Download Free cash flows of equity (FCFE)

P4 Advanced Investment Appraisal
Section C: Advanced Investment Appraisal
Designed to give you the knowledge and application of:
C1. Discounted cash flow techniques and the use of free cash flows.
C2. Application of option pricing theory in investment decisions.
C3. Impact of financing on investment decisions and adjusted present
values.
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C1: Discounted cash flow technique and the use of free cash flows
Learning Outcomes

Capital Investment Appraisal using NPV

Capital Investment Appraisal using IRR & MIRR

Forecast a company’s free cash flow and its free cash flow to equity (pre and post
capital reinvestment).

Specified capital investment programme, on a firm's current and projected
dividend capacity. [3]

Value of a firm using its free cash flow and free cash flow to equity under
alternative horizon and growth assumptions. [3]

Application of Monte Carlo simulation to investment appraisal. Demonstrate an
understanding of:
i. simple model design
ii. types of distribution controlling the key variables within the simulation
iii. simulation output and assessment of the likelihood of project success
iv. measurement and interpretation of project value at risk
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Cash flow (CF) analysis & free cash flow concept
Important in
investment
analysis
Free cash
flows of firm
(FCFF)
Profitability of investment projects
determined by evaluating CF
Estimation of CF
 FCFF are the cash inflows, net of capital expenditure
 CF available to service shareholders and lenders
 CF should be discounted to ascertain a project’s NPV
Free cash flow = Revenues – Operating – Taxation – Capital + Depreciation and
of Firm (FCFF)
expenditure
expenditure
Amortisation
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+/- Changes in
working capital
Net present value (NPV)
NPV = Present value of cash inflows
less
Present value of cash outflows
A positive NPV would indicate a potential increase in the value added to the firm if a
specified project or portfolio of projects is undertaken.
Accept / Reject criteria for a project
NPV > Zero
Accept Investment
NPV < Zero
Reject Investment
NPV = Zero
May Accept Investment
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Taxation effects of the relevant cash flows
1. Operating cash flows
Refers to revenue expenditure or income affecting operating profit
Revenues
(inflows)
Expenses
(outflows)
increase profits, resulting in tax
increases shown as cash outflows
reduce profits, resulting in tax savings
shown as cash inflows
2. Capital cash flows
Capital allowances
Disposal of assets
allowable against profits
resulting in tax savings shown
as cash inflows
Balancing allowance / charge
profit on disposal
loss on disposal
tax payment
tax relief on disposal
3. Timing
The local tax laws define the period the tax flows relate to
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Linear programming approach to multi- period capital rationing
Multi-period capital rationing arises when there is more than one cash outflow and these
cash outflows arise in different time periods for different projects.
 Firm objective is to choose that package of projects which gives the maximum total
NPV subject to the capital constraints.
 As the number of alternatives and constraints increase, the decision-making process
becomes more complex.
 Use of a mathematical programming method is recommended.
Linear programming (LP) is a mathematical technique used to arrive at the optimal
production plan & optimal resource allocation with an objective of cost minimisation and
profit maximisation.
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Internal rate of return (IRR)
Internal Rate
of Return
(IRR)
It is the required rate of return or cost of capital which
produces an NPV of zero when used to discount the project’s
cash flows.
Present value of cash inflows = present value of cash outflows
Situations for the calculation of IRR
When the project cash
inflows are identical
When the project cash
inflows are not identical
Continued …
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Continued …
Calculation of IRR when the project cash inflows are identical
Factor / Payback =
cash outflow
annual cash inflow
.
Go across the row of the year (equivalent to the life of the project) of the table of
cumulative present values and find the closest figure to the factor as calculated above
The corresponding rate of that figure is the IRR
Criteria:
IRR ≥ minimum desired rate of return, the investment project should be accepted.
IRR < desired rate of return, the project should be rejected.
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Calculation of IRR when the project cash inflows are not identical
Calculation of IRR when the project cash inflows are not identical
 In such a situation, the interpolation method is to be used.
 The NPV at two discount rates will be required (preferably a positive and negative NPV).
 A  x b - a %

A
B


IRR  a  
Where
a is lower of the two rates of return used
b is higher of the two rates used
A is NPV obtained using rate a
B is NPV obtained using rate b
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Modified internal rate of return (MIRR)
Modified Internal
Rate of Return
(IRR)
Discount rate that equates present value of the terminal cash
inflow to the initial investment in year zero
n
MIRR =
Terminal value of cash flows
--------------------------------------------------- - 1
Present value of investment outlay
n
Terminal Value = ∑ CFt (1+r) n-t
T=0
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Discount rate is IRR
Find discount rate that equates terminal
value to initial investment outlay
Calculate terminal value of project cash flows
using reinvestment rate / cost of capital
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1
Free cash flow of equity (FCFE)
Cash surplus generated by a firm which is available for
reinvestment or redistribution
Free cash flows of
equity (FCFE)
FCFF
Revenues
Less: Operating expenditure
Less: Taxation
Less: Capital expenditure
Add: Depreciation & amortisation
Add / (Less): Changes in working capital
X
(X)
X
X
(X)
X
FCFF
X
FCFE
Net income after taxation
Less: Capital expenditure
Add: Depreciation & amortisation
Add: New debts issued
Less: Debt repayments
Add / (Less): Changes in working capital
X
(X)
X
X
(X)
X
Less: Preference dividends paid
FCFE
(X)
X
Refer to Example (page 195)
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Advise on a specified capital investment programme a firm’s current &
projected dividend capacity
Function of free cash flow to equity
(FCFE)
Dividends
Other than FCFE, reasons: future
investment requirements, stability
requirements, taxation, etc.
Excess cash flow after all positive NPV can be:
 Distributed in large cash dividends to shareholders
 Share purchase schemes; or
 Higher level of gearing which increases interest payments and
reduces discretionary cash flow
Formula
Dividends + Equity repurchase
Cash to shareholders: FCFE ratio =
FCFE
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Valuation of a firm using free cash flow
Value of a firm is the discounted value of future cash flow available for payment as
dividend / for investment
FCFF at constant rate
FCFF0 (1 + g)
Vo = ------------------------Re – g
Where Vo = Value of the firm
Re = Expected rate of return
g = Expected growth rate
Terminal values- FCFF growing at a rate higher than the growth rate of economy
n
V0 = ∑
T=1
FCFFt (1 + g)
Terminal value of business
---------+ ---------------------------------------(1 + Re) t
(Re - g)
Where Re is the cost of capital
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Valuation of a firm using free cash flow to equity
Value of equity is the discounted value of future cash flow available for payment as
dividend / for investment
FCFE at constant rate
 Formulae remains same as value of firm.
 Use FCFE in place of FCFF
Terminal values- FCFE growing at a rate higher than the growth rate
 Formulae remains same as value of firm.
 Use FCFE in place of FCFF
Refer to Example (page 197)
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Monte Carlo simulation
Assessment of risk is important & must be incorporated in the investment appraisal
process. Cash flows can vary due to risks. Statistical tool of simulation can be applied to
measure such risk.
Simulation - quantitative procedure used to describe a process by developing a model of
that process, and then conducting a series of organised experiments to predict the
probable outcome of that process.
Technique of spread sheet simulation
Monte Carlo simulation
Used to calculate the NPV from a
combination of economic variables
which affect the NPV calculation
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Steps for adjustments
Market factors
Investment
cost factors
1. Select on observation from each factor
2. Assign probability values to factors
3. Generate random numbers for each factor
4. Calculate NPV by electing value of each factor
corresponding with random number
5. Repeat process several times (process is called
iteration)
6. Will generate probability distribution (PD) of NPV
7. Plot PD of NPV on a graph
Continued …
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Operating &
fixed cost
factors
Continued …
Significance of
simulation
output
Standard deviation
Used to measure risk of
projects
Expected net present
value (ENPV)
Weighted average of
returns where probabilities
of possible outcomes are
used as weights
 Process of iterations gives range of outputs.
 If number of iterations is large, outputs follow a normal probability distribution.
 Normal probability distribution can be used to further analyse the risk in the
investment appraisal process.
 Normal probability distribution is a symmetric, continuous bell-shaped curve
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Project value at risk (project VaR)
Project VaR measures the potential loss in the value of a project over a defined period for
a given confidence level
Used by management in decision
making
signifies maximum amount by which
the actual NPV of a project will be
lower than its expected NPV
Project VaR = Z x  x T
Where:
Z is the standard normal variable
 is the standard deviation
T is the time period over which the value at risk will be calculated.
Usefulness of VaR
Project VaR can be used by the management of a company to decide
whether to accept or reject a particular investment project taking into
account the expected NPV and the risk.
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Recap

Capital Investment Appraisal using NPV

Capital Investment Appraisal using IRR & MIRR

Forecast a company’s free cash flow and its free cash flow to equity (pre and post
capital reinvestment).

Specified capital investment programme, on a firm's current and projected
dividend capacity. [3]

Value of a firm using its free cash flow and free cash flow to equity under
alternative horizon and growth assumptions. [3]

Application of Monte Carlo simulation to investment appraisal. Demonstrate an
understanding of:
i. simple model design
ii. types of distribution controlling the key variables within the simulation
iii. simulation output and assessment of the likelihood of project success
iv. measurement and interpretation of project value at risk
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