Corporate Finance - Appunti

RISK ANALYSIS, REAL OPTIONS AND CAPITAL BUDGETING

Sensitivity analysis, Scenario analysis and Break-even analysis – dealing with uncertain forecasts

In the scenario analysis I don’t change just one input (as in the sensitivity one), but more than one at the same time. Breakeven analysis is another approach in order to define some thresholds in order to keep a sort of margin of safety – accounting or financial breakeven.

SENSITIVITY ANALYSIS

Example

For this baseline it is possible to consider the revenues, the variable and fixed costs, depreciation, pretax profit, we can apply the proper tax rate, we can get the net profit and the cash flow. We have all the figures to get the typical NPV calculation: we start from the initial investment and we discount for 5 yrs – discount factor, the result is positive, it seems to be attractive. In this calculation the first line is revenues, how many variables can affect it? 53

Just for the first line of the cash flow we have three

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What does sensitivity analysis tell us?

What happens in the future in your project is just a big difference with what you forecasted. When forecasting, anything is reasonable, but it can be too optimistic or too pessimistic, but it is not about being right or wrong, it is about

trying to get the best results. In our table we have just two negative NPVs and the majority is positive: probably the project is nice, and vice-versa – the project is not so attractive, or you calculated something in a non-accurate way.

What can you get?

1. If the project is valid
2. Additional info, not just one NPV and streams of cash flows

Weaknesses: you can make mistakes even in your assumptions (in the range for the ex.), and at the same time you have to think that you did the best you could. Moreover, another weakness is that you treat each variable in isolation, but in reality, more things can happen at the same time. Some of these inputs are correlated to each other so it is easier to point out the effect of the same variable if the whole system is taken into consideration.

SCENARIO ANALYSIS

Assume market size is 70 per cent of expectation = 7000

Assume market share is 2/3 of expectation = 20%

Example 55

BREAK-EVEN ANALYSIS

ACCOUNTING FINANCIAL

Find input value for a break-even profit over life

Find input value for a zero NPV.project. Investments should have a positive NPV – the Investments shouldn’t make a loss company is the sum of many projects, so the analysis you can do for one project you can do for the whole.

Why accounting and financial managers looks at the break-even point? Because it is a warning, a threshold: we are not really sure about the future, but we are sure to calculate some thresholds – if the market will be booming, we will go over the breakeven point.

Volume = # of output, machine, … - we can give a sum of the production of the company

1. Revenues = the unit price is fixed

The more I produce the more I gain. If I work in a profitable company I imagine that the

2. variable costs will be lower than the revenue; we also have
3. fixed costs that don’t depend on the output – whether you produce or not you have to pay in any case.

The company has to pay variable costs when it starts to produce, but even if it doesn’t

produce it has to payfixed costs – (4) net present value of tot costs.

56Monte Carlo simulation – random samplingMethod to get esteem through a huge number of simulations that are needed to measure a huge amountof cases. It generates random numbers that have no correlations.Example – see the slides

Real options – the option to expand; the option to abandon; timing optionsReal vs financial options – the latter is a financial tool that you can buy and sell; a real one is something thatis intrinsic, linked to some investments,A real option is an option to adjust operations once a project has started, and there are three types ofthem: the option to expand; the option to abandon; timing options.

When I start a project and I can make some adj in progress is a matter of future flexibility which has a value,and through the real option I can give such value – flexibility sometimes can be also improvement. Withouta real option, projects seem to be not enough

In any case, there is a negative attitude toward risk. However, without risk there is no "party".

Return: something coming back - it is the money that I can gain or loss over a period of time. I have to do something (investment) in order to get something back (money). Return needs to be started in order to receive something back. In corporate finance there are two main pov:

• Monetary return - it is a subtraction, a difference. I put money in the investment, and I try to get more that I put, which is a gain. This is in terms of money. It is over a period of time, for ex. I invest and I want to know the return after one year. Subtraction between cash in and cash out.
• Relative return - it is a division, a fraction. This is in terms of numbers, percentage. Fraction between the cash in and the cash out.

Monetary return: If I have to invest in stock, I expect to receive two kinds of returns: the one coming from dividend income and one from capital gains. Am I forced to sell the stock?

using the same approach so they are on the same line.

Example 60Percentage return

Example Holding Period Returns – measuring Stock Market performance

Two assumptions:

• It is total return
• It is all the money invested initially has to be left inside, and everything you get and loose each year have to be included

This was a typical financial crisis. Problem of the real economy can affect the financial stability.

61We can get a useful conclusion in terms of what is happening in the stock market: figures regarding performance, annual return looking at the index market.

Ex. Netherlands – in the first year investing in there means getting 25%, the years after it decreased. 2007 was the starting of the decline, and in 2008 it reached its apex.

Chiedi Return statistics If I apply this formula to the above graph, the mean will be something between 0 and 5. Here we are talking about arithmetical mean, which is different from the geometrical one:

1. They are not so different
2. They give two different messages

They are uses for two different purposes

Arithmetical mean is useful ex-ante, the message that it provides is: what is the most frequent thus the most probable return I can forecast by looking to what has happened so far I the last x years. I consider it more probable bc I saw that it was most frequently repeated. The geometrical one is useful ex-post: if I have invested in just an ITF in the Dutch market and I stay invested for 3 years what will I get?

COMPOUND ANALYSISà 62

Average Stock Returns and Risk-free Returns – Risk Premiums and Risk-free Rates

Do you think that we can have around us activities that have zero risk? No, everything has a risk different in size. However, we have to be practical and imagine that there are some activities with such low risk that we can consider them to be risk-free. Why do we introduce the free risk? Bc if we want to compare return with risk, we have to measure such risk. When we make a measurement, what we do is to take a sample, a meter, and

You compare something to it, but how can we do it with risk? The international community decided that the lowest risk activities can be the financial instruments issued by governments. We can measure a risky asset comparing the performance of such risk assets to the performance of a low risk one.

Government bills [BOT] – shorter maturity, within one year. We prefer to use government bills because we give up the risk coming from time.

Government bonds [BTP] – usually 5 yrs. For long-term investments, it is better to use government bonds of the same duration.

Any kind of negotiation, investment has two kinds of risk:

• Risk coming from activities, time, value coming from time
• The counterpart risk

In Italy, the difference between equity premium and government bills is 6%, that means