# Valuation using discounted cash flows

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Valuation using discounted cash flows is a method for determining the current value of a company using future cash flows adjusted for time value. The future cash flow set is made up of the cash flows within the determined forecast period and a continuing value that represents the cash flow stream after the forecast period.

## Basic formula for firm valuation using DCF model

value of firm = ${\displaystyle \sum _{t=1}^{n}{\frac {FCFF_{t}}{(1+WACC_{hg})^{t}}}+{\frac {\left[{\frac {FCFF_{n+1}}{(WACC_{st}-g_{n})}}\right]}{(1+WACC_{hg})^{n}}}}$

where ${\displaystyle FCFF_{t}}$ is the Free Cash Flow from the Firm, the ${\displaystyle WACC_{hg}}$ is the Weighted Average Cost of Capital for High Growth period (from ${\displaystyle t=1}$ to n${\displaystyle ),}$ and ${\displaystyle WACC_{st}}$t is the Weighted Average Cost of Capital for Standard Growth period.

## Process Data Diagram

The following diagram shows an overview of the process of company valuation. All activities in this model are explained in more detail in section 3: Using the DCF method.

## Using the DCF Method

### Determine Forecast Period

The forecast period is the time period for which the individual yearly cash flows are input to the Discounted Cash Flows (DCF) formula. Cash flows after the forecast period can only be represented by a fixed number such as annual growth rates. There are no fixed rules for determining the duration of the forecast period.

Example:

‘MedICT’ is a medical ICT startup that has just finished their business plan. Their goal is to provide medical professionals with software solutions for doing their own bookkeeping. Their only investor is required to wait for 5 years before making an exit. Therefore MedICT is using a forecast period of 5 years.

### Determine the yearly Cash Flow

Cash flow is the difference between the amount of cash flowing in and out a company. Make sure to consistently include the different types of cash flows.

Example: MedICT has chosen to use only operational cash flows in determining their estimated yearly cash flow:

In thousand €

 Year 1 Year 2 Year 3 Year 4 Year 5 Revenues +30 +100 +160 +330 +460 Personnel -30 -80 -110 -160 -200 Car Lease -6 -12 -12 -18 -18 Marketing -10 -10 -10 -25 -30 IT -20 -20 -20 -25 -30 Cash Flow -46 -22 +8 +102 +182

### Determine Discount Factor / Rate

Determine the appropriate discount rate and factor for each year of the forecast period based on the risk level associated with the company and its market. The higher the risk, the higher the discount rate will be.

Example:

MedICT has chosen their discount rates based upon their company maturity. As they are note already noted, they used comparable firms to estimate their risk. If such firms did not exist, their risk could still be estimated using financial characteristics (leverage, size, volatility in earnings,...). For a comprehensive treatment of how to value young companies, see Damodaran (2002).

 Year 1 Year 2 Year 3 Year 4 Year 5 Risk Group Seeking Money Early Startup Late Start Up Mature Risk Rate 50 - 100 40 – 60 30 – 50% 10- 25% Discount Rate 65% 55% 45% 35% 25% Discount Factor 0.61 0.42 0.33 0.30 0.33

### Determine Current Value

Calculate the current value of the future cash flows by multiplying each yearly cash flow by the discount factor for the year in question. This is known as the time value of money.

Example:

 Year 1 Year 2 Year 3 Year 4 Year 5 Cash Flow -46 -22 +8 +102 +182 Discount Factor 0.61 0.42 0.33 0.30 0.33 Current Value € -28.06 € -9.24 € 2.64 €30.6 €60.6

Total current value = 56.540

### Determine the Continuing Value

Calculating cash flows after the forecast period is much more difficult as uncertainty, and therefore the risk factor, rises with each additional year into the future. The continuing value, or terminal value, is a solution that represents the cash flows after the forecast period.

Example:

MedICT has chosen the perpetuity growth model to calculate the value of cash flows after the forecast period. They estimate that they will grow at about 6% for the rest of these years.

${\displaystyle {\frac {182*(1+0.25)}{0.25-0.06}}=1197.37}$

The total cash flows after the forecast period are valued at € 1197.37

This value however is a future value that still needs to be discounted to a current value:

${\displaystyle 1197.37*{\frac {1}{(1.25)^{5}}}=392.35}$

### Determining Company Value

The value of the company can be calculated by subtracting any outstanding debts from the total off all discounted cash flows.

Example:

MedICT doesn’t have any debt so it only needs to add up the current value of the continuing value and the current value of all cash flows during the forecast period:

56.540 + 392.354 = 448.894

The company or equity value of MedICT : € 448.894

## Pitfalls

As in any model, the Discounted Cash Flow has some known quirks:

• Reliance on Free Cash Flows

Some big companies (i.e. GE, Wal-Mart,...) consitently report negative free cash flows. According to the DCF formula, this has a negative impact on the value of the firm. But as noticed by Penman (2006), FCF is defined as: Cash Flow from Operations - Cash Investment.

In other words, any companies having a lot of investment oppportunies (i.e. investment in a new location or a new machine) would have their value decreased while those investments can be (if successful) value generators.

• Sensitivity to Continuing Value

As seen in our MedICT example, an error in the continuing value estimate can have a large impact on the firm value (85% of the value being determined by long term prospects). Any change in the firm discount rate or the growth rate estimate would have a huge impact on the firm value.

• Based on some Speculation

As the DCF model is mainly based on estimates (FCF estimates, discount and growth rate estimates), analyst can easily manipulate those numbers to provide a firm value that has nothing to do with the real intrinsic value.

## References

• Damodaran A., 2002, Investment Valuation: Tools and Techniques for Determining Value, Second Edition, Wiley and Sons
• Keck, T., E. Levengood, and A. Longfield, 1998, "Using Discounted Cash Flow Analysis in an International Setting: A Survey of Issues in Modeling the Cost of Capital", Journal of Applied Corporate Finance, Fall, pp. 82-99.
• Kubr, Marchesi, Ilar, Kienhuis. 1998. "Starting Up" Mckinsey & Company
• Pablo Fernandez. 2004. "Equivalence of ten different discounted cash flow valuation methods", IESE Research Papers. D549
• Penman, S. H., 2006 "Handling Valuation Methods", Journal of Applied Corporate Finance, Spring 2006, pp. 48-54
• Ruback, R. S., 1995, "An Introduction to Cash Flow Valuation Methods", Harvard Business School Case # 295-155.