# Discounted Cash Flow Model – A Simple Explanation

Investment appraisal is a key financial concept that covers how investments should be valued based on different criteria. Among the different investment appraisal methods, discounted cash flow (DCF) is one of the most used appraisal methods.

### What Is the Discounted Cash Flow Model?

As mentioned above, discounted cash flow is a method of investment appraisal or a valuation method. The defining characteristic of discounted cash flow is that it values investments based on their future cash flows. Focusing upon future cash flows means that there is a consideration of the “time value of money” in DCF calculations. Once the cash flows are adjusted for their time value, the Net Present Value (NPV) method determines cash flows.

### Time Value of Money

Time value of money refers to the concept that the value of a certain sum of money is worth more in the present than in the future.

The concept of the time value of money is rooted in the idea that money earns interest and can be invested. Any rational investor would prefer to receive money in the present rather than in the future. For instance, if an investor were to receive \$1 million today, they would invest it and hopefully start earning a return on the \$1 million. After a year, the investment would be worth more than \$1 million. If that same investor received the \$1 million a year later, that investor would have lost one year’s return on investment. Let us look at this in greater detail.

If the investor were to earn a 10% return on \$1 million, they would earn \$100,000 in one year. Thus, by the end of the year, \$1 million would have increased to \$1.1 million. On the other hand, if the investor chooses to receive the \$1 million one year later, the investor would have \$100,000 less. Therefore, because money earns interest and can be invested, the concept of the time value of money exists. This means that the value of money is connected to time.

This brings us back to discounted cash flow analysis. The purpose of DCF is to estimate the return on an investment after being adjusted for its time value. This makes discounted cash flow analysis very appropriate as it considers the present value of future cash flows.

### Discounted Cash Flow Formula and How to Calculate it

Investments in major projects such as the construction of a dam are usually spread out over many future periods. Therefore, investors will want to assess whether the return they will receive will be greater or less than the total investment they will inject into the project.

This means that the present value of all future expected cash flows from the investment will have to be calculated using a discount rate.

Calculation of Discount Factor

A discount rate is simply the rate of interest or the rate of return on a particular project.

The discount factor is the ratio used to calculate the present value of cash flow every year of the project’s lifetime.

Because today’s dollar value will intrinsically be worth less in the future due to interest and inflation, the discount factor is often between zero and one. Moreover, the discount factor gets smaller for every following year in a project.

The discount factor is used to determine the net present value. This determines the expected profits and losses based on future payments — the net future value of an investment.

The formula for the discount factor is straightforward.

```Where:
i = discount rate in %
n = number of periods```

The example above shows the discount factors for a 3-year project with a discount rate of 10%.

Knowing how to calculate the discount factor is very important for DCF calculation. To get the present value of each year’s expected cash flow, the discount factor for a particular gets multiplied by the expected cash flow for that same year.

The discounted cash flow formula is:

```Where:
CF:Cash Flow for the year
DCF: Discounted Cash Flow
i: discount rate (or interest rate) applicable to the project or investment
n: number of years```

### Discounted Cash Flow Analysis and Interpretation

To better understand DCF, let us look at an example:

Suppose an investor invests \$1 million in a 3-year project. In the first year, the expected cash flow is \$600,000, in the second year, \$700,000, and in the third year, \$800,000.

So, in the 3 years of the project, the total future cash inflow is \$2.1 million. Next, the future cash inflow gets adjusted for the time value of money. This is done by multiplying the cash inflow of each year by the discount factor for that same year. The result is a total discounted cash flow of \$1,724,400.

To calculate the project’s net present value, you take the total discounted cash flow and deduct the initial investment. The example shows that the net discounted cash flow on the \$1 million investment over the 3-year period exceeds the initial investment by \$724,400. This means that the project’s investment is profitable, and thus the investor should consider going ahead with it. On the other hand, had this figure been negative, the investor should not make the investment.

Let us now look at an example that results in a negative net present value.

The example above shows that the net present value of the project is a negative \$270,000. This indicates that the initial investment cannot be recovered in the 3-year period, so the investment should not be made.

### Terminal Value

One of the limitations of using the DCF method is that it can only forecast the cash flows for a finite number of periods. It is common practice for the cash flows to be forecasted for 5 years into the future. Beyond this point, any forecast or projection becomes highly uncertain. This is where the concept of “Terminal Value” comes into the equation.

Terminal value is the value of a project or business being appraised beyond the forecasted cash flows period. Terminal values assume that the project/business will grow at a specific growth rate in perpetuity beyond the forecasted period.

Therefore, the discounted cash flow formula stated above is used when future cash flows are for a finite period, usually 5 years. The formula must include the terminal value in situations where the forecasted cash flows are beyond this time horizon.

There are 2 ways to calculate terminal value:

#### Perpetual growth

The perpetuity method assumes that the investment interest will grow at a stable rate in perpetuity. Therefore, the terminal value can be calculated by dividing the Free Cash Flow (FCF) of a project/ business by the difference between the discount rate and the growth rate.

The formula for terminal value is, therefore:

```Where:
Free cash flow: Free cash flow of the last forecasted period
g: Growth rate in % applicable to the project or business interest
d: discount rate in %```

#### Exit multiple

While the perpetual growth model for terminal value assumes an infinite time horizon, the exit multiple assumes a finite number of years beyond the forecasted time horizon.

Exit Multiple = Financial metric x Trading multiple

The exit multiple is usually used to calculate the terminal values for business acquisitions. Terminal value through the exit multiple is calculated by multiplying any relevant and appropriate financial metric such as EBITDA with a trading multiple commonly in similar companies. This technique is used most commonly by investment banks to calculate the value of takeovers.

### What Is DCF Used For?

Discounted cash flow is a widely used appraisal technique in investment banking. It can be used to measure the value of cash flows generated by a company. If used correctly, it is an exact method of valuation. DCF can also be used to value a project or investment within a company, an entire company, the benefit of a cost-saving initiative, or stocks. Discounted cash flow is used by investment bankers, analysts, and governments alike for ease of use and possible application in various scenarios.

DCF is an inward-looking appraisal technique that relies on the company’s intrinsic value or investment interest generated through its cash flows. It is, for this reason, seen as a very objective method of investment valuation.

### How to Calculate the Fair Value of a Company through DCF

Calculating a business’s fair value through the discounted cash flow analysis requires the same principles and formulae that we discussed previously.

Free cash flow is the cash available to a company after accounting for operational and capital expenditures. The most recent free cash flow of a business can be used to project the cash flow over a period of three to five years in the future.

For example, the discounted cash flow method determines a company’s fair value in merger and acquisition negotiations.

Assume the free cash flow of a company is \$30 million per year. The expected uniform growth rate is 3% over the next 3 years and beyond.

As the calculations show, the company’s terminal value is a little more than \$482 million. Now that we know the company’s projected cash flow, the discount rate can be applied to get a present value for those cash flows. Let us assume that the discount rate is 10%.

By applying the discount rate of 10%, we get a fair market value of \$408.4 million for the company. Investors use the fair market value to determine how much to pay for a company to get a positive return on their investment. Please note that using Excel in financial modeling to determine a company’s value can save a lot of time.

### How to Determine the Fair Value of a Stock Using the Discounted Cash Flow Model

Investors also use discounted cash flow valuation to measure the fair value of a stock. Stock investors need to know whether their target stock is over or undervalued by the market. The stock price is a reflection of the value that the market places on that stock. This value can be grossly over or understated due to market sentiment. Investors look for undervalued stocks, as those stocks present opportunities to earn a profit. Undervalued stocks tend to revert to their fair value, and when this happens, the stock goes up, and the investors make a profit.

On the other hand, overvalued stocks tend to revert to their fair value, resulting in their stock price going down. Thus investors can lose money if they invest in overvalued stocks.

The DCF valuation method uses the free cash flow projections of a company and discounts them with a suitable discount rate to arrive at the stock’s present value. Then, investors can compare the stock’s present value with the stock price to analyze whether the stock is over or undervalued.

In the above-mentioned example, the fair value of the business is \$408.4 million. Let us assume that this company has issued 1 million shares. We can now calculate the fair value price of its stock by dividing the company’s fair value by the number of outstanding shares. This results in a fair value stock price of \$408.40 per share. Investors can now analyze whether the market price is above or below this fair value and make their investment decision accordingly. For example, if the current share price is \$375, then the stock is undervalued, and the investors can profit when the price goes up.

### Limitations of the Discounted Cash Flow Method

DCF is, without any doubt, a very objective way of valuing investment interests. However, it does have its limitations.

• The discount factor needs to be chosen carefully. Usually, businesses use their WACC (Weighted Average Cost of Capital) as the discount rate. However, debt and equity costs can fluctuate rapidly in times of economic uncertainty, making the DCF calculations questionable.
• Future cash flow projections are estimates at best, and if they are not calculated carefully, they might be inaccurate. Many variables are involved in calculating future projections, such as forecasting earnings, working capital, and tax rates. If any of these variables is misestimated, the discounted cash flow calculations can become unreliable. Each year in the forecast, uncertainty increases for cash flow projections, and many DCF models use five or even 10 years’ worth of estimates.
• Unforeseen events can make discounted cash flow calculations irrelevant. For instance, the Covid-19 pandemic qualifies as an unforeseen event. It has completely disrupted business activity all over the world. Investment valuations carried out in 2019 did not take this pandemic and its economic repercussions into account, thereby rendering DCF calculations useless in the present scenario.
• It looks at company’s valuation in isolation and does not consider the relative valuations of competitors.

### Conclusion

Discounted cash flow analysis is a very objective analysis of investment interests that can help investors gauge their target investments’ fair value. Care, however, must be taken to make sure that the variables used are appropriate and relevant. Otherwise, the discounted cash flow calculations can become misleading.