ACCA P4 Advanced Financial Management - 2010 - Study text - Emile Woolf Publishing
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Chapter 3: Capital investment appraisal
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Free cash flow
Valuation of a business using DCF
Definition of free cash flow
Free cash flow for the firm
Calculating free cash flow for the firm
Free cash flow for equity
Free cash flow and dividend policy
6 Free cash flow
6.1 Valuation of a business using DCF
DCF can be used to estimate a present value of the future profitability of a company.
Management might want to know the present value of expected profits of a business
in future years. One reason for wanting this information is to enable management to
put a current value on the business, possibly in order to:
decide how much to offer for a target company in a takeover bid, or
decide whether to accept or reject a takeover offer from another company.
The value of a business can be estimated by discounting expected future cash flows
from the business over a number of years into the future.
However, the cash flows that should be used for discounting are the expected
free
cash flows
of the business.
6.2 Definition of free cash flow
Free cash flow is the amount of cash generated by a company or business during a
specified period of time (say one year) minus the cash payments that the company
or business is obliged to make. Essential payments include taxation payments and
capital expenditure to replace ageing non-current assets (‘replacement’ capital
expenditure). Free cash flow is therefore the amount of cash generated by the
company that management are able to decide how to use.
However, there are differing specific definitions of free cash flow. The most
appropriate definition to use might differ according to purpose.
6.3 Free cash flow for the firm
Free cash flow for the firm is the amount of free cash flow generated by the business
as a whole, regardless of the source of finance. It is therefore calculated without
deducting interest payments as an essential cash payment.
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There are differing views about whether capital expenditure for expanding the
business is an essential cash payment.
One view is that only replacement capital expenditure should be deducted as
essential cash payments.
A different view is that replacement capital expenditure and capital expenditure
to grow the business internally (organically) should both be deducted in
calculating free cash flows, but that capital spending on acquisitions and cash
received from business disposals should be excluded.
A third view is that all capital expenditure (net of proceeds from disposals)
should be included in the calculation of free cash flow.
There is no ‘correct’ answer. However, free cash flow is the amount of cash that
management can decide how to use.
If it is assumed that expanding the business is a free decision by management,
only replacement capital expenditure should be deducted in calculating free
cash flow.
On the other hand, if it is assumed that capital expenditure to pay for expansion
of the business is necessary to grow operating cash flows in future years, a better
definition of free cash flow would be one where both replacement capital
expenditure and capital expenditure to pay for growth and expansion are
deducted.
6.4 Calculating free cash flow for the firm
There are two methods of calculating free cash flow for the firm, although they are
closely connected. One method starts with operating profit and the other starts with
cash flow from operations (as given in the cash flow statement)
Method 1 Method 2
Operating profit before interest
and tax
X
Add back: Depreciation (and any
other non-cash expenditures)
X
X
Plus or minus
Changes in working capital X /
(X)
X
Cash flow from operations X
Minus: Tax payments on profit
Minus:
Tax payments on profit (X)
Tax payments on profit (X)
Replacement capital expenditure (X)
Replacement capital expenditure (X)
Free cash flow X
Free cash flow X
(Note: You should remember that an increase in working capital reduces cash flow
and a reduction in working capital increases cash flow.)
Chapter 3: Capital investment appraisal
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6.5 Free cash flow for equity
Free cash flow for equity is the amount of free cash flow after deduction of interest
payments.
Free cash flow for the firm X
Minus: Interest payments
Equals: Free cash flow for equity (X)
Free cash flows for equity might be used in the valuation of the share capital of a
company; whereas free cash flow for the firm would be used for the valuation of the
entire business, equity plus debt capital.
Examples
Some companies explain in their annual report and accounts how they use free cash
flow as a measure of performance, and they give their definition of free cash flow.
Cadbury Schweppes has used the following definition (slightly simplified):
Cash generated by operations X
Minus: Interest payments (X)
Minus: Taxation payments (X)
Minus: Dividend payments (X)
Minus: All capital expenditure, but excluding
spending on share repurchases
(X)
Free cash flow X
6.6 Free cash flow and dividend policy
An examination question might ask you to comment on the ability of a company to
finance its capital investment programme from retained profits and free cash flows.
The ability of a company to source capital investments internally depends not only
on the amount of cash flows generated, but also on dividend policy. A situation
might easily occur where a company wants to finance a new capital investment
project and has enough cash from free cash flows, but is unwilling to invest because
using the cash in this way would involve cutting the annual dividend payment.
As a senior financial manager you might be required to consider two conflicting
financial objectives, and make a recommendation about what the company should
do.
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Paper P4
Advanced Financial Management
CHAPTER
4
DCF: risk analysis
Contents
1 Risk and uncertainty in capital investment
appraisal
2 Monte Carlo simulation
3 Project value at risk
4 Beginner’s guide to normal distribution tables
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Risk and uncertainty in capital investment appraisal
The problem of risk and uncertainty
Methods of assessing risk and uncertainty
Expected value of the NPV
Sensitivity analysis
Risk modelling
Fiscal risk
1 Risk and uncertainty in capital investment appraisal
1.1 The problem of risk and uncertainty
Investment projects are long-term projects, often with a time scale of many years. When
the cash flows for an investment project are estimated, the estimates might be incorrect.
Estimates of cash flows might be wrong for two main reasons:
risk in the investment, and
uncertainty about the future.
Risk
Risk exists when the actual outcome from a project could be any of several different
possibilities, and it is not possible in advance to predict which of the possible
outcomes will actually occur.
The simplest example of risk is rolling a dice. When a dice is rolled, the result will
be 1, 2, 3, 4, 5 or 6. These six possible outcomes are known in advance, but it is not
possible in advance to know which of these possibilities will be the actual outcome.
With risk assessment, it is often possible to estimate the probabilities of different
outcomes. For example, we can predict that the result of rolling a dice will be 1, 2, 3,
4, 5 or 6, each with a probability of 1/6.
Risk can often be measured and evaluated mathematically.
Uncertainty
Uncertainty exists when there is insufficient information to be sure about what will
happen, or what the probability of different possible outcomes might be. For
example, a business might predict that sales in three years’ time will be £500,000,
but this might be largely guesswork, and based on best-available assumptions about
sales demand and sales prices.
Uncertainty occurs due to a lack of sufficient information about what is likely to
happen.
It is possible to assess the uncertainty in a project, but with less mathematical
precision than for the assessment of risk.
Chapter 4: DCF: risk analysis
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Management should try to evaluate the risk and uncertainty, and take it into
account, when making their investment decisions. In other words, investment
decisions should consider the risk and uncertainty in investment projects, as well as
the expected returns and NPV.
1.2 Methods of assessing risk and uncertainty
There are several methods of analysing and assessing risk and uncertainty. Some of
these are fairly simple and straightforward. Others are more complex. The available
methods include:
calculating the expected value of the NPV
sensitivity analysis
simulation modelling
calculating a project value at risk (VaR).
1.3 Expected value of the NPV
An expected value is a weighted average value, calculated using estimated
probabilities of different possible outcomes. To calculate an expected value, the
probability of each possible outcome is estimated, and the mean (average) outcome
is calculated.
Expected value (EV) =
∑ px
where:
p represents the probability of each outcome and
x represents the value of each particular outcome.
When expected values are used to assess the risk in capital investment appraisal, x
would be the NPV for each possible outcome, and the EV would be the expected
value of the project net present value (the EV of the NPV).
The basic decision rule is that an investment project should be undertaken if the
expected value of its NPV is positive.
However, a project with a positive EV of NPV might not be undertaken if the risk
involved seems too great in relation to the amount of the return expected.
Example
A company is considering an investment in a project. The project would be a five-
year project, and would cost £200,000. The actual returns from the investment are
subject to uncertainty, but the following estimates have been prepared for the
different possible outcomes:
Probability NPV
£
0.10 (8,000)
0.30 4,000
0.40 12,000
0.20 20,000
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The EV of the NPV is calculated as follows:
Probability NPV EV
p x px
£ £
0.10 (8,000) (800)
0.30 4,000 1,200
0.40 12,000 4,800
0.20 20,000 4,000
EV of NPV 9,200
The EV of the NPV is positive, + £9,200. The decision would therefore be to
undertake the investment, provided that the risk does not seem too great. In this
example, there is a 10% probability that the NPV will be negative, – £8,000.
Management might therefore consider whether they consider the investment worth
undertaking, in view of this risk.
Expected value of cash flows for specific items
An alternative approach to using EVs is to use estimates of probabilities for
individual items of cash flow, such as EVs for annual sales revenue from a project
and EVs for the expected annual running costs.
Example
A company is considering an investment in a project where the prospects for
winning market share have been estimated as follows:
Market share Probability
High 40% 0.10
Medium 25% 0.50
Low 10% 0.40
The total value of market sales is expected to be $1,000,000 in Year 1, rising to $6
million in Year 5.
For the purpose of DCF analysis, we could calculate the EV of sales revenue in each
year and use this EV as the cash flow for sales revenue.
EV of market share = (0.10 × 40%) + (0.50 × 25%) + (0.40 × 10%) = 20.5%.
Estimates of sales revenue for the DCF analysis would therefore be $205,000 in Year
1 (20.5% of $1 million) rising to $1,230,000 in Year 5.
Disadvantages of using expected values
The advantage of using expected values of the NPV is that it provides a weighted
average value that allows for all the different possible outcomes.
The disadvantages of using expected values of the NPV are as follows:
The estimates of probabilities might be subjective, and based on judgement and
guesswork.
The EV of the NPV is not a value for any of the actual possible outcomes. In
other words, the EV will not happen.
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An EV is much more reliable for estimating the average outcome from events
that will happen repeatedly, many times over. A weighted average is not nearly
as suitable for estimating the expected outcome for a once-only investment
project.
Most important of all, an EV does not provide any analysis of the risk or
uncertainty. When capital investment projects are evaluated, and a decision is
made whether or not to undertake the investment, there should be a thorough
analysis of the risk as well as the expected returns.
1.4 Sensitivity analysis
Sensitivity analysis is a useful but simple technique for analysing risk and
uncertainty in an investment, when it is recognised that estimates of cash flows
could be inaccurate, or that events might occur that will make the estimates wrong.
Sensitivity analysis can be used:
To calculate the effect on the NPV of a given percentage reduction in benefits or
a given percentage increase in costs. For example, what would the NPV of the
project be if sales volumes were 10% below estimate, or if annual running costs
were 5% higher than estimate?
To calculate the percentage amount by which benefits must fall below estimate
or costs rise above estimate before the project NPV becomes negative. For
example, by how much would sales volumes need to fall below the expected
volumes, before the project NPV became negative?
To assess the effect of an unexpected event occurring in the future that would
make the cash flow estimates for the project wrong.
To assess the effect of a delay so that the expected cash inflows from the project
occur later than planned.
Example
A company is considering the following project:
Year
Equipment
Income
Running
costs
Net cash
flow
DCF factor at
10%
PV
£ £ £ £ £
0 (8,000)
1.000 (8,000)
1 6,000
3,500
2,500
0.909 2,273
2 8,000
4,500
3,500
0.826 2,891
3 10,000
5,500
4,500
0.751 3,379
4 4,000
2,500
1,500
0.683 1,025
NPV
+ 1,568
Required
Estimate the sensitivity of the project to:
income being lower than estimate, and
running costs being higher than estimate.
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Answer
We can calculate the PV of the equipment cost, the income and the running costs
separately, as follows:
Year
Equipment
Income
Running
costs
PV PV PV NPV
£ £ £ £
0 (8,000)
1 5,454
(3,181)
2 6,608
(3,717)
3 7,510
(4,131)
4 2,732
(1,707)
PV (8,000) 22,304
(12,736)
+ 1,568
The sensitivity of the project to errors in the estimates can now be assessed as
follows:
Income. The project would cease to have a positive NPV if income is below the
estimate by more than:
1,568
22, 304
= 0.070 or 7.0%.
Running costs. The project would cease to have a positive NPV if running costs
are above the estimate by more than:
1,568
12,736
= 0.123 or 12.3%.
An assessment of risk and uncertainty could then be made on the basis of the
likelihood that income will fall below estimate or running costs will increase above
the estimate by more than these amounts.
1.5 Risk modelling
The risk in an investment can be assessed by constructing a ‘model’ for the
investment, and then considering possible variations in the possible outcomes.
For capital investment appraisal, a risk model might be constructed using a
spreadsheet.
Having constructed the model, the risk in the investment can be assessed by testing
different scenarios, such as delays in achieving the benefits from an investment, and
combinations of variations in costs and benefits.
Risk modelling can be used to consider any aspect of risk. One aspect of risk that
can be particularly significant for investment decisions by companies in certain
industries is fiscal risk.
1.6 Fiscal risk
Fiscal risk is the risk that after a capital investment project has been implemented,
the government might increase the rate of tax payable on the profits or cash flows
from the project. Higher tax payments could significantly affect the returns from a
project.