# Discounted Cash Flow

### Discounted Cash Flow Techniques The formula for the discounted cash flow of an investment involves estimating its value based on the sum of future cash flows.
The net present value formula has two parts: the sum of the cash flows and the initial investment. The summation component is the discounted cash flow (DCF). Discounted cash flow is a system of calculating the present value of forecasted future cash flows at a given discount rate.
${\rm{DCF}}=\frac{C_1}{(1+r)^1}+\frac{ C_2}{(1+r)^2}+\frac{ C_3}{(1+r)^3}+...+\frac{C_n}{(1+r)^n}$
Where:
\begin{aligned}C&=\text{Cash Flow}\\r&=\text{Discount Rate}\\n&=\text{Number of Periods (or Year})\end{aligned}
In a basic example, in year 1, Vision Inc. has a cash flow of $900. The cash flows in year 2 and year 3 are also$900. With a rate of 10 percent, discounted cash flow can be calculated.
\begin{aligned}{\rm{DCF}}=\;&\frac{900}{(1+0.10)^1}+\frac{900}{(1+0.10)^2}+\frac{900}{(1+0.10)^3}+...+\frac{C_n}{\displaystyle(1+r)^n}\\\\=\;&818+744+676+...+\frac{C_n}{(1+r)^n}\end{aligned}
The present value of the cash flow reduces over time, from $818 in year 1, to$744 in year 2, to $676 in year 3. Present value is the value in current dollars of a future payment discounted to the present and based on the required investor's return. DCF analysis is solely centered on the cash flow. The difference between net present value (NPV) and DCF is subtle but significant. DCF removes investment constraints and allows the business to create goals for funding an investment with a positive cash flow. Discounting in finance is the process of adjusting the future value of money to the present. In capital budgeting analysis, this is often the weighted average cost of capital (WACC). Weighted average cost of capital is a formula for determining the relative average a company is expected to pay to all its security holders to finance its assets. The cash flow may change based on the growth rates and then be discounted using the WACC. In another example of discounted cash flow calculations, Vision Inc. is considering generating a new line of products. This new line will increase the growth rate by 10 percent for the first two years. After the novelty of the new product wears off, the growth rate will drop to 3 percent for four years. Vision Inc.'s normal growth rate is 2 percent, the WACC is 7 percent, and its current free cash flow is$40 million.

The last term of the equation, called the terminal value, will happen at some undefined time in the future. Terminal value is the value of all expected future cash flows when a stable growth rate is expected. There are different ways to calculate this amount. Using the Gordon formula, the terminal value can be calculated. The Gordon Model, also known as the Gordon Growth Model or the dividend discount model, provides a way to calculate a stock’s value based on the present value of all future dividends.
$\text{Terminal Value}=\text{Final Year Projected Cash Flow}\times\frac{(1+\text{Normal Growth Rate})}{\;(\text {WACC}-\text{Normal Growth Rate})}$
The sum of the discounted cash flows is $1,399 million, or approximately$1.4 billion.

#### Discounted Cash Flow and Terminal Value Calculations Using Spreadsheets The assumptions used to calculate the terminal value must be accurate since the terminal value is the majority of the total discounted cash flow. Terminal value can be calculated using spreadsheets.

### Discounted Cash Flow Analysis for Capital Decision-Making In capital decision-making, earnings before interest and taxes ratios may be used to verify that the discounted cash flow assumptions are correct; discounted cash flow decisions are also part of the dividend payout ratio.

Cash flow has a fundamental impact on the financial statements and the fiscal health of a company. Cash flow assumptions are the foundation for discounted cash flow analysis, and these assumptions will need to continue throughout a business's analytical process in order for the business to make proper comparisons. Discounted cash flow (DCF) assumes a free cash flow amount, which is the difference between operating income and operating expenses net of any non-cash expenses or non-cash income. In capital budgeting decisions, it may be erroneous to assume that all of the free cash flow applies to the discounted cash flow. If Vision Inc., for instance, has diversified products, a single growth rate may not apply to all product lines. Likewise, it may not be the correct assumption to apply in the capital investment analysis. Earnings before interest and taxes (EBIT) can be used. Earnings before interest and taxes (EBIT) is the profit associated with operations; it is an important calculation for investors and business managers. Typically, EBIT ratios are used to verify that the DCF assumptions are correct, since EBIT gives information that is independent of capital structure.

An investor in Vision Inc., for example, will earn profits in the form of dividends. This profit will come from increased free cash flow as a result of new capital investments. Therefore, discounted cash flow decisions have a direct impact on the dividend payout ratio. The dividend payout ratio is the ratio of the distribution of a corporation's earnings (in the form of cash, stock, or property) to the stockholders, divided by the net income of a company. Dividends are a key component in the valuation of Vision Inc., and they may be discounted in the valuation process. For the sake of consistency, the discount amount will be equivalent to the discounting used in the DCF analysis. The time value of money will not change for different cash sources over the same periods of time, so DCF analysis will tie into all of the financial statement analysis within Vision Inc.

#### Process for Calculating Discounted Cash Flow The free cash flow assumption will affect analysis, so it needs to be accurate. There are several methods for calculating the terminal value, including the terminal growth multiple and the perpetuity method.