Fin management materials / 4 P4AFM-Session06_j08

SESSION 06 – ADVANCED INVESTMENT APPRAISAL

4MODIFIED INTERNAL RATE OF RETURN

¾Traditional Internal Rate of Return has a major limitation as it implies that the cash flows from a project can be reinvested at the IRR itself. This may be an over-optimistic assumption, particularly when the IRR is significantly higher than the firm’s hurdle rate i.e. WACC.

¾Modified Internal Rate of Return (MIRR) overcomes this problem and assumes that the cash flows arising from a project (excluding the initial investment) are reinvested at the firm’s hurdle rate.

¾Method of calculation:

Each annual cash flow is projected forward at the firm’s hurdle rate to obtain a terminal value at the end of the project

Example 3

A project has the following forecast cash flows:

The firm’s cost of capital is 8%.

Required:

Estimate the MIRR.

Solution

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SESSION 06 – ADVANCED INVESTMENT APPRAISAL

5ANALYSING PROJECT LIQUIDITY

5.1Traditional Measures

¾Traditional measures of project liquidity have significant weaknesses:

Payback period: ignores the time value of money and ignores cash flows beyond the payback date

Discounted payback; takes into account the time value of money but still ignores post-payback cash flows

¾Clearly there is a need for measures which take into account cash flows over the whole life of the project.

5.2Project Recovery

¾Recovery period is the number of years required to recover the initial investment, taking into account the time value of money.

¾Unlike discounted payback, the calculation of recovery takes into account cash flows over the whole life of the project.

¾However recovery period assumes that project returns are generated at a constant rate over the life of the project. This weakness can be resolved by calculating project duration.

5.3Project Duration

¾Duration measures the time over which half of the project’s returns are generated. Method:

Calculate the present value of each future cash flow

Express each year’s discounted cash flow as a proportion of the total present value of the project’s returns.

Multiply each proportion by the relevant year

Sum the weighted years

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SESSION 06 – ADVANCED INVESTMENT APPRAISAL

Example 4

A project has the following forecast cash flows:

The firm’s cost of capital is 8%

Required:

Estimate:

(a)project recovery period

(b)project duration

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SESSION 06 – ADVANCED INVESTMENT APPRAISAL

6ANALYSING PROJECT RISK

6.1Use of simulation

¾Traditional sensitivity analysis can be used if one project variable changes independently of all others. However, some project variables may be interdependent e.g. costs and market share.

¾Simulation is a technique which allows more than one variable to change at the same time.

¾One example of simulation is the “Monte Carlo” method. Calculations will not be required in the exam, an awareness of the stages is sufficient.

6.2Stages in a Monte Carlo simulation

(1)Specify the major variables.

(2)Specify the relationship between the variables.

(3)Attach probability distributions (e.g. the normal distribution) to each variable and assign random numbers to reflect the distribution.

(4)Simulate the environment by generating random numbers.

(5)Record the outcome of each simulation.

(6)Repeat simulation many times to obtain a frequency distribution of the NPV

(7)Determine the expected NPV and its standard deviation.

8It is not a technique for making a decision, only for obtaining more information about the possible outcomes.

8It can be very time-consuming without a computer.

8It could prove expensive in designing and running the simulation, even on a computer.

8Simulations are only as good as the probabilities, assumptions and estimates made.

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SESSION 06 – ADVANCED INVESTMENT APPRAISAL

6.5Value At Risk (VAR)

¾VAR gives an indication of the potential loss which is likely to occur at a given level of confidence

Project VAR = N(confidence level) × s × √T Where:

N(confidence level) is the number of standard deviations from the mean for the given confidence level (extracted from the normal distribution tables)

s is the annual standard deviation of the project’s returns

T is the number of years of the project.

Example 5

Monte Carlo simulation has produced the following output for a potential 10 year project:

¾Expected NPV $1.964m

¾NPV volatility $1.02m (annual standard deviation)

Required:

(a)What is the probability that the project will produce a negative NPV?

(b)What is the Value At Risk at the 95% and 99% confidence levels?

Solution

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SESSION 06 – ADVANCED INVESTMENT APPRAISAL

6.6Stress Testing

¾Stress testing is designed to test the sensitivity of a project’s value at risk under the worst set of outcomes that can reasonably be expected to occur

¾This requires a careful evaluation of the worst possible outcomes – possibly by looking at the response of the model to extreme external events e.g. major currency or interest rate changes.

Key points

Traditional NPV calculated using WACC does not deal well with a project whose finance significantly changes the firm’s capital structure.

In this situation it is preferable to use APV which splits the operational side of a project from its financing implications and values each separately before finding the overall impact of the project with the proposed financing.

Multi-period capital is where cash for investment is a limiting factor in several years. In this case it is necessary to formulate a linear programming model and solve graphically.

Traditional IRR assumes that project cash flows can be reinvested at the IRR itself – often an optimistic assumption. Modified IRR makes the more realistic assumption that cash flows can be reinvested at the cost of capital.

Various measures of project liquidity can be calculated - listed in order of increased usefulness – payback, discounted payback, recovery and duration.

Project risk can be modelled using Monte Carlo simulation, the results of which can then be used for VAR analysis.

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SESSION 06 – ADVANCED INVESTMENT APPRAISAL

FOCUS

You should now be able to:

¾calculate the APV of a project to account for its financing side-effects;

¾discuss the application of Real Options Pricing Theory in finding the full strategic value of a project;

¾deal with both single period and multi-period capital rationing;

¾calculate MIRR as a more realistic measure of project return than traditional IRR;

¾calculate measures of project liquidity and project risk.

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EXAMPLE SOLUTIONS

Solution 1

Firstly identify the operating cash flows:

(a)Current WACC

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SESSION 06 – ADVANCED INVESTMENT APPRAISAL

(c)Adjusted present value approach

Step 1 Calculate “base case” NPV

17,883

_______

Net of tax costs

(discounted at risk-freerate)=$17,883− 35%×$17,883 1.1

= $12,193

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