Applied Corporate Finance. What is a Company worth?

CRITERIA FOR THE ANALYSIS OF INVESTMENTS

Investments can be considered under a series of criteria:

• Return

• Consideration of risk

• How difficult it is to finance the project

• Safety considerations

• Convenience of completing a series of projects

• External image

• Etc

Therefore, the return is not the only criteria for valuing an investment. In this section we will focus exclusively on the criteria of return as it is present in every analysis of investments. In general it is the most determining.

In no way is the matter trivial. Furthermore, to be able to deal with the question straightforwardly we are going to create a world of certainties: we assume all forecasts will be true. At the end of the section we introduce the impact of the inflation.

Another way to make the subject easy to understand is avoiding unnecessary mathematics, such as equations and formula. The quantitative concepts dealt with are illustrated using numerical examples in the most straightforward way.

PROJECT DEFINITION

An example:

The following example helps to understand the concept. We will consider the choice between two investment projects, set out below:

Cash necessities, debtors and stocks that must be financed. These are investments in working capital made necessary by the project being put into operation. They will be net as some financing may be provided spontaneously (suppliers, etc.), by the project

To simplify the matter and isolate the return as much as possible, we will suppose that the duration of 5 years is pure: there is no residual value and after 5 years the Project is abruptly stopped, recovering the money invested in working capital (stocks are sold and debts received, etc.)

Our question is which of the two projects is most attractive in terms of return? Which has the highest return?

PROCEDURE TO MEASURE RETURN

SIMLE RETURN ON INVESTMENT

This is defined as the percentage given by the net profit divided by the total investment total. It is a simple and intuitive measure of the return. For both of our projects it will be the same in both cases:

Net profit: 14,000 €

Total investment: 100,000 €

Simple rate of return: 14%

In the example of our projects, the calculation is simplified because we assume the annual profits remain constant over the project’s life. When this is not the case, the simple return is usually calculated using the average annual profit foreseen for each of the years of the project life. Naturally, when the profits foreseen are constant, the average coincides with the estimated annual profit.

A concept slightly different to simple return is to consider the investment not as the total amount committed to the project, but rather the average accounting value of the amounts tied up every year, obtained by subtracting the corresponding amortizations from the initial investment.

Project A gives us the following data:

We subtract from the 80 original the amortization of 16 for every year that goes by(80/ 5= 16)

Average Investment 52

Average return on investment: (14 / 52) * 100 = 26, 92%

FIRST CONSIDERATIONS ON OTHER METHODS : CALCULATION OF CASH-FLOWS

According to the Simple rate of return on Investment, both projects are equally enticing as both of them offer a net profit of 14,000 x 5 years = 70.000 €. Having come this far, perhaps we should ask if any reason intuitively makes us prefer one project over another.

We could try to answer this question looking at it this way:

We agree the two projects produce 70, 000 €, made up of 14,000 € each year. However, when is the company really going to receive these profits in the books? Looked at in this way, the two projects are no longer the same.

If the reader does the exercise of checking the money flow of funds in each of the years, they are seen to be the following (1):

(1) Remember that amortization is an expenditure that does not mean the paying out of funds. Another factor is that the necessities of investment in Working capital are constant until the end of the life of the projects, when we suppose that the Working capital is settled (suppliers pay) and becomes money

We can see that the net Flow of funds over the life of the projects coincide with the total accumulated profits. From this point of view, the two projects give the same return. However, the Flows of funds shows that in project A the cash return come earlier than in project B. As the investor has the cash earlier, they can then obtain an interest from it and this makes project more desirable.

This advantage of project A is not revealed by the simple rate of return. In the following section we will analyze other methods for measuring the rate of return.

THE PAY BACK PERIOD

Sometimes this is calculated by dividing the total investment by the annual profits. This gives the number of years that are needed for the accumulated profits to compensate the initial investment. In stock market circles this division is called PER – Price earnings rate).

We can see that the payback period calculated in this way is the reciprocal of the simple rate of return (i divided by). However, though this formula is sometimes used for rapid calculation, it does not really always make too much sense. To realize this, it is necessary only to see that in our projects the period is 100/ 14 = 7,14 years, which is longer than the real life of the projects.

The correct way to calculate the payback period for the investment in a project is firstly to work out the Flow of funds and then calculate the time when the in-flows have returned in full the initial outlay.

Working in this way from the Flow of funds for the projects in our example, set out in the previous table we can see that the pay-back for project A is 3 years 4 months and for project B it is until the end of the 5th year, moment in which the Working capital is liquidated and the initial 100, 000€ invested are recovered.

Therefore the payback period for project B is 5 years.

We can see that when the pay-back period for an investment is correctly calculated it automatically classifies the two projects in the correct order.

However, the greatest objection to this method is that it does not take into account the flow of funds once the investment is paid back. If , for example, we consider a project c with the same Flow of funds as project b in the first five years, but which has a sixth year with a very high return (let’s say 500,000 €), it is obvious that project c is superior to project c. nevertheless, the pay-back analysis would rate project A (pay back period only 3,3 years) as project c and project b has a payback period of 5 years.

NET PRESENT VALUE METHOD (NPV)

The present value method tries to overcome the mentioned difficulties of working with Flows of funds. It considers the total Flows of funds.

The basic idea of the method is comparing amounts of Money at different points of time, using the interest obtained from investing or depositing this Money. For example, if the interest rate available is 10%, we believe having 1 euro in our pocket today is the same as having 1,10 euros in our pocket one year in the future. In the same way, we must state that one euro in our pocket today is the same as having received 1/1,10= 0,91 euros one year ago or 0,91/1,10= 0,83 euros 2 years ago.

When we express various flows of funds foreseen in the future calculated using this technique, and we give their value today, working with a defined interest rate – called the discount rate – the process is called discounting flows", or valuing them in today’s terms.

This means that we can express all the flows in currency units of today and we can operate with them (for example sum them).

For this affirmation to be strictly true we must have available the alternative of investing the Money at 10% and this is the unique alternative for any amount of Money available.

If this hypothesis is accepted as true, or in great part, we can transfer the Flows of funds of a defined project into incomes and outgoings of Money all of them realized now, in the present.

We will illustrate this taking project A as an example:

Therefore, Project A is the equivalent of investing 100 and in the same moment receiving:

27.27 + 24.79 + 22.54 + 20.49 + 31.05 = 126. 14

(These figures are in thousands of euros : 126,140 €, after investing 100,000€)

This means a gift of 26,140 euros. This amount is known as the net present value of the Project, a name that comes from the simple fact that accepting the hypothesis of the alternative investment with an interest rate of 10%, the opportunity to carry out Project A turns out to offer a gift of 26,140 €.

The net Present value is therefore a clear intuitive indicator for selecting projects. If the net Present value is the gift , the larger the gift , the better the project.

The Present value of Project A, at a rate of 10% is 26,140 €, as we have calculated before. Project B’s NPV is 17,900 €, and this is because the Project is not so attractive .

Here the method has been explained through an example.

The procedure to calculate the Present value is always following the same four steps:

1-Calculate the Flows of funds

2-decide what is the alternative interest rate available (1)

3- Divide all the incomes and expenditures by one plus the chosen interest rate to the power of the number of years that separate this flow from now (moment zero).

4-add up or subtract the resulting amounts according to their respective signs ( they are now homogeneous as they are all expressed as present values, their current value)

(1)The election of the discount rate is a well-discussed financial question, beyond the scope of this guide. It is very common to use the average cost of capital to finance all the projects. This could be considered as an alternative interest rate because it represents the interest saved at the average rate. The concept of the cost of funds used to finance the company is complicated in its own right and even more so because of the cost of capital. Later on in this guide, we will go in to this thoroughly.

INTERNAL RATE OF RETURN , IRR

If the interest rate used in the calculation of the Present value of a certain project is increased, the present value decreases.

The value that makes the net Present value of a Project zero is called the internal rate of return.

Calculating it is quite tedious, however simple the project may be. Today there are powerful calculators and spread sheets that easily calculate the IRR for any type of project.

For our Project A, the IRR is 19 %. With this internal rate of return, the net present value of the different flows is zero:

NET PRESENT VALUE: -100+ 25.2 +21.2+17.6 + 15 +21 = 0

If the Present value is equal to zero, the Project is no more or less attractive than the alternative interest rate. This is why the alternative interest rate (which makes the Present value equal to 0) is called the project’s internal rate of return.

RELATIONSHIP BETWEEN THE PRESENT VALUE AND THE IRR

Before we said that as the interest rate employed in the calculation of the Present value is increased , the latter falls. This relationship may be expressed graphically in the diagram, drawn up with the figures of project A.

In the diagram we have presented the Present value with the interest rate of 10%, which gives a value of 26,140€, and at the interest rate of 19% the Present value is zero (and this is the internal rate of return).

The slope of the graphic clearly shows that while the discount rate applied to a project is less than the internal rate of return, the Project’s present value is positive and vice versa.

This shows that the decision as to whether a Project should go ahead is always the same under the Present value and the IRR criteria. If the Present value is positive, the