So discounting cash flows, what does it entail?

Why do we consider it to be the gold standard in finance?

Let's take a closer look.

We start with a simple example.

I've got two propositions for you, which one would you prefer?

I either give you $100 now or I promise to give you $100 in a year's time.

Which one do you prefer?

Wouldn't be surprised if you said that you very much preferred the $100 right now,

thank you very much.

And that is indeed what most people would intuitively reply.

They prefer money in hand rather than to wait for

the same amount of money at some point in the future.

But why is that?

Why is the $100 today somehow valued differently from $100 in the future?

Well, we have at least three good reasons why you might want

to prefer the $100 right now, expected inflation.

We've seen over many, many years that dollars,

over time reduce in value due to price increases.

Inflation erodes the value of money over time.

So what you can buy with $100 today is going to be worth

probably more than what you can buy with the $100 in a year's time.

Second reason why you might want to prefer the $100 now is that you might not get it.

I might walk away and you'll end up empty-handed in one year's time.

Risk, will the cash flow actually occur?

If you get the money now, there is no risk.

But one year from today, who knows what can happen in that time period.

And lastly, opportunity costs.

We'll discuss the opportunity costs in a lot more detail

in the remainder of this module.

The key point is that we cannot directly compare dollars,

cash flows, that occur at different points in time.

We need to consider the actual date that a cash flow eventuates.

So, we need to consider the value of those cash flows at different points in time,

somehow accounting for expected inflation, for risk, and for

opportunity costs, alternative investment opportunities for investors.

The way we do that is as follows.

So, we account for what we labeled the time value of money,

how a dollar changes in value from one time period to the next time period

by systematically discounting future cash flows.

The formula here tells you how we do that.

We take the cash flow and we divide through by 1 plus

a discount rate, r, to the power of n.

And n indicates the number of years you have to wait until you're entitled

to the cash flow, where the cash flow is indicated for

the year that it will occur, cash flow at n.

If we divide the cash flow through by 1 plus the discount rate,

we divide through by something that is larger than 1,

we’ll end up with a value which is going to be smaller than the cash flow.

That is the present value.

The present value in the presence of expected inflation risks and opportunity

costs will be less than the cash flow entitlement, and years down the track.

It allows us to express future cash flows into present dollars,

equivalent present dollars.

We label those equivalent present dollars, the present value of a future cash flow.

That, then, will allow us to bring all future cash flows,

whether they occur in one year's time, two years' time or

ten years' time, we can bring them back to the present.

And once we've got them all valued at the same decision period, today, now, we've

got comparable cash flows that allow us to make an informed investment decision.

So, let me give you an example.

What is the present value of that $100 that I promised you earlier, but

I will only give it to you in one year's time?

And an appropriate discount rate, we'll discuss the choice of that discount rate

a little later, and appropriate discount rate being 5% per annum.

Take the cash flow, $100 in one year's time,

divide by 1 plus that discount rate of 5%,

1.05 to the power, the number of the years, 1 in this case,

and that tells us that the present value in this example is $95.24.

So, $100 in one year's time is valued today at

a discount rate of 5% at only $95.24.

So, what's the intuition here?

Or, consider it another way,

take that $95.24, and take that right now,

borrow $95.24, invest it at the discount rate.

Let's assume a bank is offering you a 5% interest rate per annum.

Invest the $95.24 at that 5% and what do you get?

Exactly the $100 in one year's time.

So that suggests a neat link between an opportunity

to invest at 5% over a one-year period,

linking a future cash flow to a present value of $95.24.

Now what would happen if that cash flow didn't occur in one year's time, but

in two years' time instead?

No problem, same formula.

Take that cash flow.

In two years, n equals 2 of $100, but

now discount by a slightly higher discount factor,

and that is going to be 1 plus the same discount rate of 5%, but

now to the power of n equals 2 years.

And it will tell us that the present value of a $100 cash flow that you will be

entitled to in two years' time, today is only worth the present value of $90.70, so

you've lost the further $5, almost $5, in terms of present value.

The further away the cash flow entitlement,

the smaller the present value.

So the intuition here is the same.

Borrow the $90.70 today.

Go to the bank, invest it now for two years.

And what will you get after two years?

Exactly the $100.

So there is a very clear link between

future values of cash flows and present values of cash flows.

And we can in fect move either way.