Discounting Cash Flows Explained

In this article we’re going to explore what discounting cash flows is, including what it means, how it works, and why we should even bother doing it. Let’s get into it.

What is discounting cash flows?

Firstly, what is “discounting cash flows”?

In a nutshell, it’s about expressing future cash flows in today’s terms.

Specifically, it’s about expressing future cash flows in today’s terms after incorporating the time value of money, firm specific risk, and market risk.

What is discounting?

Discounting is just the process of estimating the value of future cash flows today.

Discounting allows us to establish how much future cash flows are worth in today’s terms.

Why bother with discounting cash flows?

Fundamentally, we discount cash flows because $1,000 today is worth more than $1,000 in the future.

And that is because money loses value over time. This fact is defined as the “time value of money”.

Time Value of Money

Consider an example. Imagine you have $1,000 in your wallet right now. Further imagine that you live in Cloud Cuckoo Land where the price of 1 banana is $1.

How many bananas can you buy right now?

You can buy 1,000 bananas with your $1,000 given each banana costs $1.

Now fast forward to a year later. The price of bananas have increased because of inflation. 1 banana now costs $1.05.

How many bananas can you buy now?

You can buy about 952 bananas with the same $1,000.

Thanks to inflation, you’re now worse off by 48 bananas.

You still have the same amount of money, but you can’t do as much with it as you could before.

Put differently, your money lost value over time.

That, is the Time Value of Money.

Discounting cash flows process

If we think about discounting at the process level, ultimately it allows us to see how much future cash flows are worth to us today, given the time value of money, as well as other risks.

Consider the following cash flow stream:

We’re here, in Year 0 (the present, right here, right now).

And we’re going to get this future cash flow, in Year 1, then in Year 2, in Year 3, and so on and so forth all the way until Year N.

For simplicity, let’s assume that all of these cash flows are equal, in nominal terms.

So is the same as , which is the same as , and so on and so forth.

But of course, given the time value of money we know that the first cash flow () will be worth more than the second cash flow (), because money loses value over time.

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So we need to get this cashflow one , and we need to bring it back to Year 0 to see how much it’s worth to us right here right now.

Then we need to take the second cash flow, the cash flow we get in year two and do the same thing – discount it back to year zero (today), to see how much it’s worth now.

And then we need to do the same thing for the third year, the fourth year and so on and so forth, until the nth year.

Ultimately we’re just taking these future cash flows and we’re discounting them back to the present.

Consider any future cash flow that you’ve got…

You’re going to take the future cash flow, and then incorporate these three different kinds of risks:

• firm specific risk,
• market risk, and
• time value of money

And what you’re going to get then is the PV or the Present Value of future expectations.

The Discount Rate

And these three risks over here are incorporated in what we call the discount rate or .

This rate is the crucial ingredient for discounting future cash flows. If you don’t have this discount rate, you don’t have anything, you don’t have any sort of discounting.

So this is like the Holy grail of understanding discounting.

This rate, which is expressed as a percentage, incorporates all of the risks associated with a given project or firm.

There are of course, a variety of other terms that are used to describe it including:

• cost of capital
• opportunity cost of capital
• hurdle rate
• required rate
• required rate of return
• 
• 
• weighted average cost of capital (WACC), under certain conditions

Some people call it because it refers to a sort of “capital”.

So any one of these are fine. The key takeaway really is that they’re all essentially the discount rate. I’m going to be using them interchangeably throughout the course so that you really get comfortable with it.

The Present Value

Ultimately, we’re just taking these future cash flows and we’re discounting it back to the present. And in the general case, we do this by applying the formula for the Present Value (PV), which looks like this…

   

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So here refers to the Present Value of future cash flows. is the cash flow or the future cash flow occurring at time .

is your discount rate, aka hurdle rate, or cost of capital or required rate, whatever you want to call it.

It’s just the rate that discounts the future cash flows.

Let’s consider an example and see what this process actually looks like.

Discounting cash flows Example

Consider a cash flow stream where you get $7,500 every year for the next 5 years. Assume the appropriate discount rate is 10%.

How much are these cash flows worth today?

Although the cash flows are constant, meaning each cash flow is equal to the other…

Given the time value of money,  the $7,500 that you get in Year 1 is actually worth more than the $7,500 you get in Year 2, which in turn is worth more than the $7,500 you get in Year 3, 4, and so on and so forth.

In other words,  the cash flows are constant and they’re equal in nominal terms, but they’re not equal when you consider them in real terms. And when you consider the other risks.

To really evaluate a project then, you’d need to discount these future cash flows.

What does that look like?

Well it’s literally just a simple case of applying the equation for the Present Value.

   

In our case, we’re looking at a 5 year timeframe, so the equation can be seen as…

   

Expanding / opening the equation looks like…

   

Consider the specific case of the cash flow in Year 2:

   

Here, we’re raising to the power of 2 because we’re discounting the $7,500 which occurs in 2 years time back to the present.

Put differently, in order to express that future cash flow in today’s terms, we need to discount it over 2 years. That is why we’re raising it to the power of 2.

Now, given that the discount rate is 10%, the equation becomes…

   

Solve for that, and you’ll find that the PV (or discounted cash flow) is approximately equal to $28,430.90

In other words, the discounted cash flow of $28,430.90 represents the value of $7,500 paid out every year for the next 5 years, in today’s terms.

Importantly, this is true if and only if the appropriate discount rate is in fact 10%.

Estimating the discount rate itself is a whole other topic, and way outside the scope of this article.

But the key thing you need to know right now is that this is how we go about discounting future cash flows.

And now that you know that, let’s consider some of its applications.

Applications of discounted cash flows

Discounted cash flows have a wide scope of application, but they’re predominantly used for:

• Investment Appraisal (e.g., using the Net Present Value capital budgeting tool)
• Valuation (e.g., using a discounted cash flow valuation model / DCF valuation)

Investment Appraisal

Investment Appraisal (aka Capital Budgeting) can end up making quite an extensive use of discounted cash flows, especially when one considers the Net Present Value (NPV) or Discounted Payback Period appraisal tools.

Valuation

As far as valuation goes, this includes everything from company / business valuation, to stock valuation, bond valuation, real estate valuation, etc.

One way or another, they all can, and often to, end up using a discounted cash flow model to obtain a fair value estimate for the asset.

For instance, the DCF method / DCF valuation is one of the most commonly used approaches for valuation, globally.

Sure, complexities arise when one starts thinking about the types of cash flows in a DCF analysis – free cash flow (FCF) vs. free cash flow to equity (FCFE) or “flow to equity”.

Or in terms of the specific discount rate – the cost of equity vs. cost of debt vs. weighted average cost of capital.

Or indeed, capital structure, which in turn further complicates the discount rate; levered vs. unlevered FCF for instance.

Yes, complexities do increase. However, the core fundamentals still remain unchanged. It’s still, fundamentally, about discounting future cash flows.

Importance of discounting cash flows

Failure to discount future cash flows will mean that we make suboptimal decisions.

Because we won’t be able to compare cash flows like for like.

When you discount cash flows to the present, you’re able to compare them like for like, because you’re comparing them at the same time.

Remember that in the example, we had cash flows that occurred at different time periods over the future. But after discounting them all back to Year 0, we’re able to see all of them like for like.

So when we’re looking at this investment opportunity, we’re looking at all of the cash flows as at Year 0, as opposed to different timeframes and different risk factors, et cetera. It’s all like for like, it’s all at the same time.

Another important relationship that you need to know and understand is the relationship between the discount rates and the present value, or just value in general.

Since the discount rate is a measure of risk, we can say that the value of an asset increases as the discount rate decreases.

And the value of an asset decreases as the discount rate increases.

Risk and value thus have an inverse relationship.

On the flip side, risk and (expected) return have a proportional relationship.

The higher the risk, the higher the expected return, and the lower the risk, the lower the expected return.

Risk increases with expected return, or expected return increases with risk. These two go in the same direction.

This relationship is something that you need to know not just for discounting cash flows, but for finance in general.

You need to know that as risk increases, the expected return increases, but the value decreases.

And as risk decreases, the expected return decreases, but crucially, the value increases.

Wrapping Up

Alright, in summary…

You’ve learned that discounting is the process of estimating the value of future cash flows in today’s terms, given the time value of money, firm specific risk, as well as market risk.

And you’ve learned the cash flows are discounted by estimating the Present Value, which is estimated as…

   

Finally, you learned that risk and expected return are proportional to one another. And risk and value are inversely proportional to one another, so they go in opposite directions.

Okay, hopefully this makes sense and you now know how to go about discounting cash flows.

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