# Discounted cash flow

Suppose you are a big investor, and an investment banker suggests that you buy a stock or a company, and tells you that the price quoted is fair price. You will likely wonder how he ascertained that the price is indeed fair. You will find out that the banker has used DCF analysis to arrive at the “fair price.”

## What is DCF?

The full form of DCF is Discounted Cash Flow.

DCF is a valuation method to estimate the present value of an investment using its future cash flows — cash flows are payments an investor receives in a given period for making an investment in a project, for owning shares or bonds, etc.

DCF is used by investment bankers and financial analysts to recommend to investors a fair price for selling or buying a company and to find out whether a stock is a good buy or not.

A DCF analysis is based on the concept of “time value of money” (TVM), according to which, money available now — that is, at the present time — is worth more than an identical sum in the future.

This is because money available now can be invested immediately to earn returns (interest, dividend, etc.), but an identical sum that may be available in the future may be of a lower value than money available now due to factors such as inflation acting on it.

The goal of a DCF analysis is to calculate how much an asset that is expected to provide returns over a few years is worth at present.

Using the concept of TVM, and forecasts about the future returns that an investment is expected to bring, a DCF analysis evaluates the viability of the investment using a “discount rate.”

The investment is viable if the “net present value” (NPV, calculated by discounting future cash flows using the discount rate; see below) of expected future cash flows is positive—that is, if it adds up to more than the initial investment–and it is not viable if the NPV is negative (less than the initial investment).

In a DCF analysis, the “terminal value,” the growth rate for future years outside the timeframe of a project, may also be taken into account.

## Discount rate

Usually, a DCF analysis estimates how much cash flow an investment will generate in five years. These future cash flows are “discounted” to assess their value at present—that is, adjustments are made to know their value over time.

The discount rate reflects TVM (investors would demand to be compensated for the delay in returns being paid later rather than at present) and a risk premium (future cash flows carry the risk that they may not come at all).

In business, the discount rate is typically a company’s “weighted average cost of capital” (WACC), the required rate of return that investors expect from investments in the company.

Simply put, for a bond, the discount rate is equal to the interest rate on the security. The discount rate can also be conceived as the money you would earn if you invested it in another opportunity that carries the same risk. A good guideline is to use the current interest rate on loans.

To use the DCF formula effectively, the investor should set an appropriate discount rate depending on the project or investment opportunity.

If the project is too complex, and the investor cannot make a reasonable estimate of future cash flows, then the DCF formula cannot be used to assess the returns from the project.

## Discount rate and real returns

In a DCF analysis, the discount rate is the degree to which future cash flows are discounted in the NPV calculation.

For example, if a project, with an initial investment of \$3,000, is estimated to give returns of \$1,000 each year for five years, one might assume that the total returns equal \$5,000.

But that is not accurate.

Let’s assume that the discount rate is estimated at 10 percent. At the end of the first year, say the return is \$1,000.

Applying a discount rate of 10 percent, the return is \$900 (\$1,000 – \$1,000 x 10/100), that is, the cash flow minus the discount rate.

After year 2, it will be \$810 (\$900 – \$900 x 10/100), year 3, \$729 (\$810 – \$810 x 10/100), year 4, \$656.1 (\$729 – \$729 x 10/100), and year 5, \$590.49.

The total returns in the five years will be \$3,685.59, not \$5,000.

## Net present value

Deducting the initial investment of \$3,000 from the total returns of \$3,685.59, we get \$685.59 as the NPV, which is a positive number.

Therefore, the cost of your investment is worth it, as the project will give you positive discounted cash flows that are greater than your initial investment.

However, if your initial investment had been \$4,000 instead of \$3,000, for example, the discounted cash flows would have added up to less than the initial investment, and the project would not have been worth putting your money in.

## DCF formula

The formula for calculating DCF is as follows:

DCF = CF1/(1 + r)1 + CF2/(1 + r)2 + CF3/(1 + r)3 + CF4/(1 + r)4 + CF5/(1 + r)5

where “CF” is the cash flow for a particular year (CF1 for year one, CF2 for year two, etc.), “r” is the discount rate, and the superscript figure denotes the year.

Let’s take an example. Suppose a company plans to invest \$1,000,000 to buy new equipment to improve its processes and increase profits.

Say the discount rate of the investment is estimated at 5 percent (in such instances, a company uses its “weighted average cost of capital,” or WACC, which reflects the shareholders’ expectation of the average rate of return from investments in the company).

After year 1, the project sees a cash flow of \$100,000 (using the DCF formula, the discounted cash flow is \$95,238).

After year 2, the cash flow is \$200,000 (DCF is \$181,405), year 3 \$300,000 (\$259,291), year 4 \$400,000 (\$300,525), and year 5 \$500,000 (\$398,089). The total DCF is \$1,234,508.

Deducting the initial investment of \$1,000,000, you get an NPV of \$234,508, which is a positive number. The investment is, therefore, worth it.

What if the initial investment had been \$2,000,000?

With the same cash flows, you would have got an NPV of \$1,234,508 – \$2,000,000, or -\$765,492, a negative number, and the investment would have not have been worth it.

## Variables

However, as an investor, you cannot take a “fair price” estimated by an investment banker or financial analyst through a DCF analysis as the last word.

It doesn’t have to be accurate, after all. This is because the formula to calculate DCF contains variables, particularly the “discount rate”, or estimated value of money in the future, and they can go up or down depending on many circumstances, affecting a DCF analysis.

If you make a few adjustments to the variables, the estimated value of an investment can change easily.

If highly optimistic projections of cash flows are made, the return is going to be exaggerated; if low projections are made, the investor may not participate in the project and may lose the investment opportunity.

Often, the terminal value of a DCF analysis accounts for a large percentage (sometimes up to 50 percent) of the estimated total value of a company being evaluated for purchase.

Any changes in the terminal value may significantly impact the result of the DCF analysis.

## Uses of DCF analysis

A DCF analysis is used to estimate the value of an entire business, to value a bond or shares in a company, to value revenue-earning property, and to value the benefit of cost-saving program in a company.

The analysis also comes in handy when you need to find out how much money to invest for getting a certain expected return.

Examples of businesses that can use a DCF analysis include:

• a restaurateur estimating the value of a restaurant to buy
• a merger and acquisition firm using the analysis to determine the value of another company
• a tax consultant using it to find out whether an investment in new office furniture will be worth it over the years
• a construction company using the method to find the value of equipment several years on

Although the time-frame that is usually used is five years, longer timeframes may also be used. For investments in equipment, etc., shorter timeframes may be used, but for investments in whole businesses, a longer timeframe of ten years or longer could be more appropriate.

## DCF Alternatives

Alternatives to a DCF analysis include the following:

• Comparables Method: Takes into account how a company is actually performing at present.
• Precedent Transaction Analysis: Values a company based on its merger and acquisition transactions or those in the industry generally.
• Adjusted Present Value: Ignores taxes and loan interest for calculating the discount rate.

• Evaluates the intrinsic value of a business
• Calculates the internal return rate of an investment
• Takes into account all major assumptions and future expectations
• Analyses mergers and acquisitions
• Is Excel-friendly