ACCA F9 Financial Management - 2010 - Study text - Emile Woolf Publishing
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Chapter 8: Discounted cash flow
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At a discount rate of 11%, the present value (Year 0 value) of $50,000 as at the
end of Year 3
= $50,000 × discount factor for Year 3 at 11%
= $50,000 × 0.731
= $36,550.
Exercise 4
A company is planning a long-term investment costing $800,000. The project cash
flows would be $100,000 each year for the first five years and then $80,000 per year
in perpetuity, from Year 6 onwards. The cost of capital is 12%.
What is the NPV of this project, and should it be undertaken? (Ignore all other
factors, including risk and uncertainty).
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Layout of NPV calculations
Two methods of presentation
Workings for relevant costs
5 Layout of NPV calculations
5.1 Two methods of presentation
If you are required to present NPV calculations in the answer to an examination
question, it is important that you should be able to present your calculations and
workings clearly. There are two normal methods of presenting calculations, and you
should try to use one of them.
The two methods of presentation are shown below, with illustrative figures.
Format 1
Year
Descriptionofitem
Cashflow
Discount
factorat10%
Present
Value
$$
0 Machine (40,000) 1.000 (40,000)
0 Workingcapital (5,000) 1.000 (5,000)
1‐3 Cashprofits 20,000 2.487 49,740
3 Saleofmachine 6,000 0.751 4,506
3 Recoveryofworkingcapital 5,000 0.751 3,755
NPV 13,001
Format 2
Year 0 1 2 3
Descriptionofitem $ $ $ $
Machine/saleofmachine (40,000) 6,000
Workingcapital (5,000) 5,000
Cashreceipts50,000 50,000 50,000
Cashexpenditures (30,000) (30,000) (30,000)
–
–––––––
–
–––––––
–
––––––– ––––––––
Netcashflow (45,000) 20,000 20,000 31,000
–
–––––––
–
–––––––
–
––––––– ––––––––
Discountfactorat10% 1.000 0.909 0.826 0.751
Presentvalue (45,000) 18,180 16,520 23,281
NPV + 12,981
–
–––––––
Chapter 8: Discounted cash flow
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For computations with a large number of cash flow items, the second format is
probably easier. This is because the discounting for each year will only need to be
done once.
Note that
changes in working capital are included as cash flows. An increase in
working capital, usually at the beginning of the project in Year 0, is a cash outflow
and a reduction in working capital is a cash inflow. Any working capital investment
becomes $0 at the end of the project.
5.2 Workings for relevant costs
You should also show all your workings to calculate specific cash flows. For
example, you might need to show your workings to obtain the cash flows for:
annual cash profits from a project, or
taxation.
Where you are required to identify the relevant costs for an item, present your
calculations or reasoning clearly in workings or notes. If there are sunk costs that
have already been incurred or committed by an earlier decision, these are not
relevant costs: it might be appropriate to tell the examiner that you have recognised
the irrelevance of the sunk cost or committed cost, by making a note in your answer.
Example
A company is considering a new large project. It owns a piece of land that it bought
for $6,000 over forty years ago. This land is currently not being used but could be
sold now for $1.2 million. If it is used it could be sold in three years time for $1.3
million.
The company will spend $500,000 building a work processing plant for the project.
The company finances the plant with a three-year bank loan at 5%. The resale value
of the plant is $50,000 at the end of year 3.
The company also will use various types of raw material. The raw material
requirements for the project output of 100 tonnes of Product X are as follows:
Rawmaterial A B
Currentamountsininventory(tonnes) 100 100
Cost(pertonne) $95 $80
Scrapvalue(pertonne) $30 Toxic
Replacementcost(pertonne) $100 $90
Usedelsewhere? Yes No
Contributionpertonneusedonotherproducts**
(**contribution=afterdeductionofcurrentreplacementcost)
$40 $400
Annualrequirement(tonnes) 200 100
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Notes
Raw material B is toxic. No further supplies are available until the end of the
first year. Material B is also being used in another product, for which 50 tonnes
are required annually. This other product is being discontinued from the end of
year 1.
There are no other uses for Material B. To dispose of material B would cost the
company $25 per tonne.
The standard cost card prepared by the management accountant shows a cost
for Product X of $450 per tonne produced. This includes a direct labour cost of
$100 per unit of Product X.
There is spare capacity in the labour force – no extra personnel or overtime will
be needed to produce the new product.
Receipts from sales will be:
Year 1 $500,000
Year 2 $500,000
Year 3 $300,000
The project will last three years. Assume that all cash flows occur at the end of
the relevant year.
Required
Calculate the NPV if the company has a cost of capital of 10%. Ignore taxation.
Answer
Notes
(1) Land. By undertaking the project, the company will forgo the immediate sale of
the land, for which it could obtain $1,200,000. This revenue forgone is an
opportunity cost. However, if the project is undertaken, the land can be sold at
the end of Year 3 for $1,300,000
(2)
Plant. The relevant cash flows are its current cost (the $500,000 is assumed to be a
cash cost) and its eventual disposal value. The 5% financing of the plant is
irrelevant and must be ignored: interest costs are implied in the cost of capital,
which is 10%, not 5%.
(3)
Labour costs – Labour costs are irrelevant because they are not incremental cash
flows. The wages or salaries will be paid whether or not the project goes ahead.
(4)
Material A costs – Material A is in regular use; therefore its relevant cost is its
replacement cost. Annual cost = 200 tonnes × $100 = $20,000.
(5)
Material B costs – 100 tonnes are currently in inventory and no additional units
can be obtained until Year 2. The choices are to use all 100 tonnes to make
Product X, or to use 50 tonnes to make the other product and dispose of the
remaining 50 tonnes.
The other product earns a contribution of $400 per tonne of Material B used, and the
contribution is after deducting the replacement cost of the material. The opportunity
cost of using the 50 tonnes to make Product X instead of this other product in Year 1
Chapter 8: Discounted cash flow
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is therefore $490 per tonne. The total opportunity cost of lost cash flow is therefore
50 tonnes at $490 each = $24,500, but in Year 1 only.
However, by making Product X, the company will also avoid the need to dispose of
50 tonnes of Material B at a cost of $25 per tonne. It is assumed that these costs
would be incurred early in Year 1 (Year 0). Making and selling Product X will
therefore save the company disposal costs of 50 tonnes × $25 = $6,250 in Year 0.
Year 0 1 2 3
$ $ $ $
Land (1,200,000)1,300,000
Plant (500,000)50,000
MaterialA(20,000) (20,000) (20,000)
MaterialB:disposalcostssaved 6,250
MaterialB:cashprofitsforgone(24,500)
MaterialB:purchasecosts(9,000) (9,000)
Sales 500,000 500,000 300,000
–
–––––––
–
–––––––
–
––––––– ––––––––
Netcashflow (1,193,750) 455,500 271,000 1,321,000
Discountfactorat10% 1.000 0.909 0.826 0.751
Presentvalue (1,193,750) 414,050 223,846 992,071
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Paper F9
Financial management
CHAPTER
9
DCF: taxation and inflation
Contents
1 DCFandtaxation
2 Tax‐allowabledepreciation(capitalallowances)
3 DCFandinflation
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DCF and taxation
Taxation cash flows in investment appraisal
Interest costs and taxation
Timing of cash flows for taxation
1 DCF and taxation
1.1 Taxation cash flows in investment appraisal
In project appraisal, cash flows arise due to the effects of taxation. When an
investment results in higher profits, there will be higher taxation. Tax cash flows
should be included in DCF analysis. In DCF analysis it is normally assumed that tax
is payable on the amount of cash profits in any year.
For example, if taxation on profits is 25% and a company earns $10,000 cash profit
each year from an investment, the pre-tax cash inflow is $10,000, but there is a tax
payment of $2,500.
Similarly, if an investment results in lower profits, tax is reduced. For example, if an
investment causes higher spending of $5,000 each year and the tax on profits is 30%,
there will be a cash outflow of $5,000 but a cash benefit from a reduction in tax
payments of $1,500.
1.2 Interest costs and taxation
Interest costs are also allowable expenses for tax purposes, but interest cash flows
are not included in DCF analysis. This is because the interest cost is in the cost of
capital (discount rate).
In DCF analysis, an after-tax cost of capital is used to calculate present values. An
after-tax cost of capital is a discount rate that allows for the tax relief on interest
payments. This means that because interest costs are allowable for tax purposes, the
cost of capital is adjusted to allow for this and is reduced accordingly.
By using an after-tax cost of capital, we are able to exclude both interest cash flows
and tax relief on interest from the estimated cash flows of a project.
The cost of capital is explained in more detail in a later chapter. Briefly however, if
interest on debt capital is 8% and the rate of tax on company profits is 25%, the
after-tax cost of the debt capital will be 8% × (1 – 0.25) = 6%. In other words, when t
is the rate of taxation as a proportion, the after-tax cost of debt capital is:
r (1 – t).
Chapter 9: DCF: taxation and inflation
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1.3 Timing of cash flows for taxation
When cash flows for taxation are included in investment appraisal, an assumption
must be made about when the tax payments are made. The actual timing of tax
payments depends on the tax rules that apply in the relevant country. In DCF
analysis, one or other of the following assumptions is used.
Assumption 1. Tax is payable in the same year as the profits to which the tax
relates.
Assumption 2. Tax is payable one year later (‘one year in arrears’). For example,
tax on the cash profits in Year 1 is payable in Year 2.
Either of these two assumptions could be correct. An examination question should
specify which assumption you should use.
Example
The after-tax cost of capital is 8%. A project costing $60,000 will be expected to earn
cash profits of $40,000 in year 1 and $50,000 in year 2. Taxation at 30% occurs one
year in arrears of the profits or losses to which they relate.
For the purpose of this exercise, assume that the cost of the project is not an
allowable cost for tax purposes (i.e. capital allowances should be ignored).
Required
Calculate the NPV of the project.
Answer
Year
Investment/pre‐
taxcashprofit
Taxat
30%
Netcash
flow
Discount
factorat8%
Present
value
$ $ $$
0 (60,000)(60,000) 1.000 (60,000)
1 40,00040,000 0.926 37,040
2 50,000 (12,000) 38,000 0.857 32,566
3(15,000) (15,000) 0.794 (11,910)
––––––––
NPV (2,304)
––––––––
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Tax-allowable depreciation (capital allowances)
The nature of caapital allowances
Straight-line method
Reducing balance method
Balancing charge or balancing allowance on disposal
2 Tax-allowable depreciation (capital allowances)
2.1 The nature of capital allowances
When a business buys a non-current asset, depreciation is charged in the financial
accounts. However, depreciation in the financial accounts is not an allowable
expense for tax purposes.
Instead, the tax rules provide for ‘tax-allowable depreciation’ or capital allowances,
according to rules determined by the government.
Tax-allowable depreciation affects the cash flows from an investment, and the tax
effects must be included in the project cash flows.
There are two ways of allowing depreciation for tax purposes:
the straight-line method
the reducing balance method.
2.2 Straight-line method
With the straight-line method of tax-allowable depreciation, the annual depreciation
expense allowed for tax purposes =
Cost of the asset minus any expected residual value
Expected years of life
Example
An asset costs $80,000 and has an expected economic life of four years with no
residual value. If depreciation is allowed for tax purposes over four years using the
straight-line method, the allowable depreciation would be $20,000 each year.
If the rate of tax on profits is 25%, the annual reduction in tax from the capital
allowance is $20,000 × 25% = $5,000 for four years.