# DCF for Dummies

/I used Discounted Cash Flow (DCF) for many years without actually understanding it. I am sure there are many people who are a bit scared of really testing their understanding of DCF in public, so herewith a simple DCF for Dummies.

DCF is a valuation method used to estimate the attractiveness of an investment opportunity. It does this by calculating the value of all cash flows - e.g. a series of deposits over a period of time. Remember that there may be cash flow IN and cash flow OUT - and it won't matter to the formula because it just means it is a plus or a minus.

So, a DCF answers the question: Is $1m today worth more or worth less than a stream of cash flow payments of $125,000 for 10 years? Because $125,000 x 10 > than $1m, you may be tempted to think so.

But, the $125,000 in-flow in year 10 is not quite worth $125,000 because of the time-value of money. Your $1m investment could have attracted interest or be affected by inflation; and this must be factored into the equation.

Of course if you want to 'value' a cash flow, you must put a value on cash. How much is the cash worth? This is expressed in terms an 'interest rate' - which is sensible because money either earns interest or pays interest. Technically this is called the discount rate, because this is the percentage by which the future cash flows will be discounted in order calculate its value today.

A discount rate of 8% will mean that in each successive year the same amount of money will be worth 8% less than the previous year. (The formula actually accounts for the cumulative nature of these changes and more about that later.)

The underlying assumption is that future cash inflows are worth less than current cash inflows and future cash-outflows are not as bad as current cash-outflows. (A bird in the hand and all that.)

Analysts must pick a number and there are many different ways to arrive at a percentage for the discount rate. The most common way is to look at all the sources of capital (e.g. debt, equity etc.) and to work out some kind of average cost. Technically this 'average' interest rate is a weighted average cost of capital - rather than a simple average.

The formula looks as follows:

At first glance it seems scary, but just take a deep breath. Read this sentence by sentence and think about the meaning:

Every CF is a cash flow. This formula adds up all the cash flows (positive or negative).

But it reduces the value of each successive cash flow by a certain amount by dividing it by a denominator (below the line): This number is 1 + the discount rate (percentage).

Let us assume the discount rate is 10%. The first cash flow will be discounted (divided by) by 1 + 10% = 1.1. So the first cash flow received at the end of year 1 is $113,636. [Calculated as $125,000÷ 1.1]

This makes sense because if I had the $125000 in the bank I could have earned interest so the future cash flow is worth less than the $125000.

The next cash flow will be divided by a number that is bigger than 1.1 making that cash flow slightly smaller than the one before. The next number in the denominator is bigger because we add the exponential element. The next denominator in period 2 = (1+ 10%)to the power of 2, which is equal to 1.21.

So the cash flow at the end of year 2 is $103,305 [Calculated as $125,000÷ 1.21.]

Basically we are saying that the cash flow received in the future becomes progressively smaller because it is discounted by an ever-increasing number.

If the end value arrived at (sum total all individual in/out flows) through DCF analysis is higher than the current cost of the investment, the opportunity may be a good one.

Despite the complexity of the calculations involved, the purpose of DCF analysis is just to estimate the money you'd receive from an investment and to adjust for the time value of money.

DCF models have shortcomings. DCF is merely a mechanical valuation tool, which means "garbage in, garbage out". Small changes in inputs can result in large changes in the value of a company.

Instead of trying to project the cash flows to infinity, a terminal value approach is often used, effectively capping the number of cash flows at say 10.

In sum: Adding up a whole series of cash flows (e.g. deposits) is not a straightforward addition; you must make each cash flow further out worth slightly less because money in hand today is worth more than that same amount of money in the future.

DCF is a valuation method used to estimate the attractiveness of an investment opportunity. It does this by calculating the value of all cash flows - e.g. a series of deposits over a period of time. Remember that there may be cash flow IN and cash flow OUT - and it won't matter to the formula because it just means it is a plus or a minus.

So, a DCF answers the question: Is $1m today worth more or worth less than a stream of cash flow payments of $125,000 for 10 years? Because $125,000 x 10 > than $1m, you may be tempted to think so.

But, the $125,000 in-flow in year 10 is not quite worth $125,000 because of the time-value of money. Your $1m investment could have attracted interest or be affected by inflation; and this must be factored into the equation.

Of course if you want to 'value' a cash flow, you must put a value on cash. How much is the cash worth? This is expressed in terms an 'interest rate' - which is sensible because money either earns interest or pays interest. Technically this is called the discount rate, because this is the percentage by which the future cash flows will be discounted in order calculate its value today.

A discount rate of 8% will mean that in each successive year the same amount of money will be worth 8% less than the previous year. (The formula actually accounts for the cumulative nature of these changes and more about that later.)

The underlying assumption is that future cash inflows are worth less than current cash inflows and future cash-outflows are not as bad as current cash-outflows. (A bird in the hand and all that.)

Analysts must pick a number and there are many different ways to arrive at a percentage for the discount rate. The most common way is to look at all the sources of capital (e.g. debt, equity etc.) and to work out some kind of average cost. Technically this 'average' interest rate is a weighted average cost of capital - rather than a simple average.

The formula looks as follows:

At first glance it seems scary, but just take a deep breath. Read this sentence by sentence and think about the meaning:

Every CF is a cash flow. This formula adds up all the cash flows (positive or negative).

But it reduces the value of each successive cash flow by a certain amount by dividing it by a denominator (below the line): This number is 1 + the discount rate (percentage).

Let us assume the discount rate is 10%. The first cash flow will be discounted (divided by) by 1 + 10% = 1.1. So the first cash flow received at the end of year 1 is $113,636. [Calculated as $125,000÷ 1.1]

This makes sense because if I had the $125000 in the bank I could have earned interest so the future cash flow is worth less than the $125000.

The next cash flow will be divided by a number that is bigger than 1.1 making that cash flow slightly smaller than the one before. The next number in the denominator is bigger because we add the exponential element. The next denominator in period 2 = (1+ 10%)to the power of 2, which is equal to 1.21.

So the cash flow at the end of year 2 is $103,305 [Calculated as $125,000÷ 1.21.]

Basically we are saying that the cash flow received in the future becomes progressively smaller because it is discounted by an ever-increasing number.

If the end value arrived at (sum total all individual in/out flows) through DCF analysis is higher than the current cost of the investment, the opportunity may be a good one.

Despite the complexity of the calculations involved, the purpose of DCF analysis is just to estimate the money you'd receive from an investment and to adjust for the time value of money.

DCF models have shortcomings. DCF is merely a mechanical valuation tool, which means "garbage in, garbage out". Small changes in inputs can result in large changes in the value of a company.

Instead of trying to project the cash flows to infinity, a terminal value approach is often used, effectively capping the number of cash flows at say 10.

In sum: Adding up a whole series of cash flows (e.g. deposits) is not a straightforward addition; you must make each cash flow further out worth slightly less because money in hand today is worth more than that same amount of money in the future.