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  • 20 Marks

FM – L2 – Q63 – DCF: Risk and uncertainty

Calculate NPV for two machines under different sales demand levels for Kofi Enterprises Ltd.

Kofi Enterprises Ltd must purchase a new machine for making a new product. There is a choice between two machines, Machine A and Machine B. Each machine has an estimated life of three years with no expected scrap value.
Machine A costs N₦15,000 and Machine B costs N₦20,000.
The variable costs of manufacture would be N₦1 per unit if Machine A is used and N₦0.50 per unit if Machine B is used. The product will sell for N₦4 per unit.
The demand for the product is uncertain. Following some market research, the following estimates of annual sales demand have been made:

Annual demand (Units) Probability
2,000 0.2
3,000 0.6
5,000 0.2

The sales demand in each year will be the same. For example, if the demand is 2,000 units in Year 1, it will be 2,000 units for every year of the project.
Taxation and fixed costs will be unaffected by any decision made.
Kofi Enterprises Ltd’s cost of capital is 6%.

Required:
(a) Calculate the NPV for each of investment options, Machine A and Machine B, for each of the possible levels of sales demand.

(b) Calculate the expected NPV for each of the investment options.

(c) Assume now that the decision is taken to buy Machine A.

(i) Calculate the probability that the NPV of the project will be negative.

(ii) Calculate the minimum annual sales required for the NPV of the project to be positive.

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  • 21 Marks

FM – L2 – Q62 – Discounted cash flow

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

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

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  • 15 Marks

FM – L2 – Q61 – Discounted Cash Flow

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

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.

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  • 12 Marks

FM – L2 – Q60 – Discounted Cash Flow

Calculate NPV of ZQR Ltd's project ignoring inflation, with given cash flows and 10% cost of capital

ZQR Ltd, a manufacturing company, is considering a proposal to invest in machinery that it will use to increase its output and sales by 10,000 units in each of the next five years. The full purchase cost of the machinery would be GH¢225,000. This price includes a payment of GH¢20,000 made 12 months ago to the machinery supplier for a non-refundable down-payment for purchase of the machinery.

The company currently makes and sells a single product. This has a selling price of GH¢15 per unit and at present-day prices the direct costs per unit are GH¢3.75 for material and GH¢2.50 for labour. Incremental production overheads (all cash expenses) would be GH¢37,500 in each year, at current price levels.

Assume that all cash flows occur at the end of the year to which they relate.

ZQR’s cost of capital is 10%.

Required

(a) Calculate the NPV of the project, ignoring inflation.

(b) Calculate the NPV of the project, at a cost of capital of 10%, taking the following inflationary increases in revenues and costs into consideration:

Because of inflation, selling prices will rise by 7% in each year.

Material costs will rise by 5% each year, labour costs by 6% each year and overheads by 2% each year.

Comment on the differences in your results, compared with the NPV you calculated in part (a)

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  • 12 Marks

FM – L2 – Q59 – Discounted Cash Flow

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

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.

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  • 12 Marks

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.

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.

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  • 10 Marks

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.

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.

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  • 5 Marks

FM – L2 – Q56 – Discounted Cash Flow

Calculate NPV for a four-year project with equipment purchase, tax, and capital allowances.

Zest Ltd is considering whether or not to invest in a four-year investment project. The project will require the purchase of equipment costing GH¢800,000. This will have an estimated residual value of GH¢200,000 at the end of Year 4. The equipment will be depreciated by the straight-line method.
The profits before interest and tax from the project are expected to be GH¢400,000 each year. Tax is payable at 30% one year in arrears.
The equipment will qualify for capital allowances (tax depreciation allowances) of 25% each year, using the reducing balance method. The first claim for an allowance would be made against Year 0 profits.
The after-tax cost of capital is 15%.
Required:
Calculate the NPV of the project.

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  • 15 Marks

FM – L2 – Q55 – Discounted Cash Flow

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

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.

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  • 15 Marks

FM – L2 – Q52 – Discounted cash flow

Calculate NPV and IRR for two mutually exclusive projects for Dambai Energy Ltd.

Dambai Energy Ltd is considering whether to invest in either of two mutually-exclusive projects, Project 1 and Project 2. Both projects involve the purchase of machinery with a life of five years.
Project 1: The machine would cost GH₵556,000 and would have a net disposal value of GH₵56,000 at the end of Year 5. The project would earn annual cash flows (receipts minus payments) of GH₵200,000.
Project 2: The machine would cost GH₵1,616,000 and would have a net disposal value of GH₵301,000 at the end of Year 5. The project would earn annual cash flows (receipts minus payments) of GH₵500,000.
Dambai Energy Ltd uses the straight-line method of depreciation. Its cost of capital is 15%.
Ignore taxation, inflation, and investment in working capital.

Required
(a) For each of the two projects, calculate:
(i) the net present value, and
(ii) the internal rate of return to the nearest one per cent.

(b) State which project, if any, you would select for acceptance.

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