Cash Flows – Page 2

FM – L2 – Q119 – Business valuations

Calculate offer price for SmallCorp using a forward P/E multiple of 8.0 based on expected earnings

Question

LargeCorp is considering a takeover bid for SmallCorp, another company in the same industry. SmallCorp is expected to have earnings next year of GH₵86,000. If LargeCorp acquires SmallCorp, the expected results from SmallCorp will be as follows:

	Year after the acquisition
	Year 1	Year 2	Year 3
Sales	GH₵200,000	GH₵280,000	GH₵320,000
Cash costs/expenses	120,000	160,000	180,000
Capital allowances	20,000	30,000	40,000
Interest charges	10,000	10,000	10,000
Cash flows to replace assets and finance growth	25,000	30,000	35,000

From Year 4 onwards, it is expected that the annual cash flows from SmallCorp will increase by 4% each year in perpetuity. Tax is payable at the rate of 30%, and the tax is paid in the same year as the profits to which the tax relates. If LargeCorp acquires SmallCorp, it estimates that its gearing after the acquisition will be 35% (measured as the value of its debt capital as a proportion of its total equity plus debt). Its cost of debt is 7.4% before tax. LargeCorp has an equity beta of 1.60. The risk-free rate of return is 6% and the return on the market portfolio is 11%.
Required:

(a) Suggest what the offer price for SmallCorp should be if LargeCorp chooses to value SmallCorp on a forward P/E multiple of 8.0 times.

(b) Calculate a cost of capital for LargeCorp.

Answer

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Tags: Acquisition, Business valuations, Cash Flows, DCF, Perpetuity, WACC
Level: Level 2

Topic: Business valuations

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 – 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 – Q62 – Discounted cash flow

Calculate contribution PV for two strategies and evaluate machine investment using IRR for Volta Fabrication Ltd.

Question

DOME FABRICATION LIMITED
(a) Contribution
Strategy 1

Year	1	2	3	4	5
Demand (units)	10,000	12,000	15,000	18,000	20,000
Selling price (unit)	GH¢25	GH¢25	GH¢25	GH¢25	GH¢25
Variable cost (unit)	GH¢15	GH¢15	GH¢15	GH¢15	GH¢15
Contribution (unit)
Inflated contribution
Total contribution (GH¢)

10% discount factors
PV of contribution (GH¢)

Total PV of Strategy 1 contributions =

Strategy 2

Year	1	2	3	4	5
Demand (units)	12,000	14,000daf	16,000	18,000	20,000
Selling price (unit)	GH¢22	GH¢22	GH¢22	GH¢22	GH¢22
Variable cost (unit)	GH¢12	GH¢12	GH¢12	GH¢12	GH¢12
Contribution (unit)
Inflated contribution
Total contribution
Total contribution
PV of contribution (GH¢)

Total PV of strategy 2 contributions =

Strategy 2 is preferred as it has the higher present value of contributions.

(b) Evaluating the investment in the new machine using internal rate of return

Year	1	2	3	4	5
Total contribution
Fixed costs
Profit
10% discount factors
Present value
20% discount factors
Present value of profits

Answer

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Tags: Cash Flows, Contribution, Cost of Capital, Discounted cash flow, Financial analysis, Inflation, investment appraisal, IRR, NPV
Level: Level 2

Topic: Discounted cash flow

FM – L2 – Q61 – Discounted Cash Flow

Calculate NPV for Coastline Plc's project with equipment purchase, considering inflation and taxation.

Question

Coastline Plc is considering whether to invest in a project whose details are as follows.
The project will involve the purchase of equipment costing GH¢2,000,000. The equipment will be used to produce a range of products for which the following estimates have been made.

Year	Average unit sales price	Average unit variable cost	Incremental fixed costs	Sales volume (units)
1	GH¢73.55	GH¢50	GH¢1,200,000	65,000
2	GH¢76.03	GH¢45	GH¢1,200,000	110,000
3	GH¢76.68	GH¢45	GH¢1,200,000	125,000
4	GH¢81.86	GH¢45	GH¢1,200,000	80,000

The sales prices allow for expected price increases over the period. However, cost estimates are based on current costs and do not allow for expected increases in costs. Inflation is expected to be 3% per year for variable costs and 4% per year for fixed costs. The incremental fixed costs are all cash expenditure.
Tax on profits is at the rate of 30%, and tax is payable in the same year.
The cost of capital is 10%.

Required:
Calculate the NPV of the project.

Answer

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

Topic: Discounted cash flow

FM – L2 – Q59 – Discounted Cash Flow

Calculate NPV of a project by Zenith Ltd, ignoring and including inflation effects.

Question

ZENITH LTD
(a) Calculate the NPV of an investment with the following estimated cash flows, assuming a cost of capital of 8%:

Years	Annual cash flow
0	(3,000,000)
1–4	500,000
5–8	400,000
9–10	300,000
11 onwards	100,000

ZENITH LTD
(b) The cash flows for an investment project have been estimated at current prices, as follows:

Year	Equipment	Revenue	Running costs
0	(900,000)
1		800,000	(400,000)
2		800,000	(350,000)
3		400,000	(300,000)
4		400,000	(300,000)

It is expected that the cash flows will differ because of inflation. The annual rates of inflation are expected to be:
Equipment value: 4% per year
Revenue: 3% per year
Running costs: 5% per year.
The cost of capital is 12%.

Required
(a) Calculate the NPV of the project ignoring inflation.
(b) Calculate the NPV of the project allowing for inflation.

Answer

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Tags: Cash Flows, Discounted cash flow, Financial management, Inflation, investment appraisal, NPV
Level: Level 2

Topic: DCF: Taxation and Inflation

FM – L2 – Q58 – Discounted Cash Flow

Calculate NPV for a project by Apex Ltd involving a new machine, considering tax, capital allowances, and working capital.

Question

Apex Ltd is considering whether to invest in the purchase of a new machine costing GH¢250,000. The machine will have a four-year life and a net disposal value of GH¢100,000 at the end of Year 4.
In addition, GH¢38,000 of working capital will be required from the start of the project, increasing to GH¢50,000 at the beginning of the second year. All the working capital will be recovered at the end of Year 4.
The project is expected to generate extra annual revenues of GH¢200,000 and incur annual cash operating costs of GH¢80,000 for each year of the project. Apex Ltd’s cost of capital is 10% after tax.
Corporation tax is charged on profits at 35%. Tax is payable in the year following the year in which the profits occur. There will be a 25% annual writing-down allowance on capital expenditure, for tax purposes. The tax-allowable depreciation is calculated by the reducing balance method.

Required
Calculate the NPV of the project and state whether or not it should be undertaken.

Answer

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Tags: capital allowances, Cash Flows, Discounted cash flow, Financial management, investment appraisal, NPV, Taxation, Working Capital
Level: Level 2

Topic: Discounted cash flow

FM – L2 – Q57 – DCF: Taxation and Inflation

Calculate the NPV of a project for CVB Ltd, considering tax, capital allowances, and cash flows over five years with a 15% cost of capital.

Question

CVB Ltd is considering whether to invest in new equipment costing GH¢600,000. The equipment is expected to have an economic life of five years and will have no disposal value at the end of Year 5 (and no disposal costs).
CVB’s after-tax cost of capital is 15%. Tax is charged at an annual rate of 35% and is payable in the year following the year in which the taxable profits arise.
The following forecasts relate to the project under consideration:

Year	GH¢000
	1	2	3	4	5
Sales income	250	250	300	350	400
Direct materials	50	55	58	64	70
Direct labour	25	25	30	30	35
Total direct costs	75	75	88	94	105
Depreciation	120	120	120	120	120

There will be tax allowances on the cost of the equipment, calculated at 25% each year on the reducing balance basis. The first depreciation tax allowance (capital allowance) would be claimed in year 0 (or very early in year 1).
Assume that:
(1) taxable profits are defined as income minus direct costs and capital allowances
(2) cash profits in each year = sales minus direct costs
Required
Calculate the net present value of the project and recommend whether or not the project should be undertaken.

Answer

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Tags: capital allowances, Cash Flows, Cost of Capital, Discounted cash flow, Financial analysis, investment appraisal, NPV, project evaluation, Tax Savings, Taxation
Level: Level 2

Topic: DCF: Taxation and Inflation

FM – L2 – Q55 – Discounted Cash Flow

Calculate NPV for Unified Energy Ltd's project with given cash flows and 10% discount rate.

Question

Unified Energy Ltd is evaluating a project with the following cash flows:

Year	0	1	2	3	4	5
	GH₵000	GH₵000	GH₵000	GH₵000	GH₵000	GH₵000
Sales			7,400	8,300	9,800	5,800
Wages			(550)	(580)	(620)	(520)
Materials			(340)	(360)	(410)	(370)
Licence fee		(300)	(300)	(300)	(300)	(300)
Overheads			(100)	(100)	(100)	(100)
Equipment	(5,200)	(5,200)				2,000
Specialised equipment			(150)
Working capital		(650)				650
	(5,200)	(6,150)	5,960	6,960	8,370	7,160
Discount factor at 10%	1.000	0.909	0.826	0.751	0.683	0.621

The company’s cost of capital is 10%.
Required:
Calculate the net present value (NPV) of the project and recommend whether it 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

Tag (SQ): Cash Flows

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FM – L2 – Q119 – Business valuations

Calculate offer price for SmallCorp using a forward P/E multiple of 8.0 based on expected earnings

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 – 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 – Q62 – Discounted cash flow

Calculate contribution PV for two strategies and evaluate machine investment using IRR for Volta Fabrication Ltd.

FM – L2 – Q61 – Discounted Cash Flow

Calculate NPV for Coastline Plc's project with equipment purchase, considering inflation and taxation.

FM – L2 – Q59 – Discounted Cash Flow

Calculate NPV of a project by Zenith Ltd, ignoring and including inflation effects.

FM – L2 – Q58 – Discounted Cash Flow

Calculate NPV for a project by Apex Ltd involving a new machine, considering tax, capital allowances, and working capital.

FM – L2 – Q57 – DCF: Taxation and Inflation

Calculate the NPV of a project for CVB Ltd, considering tax, capital allowances, and cash flows over five years with a 15% cost of capital.

FM – L2 – Q55 – Discounted Cash Flow

Calculate NPV for Unified Energy Ltd's project with given cash flows and 10% discount rate.

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FM – L2 – Q119 – Business valuations

Calculate offer price for SmallCorp using a forward P/E multiple of 8.0 based on expected earnings

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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.

You're reporting an error for "FM – L2 – Q82 – 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 – Q62 – Discounted cash flow

Calculate contribution PV for two strategies and evaluate machine investment using IRR for Volta Fabrication Ltd.

You're reporting an error for "FM – L2 – Q62 – Discounted cash flow"

FM – L2 – Q61 – Discounted Cash Flow

Calculate NPV for Coastline Plc's project with equipment purchase, considering inflation and taxation.

You're reporting an error for "FM – L2 – Q61 – Discounted Cash Flow"

FM – L2 – Q59 – Discounted Cash Flow

Calculate NPV of a project by Zenith Ltd, ignoring and including inflation effects.

You're reporting an error for "FM – L2 – Q59 – Discounted Cash Flow"

FM – L2 – Q58 – Discounted Cash Flow

Calculate NPV for a project by Apex Ltd involving a new machine, considering tax, capital allowances, and working capital.

You're reporting an error for "FM – L2 – Q58 – Discounted Cash Flow"

FM – L2 – Q57 – DCF: Taxation and Inflation

Calculate the NPV of a project for CVB Ltd, considering tax, capital allowances, and cash flows over five years with a 15% cost of capital.

You're reporting an error for "FM – L2 – Q57 – DCF: Taxation and Inflation"

FM – L2 – Q55 – Discounted Cash Flow

Calculate NPV for Unified Energy Ltd's project with given cash flows and 10% discount rate.

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