5.3. Calculating the value of the company using the free cash flow
In order to calculate the value of the company using this method, the free cash flows are discounted
(restated) using the weighted average cost of debt and equity or weighted average cost of capital (WACC):
E + D = present value [FCF; WACC] where WACC =
E Ke + D Kd (1- T)
E + D
D = market value of the debt. E = market value of the equity
Kd = cost of the debt before tax = required return to debt. T = tax rate
Ke = required return to equity, which reflects the equity’s risk
The WACC is calculated by weighting the cost of the debt (Kd) and the cost of the equity (Ke) with
respect to the company’s financial structure. This is the appropriate rate for this case as, since we are valuing the
company as a whole (debt plus equity), we must consider the required return to debt and the required return to
equity in the proportion to which they finance the company.
5.4. Calculating the value of the company as the unlevered value plus the value of the tax shield
In this method, the company’s value is calculated by adding two values: on the one hand, the value of
the company assuming that the company has no debt and, on the other hand, the value of the tax shield obtained
by the fact that the company is financed with debt.
The value of the company without debt is obtained by discounting the free cash flow, using the rate of
required return to equity that would be applicable to the company if it were to be considered as having no debt.
This rate (Ku) is known as the unlevered rate or required return to assets. The required return to assets is smaller
than the required return to equity if the company has debt in its capital structure as, in this case, the shareholders
would bear the financial risk implied by the existence of debt and would demand a higher equity risk premium.
In those cases where there is no debt, the required return to equity (Ke = Ku) is equivalent to the weighted
average cost of capital (WACC), as the only source of financing being used is capital.
The present value of the tax shield15 arises from the fact that the company is being financed with debt,
and it is the specific consequence of the lower tax paid by the company as a consequence of the interest paid on
the debt in each period. In order to find the present value of the tax shield, we would first have to calculate the
saving obtained by this means for each of the years, multiplying the interest payable on the debt by the tax rate.
Once we have obtained these flows, we will have to discount them at the rate considered appropriate. Although
the discount rate to be used in this case is somewhat controversial, many authors suggest using the debt’s market
cost, which need not necessarily be the interest rate at which the company has contracted its debt.
Consequently, the APV condenses into the following formula:
D + E = NPV(FCF; Ku) + value of the debt’s tax shield (VTS)
Basic stages in the performance of a valuation by cash flow discounting
1. Historic and strategic analysis of the company and the industry
A. Financial analysis B. Strategic and competitive analysis
Evolution of income statements and balance sheets Evolution of the industry
Evolution of cash flows generated by the company Evolution of the company’s competitive position
Evolution of the company’s investments Identification of the value chain
Evolution of the company’s financing Competitive position of the main competitors
Analysis of the financial health Identification of the value drivers
Analysis of the business’s risk
A. Financial forecasts B. Strategic and competitive forecasts
Income statements and balance sheets Forecast of the industry’s evolution
Cash flows generated by the company Forecast of the company’s competitive position
Investments Competitive position of the main competitors
Financing C. Consistency of the cash flow forecasts
Terminal value Financial consistency between forecasts
Forecast of various scenarios Comparison of forecasts with historic figures
Consistency of cash flows with the strategic analysis
For each business unit and for the company as a whole
Cost of the debt, required return to equity and weighted cost of capital
Net present value of the flows at their corresponding rate. Present value of the terminal value.
Value of the equity.
Benchmarking of the value obtained: comparison with similar companies
Identification of the value creation. Sustainability of the value creation (time horizon)
Analysis of the value’s sensitivity to changes in the fundamental parameters
Strategic and competitive justification of the value creation
2. Projections of future flows
3. Determination of the cost (required return) of capital
4. Net present value of future flows
5. Interpretation of the results
5.5. Calculating the value of the company’s equity by discounting the equity cash flow
The market value of the company’s equity is obtained by discounting the equity cash flow at the rate of
required return to equity for the company (Ke). When this value is added to the market value of the debt, it is
possible to determine the company’s total value.
The required return to equity is often using any of the following methods:
1. Gordon and Shapiro’s constant growth valuation model:
Ke = [Div1 / P0] + g. Div1 = dividends to be received in the following period = Div0(1+g)
P0 = share’s current price. g = constant, sustainable dividend growth rate
For example, if a share’s price is 200 dollars, it is expected to pay a dividend of 10 dollars and the
dividend’s expected annual growth rate is 11%: Ke = (10/200) + 0.11 = 0.16 = 16%
2. The capital asset pricing model (CAPM), which defines the required return to equity in the following terms:
Ke = RF + ß (RM - RF). RF = rate of return for risk-free investments (Treasury bonds)
ß = share’s beta16. RM = expected market return. RM – RF = market risk premium or equity premium
And thus, given certain values for the equity’s beta, the risk-free rate and the market risk premium; it is
possible to calculate the required return to equity17.
5.6. Calculating the company’s value by discounting the capital cash flow
According to this model, the value of a company (market value of its equity plus market value of its
debt) is equal to the present value of the capital cash flows (CCF) discounted at the weighted average cost of
capital before tax (WACCBT):
E + D = present value [CCF; WACCBT] WACCBT =
E Ke + D Kd
E + D
CCF = (ECF + DCF)
There are more methods to value companies discounting the expected cash flows. Chapter 6 (Valuing
Companies by Cash Flow Discounting: 10 Methods and 9 Theories http://ssrn.com/abstract=256987) shows that all ten
methods always give the same value. This result is logical, as all the methods analyze the same reality under the
same hypotheses; they differ only in the cash flows taken as the starting point for the valuation.
6. Which is the best method to use?
Table 8 shows the value of the equity of the company Alfa Inc. obtained by different methods based on
shareholders’ equity, earnings and goodwill. The fundamental problem with these methods is that some are
based solely on the balance sheet, others are based on the income statement, but none of them consider anything
but historic data. We could imagine two companies with identical balance sheets and income statements but
different prospects: one with high sales, earnings and margin potential, and the other in a stabilized situation with
fierce competition. We would all concur in giving a higher value to the former company than to the latter, in
spite of their historic balance sheets and income statements being equal. The most suitable method for valuing a
company is to discount the expected future cash flows, as the value of a company’s equity -assuming it continues
to operate- arises from the company’s capacity to generate cash (flows) for the equity’s owners.
Table 8. Alfa Inc. Value of the equity according to different methods. (Million dollars)
Book value 80
UEC method 167
Adjusted book value 135
Indirect method 197
Liquidation value 75
Direct or Anglo-Saxon method 218
PER 173
Annual profit purchase method 197
Classic valuation method 213
Risk-bearing and risk-free rate method 185
Simplified UEC method 177
7. The company as the sum of the values of different divisions. Break-up value
On many occasions, the company’s value is calculated as the sum of the values of its different divisions
or business units18.
The best way to explain this method is with an example. Table 9 shows the valuation of a North
American company performed in early 1980. The company in question had 3 separate divisions: household
products, shipbuilding, and car accessories. A financial group launched a takeover bid on this company at 38
dollars per share and a well-known investment bank was commissioned to value the company. This valuation,
which is included in Table 9, would serve as a basis for assessing the offer.
Table 9 shows that the investment bank valued the company’s equity between 430 and 479 million
dollars (or, to put it another way, between 35 and 39 dollars per share). But let us see how it arrived at that value.
First of all, it projected each division’s net income and then allocated a (maximum and minimum) PER to each
one. Using a simple multiplication (earnings x PER), it calculated the value of each division. The company’s
value is simply the sum of the three divisions’ values.
We can call this value (between 387 and 436 million dollars) the value of the earnings generated by the
company. We must now add to this figure the company’s cash surplus, which the investment bank estimated at
77.5 million dollars. However, the company’s pension plan was not fully funded (it was short by 34.5 million
dollars), and consequently, this quantity had to be subtracted from the company’s value.
The offer made of 38 dollars per share was in the interval between 35 and 39 dollars: luck?
Table 9.