The rationale behind the discounted cash flow (DCF) model is that a company is worth the sum of all the future cashflows discounted at the present value.

## FREE CASH FLOW

###### What is free cash flow (FCF)?

What is always used when running a discounted cash flow model is the free cash flow, which is a measure of profitability and given that it removes all non cash items, it is tougher to manipulate. It is in fact computed starting from EBIT, subtracting the taxes at the marginal tax rate, then adding Depreciation and Amortization, subtracting Capex(Capital Expenditures) and finally subtracting the change in NWC(net working capital), which is the difference between a company’s current assets and its current liabilities.

###### Why the marginal tax rate?

Most times, companies’ financial data published to investors and the one on which they based their tax payments are completely different. In fact, when presenting the two data goals are the opposite, on one hand they want to show high profits to investors, while on the other hand they prefer to have the lowest net income possible so that they need to pay less taxes. For this reason, the tax rate shown or publicly available financial statements

## THE DISCOUNT RATE

The discount rate is an essential part of the valuation tool, in fact it is used to discount all cash flows at the present value. The appropriate rate to use is the cost of capital, which is the cost of financing for the firm, the most common way to compute it is the WACC (weighted average cost of capital), where the cost of capital is the average between cost of debt and cost of equity weighted by the debt to equity ratio(D/E) of the firm.

###### Beta

In this section we will be explore what the beta is, so that it can be used later on to compute the cost of equity. The Beta is a financial coefficient which indicates how an asset moves with respect to the market. Beta is a concept that measures the expected move in a stock relative to movements in the overall market. A beta greater than 1.0 suggests that the stock is more volatile than the broader market, while a beta less than 1.0 indicates a stock with lower volatility. The Beta can in fact be computed as the ratio between the covariance of the asset and the market and the variance of the asset. It is worth mentioning that probably the fastest way to compute the beta is by using excel and downloading markets’ and assets’ data from Yahoo Finance. Moreover, both Bloomberg terminal and Refinitiv provide data regarding Beta for most of the stocks on the market.

###### The cost of equity

The most common way to compute the cost of equity is using the CAPM (capital assets pricing model), according to which the cost of equity (Ke) is the sum of the risk-free rate(rf) and the product between the risk premia (rm- rf) and the Beta. While the risk-free rate commonly used is the ten-year yield of the country taken into account, the risk premium(rm-rf) can be derived by analyzing historical data. Luckily for us, one of the greatest value investors and Stern’s University’s professor, Aswath Damodaran, calculate the Equity risk premium data for basically all countries on earth at: https://pages.stern.nyu.edu/~adamodar/New_Home_ Page/datafile/ctryprem.html

###### The cost of debt (Kd)

The cost of debt is an opportunity cost, and it measures the rate of return that is deemed acceptable by the holders of the firm debt, counterpart of risks such as defaults or inability of the firm to thoroughly fulfill its obligation. It expresses the costs that a firm must bear to finance new investments with debt. The computation of this rate depends on different assumption such asthe financial equilibrium of the firm and stable macroeconomic prospects. We can use different methods to calculate the cost of debt, the most used are the following:

Yields to maturity (YTM) on listed bonds: If the company has different bonds, we can make a weighted- average YTM on the analyzed company’s bonds. If we don’t have the YTM of our specific bonds, we can take this value from bonds with a comparable rating.

Model based on rating: according to this method the cost of debt is the sum of the base rate (Rf) and the spread. The first is expressed by the current return on long term risk-free investments, chosen regarding geographic location and accessible opportunities of the firm. The second, also known as risk premium, is defined by industry, geographical location and rating which allow us to create different bands of spread. To compute this value, we can use the spread calculator offered by Damodaran which considers the opinions of the two main rating agencies and the EBIT/Interests ratio.

Contractual: weighted average contractual interest rate for each type of debt (used for small-medium companies)

Accounting/Effective interest rate: according to this method the cost of debt is equal to the effective interest rates reported in the Income Statement divided by the Total Debt.

## FORCASTING FREE CASH FLOW

As mentioned above, according to the discounted cash flow model a business’ intrinsic value is equal to the sum of the present value of all its future cash flow. Therefore, it would be necessary to forecast all cash flows occurring from the date of the valuation to when the business ceased to exist.

###### Forecasting what predictable

To avoid forecasting all future cash flows, most textbooks usually suggest to project FCF to a point in the future when the company financial performance reaches a steady state. For financial analyst this usually means around 5 years, a time span during which allows businesses to go over an entire business cycle and for the realization of in process or planned initiatives. Instead, Value Investors many times opt for longer time spans, commonly 10 years. This is done, because before markets quit being irrational and go back to sanity, revaluing the acquired stock properly it can take long periods. Moreover, in other occasions, value investors can decide to invest in a company because the market is pricing current events too heavily and not seeing the end of a downturn, there is therefore need to wait a long time before being able to collect the desired gains.

###### Consideration for projecting FCF

Determining what free cash flow will be in future years is undoubtably one of the most difficult part of the discounted cash flow model. In fact, while for the modelling side it is easier to learn the process, projecting FCF is more of an art and requires a lot of past experience and expertise. Firstly it is definitely helpful to look for historical performance, however there is no guarantee that they will repeat in the future. It is important to oversee how a company behaved during a full business cycle and during crisis. Being optmisitic when projecting FCF is strongly not advised, instead it is better to be conservative, this way even if things don’t turn out as well as we hoped, the investment will deliver a decent return. For instance if you are projecting FCF for the next ten years, it is probable that the economy will incur at least a mild recession and it must therefore be included in the projections. It is also important to look out for analyst forecast, which can be found easily on Yahoo finance, but also on Bloomberg or Refinitiv. For most companies, analyst are usually excessively optimistic and Value Investors need to bear this in mind, however looking at their projections definitely gives a general idea of where the company is headed. In order to balance between conservatism and optimism analyst many times have different forecasts, a base case a worse case and a best case, so that we can have a range of valuation. Understanding companies performance drivers, such as customer strength, the completion of a new plant, strong dependency on certain customers or sector trends. In order to project any financial measure it is essential to determine revenue growth. While profitability measures depend a lot on the single company, sector trends and different growth drivers can send strong signal of what revenues will do in the next years.

Moreover, industry reports and consulting studies can definitely be helpful. COGS (cost of sales) and SG&A (Selling General and Administrative expenses) are estimated as a percentage of revenues, using historical data from the most recent years. It is however of extreme importance that banker find out whether the company had extremely high gross margins for a certain year and therefore avoid using it in the forecasts. For instance this is what happened with tech companies in 2020 and 2021, in this case when running a DCF it was appropriate to use as a growth margin number which is was a middle way between the 2020 and 2019 data. To project free cash flow it is instead essential to start from EBIT and EBITDA. In this case consensus estimates can be used for the first two or three years if available, after that it is common to hold EBIT and EBTIDA margins constant, however they can still be momentously reduced or increased to align them with a full business cycle performance. After determining EBIT, all the component of the FCF computation needs to be determined so that cash flow can be adequately projected.

The tax rate can be easily projected using the marginal tax rate, which can be found in the company annual report, in the US it is common to use a 25% for modelling purposes. The effective tax rate can also serve as a reference point.

Depreciation are scheduled over several years corresponding to the useful life of each of the company’s respective asset classes. Depreciation can therefore be projected as percentage of sales or capex. Building a PP&E schedule based on company’s existing depreciable and future capex projections or also the company specific assets. Watching the following video, you will be able to understand how different financial statements and especially PP&E and depreciation (from minute 16:00) are linked together, this will definitely help improving your modeling skill.

Ammortization instead it reduces the values of definite life intangible assets. Again ammortization can be projected as a percentage of sales or by building a detailed schedule upon a company’s existing intangible assets. In general it is common to forecast D&A together.

Change in Net working capital (NWC). While forecasting NWC as a percentage of revenues might work It is strongly suggested to forecast current assets and liabilities components, on the basis of historical ratio, historical performance and management guidance (mainly from earnings calls 10-Q or 10-K). In particular, capital efficiency ratios as DSO DIH DPO and Inventory turnover can all signal where NWC components are headed. For instance, accounts receivable are projected on the basis of DSO, while Inventory on DIH and accounts payable on DPO.

###### The terminal value (TV)

After having forecasted the first five or ten years it is necessary to find a way to determine the discounted value of al cash flows after that date. In order to do that it issufficient to determine the value of the business at that point in time and discount it to the present, this is called Terminal value as it represents the value of the company at the point in time during which we terminate to forecast cash flows. In order to do so there are two possible approaches listed here below:

The Perpetuity growth method, which assumes that after the business reached its financial steady state, it will grow at a fixed rate for ever. This rate of growth is usually low and can lie between 2.5 and 3.5 per cent, depending mostly on macroeconomic factor such as GDP growth. The formula to calculate the present value of a perpetually growing cash flow can be found starting from the cash flow at period n, the one at which terminal value is calculated. The formula here below assumes g being the perpetual rate of growth and WACC being the discount rate computed.

The exit multiple method, which consists in computing the Terminal Value by multiplying a financial metrics by a multiple which allows to discern the Enterprise Value or the Equity Value. In Investment Banking the most used is the EV/EBITDA (Enterprise Value over EBITDA) multiple. Therefore, by forecasting EBITDA (earnings before interest taxes depreciation and amortization, one of the most common metrics used in finance) until the final year of projections and then multiplying it by the multiple to obtain the Enterprise Value. When considering the world of investing it is however worth mentioning the importance of the P/E (price to earnings) ratio, which is probably the dominant ratio used when talking about financial markets. In case the P/E is used it is however essential to forecast the net income and then multiply it by the P/E multiple to compute the TV. The latter ratio for many companies can be found on most financial websites, including for instance Yahoo Finance. The EV/EBITDA multiple instead is less common to find and can be found mostly on pay-toaccess platforms as Capital IQ, Bloomberg (accessible at the Bocconi library) or Refinitiv (to which BSVI supervisors have remote access) which are widely available to investment banks. Moreover, professor Damodaran published a list of the average EV/EBITDA multiple in different industries at this link: https://pages.stern.nyu.edu/~adamodar/New_Hom e_Page/datafile/vebitda.html It is strongly suggested to our members to gain an understanding on what values those multiples usually take on, so that when estimating the one for the target company, a more accurate one will be chosen, leading to a better and precise valuation. When deciding the multiple to apply for the selected company it is crucial to look at what were the historical multiples for companies similar to the target at the valuation end period, with regard to size, margins, industry and growth expectation. When mentioning historical multiples, I did so because in case a relative valuation tool as the multiples method is used it is common to overvalue a companies because others are overvalued. If instead, the analyst or investor looks at how multiples moved historically forsimilar company, it is easier but not easy to better understand which multiple values the company correctly.

## DISCOUNTING THE CASH FLOWS

After having projected all the cash flows and computed the terminal values on Excel we will have a table like the one below, therefore it is then necessary to discount each year cash flow with to the present value and then sum all of them together. When discounting the cash flows, It is common to use the discount factor, a value equal to 1 over the sum between one and the discount rate powered to the number of years for which you need to discount. The discount factor multiplied by the cash flows gives us the present value of those cash flows. By summing all the discounted cash flows we obtain the Enterprise Value.

## DETERMINING THE BUY PRICE

As the most attentive reader probably noted, from the discounted cash flow model we do not obtain neither the market cap nor the share price, but the Enterprise Value. How do we therefore determine whether the stock is overvalued or undervalued?

###### What is Enterprise Value?

Enterprise Value tells us how much money it would be needed to buy a company. This is considered a more accurate representation of a firm value than the market cap or equity value. The Enterprise Value is in fact computed starting from the equity value, adding net debt, the difference between total debt and cash and cash equivalents, then adding Preferred Stock (which is treated as debt, given that in the event of an acquisition it is repaid by the acquirer) and Noncontrolling interest (any minority stake the target has, which produces cash flows but can be sold if we are solely interested in the business itself).

###### From EV to the stock price

From the formula mentioned in the previous paragraph it is easy to understand how to compute the Equity Value starting from the Enterprise Value. Once the Equity value or Market cap is calculated it is just necessary to divide it by the number of shares, which can be easily found in the most recent 10-Q a quarterly report, to the number of stocks it is also important to add in the money stock options, which will be exercised by their owners.

###### Margin of safety (MOS)

An important concept in Value Investing is Margin of Safety. Value investors usually prefer to buy a security when its stock price is below the fair price. To add a margin of uncertainty to the projections made and to minimize losses it is therefore used a Margin of safety, which is the discount from the fair price the investor believes necessary in order to minimize losses and risks. The Margin of Safety can depend on the uncertainty of the projections, underlying risk in the business or also the mere lack knowledge and experience with regard to a specific sector. Normally used margins of safety are in the range of 20%-30%. If a company carries significant risks, maybe liabilities in their balance sheets or the fact that the company is at an early stage of growth, investors can also opt for margins of safety of around 50%.