State any reservations about making an investment decision based on these NPV figures. (3 Marks)

Answer:

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  • 15 Marks

PSAF – Nov 2014 – L2 – Q7 – Public Sector Reforms

Advising on investment projects based on expected returns and understanding cost-benefit analysis features in public project appraisal.

a. Mr. Make-No-Mistake has N200,000 which he decides to invest if he can secure an assurance that the investment will earn at least 10% p.a. He is considering three projects:

  • Project A: Will earn N218,000 at the end of the 1st year.
  • Project B: Will earn N250,000 at the end of the 2nd year.
  • Project C: Will earn N140,000 at the end of 1st year and another N100,000 at the end of 2nd year.

If none of the projects is undertaken, Mr. Make-No-Mistake will invest his N200,000 in something else that will earn him 10% p.a.

You are required to assess and advise Mr. Make-No-Mistake on which of the projects he should undertake. (12 Marks)

b. Identify THREE main features of Cost-Benefit Analysis in public project appraisal. (3 Marks)

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  • 15 Marks

PSAF – May 2022 – L2 – SA – Q7 – Public Sector Reforms,

Discuss reasons for divergence between private and public appraisal of projects and explain key differences in cost-benefit and cost-effectiveness analysis.

Investment appraisal is a process of finding out the least possible costs of an investment and the maximum economic benefits, which may accrue from the commitment of resources.

Required:
a. Highlight FOUR reasons for divergence between private and public appraisal of a project. (4 Marks)
b. How does cost-benefit analysis (CBA) differ from cost-effectiveness analysis (CEA)? (5 Marks)
c. Identify THREE procedures and THREE limitations of cost-effectiveness analysis. (6 Marks)

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  • 15 Marks

PSAF – Nov 2021 – L2 – Q7 – Government Accounting Concepts and Principles

Calculate NPV for projects, profitability index, and discuss ranking differences.

Otunba Local Government wishes to boost its revenue generation and six possible capital investments have been identified. However, the Local Government only has access to a total of N6,200,000. The projects may not be postponed until a future period, and it is unlikely that similar investment opportunities will occur.

Expected net cash flows are:

Projects A and E are mutually exclusive while all the projects are believed to be of similar risk to the Local Government’s existing capital investments. Any surplus funds may be invested in the money market to earn a return of 9% per year. The money market may be assumed to be an efficient market. The Local Government’s cost of capital is 12% per year.

Required:

(a) Calculate the expected net present value for each project, and rank the projects. (8 Marks)
(b) Assuming the projects are divisible, calculate the Profitability Index for each project and rank the projects to determine how the money would be best invested. (6 Marks)
(c) State why the rankings in (b) differ from that in (a) above. (1 Mark)

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  • 15 Marks

MA – Dec 2023 – L2 – Q4a – Discounted Cash Flow

This question involves calculating the NPV for three projects being considered by Kanfa Ltd and recommending the best project based on financial grounds.

Kanfa Ltd received GH¢50 million as compensation from Ghana Highways Authority (GHA) when one of its properties was destroyed to pave way for the Accra–Kumasi highway construction. Management of Kanfa Ltd has decided to invest the amount received in one of three capital investment opportunities identified.

Project A:

This is a long-term project, which would run for 20 years and will require an immediate outlay of GH¢50 million and net annual cash profits as follows:

  • 1st to 5th years: GH¢2 million
  • 6th to 10th years: GH¢8 million
  • 11th to 15th years: GH¢15 million
  • 16th to 20th years: GH¢5 million

At the end of the 20th year, the project would be decommissioned at a cost of GH¢2 million.

Project B:

Kanfa Ltd is considering opening a Tourist Attraction Centre in Cape Coast, with an initial capital investment of GH¢50 million. It will operate for five years and be sold at an estimated price of GH¢5 million. The market research survey estimates the following visitor numbers and probabilities:

  • 800,000 visitors (30%)
  • 600,000 visitors (50%)
  • 400,000 visitors (20%)

Entrance fee: GH¢40 per visitor, and each visitor is expected to spend GH¢15 on souvenirs and GH¢5 on refreshments. Variable costs per visitor: GH¢25 (including souvenirs and refreshments). Maintenance costs: GH¢2 million per annum.

Project C:

This project involves a current outlay of GH¢50 million on equipment and GH¢15 million on working capital immediately. The working capital will increase to GH¢21 million in year one. Net annual cash profits: GH¢18 million for six years. The capital equipment can be sold for GH¢5 million at the end of the project.

Other information:

  • The company’s cost of capital is 12% for the three projects.
  • Ignore taxation and inflation.

Required:
Calculate the Net Present Value (NPV) of each project and recommend which project the company should undertake on financial grounds.

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  • 12 Marks

MA – Nov 2021 – L2 – Q4a – Discounted Cash Flow

Calculate and evaluate the payback period for the Ohenewa project based on provided cash flows.

a) Bee Ltd manufactures high-quality mobile phones for its local market. Due to less competition, Bee Ltd sales have grown significantly over the past few years and are expected to grow. Bee Ltd is planning to launch a new model, ‘Ohenewa’.

The company has already spent GH¢1 million on Research and Development and will require a further investment of GH¢5.5 million in production equipment. This cost excludes the GH¢1.1 million installation fee. The project has a life span of five years. In the end, the equipment will have a residual value of GH¢0.6 million. Sales and production of Ohenewa over its lifecycle are expected to be:

Year Units
1 6,500
2 7,500
3 8,000
4 7,800
5 7,000

The selling price in Year 1 and Year 2 will be GH¢750 per unit. However, the selling price will be reduced to GH¢600 per unit in Year 3 and will remain at this level for the remainder of the project. The variable cost as a percentage of sales is 55% over the entire product lifecycle. The fixed overhead, including depreciation cost expected to be incurred directly due to increasing the production capacity, is GH¢2 million per annum.

Other information:

  • A cost of capital of 12% per annum is used to evaluate projects of this type.
  • Bee Ltd has a history of accepting similar projects which pay back within three years.
  • Ignore inflation and taxation.

Required:
i) Calculate the Payback Period for the Ohenewa project. (10 marks)
ii) Evaluate the acceptability of the project based on the calculation in i) above. (2 marks)

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  • 15 Marks

MA – April 2022 – L2 – Q4a – Discounted cash flow

Evaluate the acceptability of a project using the Net Present Value (NPV) method considering cash flows and cost of capital.

Phil Company is considering replacing its existing machine on the introduction of a new product. The existing machine would be sold for GH¢2 million and replaced with a new machine at the beginning of the year at the cost of GH¢16 million. This new machine would be sold at the end of year 4 for GH¢1 million.

A market research recently carried out at a cost of GH¢1.5 million indicates a unit selling price of GH¢300 in year 1, rising by 10% per annum. Sales volume for the four-year life of the project has been estimated as follows:

Year Units
1 60,000
2 85,000
3 85,000
4 80,000

Possible unit variable costs are as follows:

Probability GH¢
0.4 240
0.6 260

Incremental fixed cost as a result of the project is GH¢15 per unit plus GH¢1,000,000 per annum staff cost.

The introduction of the new product is expected to reduce the market demand for an existing product by 5,000 units per annum. The existing product has a unit contribution of GH¢75.

Other annual fixed costs associated with the new product include the following:

  • Amortization of goodwill: GH¢50,000
  • Depreciation: GH¢250,000

Phil Company’s cost of capital is 12%.

Required:

Evaluate the acceptability of the project.

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  • 12 Marks

MA – Nov 2016 – L2 – Q5a – Discounted cash flow

Calculate the NPV break-even point under different cost of capital scenarios and determine the project's duration based on given cash inflows.

DDB Limited has decided to set up a factory to process groundnuts into oil. The feasibility studies cost them GH¢35,000. The consultants have advised that the initial outlay will be GH¢250,000; however, they were unable to estimate the cash inflow due to the uncertain economic environment.

Required:
Using NPV as an appraisal technique, you are required to calculate:

i) The constant cash inflow needed to break even if the cost of capital is 15% and the project is to last for 10 years.

(4 marks)

ii) By how much should the cash inflow increase to break even if the cost of capital is increased to 20%. (4 marks)

iii) If the cash inflow is GH¢45,000, for how long should the project run to break even if the cost of capital is 15%.

(4 marks)

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  • 10 Marks

FM – April 2022 – L2 – Q4b – Introduction to Investment Appraisal

Calculate the Accounting Rate of Return (ARR) for three projects and provide advice on which projects should be undertaken based on a target ARR.

SAKAMA Ghana Ltd uses the Accounting Rate of Return (ARR) as the basis of evaluating projects for investment of its scarce financial resources. It uses its predetermined expected return on capital as the basis for the choice of investment projects. The company’s Finance team has provided the information below regarding various projects and their initial investments and net cash flows. The hurdle rate or target Accounting Rate of Return for SAKAMA Ghana Ltd is 25%.

Required:
i) Calculate the Accounting Rate of Return for each project (Average Investment basis). (7 marks)
ii) Using the target return of 25%, advise SAKAMA Ghana Ltd which projects should be undertaken. (3 marks)

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  • 15 Marks

FM – May 2017 – L3 – Q7 – Investment Appraisal Techniques

Provide background on the Capital Asset Pricing Model (CAPM) and its use in project evaluation.

ou were recently appointed by a major manufacturing company as the senior accountant at one of the divisions of the company, which is located in Makurdi. You have received the following memorandum from the divisional manager:

“I tried to see you today, but you were busy with the auditors.
I have to go to a meeting at the head office on Friday about the new project. We sent to the head office its projected cash flow figures before you arrived. Apparently, one of the head office finance people has discounted our figures, using a rate which was calculated from the Capital Asset Pricing Model. I do not know why they are discounting the figures, because inflation is predicted to be negligible over the next few years. I think that this is all a ploy to stop us from going ahead with the project and let another division have the cash.
I looked up Capital Asset Pricing Model in a finance book which was lying in your office, but I could not make a head or tail of it, and anyway it all seemed to be about buying shares and nothing about our project.
We always use payback for the smaller projects which we do not have to refer to head office. I am going to argue for it now because the project has a payback of less than five years, which is our normal yardstick.
I am very keen to go ahead with the project because I feel that it will secure the medium-term future of our division.
I will be tied up all day tomorrow, so again I will not be able to see you. Could you please make a few notes for me which I can read on the way on Friday morning? I want to know how the Capital Asset Pricing Model is supposed to work, plus any other things which you feel I ought to know for the meeting. I do not want to look like a fool or lose the project because they blind me with science.
As you have probably discovered, I do not know much about finance, so please do not use any technical jargon or complicated maths.”

Required:
Prepare notes for the divisional manager which provide helpful background for the meeting.

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  • 20 Marks

FM – Nov 2023 – L3 – SB – Q3 – Investment Appraisal Techniques

Calculate and compare NPV for two proposals involving equipment purchase vs. existing machinery for contract fulfillment.

Niko Plc, a large equity-financed company, has a year-end of December 31. It must fulfill a contract in Abuja and has two proposals to choose from: Proposal A (purchasing new machinery) and Proposal B (using existing machinery).

Proposal A:

  • Outlay of N312,500,000 on December 31, 2023, for new plant and machinery.
  • Projected net cash inflows (before tax, in nominal terms):
    • 2024: N200,000,000
    • 2025: N275,000,000
    • 2026: N350,000,000
  • Scrap value: N25,000,000 at end of 2026.

Proposal B:

  • Uses a machine with a net realizable value of N250 million, with an alternative sale value of N300 million on January 1, 2025, if unused.
  • Cash inflows (in nominal terms):
    • 2024: N350,000,000
    • 2025: N350,000,000
  • Labour costs:
    • 2024: N100 million (replacement staff cost of N110 million)
    • 2025: N108 million (replacement staff cost of N118.8 million)
  • Machine residual value: N0 at project end in 2025.

Additional Details:

  • Working capital: 10% of year-end cash inflows, released upon project completion.
  • Expected annual inflation rates: 2024 – 10%, 2025 – 8%, 2026 – 6%, 2027 – 5%.
  • Real cost of capital: 10%.
  • Income tax: 40%, payable one year after the accounting period.
  • Capital allowances: 20% reducing balance for Proposal A’s plant and machinery.

Required:

  • a. Calculate the NPV at December 31, 2023, for each proposal. (17 Marks)
  • b. State any reservations about making an investment decision based on these NPV figures. (3 Marks)

Answer:

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  • 15 Marks

PSAF – Nov 2014 – L2 – Q7 – Public Sector Reforms

Advising on investment projects based on expected returns and understanding cost-benefit analysis features in public project appraisal.

a. Mr. Make-No-Mistake has N200,000 which he decides to invest if he can secure an assurance that the investment will earn at least 10% p.a. He is considering three projects:

  • Project A: Will earn N218,000 at the end of the 1st year.
  • Project B: Will earn N250,000 at the end of the 2nd year.
  • Project C: Will earn N140,000 at the end of 1st year and another N100,000 at the end of 2nd year.

If none of the projects is undertaken, Mr. Make-No-Mistake will invest his N200,000 in something else that will earn him 10% p.a.

You are required to assess and advise Mr. Make-No-Mistake on which of the projects he should undertake. (12 Marks)

b. Identify THREE main features of Cost-Benefit Analysis in public project appraisal. (3 Marks)

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  • 15 Marks

PSAF – May 2022 – L2 – SA – Q7 – Public Sector Reforms,

Discuss reasons for divergence between private and public appraisal of projects and explain key differences in cost-benefit and cost-effectiveness analysis.

Investment appraisal is a process of finding out the least possible costs of an investment and the maximum economic benefits, which may accrue from the commitment of resources.

Required:
a. Highlight FOUR reasons for divergence between private and public appraisal of a project. (4 Marks)
b. How does cost-benefit analysis (CBA) differ from cost-effectiveness analysis (CEA)? (5 Marks)
c. Identify THREE procedures and THREE limitations of cost-effectiveness analysis. (6 Marks)

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  • 15 Marks

PSAF – Nov 2021 – L2 – Q7 – Government Accounting Concepts and Principles

Calculate NPV for projects, profitability index, and discuss ranking differences.

Otunba Local Government wishes to boost its revenue generation and six possible capital investments have been identified. However, the Local Government only has access to a total of N6,200,000. The projects may not be postponed until a future period, and it is unlikely that similar investment opportunities will occur.

Expected net cash flows are:

Projects A and E are mutually exclusive while all the projects are believed to be of similar risk to the Local Government’s existing capital investments. Any surplus funds may be invested in the money market to earn a return of 9% per year. The money market may be assumed to be an efficient market. The Local Government’s cost of capital is 12% per year.

Required:

(a) Calculate the expected net present value for each project, and rank the projects. (8 Marks)
(b) Assuming the projects are divisible, calculate the Profitability Index for each project and rank the projects to determine how the money would be best invested. (6 Marks)
(c) State why the rankings in (b) differ from that in (a) above. (1 Mark)

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  • 15 Marks

MA – Dec 2023 – L2 – Q4a – Discounted Cash Flow

This question involves calculating the NPV for three projects being considered by Kanfa Ltd and recommending the best project based on financial grounds.

Kanfa Ltd received GH¢50 million as compensation from Ghana Highways Authority (GHA) when one of its properties was destroyed to pave way for the Accra–Kumasi highway construction. Management of Kanfa Ltd has decided to invest the amount received in one of three capital investment opportunities identified.

Project A:

This is a long-term project, which would run for 20 years and will require an immediate outlay of GH¢50 million and net annual cash profits as follows:

  • 1st to 5th years: GH¢2 million
  • 6th to 10th years: GH¢8 million
  • 11th to 15th years: GH¢15 million
  • 16th to 20th years: GH¢5 million

At the end of the 20th year, the project would be decommissioned at a cost of GH¢2 million.

Project B:

Kanfa Ltd is considering opening a Tourist Attraction Centre in Cape Coast, with an initial capital investment of GH¢50 million. It will operate for five years and be sold at an estimated price of GH¢5 million. The market research survey estimates the following visitor numbers and probabilities:

  • 800,000 visitors (30%)
  • 600,000 visitors (50%)
  • 400,000 visitors (20%)

Entrance fee: GH¢40 per visitor, and each visitor is expected to spend GH¢15 on souvenirs and GH¢5 on refreshments. Variable costs per visitor: GH¢25 (including souvenirs and refreshments). Maintenance costs: GH¢2 million per annum.

Project C:

This project involves a current outlay of GH¢50 million on equipment and GH¢15 million on working capital immediately. The working capital will increase to GH¢21 million in year one. Net annual cash profits: GH¢18 million for six years. The capital equipment can be sold for GH¢5 million at the end of the project.

Other information:

  • The company’s cost of capital is 12% for the three projects.
  • Ignore taxation and inflation.

Required:
Calculate the Net Present Value (NPV) of each project and recommend which project the company should undertake on financial grounds.

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  • 12 Marks

MA – Nov 2021 – L2 – Q4a – Discounted Cash Flow

Calculate and evaluate the payback period for the Ohenewa project based on provided cash flows.

a) Bee Ltd manufactures high-quality mobile phones for its local market. Due to less competition, Bee Ltd sales have grown significantly over the past few years and are expected to grow. Bee Ltd is planning to launch a new model, ‘Ohenewa’.

The company has already spent GH¢1 million on Research and Development and will require a further investment of GH¢5.5 million in production equipment. This cost excludes the GH¢1.1 million installation fee. The project has a life span of five years. In the end, the equipment will have a residual value of GH¢0.6 million. Sales and production of Ohenewa over its lifecycle are expected to be:

Year Units
1 6,500
2 7,500
3 8,000
4 7,800
5 7,000

The selling price in Year 1 and Year 2 will be GH¢750 per unit. However, the selling price will be reduced to GH¢600 per unit in Year 3 and will remain at this level for the remainder of the project. The variable cost as a percentage of sales is 55% over the entire product lifecycle. The fixed overhead, including depreciation cost expected to be incurred directly due to increasing the production capacity, is GH¢2 million per annum.

Other information:

  • A cost of capital of 12% per annum is used to evaluate projects of this type.
  • Bee Ltd has a history of accepting similar projects which pay back within three years.
  • Ignore inflation and taxation.

Required:
i) Calculate the Payback Period for the Ohenewa project. (10 marks)
ii) Evaluate the acceptability of the project based on the calculation in i) above. (2 marks)

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  • 15 Marks

MA – April 2022 – L2 – Q4a – Discounted cash flow

Evaluate the acceptability of a project using the Net Present Value (NPV) method considering cash flows and cost of capital.

Phil Company is considering replacing its existing machine on the introduction of a new product. The existing machine would be sold for GH¢2 million and replaced with a new machine at the beginning of the year at the cost of GH¢16 million. This new machine would be sold at the end of year 4 for GH¢1 million.

A market research recently carried out at a cost of GH¢1.5 million indicates a unit selling price of GH¢300 in year 1, rising by 10% per annum. Sales volume for the four-year life of the project has been estimated as follows:

Year Units
1 60,000
2 85,000
3 85,000
4 80,000

Possible unit variable costs are as follows:

Probability GH¢
0.4 240
0.6 260

Incremental fixed cost as a result of the project is GH¢15 per unit plus GH¢1,000,000 per annum staff cost.

The introduction of the new product is expected to reduce the market demand for an existing product by 5,000 units per annum. The existing product has a unit contribution of GH¢75.

Other annual fixed costs associated with the new product include the following:

  • Amortization of goodwill: GH¢50,000
  • Depreciation: GH¢250,000

Phil Company’s cost of capital is 12%.

Required:

Evaluate the acceptability of the project.

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  • 12 Marks

MA – Nov 2016 – L2 – Q5a – Discounted cash flow

Calculate the NPV break-even point under different cost of capital scenarios and determine the project's duration based on given cash inflows.

DDB Limited has decided to set up a factory to process groundnuts into oil. The feasibility studies cost them GH¢35,000. The consultants have advised that the initial outlay will be GH¢250,000; however, they were unable to estimate the cash inflow due to the uncertain economic environment.

Required:
Using NPV as an appraisal technique, you are required to calculate:

i) The constant cash inflow needed to break even if the cost of capital is 15% and the project is to last for 10 years.

(4 marks)

ii) By how much should the cash inflow increase to break even if the cost of capital is increased to 20%. (4 marks)

iii) If the cash inflow is GH¢45,000, for how long should the project run to break even if the cost of capital is 15%.

(4 marks)

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  • 10 Marks

FM – April 2022 – L2 – Q4b – Introduction to Investment Appraisal

Calculate the Accounting Rate of Return (ARR) for three projects and provide advice on which projects should be undertaken based on a target ARR.

SAKAMA Ghana Ltd uses the Accounting Rate of Return (ARR) as the basis of evaluating projects for investment of its scarce financial resources. It uses its predetermined expected return on capital as the basis for the choice of investment projects. The company’s Finance team has provided the information below regarding various projects and their initial investments and net cash flows. The hurdle rate or target Accounting Rate of Return for SAKAMA Ghana Ltd is 25%.

Required:
i) Calculate the Accounting Rate of Return for each project (Average Investment basis). (7 marks)
ii) Using the target return of 25%, advise SAKAMA Ghana Ltd which projects should be undertaken. (3 marks)

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