Discounted cash flow

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 – Q78 – Discounted cash flow

Calculate NPV for Woodland Enterprises' new product investment with inflation and advise on project viability.

Question

Woodland Enterprises 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₵1.4m per annum will also be needed. Expenditure of GH₵1.3m per annum will be required to replace existing assets which will now be used on the project but are getting to the end of their useful lives. This expenditure will be incurred at the beginning of each year. Additional investment in working capital equivalent to 10% of contribution will need to be in place at the start of each year. Working capital will be released at the end of the project. The following forecasts are made of the rates of inflation each year for the next five years:

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

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

Required:
Calculate the net present value of the project and appraise whether it is a worthwhile project.

Answer

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Tags: Capital Investment, Contribution, Cost of Capital, Discounted cash flow, Inflation, NPV, Working Capital
Level: Level 2

Topic: Discounted cash flow

FM – L2 – Q75 – Discounted cash flow

Calculate NPV to decide between maintaining old equipment or buying new equipment for Wisdom Ltd, using a 20% cost of capital.

Question

The maintenance manager of Wisdom Ltd insists that management should maintain an old piece of equipment that had been used for 5 years and is fully depreciated rather than buy a new one. The old equipment has a current operating cost of GH₵53,000.00 per annum. The operating cost of the equipment is expected to increase at 5% every year over the next four years, with a sale value of GH₵6,500.00 in the fifth year.

The maintenance manager has proposed that a new system with enhanced technology to reduce operating cost to GH₵32,000.00 for the next three years and GH₵33,600.00 for the fourth and fifth years be introduced. The new equipment will cost GH₵60,000.00 and when introduced, a redundancy cost of GH₵25,000.00 will be paid, with the old equipment sold for GH₵12,000.00. The sale value of the new equipment will be GH₵10,200.00 after its five years’ useful life.

Required:

Using net present value (NPV) method of capital appraisal with 20% cost of capital, advise management on which option Wisdom Ltd should go for.

Answer

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Tags: Cost of Capital, Discounted cash flow, Equipment replacement, NPV, operating costs
Level: Level 2

Topic: Discounted cash flow

FM – L2 – Q74 – Discounted Cash Flow

Calculate NPV for TechNova Ltd's new game Zestora, considering sales, costs, and tax over four years.

Question

TechNova Ltd

(a) TechNova Ltd, a software company, has developed a new game “Zestora” which it plans to launch in the near future. Sales volumes, production volumes, and selling prices for “Zestora” over its four-year life are expected to be as follows:

Year	Sales and production (units)	Selling price (GH₵ per game)
1	15,000	45
2	25,000	40
3	20,000	38
4	10,000	35

Financial information relating to the production of Zestora:

Item	GH₵ per game
Direct materials	6
Direct labour	8
Variable production overheads	4

Additional information:

Annual fixed production overheads will be GH₵150,000.
Initial investment in equipment will be GH₵800,000.
Additional working capital of GH₵50,000 will be needed at the beginning of the project and will be released at the end of year four.
Tax at the rate of 25% is payable on profits one year in arrears.
Capital allowance is available at 25% per year on a reducing balance basis.
TechNova Ltd’s cost of capital is 10%.
The equipment will have no residual value at the end of year four.

Required: Calculate the net present value of the proposed investment and comment on your findings.

Answer

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Tags: Capital Investment, Cost Estimation, Discounted cash flow, Financial analysis, Inflation, NPV, Project Appraisal, Sales Forecast, Software Industry, Taxation
Level: Level 2

Topic: Taxation and Inflation

FM – L2 – Q73 – Discounted Cash Flow

Calculate the breakeven rate of return for Kofi's taxi service project using NPV criteria with given cash flows and costs.

Question

Kofi, after his National Service and with no hope of securing a job in the formal sector, has decided to run a taxi service. The following have been made for the operation of a service between Asikrom and Sunyasi:
(i) Revenue totalling GH¢300 a week for 52 weeks in a year. This is net of fuel and other variable costs.
(ii) Tyres; four pieces for a year at GH¢120 per unit.
(iii) Maintenance and servicing; GH¢120 per month.
(iv) Salaries GH¢3,000 per year.
(v) Insurance GH¢350 per year.
The net cash flow will increase at 5% per annum for the next five years due to inflation. The cost of the vehicle is estimated at GH¢28,000. The project appears quite profitable based on the NPV criteria using the Government policy rate of 26%. However, the banks are offering rates far higher than the policy rate.

Required:
Calculate the breakeven rate of return for the project.

Answer

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Tags: Capital Budgeting, Cash Flow Analysis, Discounted cash flow, Internal Rate of Return, Net Present Value
Level: Level 2

Topic: 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.

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 – 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

Tag (SQ): Discounted cash flow

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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 – Q78 – Discounted cash flow

Calculate NPV for Woodland Enterprises' new product investment with inflation and advise on project viability.

FM – L2 – Q75 – Discounted cash flow

Calculate NPV to decide between maintaining old equipment or buying new equipment for Wisdom Ltd, using a 20% cost of capital.

FM – L2 – Q74 – Discounted Cash Flow

Calculate NPV for TechNova Ltd's new game Zestora, considering sales, costs, and tax over four years.

FM – L2 – Q73 – Discounted Cash Flow

Calculate the breakeven rate of return for Kofi's taxi service project using NPV criteria with given cash flows and costs.

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 – 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.

You're reporting an error for "FM – L2 – Q84 – 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.

You're reporting an error for "FM – L2 – Q82 – 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.

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

FM – L2 – Q78 – Discounted cash flow

Calculate NPV for Woodland Enterprises' new product investment with inflation and advise on project viability.

You're reporting an error for "FM – L2 – Q78 – Discounted cash flow"

FM – L2 – Q75 – Discounted cash flow

Calculate NPV to decide between maintaining old equipment or buying new equipment for Wisdom Ltd, using a 20% cost of capital.

You're reporting an error for "FM – L2 – Q75 – Discounted cash flow"

FM – L2 – Q74 – Discounted Cash Flow

Calculate NPV for TechNova Ltd's new game Zestora, considering sales, costs, and tax over four years.

You're reporting an error for "FM – L2 – Q74 – Discounted Cash Flow"

FM – L2 – Q73 – Discounted Cash Flow

Calculate the breakeven rate of return for Kofi's taxi service project using NPV criteria with given cash flows and costs.

You're reporting an error for "FM – L2 – Q73 – 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 – 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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