Question Tag: Sensitivity Analysis

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  • 20 Marks

FM – May 2023 – L3 – Q3 – Investment Appraisal Techniques

Evaluate Tinco Limited's expansion project using financial metrics, assess sensitivity to contribution and tax rate changes, and incorporate capital allowances.

Tinco Limited (TL) is considering an expansion project. The project will involve the acquisition of an automated production machine costing ₦11,000,000 and payable now. The machine is expected to have a disposal value at the end of 5 years, which is equal to 10% of the initial expenditure.

The following schedule reflects a recent market survey regarding the estimated annual sales revenue from the expansion project over the project’s five-year life:

Level of Demand ₦’000 Probability
High 16,000 0.25
Medium 12,000 0.50
Low 8,000 0.25

It is expected that the contribution to sales ratio will be 50%. Additional expenditure on fixed overheads is expected to be ₦1,800,000 per annum. TL incurs a 20% tax rate on corporate profits. Corporate tax is paid one year in arrears.

TL’s after-tax nominal (money) discount rate is 15.5% per annum. A uniform inflation rate of 5% per annum will apply to all costs and revenues during the life of the project. All of the values above have been expressed in terms of current prices.

You can assume that all cash flows occur at the end of each year and that the initial investment does not qualify for capital allowances.

Required:

a.
i. Evaluate the proposed expansion from a financial perspective. (10 Marks)
ii. Calculate and interpret the sensitivity of the project to changes in:

  • The expected annual contribution (3 Marks)
  • The tax rate (2 Marks)

b.
You have now been advised that the capital cost of the expansion will qualify for written down allowances at the rate of 25% per annum on a reducing balance basis. Also, at the end of the project’s life, a balancing charge or allowance will arise equal to the difference between the scrap proceeds and the tax written down value.

You are required to calculate the financial impact of these allowances. (5 Marks)

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  • 30 Marks

FM – May 2018 – L3 – SA – Q1 – Investment Appraisal Techniques

Evaluate the NPV of Plateau Plc.'s project, assess sensitivity, discuss political risk, and explore real options for the project.

Plateau Plc. (PT) is a Nigerian company that manufactures and sells innovative products. Following favourable market research that cost N4,000,000, PT has developed a new product. It plans to set up a production facility in Kano, although its board had contemplated setting up the facility in an overseas country. The project will have a life of four years.

The selling price of the new product will be N5,900 per unit, with sales in the first year to December 31, 2019, expected to be 120,000 units, increasing by 5% per annum thereafter. Relevant direct labour and material costs are expected to be N3,400 per unit, and incremental fixed production costs are expected to be N60 million per annum. The selling price and costs are stated in December 31, 2018 prices and are expected to increase at a rate of 3% per annum. Research and development costs to December 31 will amount to N25 million.

Investment in working capital will be N30 million on December 31, 2018, and this will increase in line with sales volumes and inflation. Working capital will be fully recoverable on December 31, 2022.

The company will need to rent a factory during the life of the project. Annual rent of N20 million will be payable in advance on December 31 each year and will not increase over the life of the project.

Plant and machinery will cost N1 billion on December 31, 2018. The plant and machinery are expected to have a resale value of N300 million (at December 31, 2022, prices) at the end of the project. The plant and machinery will attract 20% (reducing balance) capital allowances in the year of expenditure and in every subsequent year of ownership by the company, except in the final year when there will be a balancing allowance or charge.

Assume a corporate tax rate of 20% per annum in the foreseeable future and that tax flows arise in the same year as the cash flows which gave rise to them.

The directors are concerned by rumours in the industry of research by a rival company into a much cheaper alternative product. However, the rumours suggest that this research will take another year to complete, and if successful, it will take a further year before the alternative product comes on the market.

An appropriate weighted average cost of capital for the project is 10% per annum.

Required:

a. Calculate, using money cash flows, the NPV of the project on December 31, 2018, and advise the company whether to proceed with the project or not.
(15 Marks)

b. Calculate and interpret the sensitivity of the project to a change in:

  • (i) The annual rent of the factory (2 Marks)
  • (ii) The weighted average cost of capital (4 Marks)

c. If the board of PT decided to set up the manufacturing facility overseas, advise the board on how political risk could change the value of the project and how it might limit its effects. (4 Marks)

d. Discuss briefly FOUR real options available to PT in relation to the new project. (5 Marks)

(Total 30 Marks)

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  • 15 Marks

PM – May 2023 – L2 – SA – Q6 – Cost Management Strategies

Evaluate the financial impact of hiring equipment and assess sensitivity to changing demand.

TK is a theme park. The following information is available for the forthcoming month:

Forecast daily ticket sales and prices:

Ticket Price per ticket Forecast Sales
Pre-booked discounted ticket N580 1,500
Standard ticket N780 8,000
Premium family ticket (admits 4) N3,700 675

The theme park will be open for 30 days in the month.

Costs:

  • Variable costs per person per day are forecast to be N2050.
  • Fixed costs for the month are forecast to be N130,000,000.

Pricing Information:

  • The sales of pre-booked discounted tickets and standard tickets will be restricted to 1,500 and 8,000 per day respectively for the forthcoming month. It is forecast that all of these tickets will be sold.
  • A premium family ticket admits four people to the theme park and allows them to go to the front of the queues in the theme park. The price of a premium family ticket has been set at N3,700 to maximize profit.

Market information shows that for every N100 increase in the selling price of a premium family ticket, the demand would reduce by 25 tickets. For every N100 decrease in the selling price, the demand would increase by 25 tickets.

The theme park has adequate capacity to accommodate any level of demand for premium family tickets. It is assumed that four people would always be admitted on every premium family ticket sold. Sales of the different ticket types are independent of each other.

Equipment Hire:

TK is considering hiring some automated ticket reading equipment for the forthcoming month. The hire of this equipment would increase fixed costs by N5,000,000 for the month. However, variable costs per person would be reduced by 8% during the period of the hire.

Required:

a) Calculate the financial benefit of hiring the equipment for the forthcoming month given its impact on variable cost and the price charged for premium family tickets. (11 Marks)

b) It has now been realized that a competing theme park is planning to offer discounted ticket prices during the forthcoming months. It is thought that this will reduce the demand for TK’s standard tickets. TK will not be able to reduce the price of the standard tickets for the forthcoming month.

Discuss the sensitivity of the decision to hire the equipment to a change in the number of standard tickets sold per day. (Note: Your answer should include the calculation of the sensitivity.) (4 Marks)

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  • 15 Marks

MA – Nov 2017 – L2 – Q4 – Cost-volume-profit (CVP) analysis

Analyze the profit statement for two complementary products and evaluate the impact of various proposals on profit optimization.

Zumah Ltd manufactures and sells two complementary products: Hyline and Glycerin in the ratio 3:2. The result for the just ended period showed the following:

Product Hyline Glycerin
Selling price (GH¢) 20 15
Contribution/sales ratio 60% 40%
Profit/ (loss) (GH¢) 97,200 (3,600)

Joint fixed costs of GH¢180,000 are apportioned in proportion to the number of units of each product sold.

The company is in the process of preparing the budget for the coming year and is desirous of improving the performance of Glycerin. Therefore, the following proposals are being considered for implementation:

  1. Increase the price of Glycerin by 25% in expectation that the quantity demanded will reduce by 10%; or
  2. Retool the production process, which will result in a reduction of joint fixed costs by 15% and an increase in variable costs of each product by 10%; or
  3. Introduce proposals 1 and 2.

Required:

a) Determine the units of each product sold, and hence, prepare the profit statement for the just ended period.
b) Advise the management of Zumah Ltd as to which proposal to implement with a view to optimizing profits.

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  • 15 Marks

FM – May 2021 – L2 – Q4a – Introduction to investment appraisal

Evaluate the financial viability of an investment using NPV, IRR, and explain the concept of sensitivity analysis.

CVD Ghana Ltd, which is into the production and sale of COVID-19 vaccine in Ghana and abroad, plans to buy a new machine to expand the scope of its operations due to increased demand in both the local and the international markets.

The cost of the machine is GH¢24,000,000 and has a useful life of five years. The machine will require additional investment in working capital of GH¢2,700,000 at the beginning of the first year of operations. At the end of year five, the machine will be sold for scrap, with the scrap value expected to be 5% of the machine’s initial purchase cost. The company has no intention to replace the machine. Production and sales from the new machine are expected to be 1,000,000 packs per year.

The selling price per pack and variable cost per pack are as follows:

Year Selling Price per Pack (GH¢) Variable Cost per Pack (GH¢)
1 48 33
2 48 33
3 55 38
4 55 38
5 60 42

It is also estimated that incremental fixed costs arising from the machine’s operations will be GH¢4,800,000 per year. CVD Ghana Ltd has an after-tax cost of capital of 20%, which it uses as a discount rate in its investment appraisal. The company pays corporate tax at an annual rate of 25% per year. Capital allowance should be ignored.

Required:

i) Compute the Net Present Value of this project and advise CVD Ghana Ltd whether the investment is financially viable. (8 marks)

ii) Calculate the Internal Rate of Return of investing in the machine and advise whether it is financially viable. (5 marks)

iii) Explain the meaning of the term “sensitivity analysis” in the context of investment. (2 marks)

 

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  • 20 Marks

FM – Nov 2019 – L2 – Q4 – Capital rationing | Discounted cash flow

Compute NPV and IRR, assess sensitivity, and recommend a project portfolio under capital rationing.

The current financial year of General Kapito Ltd, a sports apparel company based in Ghana, will be ending in two months’ time. The directors of the company will be meeting next week to approve capital projects that will be implemented in the coming financial year. A major concern for the coming year is the availability of finance to meet investment requirements.

The cost of raising new capital in Ghana’s capital market has risen so high that it is not cost-effective to raise small blocks of capital. Consequently, the directors of the company have decided to finance new projects in the coming year with retained earnings and not raise new external capital from the capital market to bridge any financing gap. The maximum amount of retained earnings that will be available for financing new capital projects in the coming year is GH¢62 million.

There are six independent projects that will be presented before the board of directors for approval in their upcoming meeting. Five of the projects have been appraised already (see a summary of the projects in the table below).

Project Investment requirement Net present value (NPV) Internal rate of return (IRR)
PROJECT-01 25 50 36.2%
PROJECT-02 15 45 37.1%
PROJECT-03 9 35 39.5%
PROJECT-04 12 20 34.8%
PROJECT-05 34 To be computed To be computed
PROJECT-06 5 2 33.5%

Project-05 refers to a 5-year contract with a local football club for the manufacture and supply of a special football boot for playing under rainy conditions. It is estimated that this project will require an investment of GH¢34 million in plant and equipment at the start of the first year. The estimated cost of required plant and equipment might change as there are speculations about probable change in technology in the coming year. That notwithstanding, this project is expected to return an after-tax net operating cash flow of GH¢13.5 million every year over the coming five years. The estimated after-tax salvage value of the plant and equipment is GH¢10 million at the end of the fifth year.

The company’s required rate of return is 25%.

Required:

a) Compute the NPV and IRR of Project-05. (10 marks)

b) Assess the sensitivity of the outcome of Project-05 to variations in the cost of plant and equipment. Interpret your result. (5 marks)

c) Assuming the projects are divisible, recommend the portfolio of projects that should be funded in the coming year. (5 marks)

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  • 20 Marks

FM – May 2023 – L3 – Q3 – Investment Appraisal Techniques

Evaluate Tinco Limited's expansion project using financial metrics, assess sensitivity to contribution and tax rate changes, and incorporate capital allowances.

Tinco Limited (TL) is considering an expansion project. The project will involve the acquisition of an automated production machine costing ₦11,000,000 and payable now. The machine is expected to have a disposal value at the end of 5 years, which is equal to 10% of the initial expenditure.

The following schedule reflects a recent market survey regarding the estimated annual sales revenue from the expansion project over the project’s five-year life:

Level of Demand ₦’000 Probability
High 16,000 0.25
Medium 12,000 0.50
Low 8,000 0.25

It is expected that the contribution to sales ratio will be 50%. Additional expenditure on fixed overheads is expected to be ₦1,800,000 per annum. TL incurs a 20% tax rate on corporate profits. Corporate tax is paid one year in arrears.

TL’s after-tax nominal (money) discount rate is 15.5% per annum. A uniform inflation rate of 5% per annum will apply to all costs and revenues during the life of the project. All of the values above have been expressed in terms of current prices.

You can assume that all cash flows occur at the end of each year and that the initial investment does not qualify for capital allowances.

Required:

a.
i. Evaluate the proposed expansion from a financial perspective. (10 Marks)
ii. Calculate and interpret the sensitivity of the project to changes in:

  • The expected annual contribution (3 Marks)
  • The tax rate (2 Marks)

b.
You have now been advised that the capital cost of the expansion will qualify for written down allowances at the rate of 25% per annum on a reducing balance basis. Also, at the end of the project’s life, a balancing charge or allowance will arise equal to the difference between the scrap proceeds and the tax written down value.

You are required to calculate the financial impact of these allowances. (5 Marks)

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  • 30 Marks

FM – May 2018 – L3 – SA – Q1 – Investment Appraisal Techniques

Evaluate the NPV of Plateau Plc.'s project, assess sensitivity, discuss political risk, and explore real options for the project.

Plateau Plc. (PT) is a Nigerian company that manufactures and sells innovative products. Following favourable market research that cost N4,000,000, PT has developed a new product. It plans to set up a production facility in Kano, although its board had contemplated setting up the facility in an overseas country. The project will have a life of four years.

The selling price of the new product will be N5,900 per unit, with sales in the first year to December 31, 2019, expected to be 120,000 units, increasing by 5% per annum thereafter. Relevant direct labour and material costs are expected to be N3,400 per unit, and incremental fixed production costs are expected to be N60 million per annum. The selling price and costs are stated in December 31, 2018 prices and are expected to increase at a rate of 3% per annum. Research and development costs to December 31 will amount to N25 million.

Investment in working capital will be N30 million on December 31, 2018, and this will increase in line with sales volumes and inflation. Working capital will be fully recoverable on December 31, 2022.

The company will need to rent a factory during the life of the project. Annual rent of N20 million will be payable in advance on December 31 each year and will not increase over the life of the project.

Plant and machinery will cost N1 billion on December 31, 2018. The plant and machinery are expected to have a resale value of N300 million (at December 31, 2022, prices) at the end of the project. The plant and machinery will attract 20% (reducing balance) capital allowances in the year of expenditure and in every subsequent year of ownership by the company, except in the final year when there will be a balancing allowance or charge.

Assume a corporate tax rate of 20% per annum in the foreseeable future and that tax flows arise in the same year as the cash flows which gave rise to them.

The directors are concerned by rumours in the industry of research by a rival company into a much cheaper alternative product. However, the rumours suggest that this research will take another year to complete, and if successful, it will take a further year before the alternative product comes on the market.

An appropriate weighted average cost of capital for the project is 10% per annum.

Required:

a. Calculate, using money cash flows, the NPV of the project on December 31, 2018, and advise the company whether to proceed with the project or not.
(15 Marks)

b. Calculate and interpret the sensitivity of the project to a change in:

  • (i) The annual rent of the factory (2 Marks)
  • (ii) The weighted average cost of capital (4 Marks)

c. If the board of PT decided to set up the manufacturing facility overseas, advise the board on how political risk could change the value of the project and how it might limit its effects. (4 Marks)

d. Discuss briefly FOUR real options available to PT in relation to the new project. (5 Marks)

(Total 30 Marks)

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  • 15 Marks

PM – May 2023 – L2 – SA – Q6 – Cost Management Strategies

Evaluate the financial impact of hiring equipment and assess sensitivity to changing demand.

TK is a theme park. The following information is available for the forthcoming month:

Forecast daily ticket sales and prices:

Ticket Price per ticket Forecast Sales
Pre-booked discounted ticket N580 1,500
Standard ticket N780 8,000
Premium family ticket (admits 4) N3,700 675

The theme park will be open for 30 days in the month.

Costs:

  • Variable costs per person per day are forecast to be N2050.
  • Fixed costs for the month are forecast to be N130,000,000.

Pricing Information:

  • The sales of pre-booked discounted tickets and standard tickets will be restricted to 1,500 and 8,000 per day respectively for the forthcoming month. It is forecast that all of these tickets will be sold.
  • A premium family ticket admits four people to the theme park and allows them to go to the front of the queues in the theme park. The price of a premium family ticket has been set at N3,700 to maximize profit.

Market information shows that for every N100 increase in the selling price of a premium family ticket, the demand would reduce by 25 tickets. For every N100 decrease in the selling price, the demand would increase by 25 tickets.

The theme park has adequate capacity to accommodate any level of demand for premium family tickets. It is assumed that four people would always be admitted on every premium family ticket sold. Sales of the different ticket types are independent of each other.

Equipment Hire:

TK is considering hiring some automated ticket reading equipment for the forthcoming month. The hire of this equipment would increase fixed costs by N5,000,000 for the month. However, variable costs per person would be reduced by 8% during the period of the hire.

Required:

a) Calculate the financial benefit of hiring the equipment for the forthcoming month given its impact on variable cost and the price charged for premium family tickets. (11 Marks)

b) It has now been realized that a competing theme park is planning to offer discounted ticket prices during the forthcoming months. It is thought that this will reduce the demand for TK’s standard tickets. TK will not be able to reduce the price of the standard tickets for the forthcoming month.

Discuss the sensitivity of the decision to hire the equipment to a change in the number of standard tickets sold per day. (Note: Your answer should include the calculation of the sensitivity.) (4 Marks)

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  • 15 Marks

MA – Nov 2017 – L2 – Q4 – Cost-volume-profit (CVP) analysis

Analyze the profit statement for two complementary products and evaluate the impact of various proposals on profit optimization.

Zumah Ltd manufactures and sells two complementary products: Hyline and Glycerin in the ratio 3:2. The result for the just ended period showed the following:

Product Hyline Glycerin
Selling price (GH¢) 20 15
Contribution/sales ratio 60% 40%
Profit/ (loss) (GH¢) 97,200 (3,600)

Joint fixed costs of GH¢180,000 are apportioned in proportion to the number of units of each product sold.

The company is in the process of preparing the budget for the coming year and is desirous of improving the performance of Glycerin. Therefore, the following proposals are being considered for implementation:

  1. Increase the price of Glycerin by 25% in expectation that the quantity demanded will reduce by 10%; or
  2. Retool the production process, which will result in a reduction of joint fixed costs by 15% and an increase in variable costs of each product by 10%; or
  3. Introduce proposals 1 and 2.

Required:

a) Determine the units of each product sold, and hence, prepare the profit statement for the just ended period.
b) Advise the management of Zumah Ltd as to which proposal to implement with a view to optimizing profits.

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  • 15 Marks

FM – May 2021 – L2 – Q4a – Introduction to investment appraisal

Evaluate the financial viability of an investment using NPV, IRR, and explain the concept of sensitivity analysis.

CVD Ghana Ltd, which is into the production and sale of COVID-19 vaccine in Ghana and abroad, plans to buy a new machine to expand the scope of its operations due to increased demand in both the local and the international markets.

The cost of the machine is GH¢24,000,000 and has a useful life of five years. The machine will require additional investment in working capital of GH¢2,700,000 at the beginning of the first year of operations. At the end of year five, the machine will be sold for scrap, with the scrap value expected to be 5% of the machine’s initial purchase cost. The company has no intention to replace the machine. Production and sales from the new machine are expected to be 1,000,000 packs per year.

The selling price per pack and variable cost per pack are as follows:

Year Selling Price per Pack (GH¢) Variable Cost per Pack (GH¢)
1 48 33
2 48 33
3 55 38
4 55 38
5 60 42

It is also estimated that incremental fixed costs arising from the machine’s operations will be GH¢4,800,000 per year. CVD Ghana Ltd has an after-tax cost of capital of 20%, which it uses as a discount rate in its investment appraisal. The company pays corporate tax at an annual rate of 25% per year. Capital allowance should be ignored.

Required:

i) Compute the Net Present Value of this project and advise CVD Ghana Ltd whether the investment is financially viable. (8 marks)

ii) Calculate the Internal Rate of Return of investing in the machine and advise whether it is financially viable. (5 marks)

iii) Explain the meaning of the term “sensitivity analysis” in the context of investment. (2 marks)

 

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  • 20 Marks

FM – Nov 2019 – L2 – Q4 – Capital rationing | Discounted cash flow

Compute NPV and IRR, assess sensitivity, and recommend a project portfolio under capital rationing.

The current financial year of General Kapito Ltd, a sports apparel company based in Ghana, will be ending in two months’ time. The directors of the company will be meeting next week to approve capital projects that will be implemented in the coming financial year. A major concern for the coming year is the availability of finance to meet investment requirements.

The cost of raising new capital in Ghana’s capital market has risen so high that it is not cost-effective to raise small blocks of capital. Consequently, the directors of the company have decided to finance new projects in the coming year with retained earnings and not raise new external capital from the capital market to bridge any financing gap. The maximum amount of retained earnings that will be available for financing new capital projects in the coming year is GH¢62 million.

There are six independent projects that will be presented before the board of directors for approval in their upcoming meeting. Five of the projects have been appraised already (see a summary of the projects in the table below).

Project Investment requirement Net present value (NPV) Internal rate of return (IRR)
PROJECT-01 25 50 36.2%
PROJECT-02 15 45 37.1%
PROJECT-03 9 35 39.5%
PROJECT-04 12 20 34.8%
PROJECT-05 34 To be computed To be computed
PROJECT-06 5 2 33.5%

Project-05 refers to a 5-year contract with a local football club for the manufacture and supply of a special football boot for playing under rainy conditions. It is estimated that this project will require an investment of GH¢34 million in plant and equipment at the start of the first year. The estimated cost of required plant and equipment might change as there are speculations about probable change in technology in the coming year. That notwithstanding, this project is expected to return an after-tax net operating cash flow of GH¢13.5 million every year over the coming five years. The estimated after-tax salvage value of the plant and equipment is GH¢10 million at the end of the fifth year.

The company’s required rate of return is 25%.

Required:

a) Compute the NPV and IRR of Project-05. (10 marks)

b) Assess the sensitivity of the outcome of Project-05 to variations in the cost of plant and equipment. Interpret your result. (5 marks)

c) Assuming the projects are divisible, recommend the portfolio of projects that should be funded in the coming year. (5 marks)

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