1.7. PV calculation shortcut (2) – annuities

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Principles of Corporate Finance – A Tale of Value

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Moscow Institute of Physics and Technology

Principles of Corporate Finance – A Tale of Value

5 classificações

Curso 2 de 5 em Specialization Understanding Modern Finance

The study of Corporate Finance seems to be a very generic part of business education. Still, it either falls in the trap of intimidating formulas or is superficially journalistic. Both extremes preclude the understanding of the core finance ideas, concepts, and models. This Course is an attempt to avoid the above extremes. We discuss the core basis and mechanisms of modern corporate finance in a learner-friendly way. We will analyze the market’s most fundamental problems, realize the intrinsic interests and preferences of investors, reveal the true meaning of specific financial terms, and uncover important issues that are so often ignored in choosing and valuing investment projects. The learners will gain insight into the essence of corporate finance. They will be able to use the obtained knowledge and skills to successfully advance in their career at a financial institution, as well as in the area of financial management at non-financial businesses.

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Why Finance Matters? Net Present Value. How to Calculate NPV

In Week 1 we propose the game plan for our study of value. Then we analyze the key assumptions for the general valuation model. We focus on the understanding of the sources of value and the fundamental ideas of investor’s choice, the opportunity cost of capital, risk and return. We discuss the importance of time and expectations in determining value. Then we discuss the present value approach to studying the projects’ value and choice. We present the general PV formula and introduce the key concept of net present value (NPV) as a criterion of the choice of good investment projects. Then we study some most widely used shortcuts and apply the formulas to find the NPV’s of certain projects that play a special role in valuation. We end up with the general NPV formula and discuss the challenges in using it.

1.1. Introduction – the idea of value6:48

1.2. The game plan – a jumbo jet taking off5:09

1.3. The valuation model – key assumptions11:27

1.4. The opportunity cost of capital6:56

1.5. Introducing PV and NPV12:50

1.6. PV calculation shortcut (1) – perpetuities9:16

1.7. PV calculation shortcut (2) – annuities6:14

1.8. A fixed rate mortgage – an example of PV11:44

1.9. The general NPV formula4:57

Conheça os instrutores

Konstantin Kontor
Director and Professor of Finance and Strategy
American Institute of Business and Economics (AIBEc)

Now let's talk about the annuities.

Well this is a very widespread shortcut.

So the annuities looks like this.

So, looks very much like perpetuity in the beginning,

but it has- so we have CCCC but not forever.

But up to the point T. Now,

the formula to find the PV of perpetuity can- over the new item,

I'm sorry, can be very easily derived,

if we use the following trick.

If we prolong this timeline for infinity,

and then, we'll have CCC up there.

And then, to make it equal to this,

we have from to point T plus one,

we have to add another perpetuity.

Starting here, and it will be minus C,

minus C, minus C, and so on.

So, that will be clearly zero all the way through.

But the good news is,

that we would know the PV of the top perpetuity.

We would know the PV of the negative.

This perpetuity and the only thing is

to discount the PV of this law perpetuity back T times.

So, the formula would look like this,

that the PV of an annuity is equal C over r,

and here comes one minus one,

one plus r to power T. Well,

you can see that if C goes to infinity that disappears and we are back to perpetuity,

which is great as that which is consistent.

Now, the first question is,

why are we studying this?

Well, one clear answer is that there-

do we exist certain important financial instruments?

The cash flows of which are very close to this.

Well, the most well-known application of annuity is a fixed-rate mortgage.

So, it's structured that well the home buyer takes this loan from the bank,

then you repays this loan with equal installments over a long period of time.

We will study of the value of a fixed-rate mortgage in the next episode,

we will use of some merical example.

But it's worthwhile using these things.

And now we can see how the annuity formula is applied.

Then it's not only a mortgage because

some life insurance contracts also make these payments and then,

this approach is very helpful in finding the use of installment payments.

And there is another thing,

which doesn't seem to be a very much on the surface but that is extremely important.

Let's say that, you are comparing some investment options and let's say,

that their revenue stream is the same,

and you are making usually is based on the lower costs.

And oftentimes, if this projects have different length,

and if some of these costs are different at various points,

you might be interested in finding inequivalent.

So that your project would look like that,

let's say couple of years and every year,

you incur the same costs.

So that it has a special name that's called the equivalent annual cost,

and we study that in greater detail in a third week.

But for now, the important thing is that

in order to come up what these equivalent annual costs are,

people also use these the lesion approach for an annuity.

And I would say that

in annuity is probably the most widely used shortcut.

Although it's kind of simplistic.

And again let me remind you,

that holds only if r is equal to is constant because for example,

we can also say that coupon payments of a bond,

they also look like this.

Well, here is another bill of payment of

the- with you with your face value at the very end.

But as you will see,

later on in this course in the second week actually,

then even before the bonds that do not involve a lot of risk,

this assumption is poor.

And although, we will identify

a very special parameter of a bond namely yield to maturity that will be sort of

at replacement of this assumption was that this is very vaguely.

Said now, but whether we will arrive at this point, we will see what I mean.

But still, it's a widely used thing.

Now, it doesn't seem to be very clear how this formula works,

until we study that in some detail and on some example.

So, as an exercise for both you and me,

will- what we will do in the next episode,

we will apply this valuation approach

to find the payments that are associated with a fixed-rate mortgage.

Not only will we do that,

but we will see that the fact that the mortgage is really

a long term loan of that sort of forces,

the borrower, to pay a lot of money in the form of end of the interest payments.

And we will see that this is extremely dependent on these r's

and I will have two options of a lower r and of a higher

r. And you will see how the contribution of

this interest plays a significant role when r's grow.

So, let's now take a pause and in the next episode,

we will come back to a fixed-rate mortgage in some greater detail.

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