Discounted cash flow (“DCF”) is a magnificent tool. Although discounted cash flow may look complex with a series of cash flows discounted by the discount rate involved, it is a familiar concept to business professionals in the workplace. Discounted cash flow technique can be used in many aspects and we are going to take a look at them in the following examples. 

1. Net Present Value (“NPV”)

In financial management, evaluation of whether a project is worth investing often involves net present value calculation. The net present value simply considers a series of cash flows generated from the project discounted by required rate of return and the initial investment needed for the project. If the net present value is positive, meaning the net payoff /return from the project is a gain, accepting a positive NPV project will be beneficial. 

2. Financial Product Valuation/Modeling

Industry practitioners also make use of discounted cash flow technique when it comes to financial product valuation/modeling. Take plain vanilla bond valuation as an example. Its valuation is simply the coupon payment at different payment periods (i.e. the cash flows at various time horizons) discounted by the interest rate yield curve. It is obvious that discounted cash flow technique is employed in valuation. 

For more sophisticated financial products like financial derivatives, its valuation can, in fact, also be derived by multiple discounted cash flows techniques. Considering an interest rate swap (“IRS”) like a pay fixed-receive floating IRS, its valuation involves two discounted cash flows, where the pay-leg and receive-leg of a series of floating-rate and fixed-rate payments are both discounted by the interest rate yield curve.

3. Gordon Growth Model

Gordon Growth Model is one of the dividend growth modelling methods used to estimate the value of a company stock. This model often exists in many textbooks in the form of a short formula and it also makes use of the discounted cash flow model. 

Let us take a look at a simplified numerical illustration below.

Assuming we would like to do the addition of the following numbers which have a geometric series of pattern, starting with first term as a positive number (a), followed by the second term being the first term multiplied by a constant ratio (r), and the third term being the second term multiplied by the same constant ratio (r), so on and so forth. Each of the following terms gets multiplied by the same constant ratio (r), and the total number of terms is N+1

a + (a x r) + (a x r²) + ….+ (a x r^N)

Using the geometric sum of series formula, a + (a x r) + (a x r²) + ….+ (a x r^N) can be simplified as [ a x (1- r^N+1)/(1-r) ]

Secondly, assuming that the share price is equal to dividends paid in perpetuity discounted by the shareholder’s required rate of return.

D denotes the dividend paid at the first year end
R denotes the shareholder’s required rate of return 
G denotes a constant growth rate of dividend for each year and G is smaller than R
P denotes the current share price of a company
N denotes last period of dividend 

P = D/(1+R) + D(1+G)/(1+R)²+…..+D(1+G)^N-1/(1+R)^N

The right side of the above equation has a geometric sum of series pattern in that the first term is D/(1+R), the constant ratio is (1+G)/(1+R) , the number of terms is N

As a result, substituting geometric sum of series formula, 

P = D/(1+R) x (1- [(1+G)/(1+R)]^N)/(1-[(1+G)/(1+R)])

When N is close to infinity given dividends paid in perpetuity, and given G is assumed to be smaller than R, the above equation with the aid of Mathematics Limit function will be further simplified as 

P = D/(1+R) x [ 1/(1-[(1+G)/(1+R)]) ]

P = D/(R-G) (also known as the Gordon growth model equation)

In short, the dividend growth model generally considers a series of dividend payment which grows at certain percentages every year and then gets discounted by the required rate of return correspondingly. But when the growth rate of dividend is at a constant rate till infinity given a company life can be no end theoretically, through mathematical technique, the entire series of discounted cash flows for all time periods can be consolidated and be represented in a short golden equation with the aid of the geometric sum of series formula.

4. Free Cash Flow Analysis 

Free cash flow analysis to quantify a capital budgeting opportunity is very common in corporate finance. It considers real free cash flow to the firm by taking into consideration such factors as operating profit, depreciation and changes in working capital at a definite period of time discounted by the weighted average cost of capital (“WACC”). Again the underlying concept used is the discounted cash flow technique.

Key Takeaways

The discounted cash flow technique is embedded in many financial management contexts, such as enterprise valuation, NPV calculation, and financial product modeling. A good understanding of its key essence is of utmost importance, rather than memorizing the formulae or equations by rote. For instance, the denominator of discounted cash flow (also known as the “Discount Rate”) will be different depending on the context, ranging from the required rate of return for a particular project for special purpose, the weighted average cost of capital of the company to interest rate yield curve, etc. Take the interest rate yield curve as an example. The interest rate yield curve varies across business contexts and situations. There are short rates, such as within one year, and long rates, which can be up to 10 years. The interest rate yield curve will also differ based on the currency, for instance, whether it is USD Secured Overnight Financing Rate (USD-SOFR) or HKD Hong Kong Interbank Offered Rate (HKD-HIBOR). Misuse of any of the parameters during the discounted cash flow analysis can give rise to wrong output results, and the decisions made based on these results can be fatal in real life.

Although the technique and formula of discounted cash flow may seem easy, it is important to be more cautious about applying different discount rates in the right contexts and at the right timing. Similarly, the series of cash flows (the numerators in the DCF model) will involve the application of relevant cash flows, which may appear straightforward, but is it really? There are expenses that have already been incurred before the investment decision starts, like suck cost, and they should not be considered. As a result, every discounted cash flow analysis should carefully consider and select the numerator and denominator. A careless or wrong application of any components of the numerator or denominator of the discounted cash flow would lead not just to incorrect calculations on paper, but more severely, to wrong decisions which may be costly.

The discounted cash flow technique is very useful and has a wide range of applications. However, it may have limitation due to the initial data used, simply because of the principle of ‘garbage in, garbage out.’ Periodical review of relevant data, assumptions, scenarios, and fine-tuning of input data and variables will enhance the performance of the discounted cash flow model.

It is foreseeable that the algorithms and calculations in the financial management context will only become more complex, and the performance of such models is expected to increase thanks to state-of-the-art technology. Nonetheless, the underlying fundamental principle is still at the heart of all models and calculations.

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About the author
Isaac Cheng
Head of Finance, General Manager, SPDB Hong Kong
Incorporated in the People’s Republic of China with limited liability