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ACCA P4 course notes

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Having studied this chapter you will be able to:
Evaluate the potential value added to a firm arising from a
specified capital investment project or portfolio using the net present value model. Project modelling should include explicit treatment of:
(a) Inflation & specific price variation
(b) Taxation including capital allowances and tax exhaustion
(c) Single & multi-period capital rationing to include the formulation of programming methods and the interpretation of their output
(d) Probability analysis and sensitivity analysis when adjusting for risk and uncertainty in investment appraisal
(e) Risk adjusted discount rates (covered in chapter 7)

Outline the application of Monte Carlo simulation to investment appraisal. Candidates will not be expected to undertake simulations in the exam but will be expected to demonstrate understanding of
(a) simple model design
(b) the different types of distribution controlling the key variables in the simulation
(c) the significance of the simulation output and the assessment of the likelihood of project success
(d) the measurement and interpretation of project value at risk Establish the potential economic return using IRR and modified IRR & advise on a project’s return margin. Discuss merits of NPV & IRR.

Discounted cash flow techniques are also extensively examined in the context of business valuations (business valuations are covered in chapters 9-12).

Slow Fashions
– 20 marks, June 09
Your business
– 28 marks, June 09
Seal island
– 24 marks, June
2010 Q1i,ii,iii


Internal rate of return is a discounted cash flow technique of a project that calculates the % return given by a project; accept the project if the IRR is > the cost of capital.


Step 1 ¬Ė calculate the NPV of the project at 5%
Step 2 ¬Ė calculate the project at 10%
Step 3 ¬Ė calculate the internal rate of return using the formula

IRR = a +



(you will need to learn the formula for the exam)


IRR assumes that the cash flows after the investment phase (here time 0) are reinvested at the project’s IRR. In the previous Lecture example the 20% IRR was approximate, on an excel spreadsheet the IRR is 21%. Here is the proof.

You are provided with a formula to calculate MIRR; in the formula below the return phase is the phase of the project from when cash inflows have commenced. PV return phase


Using the formula, MIRR is quicker to calculate than IRR, it makes a more realistic assumption about the reinvestment rate, and does not give the multiple answers that can sometimes arise with the conventional IRR.


The extent to which the MIRR exceeds the cost of capital is called the return margin and indicates the extent to which a new project is generating competitive advantage.


Before deciding to spend money on a project, managers will want to be able to make a judgement on its risk (predictable) and uncertainty (not predictable).

Expected values

Using probabilities to calculate average expected NPV.

Risk adjusted
discount factor

Using a higher cost of capital if the project is high risk, this is discussed in chapter 7.

Payback period

The quicker the payback the less reliant a project is on the later, more uncertain, cash flows.

Discounted payback

As above but uses the discounted cash flows and is a better method since it adjusts for time value.

Sensitivity analysis

An analysis of what % change in one variable (eg sales) would be needed for the NPV of a project to fall to zero.
Calculated as NPV of project / PV of sales (for example)


An analysis of how changes in more than 1 variable (eg earlier than expected competitor reaction and an adverse change in the exchange rate) may affect the NPV of a project

Project duration

A measure of how long it takes to recover approximately half of the value of the investment; it is calculated by weighting each year of the project by the % of the present value of the cash inflows recovered in that year.


A modern approach to quantifying risk involves estimating the likely change in the value of an investment by using the concept of a normal distribution.

The standard properties of a normal distribution curve can be seen by analysing the normal distribution table (given in the exam).


The value at risk in the above lecture example is the maximum likely loss over the next 24 hours (with only a 5% chance of being exceeded).


This can be illustrated as follows:

Value at risk can be quantified for a project using simulation to calculate the project’s standard deviation. In this context, the standard deviation needs to be adjusted by multiplying by the square root of the time period ie

95% value at risk = 1.645 x standard deviation of project x time period of the project

Technique demonstration

A four-year project has an NPV of $2m and a standard deviation of $1m per annum. Required
Analyse the project’s value at risk at a 95% confidence level.


Q7 Jonas


Where the assumption of a normal distribution is not appropriate, the risk of a project can be measured by simulating the possible NPVs and weighting the outcomes by probabilities determined by management. This could be used to assess the probability, for example, of a project’s NPV exceeding zero.

The value added to a firm from a capital investment project can be assessed using NPV.
Where inflation is present it is normally correct to inflate the cash flows and to ensure that a nominal cost of capital is used, the major exception is domestic projects where there is only one rate of inflation.
A cost of capital will be nominal because investors expect inflation, it only needs to be adjusted if a question states that it is real.

Where IRR is used, the problems with the reinvestment assumption mean that a modified IRR approach is normally a better measure of the economic return of a project. This involves compounding the cash flows after the investment phase at the firm’s cost of capital and then analysing the annual return given on the PV of the investment. Where risk is being analysed discounted payback period or project duration is a better way of assessing the reliance of a project on later cash flows. Value at risk is also a useful and commonly used risk measurement device.

Having studied this chapter you will be able to:
Apply the Black-Scholes option pricing model (BSOP) to financial product / asset valuation:
(i) Determine & discuss, using published data, the five principal drivers of option value (value of the underlying, exercise price, time to expiry, volatility and the risk-free rate)
(ii) Discuss the underlying assumptions, structure, application and limitations of the BSOP model Evaluate embedded real options within a project, classifying them into one of the real option archetypes. Assess, calculateand advise on the value of options to delay, expand, redeploy and withdraw using the BSOP model.

This chapter is most likely to be tested in numerical questions that ask you to value call and put options in a variety of different contexts.

Maximisation of shareholder wealth

Investment decision

Application of option pricing theory
Some investments offer flexibility or real options. Management need to be aware of these and can attempt to value them using the Black-Scholes option valuation model.

Financing decision

Dividend decision



Projects can be analysed to assess their value under different business scenarios.

Entraq plc is considering two proposals to invest in the manufacture of solar panels: Proposal A Рto build a customised plant with specialist staff in Cornwall, which can only be used to construct solar panels. This proposal would build Entraq’s profile in the solar panel industry. Proposal B Рto use more expensive machinery in Entraq’s existing premises in Basingstoke that could be adapted to produce components for the wind power industry. A general election is expected next year that will affect the likely growth of the solar panel industry. Required

Identify the real options present in these investments.

Proposal A

Proposal B


There are five main components to the value of an option. Here these are applied to an option to buy a share for £4 in 3 years time; the share price today is £5. (a)

Intrinsic value, the difference between
(i) the current value of the asset = share price e.g. £5
(ii) the exercise price of the option = option price e.g. £4


The time value of the premium, reflecting the uncertainty surrounding the intrinsic value between now and the exercise date. Relevant factors are:

variability in the value of the asset = standard deviation of the share time until expiry of the option = 3 years
interest rates = risk free rate


If you had been told that the time value of an option was £2, then the value of this share option would be £2 time value + £1 intrinsic value = £3. The full mechanics of the calculation of the value of options are covered below.


Technique demonstration

Project A has an NPV of ¬Ė ¬£10,000; it will also develop expertise so that Entraq would be ready to penetrate the European market with an improved product in four years’ time. The expected cost at time 4 of the investment is ¬£600,000. Currently the European project is valued at 0 NPV but management believe that economic conditions in four years’ time may change and the NPV could be positive. The standard deviation is 30%, the risk free rate is 4%% and the cost of capital is 10%.

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