Valuation Concepts
Corporate Valuation
When discussing the valuation of a company, practitioners will often refer to one of the following terms:
- Enterprise value – valuing a company’s productive activities
- Equity – valuing the shares of a company (e.g. when valuing all of the equity, for the purpose of a corporate acquisition)
- Debt – valuing the company’s debt. When debt is risky, its value depends on the value of the company that has issued the debt
- Other - the valuing of other securities related to a company, such as options, warrants, employee stock options, etc.
The main concept in Corporate Valuation is that of Enterprise Value - this is a measure of the value of a firm’s core business activities.
Enterprise Value
In Corporate Finance, various approaches can be taken to calculating a firm’s value - but all of them are based on computing its Enterprise value (EV)! More mathematically, a firm’s Enterprise Value can be defined as: the present value of the firm’s future unlevered free cash flows (unlevered FCFs).
The DCF WACC approach is by far the most popular method. (There are others, such as: the accounting book value approach; the efficient markets approach; multiples of EBITDA or Sales approaches; Flow to Equity approach; or Adjusted Present Value method)
The DCF WACC method values a firm’s Enterprise Value (or levered value of a firm, \(V^L\)) from its future anticipated unlevered free cash flows (unlevered FCFs) discounted by its weighted average cost of capital (WACC).
So a lot of the work involved with valuing a company is often with just these two components:
- Calculating a firm’s Unlevered Free Cash Flows, and then,
- Estimating its Weighted Average Cost of Capital
Note:
The unlevered FCFs are the cash flows produced by the firm’s productive assets, that is: its working capital, fixed assets, and goodwill, etc. – but without taking into account the way the business is financed. This is why in many FCF workings, you will often see ‘added back’, the firm’s debt interest payments, net of tax.
Note:
When a firm maintains a fixed debt-to-value ratio over the life of the investment, often the DCF WACC method is the easiest to implement. For alternative leverage policies, (e.g. if debt is maintained as constant, or the debt-to-value ratio changes) the APV method is usually the most straightforward approach.
The APV method first determines an investment’s value without leverage \(V^U\) (the investment’s value if it had no debt), by discounting its unlevered free cash flows by its unlevered cost of capital \(r_u\) ( \(r_u\) is slightly different to WACC! ). It then separately adds to this, the present value of any interest tax shields (assuming the company now has debt), to get the value of the investment with leverage \(V^L\) (i.e. its total Enterprise Value).
\(V^L\) = \(V^U\) + \(PV(\text{Tax Shields})\)
(Unlevered) Free Cash Flows
There are various ways to calculating a company’s Free Cash Flows. For example, this can be done from its Consolidated Statement of Cashflows, but also, from a set of Pro Forma (Predictive, forward-looking) Financial Statements (e.g. of its Balance Sheet, and Profit & Loss account)
Often, in order to get to a firm’s unlevered FCFs, certain items need to be eliminated, such as any operating items, or investment items that are not expected to recur. In most cases these adjustments amount to the following:
- Accepting all Operating activities
- Dispensing with all Financing activities
- Carefully examining Investment activities, eliminating those that are financial, but keeping operational items
- Adding back after-tax interest, to neutralize the interest component in Profit after Tax
Terminal Value
Most financial analysts consider it presumptuous to project an infinite number of cashflows - not to mention the the uncertainty in projecting so far out into the future. Therefore, when preparing a DCF, the projected cashflow stream is often cut off at some arbitrary date, and a terminal value (also known as Horizon value) is substituted for cashflows beyond this date – using a version of a growing annuity formula.
WACC
The WACC of a firm, is the weighted average of its cost of equity \(r_E\), and its cost of debt \(r_D\), weighted by its market equity (\(E\)) and market debt (\(D\)) values. WACC essentially measures the average cost of firm’s different sources of financing (both debt and equity). This is the discount rate that used to calculate the present value of its Free Cash Flows. In a world with Taxes, the WACC can also be used to evaluate a project with the same risk and the same financing as the firm itself.
WACC can be calculated from the following formula:
\[\begin{align*} & WACC = {E \over ( E + D)}r_E + {D \over ( E + D)}r_D(1-T_c) \end{align*}\]where,
\(E =\) market value of the firm’s equity
\(D =\) market value of the firm’s debt
\(T_c =\) firm’s corporate tax rate
\(r_E =\) firm’s cost of equity
\(r_D =\) firm’s cost of debt
Because of the number of assumptions and judgment calls involved in estimating some of the above parameters, the reader should note that the computation of a firm’s WACC is as much of an art as it is a science! There are seldom ever any exact answers!
\(\mathbf{r_E}\) – the firm’s cost of equity, can, technically, be quite challenging to compute. There are two popular methods for estimating \(r_E\):
- The Gordon’s Growth model (that is based on anticipated capital and income returns to shareholders), or
- The Capital Asset Pricing model (CAPM) (that is based on the correlation between a firm’s equity returns and the returns of a large diversified portfolio).
Variations of these models include the tax framework in which the model is defined.
\(\mathbf{r_D}\) – this can also be quite problematic to compute. Popular methods include computing this by:
- Dividing a firm’s net interest payments by its average net debt (debt minus cash and marketable securities)
- Imputing the firm’s cost of debt from a rating adjusted yield curve
- Computing the firm’s bonds as a proxy for its cost of debt
Value of Equity (\(\mathbf{E}\))
\(\mathbf{E}\) - is often computed by taking the firm’s number of outstanding shares times the current market value per share.
Value of Debt (\(\mathbf{D}\))
\(\mathbf{D}\) - is often computed by taking the firm’s market value of debt minus the market value of excess liquid assets. A common approximation is to take the balance sheet value of debt minus the firm’s balance sheet cash and marketable securities.
Firm’s Tax Rate (\(\mathbf{T_c}\))
\(\mathbf{T_c}\) - should measure the firm’s marginal tax rate, but it is common to measure it by computing the firm’s reported tax rate. Usually, this should cause no problems. (usually!)
Firm’s Cost of Debt (\(\mathbf{r_D}\))
- As a practical matter, the cost of debt can often be approximated by taking the average cost of the firm’s existing debt. The problem with this method however is that it runs the risk of confusing past costs with future anticipated cost of debt that we actually want to measure.
- You can also use the yield of similar risk, newly issued corporate securities. This method can also be somewhat problematic as the yield on a bond is its promised return, whereas the cost of debt is the expected return on a firm’s debt. As there is usually a risk of default, the promised return is generally higher than the expected return. Despite the problematics, the methods is often a good compromise.
- A model can also be used that estimates the cost of debt from data about the firm’s bond prices, estimated probabilities of default, and estimated payoffs to bondholders in case of default. The method requires a lot of work and is mathematically non-trivial. For cost of capital calculations it would only be used if the firm being analysed had significant amounts of risky debt.
Firm’s Cost of Equity (\(\mathbf{r_E}\))
CAPM
- The CAPM method is very popular for computing \(r_E\). It is based on the risk free rate, \(r_f\), the expected rate of return on the market \(E(r_m)\), and the firm specific risk measure \(\beta\), and uses the tax-adjusted Security Market Line (SML) to calculate the firms cost of equity.
The formula is:
\[\begin{align*} & r_E = r_f(1 - T_c) + \beta (E(r_m) - r_f(1-T_c)) \end{align*}\]where,
\(r_f =\) the market risk-free rate of interest
\(E(r_m) =\) the expected return on the market portfolio
\(\beta =\) a firm-specific risk measure \(= {Cov(r_{stock}, r_m) \over Var(r_m}\)
\(T_C =\) the marginal corporate tax rate in the economy
Gordon Growth Model
- Another method for computing a firm’s \(r_E\) is the Gordon model (also called Dividend Discount Model). The \(r_E\) can be calculated from the following formula:
where,
\(g =\) Anticipated growth rate of cash flow equity
- Sometimes a two-stage growth verion of the model is used to account for the fact that dividends may grow at different rates over different periods, rather than at a constant rate.
If this is used, the Gordon model can be ammended as follows::
\[\text{Share value today} = \text{Present value of dividends}\] \[= \sum_{t=1}^{m} {Div_0 * (1 + g_1)^t \over (1 + r_E)^t} + \sum_{t=m+1}^{\infty} {Div_0 * (1 + g_1)^m * (1 + g_2)^{t-m} \over (1 + r_E)^t}\]where,
\(g_1 =\) Anticipated growth rate of cash flow equity over the initial growth period \(g_2 =\) Anticipated growth rate of cash flow equity over the long term
Applying Models in Practice
Because of the application of various models to compute a firm’s WACC, and need to make several judgement calls a long the way, the advice, when performing such valuations, is to:
- Use several models to calculate the cost of capital, when practically possible
- To calculate the WACC not just for the firm being analysed , but also for other firms in the same industry
A multi-method approach is often preferred in such cases, as it can give a more reliable estimate, and is more likely to identify any anomalous or mis-approximated parameters.
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