3.3.6.1.3 Discounted cash flow (DCF)

Money has a time value. One dollar today is worth more than one dollar tomorrow.1 If Mary puts 1 dollar in the bank, and the simple annual interest rate is 4%, then at the end of one year, she will receive 1 x (1 + 0.04) = 1.04 dollar. The formula to calculate the future value of a deposit is:

FV stands for the future value; Ai is the amount of the initial deposit; r is the interest rate; and n is the number of years the deposit stays in the account.

If, in order to receive a certain amount of money in some years, one wants to know how much they have to deposit today, the present value is expressed by the inverse of the future value calculation. So the formula is:

The foregoing reasoning also works for the valuation of a corporation.2 If the future value of the company is expected to be 100 million, how much does the investors need to invest now? Put in another way, how much is the company worth at present? The equation is:

Instead of the interest rate r, here we use the letter k which is referred to as the discount rate. K is the rate of return of the next best comparable investment (also called the opportunity cost), adjusted for risk.3 For example, if the predicted return rate of the next best investment is 20 per cent, k is lower than 0.2, because risks of the investment should also be taken into account. Again, however, the answer to the question how much lower k should be adjusted is an educated guess. It is the outcome of "complicated calculation and guesswork for the opportunity cost of capital",4 and closely related to the risk of an investment. The discounted cash flow method applies the above theory: the time value of money. To calculate the present value of an entity, it first determines the future value of the entity and then discounts it by an appropriate discount rate k to the present value. According to this method, the future value of a firm includes two parts: net cash flows over some foreseeable projection period plus the terminal or residual value which represents the firm's future cash flows after the projection period.5 Then these two parts are discounted to their present value by an appropriate k. The equation is thus:

CF is the cash flows in each project year, k is the discount rate, n are the years from the present to the end of the projection period, and TV is the terminal value.

From the above equation, we can see that the DCF method involves three basic components, namely, net cash flows of the firm, terminal value and discount rate.

First, one estimates the future net cash flows available to the corporation over a project period, where possible based on contemporaneous management projections. One then, estimates a terminal value at the end of such period, which represents the firm's future cash flows generated after the projection period. The terminal value can be determined by using a perpetual growth model or capitalization of earnings.6 Lastly, one determines the discount rate, and applies it to the cash flows generated in step one and terminal value in step two.7 Here is a simple example to illustrate how this method works. Suppose Company A has a project from 2009 to 2013. The estimated net cash flows of the project years are respectively $200, $250, $ 260, $ 290, and $ 280. The averaged earnings of the last three years are $100 and the discounted rate is determined as 9%. The P/E ratio is 15.

The DCF method, though frequently used after the Weinberger case, has not been the exclusive valuation method employed. The Delaware courts have enough discretion to apply a variety of valuation techniques, subject to the facts and circumstances of a particular case. Courts are free to use the Delaware block method,8 a valuation method based on net asset value,9 a method based on a comparison with other companies,10 or a valuation based on a combination of several valuation methods.11