investment appraisal – Page 2

FM – L2 – Q84 – Discounted cash flow

Calculate NPV and estimate IRR for a project with given cash flows and discount rates.

Question

A company is considering whether to invest in a new item of equipment costing GH₵45,000 to make a new product. The product would have a four-year life, and the estimated cash profits over the four-year period are as follows.

Year	GH₵
1	17,000
2	25,000
3	16,000
4	4,000

The project would also need an investment in working capital of GH₵8,000, from the beginning of Year 1.
The company uses a discount rate of 11% to evaluate its investments.
Required
Calculate the NPV of the project at the discount rate of 11%.
Using the NPV you have calculated at 11%, and the NPV at a discount rate of 15%, estimate the internal rate of return (IRR) of the project.

Answer

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Tags: Capital Budgeting, Discounted cash flow, investment appraisal, IRR, NPV
Level: Level 2

Topic: Discounted cash flow

FM – L2 – Q82 – Discounted Cash Flow

Calculate NPV of a project with given cash flows and 10% cost of capital, and state if it should be undertaken.

Question

A company has a cost of capital of 10%. Calculate the NPV of an investment project with the following estimated cash flows:

Years	Cash flow each year
	GH₵
0	(70,000)
1	15,000
2–4	12,000
5–10	8,000

State whether the project should be undertaken.

Answer

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Tags: Cash Flows, Cost of Capital, Discounted cash flow, investment appraisal, NPV
Level: Level 2

Topic: Discounted cash flow

FM – L2 – Q79 – Discounted Cash Flow

Calculate NPV for three investment projects with varying cash flows and discount rates for Zenith Solutions Ltd.

Question

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

Investment A
This investment is similar to its current investments and requires an investment of GH₵60,000 now, GH₵40,000 for new capital equipment and GH₵20,000 for increases in working capital. This will be financed from Shareholders Funds. Sales next year would be 10,000 units, variable costs would be GH₵6 and the product would be sold for GH₵10. But due to entry of new competitors and technological improvements, the sales price would decline by 20% per annum thereafter, sales volume would fall by 10% and variable costs would fall by 20% per annum. Overheads attributed to the project would be GH₵15,000 per annum.
In year three the project would be wound up, working capital investment would be recovered and capital equipment sold off for 25% of its purchase costs the following year. Fixed costs include an annual charge of GH₵4,000 for depreciation.

Investment B
This is a long-term project in a totally new area, involving an immediate outlay of GH₵90,000, which they intend to borrow from their lenders at 6%. They expect net profits of GH₵12,000 next year, rising thereafter by 3% per annum in perpetuity.

Investment C
This is another long-term investment in a totally new area, involving an immediate outlay of GH₵25,000 which they intend financing by retained earnings. Expected annual net cash profits are as follows:
Years 1 to 4: GH₵3,000
Years 5 to 7: GH₵5,000
Year 8 onwards forever: GH₵7,000
The company discounts all projects lasting ten years duration or less at a cost of capital of 10% and all other projects at a cost of 13%. You may ignore taxation.

Required:
(a) Calculate the NPV of each project.

(b) Calculate the IRR of investments A and B (you may use 25% as the upper limit if you wish) and comment accordingly.

Answer

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Tags: Capital Budgeting, Discounted cash flow, investment appraisal, IRR, Perpetuity
Level: Level 2

Topic: Discounted cash flow

FM – L2 – Q71 – Discounted Cash Flow

Calculate NPV for a project with GH₵3M equipment cost, 5-year cash flows, and 8% cost of capital, ignoring inflation and taxation.

Question

A company, Zenith Innovations Ltd, is considering an investment in a new project to manufacture and sell a new product with a five-year lifespan. The project requires an investment of GH₵3 million in equipment. The residual value of this equipment after five years will be 30% of its original cost.

The estimates of net cash flows from operations in each year of the project are as follows:

Year	Net Cash Flow (GH₵)
1	400,000
2	800,000
3	800,000
4	700,000
5	400,000

These cash flows are based on estimates that the annual increase in cash spending on fixed costs will be GH₵200,000, and the contribution/sales ratio from transactions will be 40%. The company’s cost of capital is 8%.

The management of Zenith Innovations Ltd is aware that actual cash flows could be higher or lower than expected, and sensitivity analysis should be carried out to establish the extent to which costs or revenues could differ from the estimate before the project ceases to have a positive NPV.

The investment in working capital will be minimal. Inflation and taxation should be ignored.

Required
(a) Calculate the net present value of the project.

(b) Carry out sensitivity analysis on the following items:

(i) The cost of the equipment, assuming that the residual value will be 30% of cost.

(ii) The residual value of the equipment.

(iii) Sales revenue.

(iv) Variable costs.

(v) Annual fixed costs.

Answer

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Tags: investment appraisal, NPV, Project Risk, Risk Assessment, Sensitivity Analysis
Level: Level 2

Topic: DCF: Risk and uncertainty

FM – L2 – Q70 – DCF: Risk and uncertainty

Calculate the expected NPV of a project with uncertain cash inflows affected by multiple probabilistic factors, using a 10% cost of capital.

Question

A company is considering whether or not to invest in a project where the investment would be GH¢5,250,000. The project would have a five-year life, and estimated annual cash flows are as follows:

Year	Cash inflows	Cash outflows
	GH¢	GH¢
1	3,000,000	1,500,000
2	4,000,000	1,800,000
3	5,000,000	2,400,000
4	4,000,000	1,700,000
5	3,000,000	1,000,000

The cost of capital is 10%.
The estimates of cash outflows are considered fairly reliable. However, the estimates of cash inflows are much more uncertain. Several factors could make the annual cash flows higher or lower than expected.
Factor 1: There is a 20% probability that government measures to control the industry will reduce annual cash inflows by 20%.
Factor 2: There is a 30% probability that another competitor will also enter the market: this would reduce the estimated cash inflows by 10%.
Factor 3: There is a 40% probability that demand will be stronger than expected. The company would not be able to supply more products to the market, but it would be able to sell at higher prices and cash inflows would be 5% higher than estimated.
Required
Calculate the expected net present value of the project.

Answer

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Tags: Cash Flows, Discounted cash flow, Expected value, investment appraisal, Net Present Value, Probability Analysis, Risk Assessment
Level: Level 2

Topic: DCF: Risk and uncertainty

FM – L2 – Q68 – Discounted Cash Flow

Calculate the expected NPV of a new product launch for Accra Nova Cosmetics Limited with given cash flows and a 12% cost of capital.

Question

Accra Nova Cosmetics Limited has designed a new product that it would like to introduce to the market. It has spent GH¢250,000 on the design work so far. A market research report has indicated that the product will have a life of four years, and at a selling price of GH¢35 per unit, annual sales would be as follows:

Year	Sales (units)
1	40,000
2	60,000
3	60,000
4	20,000

It has been estimated that to produce the new product, annual fixed production costs (all cash flows) will increase by GH¢200,000, and the variable cost per unit will be GH¢10.
Other cash flows for the project will be:

Capital expenditure of GH¢1,400,000 at the beginning of the project. There will be a residual value of GH¢600,000 from this investment at the end of Year 4.
An investment of GH¢400,000 will be required in working capital. This will be recovered at the end of Year 4.
Expenditure on advertising will be required, as follows:

Year	Advertising costs
0	800,000
1	600,000
2	400,000
3	200,000

Required
(a) Calculate the expected NPV of the project to launch the new product, if the company’s cost of capital is 12%.

(b) Calculate the target cost for the product that is needed to achieve a return of 12% on investment and calculate the size of the current cost gap.

Answer

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Tags: Cost Gap, investment appraisal, NPV, Target Cost, variable costs
Level: Level 2

Topic: Discounted cash flow

FM – L2 – Q67 – Capital rationing

Determine optimal investment for Yebson Plc with GH₵800,000, assuming divisible/indivisible projects, and calculate NPV

Question

Yebson Plc is reviewing investment proposals that have been submitted by divisional managers. The investment funds of the company are limited to GH₵800,000 in the current year. Details of three possible investments, none of which can be delayed, are given below.

Project 1
An investment of GH₵300,000 in work station assessments. Each assessment would be on an individual employee basis and would lead to savings in labour costs from increased efficiency and from reduced absenteeism due to work-related illness. Savings in labour costs from these assessments in money terms are expected to be as follows:

Year	1	2	3	4	5
Cash flows (GH₵000)	85	90	95	100	95

Project 2
An investment of GH₵450,000 in individual workstations for staff that is expected to reduce administration costs by GH₵140,800 per annum in money terms for the next five years.

Project 3
An investment of GH₵400,000 in new ticket machines. Net cash savings of GH₵120,000 per annum are expected in current price terms and these are expected to increase by 3.6% per annum due to inflation during the five-year life of the machines.

Yebson Plc has a money cost of capital of 12% and taxation should be ignored.

Required:
(a) Determine the best way for Yebson Plc to invest the available funds and calculate the resultant NPV:
(i) on the assumption that each of the three projects is divisible
(ii) on the assumption that none of the projects are divisible.

(b) Explain how the NPV investment appraisal method is applied in situations where capital is rationed.

Answer

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Tags: Capital rationing, Financial constraints, Financial management, investment appraisal, Project Selection
Level: Level 2

Topic: Capital rationing

FM – L2 – Q66 – Capital rationing

Recommend investments to maximize NPV assuming divisible projects with a GH¢150,000 capital limit.

Question

A company, Kumasi Ventures Ltd, has identified five investment projects that it would like to undertake. None of the investments can be delayed. If they are not undertaken now, the opportunity to invest will be lost. Details of the five investments are as follows:

Investment	Capital investment required in Year 0	NPV of the investment
	GH¢	GH¢
A	60,000	12,000
B	80,000	21,600
C	50,000	8,500
D	45,000	10,800
E	55,000	9,900

Capital is in short supply, and only GH¢150,000 is available for investment. The company cannot therefore undertake all five investments.
Required:
In order to maximise the total NPV of its investments, recommend which investments to undertake:
(a) assuming that all five investment projects are divisible.

(b) assuming that none of the five investments is divisible, and the choice is either 0% or 100% of each investment.

Answer

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Tags: Capital rationing, Financial decision-making, Indivisible projects, investment appraisal, NPV
Level: Level 2

Topic: Capital rationing

FM – L2 – Q65 – DCF: Specific applications

Calculate the equivalent annual cost for replacing a machine every 1, 2, 3, and 4 years and recommend the optimal replacement policy.

Question

A business entity, Volta Ventures, is considering its policy for the replacement of machines. One type of machine in regular use is Machine Y. This machine has a maximum useful life of four years, but maintenance costs and other running costs rise with use. An estimate of costs and disposal values is as follows:

Machine Y: Purchase cost GH₵40,000

Year	Maintenance costs and other running costs in the year	Disposal value at the end of the year
	GH₵	GH₵
1	8,000	25,000
2	12,000	20,000
3	20,000	10,000
4	25,000	0

The cost of capital is 10%.

Required
Calculate the equivalent annual cost of a replacement policy for the machine of replacement:
(a) every one year
(b) every two years
(c) every three years
(d) every four years.
Recommend a replacement policy for the machine.

Answer

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Tags: Asset Replacement, Cash Flows, Cost of Capital, Depreciation, Discounted cash flow, Equivalent Annual Cost, Financial decision-making, investment appraisal, Machine Replacement, Net Present Value
Level: Level 2

Topic: DCF: Specific Applications

FM – L2 – Q64 – DCF: Specific applications

Evaluate whether to acquire a machine and recommend purchase or lease, considering NPV with tax and capital allowances.

Question

NexGen Enterprises is considering whether to acquire a new machine. The machine has a purchase cost of GH₵30,000, an expected useful life of five years, and a disposal value of GH₵6,000 at the end of year 5. The machine would generate additional cash flows of GH₵10,000 in each of its five years.
Two methods of financing are under consideration:
(i) To buy the machine with money obtained from a bank loan, at an interest rate of 8% after tax.
(ii) To lease the machine. The lease payments to the lessor would be GH₵7,000 at the end of each of the next five years.
The company’s cost of capital is 10% after tax.
Corporation tax is 30%. If the machine is purchased, the company will be able to claim capital allowances (tax depreciation allowances) of 25% each year on a reducing balance basis. Tax is payable at the end of the year following the year against profits earned during Year 1.

Required:
(a) Recommend whether the machine should be acquired.
(b) If your recommendation is to acquire the machine, recommend whether it should be purchased or leased.

Answer

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Tags: capital allowances, Cost of Capital, Discounted cash flow, Financing Decisions, investment appraisal, Lease vs Buy, Net Present Value, Taxation
Level: Level 2

Topic: DCF: Specific Applications

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FM – L2 – Q84 – Discounted cash flow

Calculate NPV and estimate IRR for a project with given cash flows and discount rates.

FM – L2 – Q82 – Discounted Cash Flow

Calculate NPV of a project with given cash flows and 10% cost of capital, and state if it should be undertaken.

FM – L2 – Q79 – Discounted Cash Flow

Calculate NPV for three investment projects with varying cash flows and discount rates for Zenith Solutions Ltd.

FM – L2 – Q71 – Discounted Cash Flow

Calculate NPV for a project with GH₵3M equipment cost, 5-year cash flows, and 8% cost of capital, ignoring inflation and taxation.

FM – L2 – Q70 – DCF: Risk and uncertainty

Calculate the expected NPV of a project with uncertain cash inflows affected by multiple probabilistic factors, using a 10% cost of capital.

FM – L2 – Q68 – Discounted Cash Flow

Calculate the expected NPV of a new product launch for Accra Nova Cosmetics Limited with given cash flows and a 12% cost of capital.

FM – L2 – Q67 – Capital rationing

Determine optimal investment for Yebson Plc with GH₵800,000, assuming divisible/indivisible projects, and calculate NPV

FM – L2 – Q66 – Capital rationing

Recommend investments to maximize NPV assuming divisible projects with a GH¢150,000 capital limit.

FM – L2 – Q65 – DCF: Specific applications

Calculate the equivalent annual cost for replacing a machine every 1, 2, 3, and 4 years and recommend the optimal replacement policy.

FM – L2 – Q64 – DCF: Specific applications

Evaluate whether to acquire a machine and recommend purchase or lease, considering NPV with tax and capital allowances.

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FM – L2 – Q84 – Discounted cash flow

Calculate NPV and estimate IRR for a project with given cash flows and discount rates.

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FM – L2 – Q82 – Discounted Cash Flow

Calculate NPV of a project with given cash flows and 10% cost of capital, and state if it should be undertaken.

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FM – L2 – Q79 – Discounted Cash Flow

Calculate NPV for three investment projects with varying cash flows and discount rates for Zenith Solutions Ltd.

You're reporting an error for "FM – L2 – Q79 – Discounted Cash Flow"

FM – L2 – Q71 – Discounted Cash Flow

Calculate NPV for a project with GH₵3M equipment cost, 5-year cash flows, and 8% cost of capital, ignoring inflation and taxation.

You're reporting an error for "FM – L2 – Q71 – Discounted Cash Flow"

FM – L2 – Q70 – DCF: Risk and uncertainty

Calculate the expected NPV of a project with uncertain cash inflows affected by multiple probabilistic factors, using a 10% cost of capital.

You're reporting an error for "FM – L2 – Q70 – DCF: Risk and uncertainty"

FM – L2 – Q68 – Discounted Cash Flow

Calculate the expected NPV of a new product launch for Accra Nova Cosmetics Limited with given cash flows and a 12% cost of capital.

You're reporting an error for "FM – L2 – Q68 – Discounted Cash Flow"

FM – L2 – Q67 – Capital rationing

Determine optimal investment for Yebson Plc with GH₵800,000, assuming divisible/indivisible projects, and calculate NPV

You're reporting an error for "FM – L2 – Q67 – Capital rationing"

FM – L2 – Q66 – Capital rationing

Recommend investments to maximize NPV assuming divisible projects with a GH¢150,000 capital limit.

You're reporting an error for "FM – L2 – Q66 – Capital rationing"

FM – L2 – Q65 – DCF: Specific applications

Calculate the equivalent annual cost for replacing a machine every 1, 2, 3, and 4 years and recommend the optimal replacement policy.

You're reporting an error for "FM – L2 – Q65 – DCF: Specific applications"

FM – L2 – Q64 – DCF: Specific applications

Evaluate whether to acquire a machine and recommend purchase or lease, considering NPV with tax and capital allowances.

You're reporting an error for "FM – L2 – Q64 – DCF: Specific applications"

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