Investment appraisal Flashcards
Accounting rate of return
You’re looking at the project not the company.
Average annual profit of the project / Av investment x 100
Average annual profit =
(Total net cash flows - total depreciation) / Length of project
Average investment
(Initial invetsment + scrap value) / 2
Cash flows + Accounting adjustments =
Profit
Advantages of ROCE
Advantages
It is simple to calculate
As a percentage the measure is familiar to non-accountants
It looks at the entire project
It reflects the way external investors judge the organisation
Disadvantages of ROCE
Disadvantages
No account is taken of the project life
No account is taken of the timing of the cashflows/it ignores the time value of money
The result may vary according to the accounting policy used
It may ignore working capital
It does not measure absolute gain
It does not give a definite decision
A relevant cost is defined as a future incremental cash flow. In other words for a figure to be relevant it must pass three tests:
(1) Future
– A decision being made today cannot change the past and so only future costs are considered.
– Past costs are sometimes referred to as sunk costs and are not relevant and so are
ignored e.g. the price paid for something which is already owned.
Incremental
– Only those costs that are affected by the decision are incremental and therefore relevant.
– Costs that are sometimes referred to as committed costs and are not relevant and so are ignored e.g. unavoidable fixed costs.
– Businesses need to consider lost opportunity costs (revenue / contribution lost from diverting resources away from an alternative use), which are also relevant. Commonly the diverted resources are labour and materials. The diagrams below are useful to help determine the relevant cost in these situations:
Cash flows
– These are factual and not based upon accounting conventions. Also organisations live or die due to their cash position. So non-cash flows are not relevant e.g. depreciation.
Perpetuities
Some annuities last forever, these are called a perpetuities.
How to calc deprival value?
Lower of Replacement cost and the higher of either NRV and VIU
Advantages of payback
Advantages
It is simple to calculate
It is easy to understand, especially for non-accountants
It uses relevant cash flows
It can be used as an initial screening tool on projects before undertaking a more detailed review
It (rather crudely) allows for risk
Disadvantages of payback
Disadvantages
It ignores returns after the payback period
It ignores the timing of the cash flows
It does not give a definite decision
It ignores project profitability
what is the calc for present value?
PV = FV × (1 + r)–n
Advantages of IRR
Advantages
It allows for the time value of money
It uses cash flows not profits
It does not require the exact cost of funds to be known
As a percentage, the measure is familiar to non-accountants
It looks at the entire project
It provides a relative measure of performance
Disadvantages of IRR
Disadvantages
It is not an absolute measure
Interpolation provides only and estimate and an accurate estimate requires the use of a
spreadsheet programme
It is fairly complex to calculate
Non conventional cash flows may give rise to multiple IRRs
It contains the inherent assumption that cash returned from the project will be re-invested at the project’s IRR which may not be true
The relationship between real and nominal interest rates is:
(1 + i) = (1 + r) × (1 + h)
Real rate
(excludes inflation, compensates the lender for the time value of money)
Nominal rate
(includes inflation, compensates the lender for TVM and inflation)
In choosing which rate to use we must be consistent:
If the cash flows exclude inflation (‘real’ cashflows) then so must the discount factor (‘real’ rate)
If the cash flows include inflation (‘nominal’ or ‘money’ cashflows) then so must the discount factor (‘nominal’ rate)
In the exam you may need to add inflation into the cash flows if you are using the ‘money/money’ approach, or remove inflation from the cash flows if you are using the ‘real/real’ approach.
Risk is when
there is a range of possible outcomes and the likelihood of those outcomes can be quantified in the form of probabilities.
Uncertainty is when
there is a range of possible outcomes, but the likelihood of the outcomes cannot be quantified
As a project’s life increases it becomes harder to quantify the likelihood and so the outcomes are more likely to be uncertain. There are a range of techniques to deal with both risk and uncertainty in project appraisal
When calculating the sensitivity for a particular cash flow the following formula is used:
NPV / NPV of required variable
When calculating the sensitivity to the cost of capital, the following formula is used
IRR - Cost of capital Cost of capital
× 100%
Advantages of sensitivity analysis
Advantages
Simple
Provides more information to allow management to make subjective judgements
Indicates which forecasts should be researched further
Indicates which variables require the closest control once the project starts
Disadvantages of sensitivity analysis
Disadvantages
Assumes variables change independently of each other
Does not assess the likelihood of change
Does not lead to a definite decision
Probabilities - If you want the probability of X ANd Z you?
If you want the probability of X OR Z you?
Multiply
Add
The usefulness of probability analysis in assisting investment decisions is
It allows us to evaluate risky investments
It allows us to quantify the risk
The limitations of using probability analysis are
Expected values are not meaningful in one off decision making situations since they represent a long run average value. Take the example above, achieving sales of $510k will not happen (it will either be $600k, $500k or $400k) in an individual year. Hence, expected values are more appropriate for assessing decisions or cashflows which will be repeated.
Expected values ignores the spread of possible returns (i.e. risk), as they average the outcomes. A separate measure is needed to show the spread of possible returns (such as the standard deviation or simulation).
Expected values rely on the accuracy of the probabilities used
Risk-adjusted discount rates
As we have already seen the discount factor reduces the future cash flows to allow for the time value of money.
As the future cash flows also contain risk, the discount factor can be adjusted to reflect this risk. So a project with more risk would have a higher discount factor applied to it and so the NPV would be reduced to reflect this risk.
Adjusted payback
The adjusted payback (also known as discounted payback) involves adjusting the cash flows in the payback calculation to take account of the risk.
In practice this means reducing the future cash flows to reflect the risk in the estimated figures. As forecasting is generally harder the further into the future you predict, the reduction needs to be greater for more distant figures
Asset replacement decisions using equivalent annual cost
Sometimes an investment decision will involve choosing between two alternatives where the benefits are unequal e.g. comparing renting one property for five years and an alternative for seven years.
Equivalent Annual Cost =
NPV / Annuity factor for project life
The EAC represents a
constant annual cashflow that has the same present value as the actual cashflows arising under each proposal. The proposal with the lowest EAC should be chosen
PV of annuity =
Annuity X Annuity factor
EAC =
Annuity
Single period capital rationing describes
the situation where an organisation does not have sufficient funds to undertake all positive NPV projects at one particular point in time
Profitability Index (PI)
Net present value / Initial Investment
Capital rationing can be caused by two different reasons:
(1) The organisation would like to raise more funds, but no stakeholder is prepared to invest. This is known as hard capital rationing and may result from the potential returns not being high enough to compensate for the perceived risks involved.
(2) The organisation could raise more funds, but has internally decided not to. This is known as soft capital rationing and may result from a concern that the available finance is too expensive or may result in a loss of control.
