ACCA P4 Advanced Financial Management - 2010 - Study text - Emile Woolf Publishing
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Chapter 3: Capital investment appraisal
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DCF and taxation
Taxation cash flows in investment appraisal
Interest costs and taxation
Timing of tax cash flows for taxation
Tax-allowable depreciation (capital allowances)
Tax exhaustion
4 DCF and taxation
4.1 Taxation cash flows in investment appraisal
In capital investment appraisal, cash flows arise due to the effects of taxation.
When an investment by a company results in higher profits, there will be higher
taxation. For example, if taxation on profits is 25% and a company earns $10,000
each year from an investment, the annual pre-tax cash inflow is $10,000, but
there is a tax payment of $2,500 each year.
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.
Tax cash flows should be included in DCF analysis.
4.2 Interest costs and taxation
Interest costs are allowable for tax purposes. However, interest cash flows are not
included in DCF analysis, 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 benefit of the tax
relief on interest payments.
4.3 Timing for cash flows for taxation
The payment of tax on extra profits or the savings in tax due to lower profits could
occur either:
in the same year as the profits or losses to which they relate, or
one year later (‘one year in arrears’).
Either of these assumptions could be correct. An examination question should
specify which assumption you should use.
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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. There will be no tax relief
on the initial investment of $60,000.
Required
Calculate the NPV of the project.
Answer
Year
Investment
Pre-tax
cash profit
Tax at 30%
Net cash
flow
Discount
factor at 8%
PV
0 (60,000) (60,000) 1.000 (60,000)
1 40,000
40,000
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)
4.4 Tax-allowable depreciation (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.
straight line method
reducing balance method.
Straight-line method
With the straight-line method, the amount allowed for tax purposes is a constant
amount each year. The tax-allowable depreciation is calculated as:
=
The cost of the asset minus any expected residual value
()
Expected years of life
.
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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.
These cash flows should be treated as cash inflows for the project.
The reducing balance method
With the reducing balance method, the tax allowable depreciation is a constant
percentage each year of the written down value (WDV) of the asset as at the
beginning of the year. The WDV of the asset is its cost less all accumulated capital
allowances to date.
The reducing balance method is much more likely to feature in an examination
question on DCF than the straight-line method.
Example
A company purchases an asset costing $80,000. Tax-allowable depreciation is 25%
on a reducing balance basis. Tax on profits is payable at the rate of 30%. Tax is
payable/saved one year in arrears.
It should be assumed that the first claim for tax-allowable depreciation is made
against the profits of the company for Year 1.
Required
(a) Calculate the tax-allowable depreciation (capital allowances) that would be
claimed against profits of Year 0 to Year 4, the tax saving, and the year of the
cash flow benefit from the tax saving.
(b) Calculate the effect on tax if the asset is sold in Year 5 for $24,000.
Answer
(a) The capital allowances for Years 1 – 4, and their effect on cash flows, are
calculated as follows:
Year
WDV at
start of year
Tax allowable
depreciation (25%)
Tax saved
(30%)
Year of cash
flow benefit
$ $ $
1 80,000
20,000
6,000 2
2 (80,000
–
20,000) 60,000
15,000
4,500 3
3 (60,000
–
15,000) 45,000
11,250
3,375 4
4 (45,000
–
11,250) 33,750
8,438
2,531 5
5 (33,750
–
8,438) 25,312
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(b) If the asset is sold in Year 5, it is assumed for DCF purposes that a balancing
charge or a balancing allowance will arise.
There is no annual capital allowance in the year of disposal.
If the asset is sold for more than its WDV at the beginning of the year of
disposal, a
balancing charge will arise. This increases taxable profits, and
so increases the amount of tax payable (in the following year, since it is
assumed that tax payments occur one year in arrear of profits).
If the asset is sold for less than its WDV at the beginning of the year of
disposal, a
balancing allowance will arise. This reduces taxable profits,
and so reduces the amount of tax payable (in the following year).
In this example:
$
Sale value in Year 5 24,000
WDV at the start of the year
25,312
Balancing allowance 1,312
Since there is a balancing allowance of $1,312 for Year 5, there will be a tax
saving of $1,312 × 30% = $394 in Year 6, one year in arrears. The effect of
capital allowances on the cash flows of the project is therefore as follows:
Year
WDV at
start of
year
Capital
allowance
(25%)
Tax saved
(30%) = cash
flow benefit
Year of
cash flow
benefit
$ $ $
1 80,000
20,000
6,000 2
2 60,000
15,000
4,500 3
3 45,000
11,250
3,375 4
4 33,750
8,438
2,531 5
5 25,312
5 Disposal value (24,000)
5 Balancing allowance
1,312
394 6
The disposal value of the asset in Year 5, $24,000, is also a cash flow of the
project.
Example
A company is considering an investment in a non-current asset (fixed asset) costing
£80,000. The project would generate the following cash profits:
Year £
1 30,000
2 40,000
3 20,000
4 10,000
The asset is eligible for capital allowances each year at 25%, by the reducing balance
method. It is expected to have a residual value of £40,000 at the end of year 4. The
after-tax cost of capital is 9%. The rate of tax on profits is 30%. Taxation cash flows
occur one year in arrears.
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The first annual capital allowance can be claimed against the company’s profits for
Year 1.
Required
Calculate the NPV of the project.
Answer
The balancing charge or balancing allowance?
The previous example shows that if the first annual capital allowance is claimed
against Year 1 profits, the WDV of the asset at the beginning of year 4 (the year of
disposal) will be £33,750. The disposal value of the asset at the end of year 4 is
£40,000. This means that there is a balancing charge in Year 4, because the disposal
value is higher than the WDV.
Balancing charge = £40,000 - £33,750 = £6,250.
There will be extra tax payable in Year 5 for the balancing charge. Extra tax payment
= £6,250 × 30% =
£1,875.
(If the residual value had been lower than £33,750, there would have been a
balancing allowance and a saving in tax the following year).
Project cash flows and NPV
Year
Investment
Cash
profits
Tax on
profits at
30%
Tax-allowable
dep’n – tax
saved/ (extra tax)
Net
cash
flow
Disc
factor
at 9%
PV
£ £ £ £ £ £
0 (80,000)
(80,000
)
1.000 (80,000)
1 30,000
30,000 0.917 27,510
2 40,000
(15,000)
6,000
31,000 0.842 26,102
3 20,000
(12,000)
4,500
12,500 0.772 9,650
4 40,000 10,000
(6,000)
3,375
47,375 0.708 33,542
5
(3,000)
(1,875)
(4,875) 0.650 (3,169)
NPV + 13,635
4.5 Tax exhaustion
It is normally assumed in DCF analysis that when capital allowances are available,
the company has sufficient taxable profits against which the capital allowances can
be set. This means that the tax benefit from the capital allowances can be claimed as
soon as possible.
A different situation would apply if a company does not have sufficient taxable
profits, for example if it has accumulated losses. In this situation, the company
might be unable to claim the capital allowances as soon as if sufficient taxable
profits existed.
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If tax allowances are not claimed as soon as possible, the cash flow benefit from the
tax savings will be deferred, and this will affect the cash flows and the NPV of the
proposed investment project.
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DCF and inflation
Real cost of capital and money cost of capital
The DCF rule on inflation
5 DCF and inflation
5.1 Real cost of capital and money cost of capital
Inflation will affect future cash flows. Future rates of inflation cannot be predicted
with certainty, but can be estimated. It is therefore possible to estimate future cash
flows to allow for expected inflation. If the future rate of inflation is expected to be i%.
Inflation-adjusted cash flow = [Cash flow at today’s value × (1 + i)
n
]
where:
i = the annual rate of inflation, expressed as a proportion (4% = 0.04, and so on)
n = the number of years in the future that the cash flow will occur.
For example, if sales revenue at today’s prices is expected to be $100,000 in four
years’ time, and the rate of sales price inflation is expected to be 3% each year, sales
revenue in Year 4 at inflation-adjusted prices will be:
$100,000 × (1.03)
4
] = $112,551.
There is a real cost of capital and a money cost of capital.
The money cost of capital is the required return on investment, allowing for
inflation
The real cost of capital is the required rate of return at today’s price levels.
There is a mathematical connection between the real cost of capital and the money
cost of capital.
(1 + r) (1 + i) = (1 + m)
where:
r = real cost of capital
i = annual rate of inflation
m = money cost of capital
A cost of capital is normally calculated as and expressed as a money cost of capital.
It is much less common to use a real cost of capital for DCF analysis.
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Example: real cost and money cost of capital
The rate of inflation in the future is expected to be 5% each year. A business has a
weighted average cost of capital of 11%. This is its money cost of capital.
The real cost of capital is calculated as follows:
1+ r
()
1.05
()
=1.11
1+ r
()
=
1.11
1.05
r =1.057 −1 = 0.05 or 5.7%
5.2 The DCF rule on inflation
When inflation is expected to have a significant effect on the future cash flows of a
project, it should be included in the DCF analysis. There are two ways of dealing
with expected inflation in DCF. Both methods are acceptable.
Method 1. Estimate the cash flows of the project at today’s prices, with no
adjustment for inflation. Discount these cash flows at the real cost of capital.
Method 2. Calculate the cash flows of the project to allow for inflation. Discount
these inflation-adjusted cash flows at the money cost of capital.
Both methods give the same NPV.
You might be expected to use either method in
your examination.
Method 2 is usually the easiest
in practice, especially when items of cost and
revenue are expected to increase in price at different annual rates.
Example: real cost and money cost of capital
A company has a money cost of capital of 15.5%. The expected future rate of
inflation is 10% each year. The real cost of capital is therefore 5%. (This is calculated
as [(1.155/1.10) – 1]).
The company is considering an investment for which the expected future cash flows
and NPV are as follows:
Year
Cash flows:
today’s prices
$
0 (60,000)
1 18,000
2 35,000
3 20,000
4 10,000
What is the NPV of the project?
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Answer
Method 1 – Today’s prices:
Discount at the real cost of capital
Method 2 – Inflated prices:
Discount at the money cost of capital
Year
Cash flows:
today’s
prices
Discount
factor at
5%
PV
Cash flows:
inflated
prices
Discount
factor at
15.5%
PV
$ $ $ $
0 (60,000) 1.000
(60,000)
(60,000)
1.000 (60,000)
1 18,000 0.952
17,136
19,800
0.866 17,147
2 35,000 0.907
31,745
42,350
0.750 31,762
3 20,000 0.864
17,280
26,620
0.649 17,276
4 10,000 0.823
8,230
14,641
0.562 8,228
NPV
14,391
14,413
These numbers should be
exactly the same. They differ slightly due to ‘rounding
errors’ in the arithmetic.
Example: calculating an NPV with inflation in the cash flow
A business is planning an investment in new equipment that would have an
expected useful life of three years. The cash flows from the project have been
estimated as follows:
Year 0 1 2 3
$
$
$
$
Equipment cost/residual value (50,000)
20,000
Sales revenue
25,000
25,000
20,000
Running costs
(10,000)
(10,000)
(8,000)
The expected annual rates of inflation for the next three years are:
Equipment cost/residual value
5%
Sales revenue 4%
Running costs 7%
In addition, the project will require a working capital investment of $10,000
immediately, with an increase to $11,000 at the end of Year 1 and a further increase
to $12,000 at the end of Year 2. This estimate allows for inflation. The weighted
average cost of capital, which is the money cost of capital, is 10%.
Required
Calculate the NPV of the project and recommend whether the project should be
undertaken.
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Answer
Since different rates of inflation apply to different items of cash flow, the NPV
should be calculated by discounting inflation-adjusted cash flows at the money cost
of capital.
Workings
Equipment residual value = 20,000 × (1.05)
3
= 23,153
Sales, Year 1 = 25,000 × (1.04) = 26,000
Sales, Year 2 = 25,000 × (1.04)
2
= 27,040
Sales, Year 3 = 20,000 × (1.04)
3
= 22,497
Running costs, Year 1 = 10,000 × (1.07) = 10,700
Running costs, Year 2 = 10,000 × (1.07)
2
= 11,449
Running costs, Year 3 = 8,000 × (1.07)
3
= 9,800.
These cash flows should be discounted at the money cost of capital, which is 10%.
Year 0 1 2 3 NPV
$ $ $ $ $
Equipment (60,000)
23,153
Working capital
(10,000)
(1,000)
(1,000)
12,000
Sales revenue
26,000
27,040
22,497
Running costs
(10,700)
(11,449)
(9,800)
Net cash flow (70,000)
14,300
14,591
47,850
Discount factor at 10% 1.000
0.909
0.826
0.751
Present value (70,000)
12,999
12,052
35,935
(9,014)
Conclusion
The project has a negative NPV. The decision should therefore be: – Do not invest.