09 Nov, 2017
Company Valuation Methods. Cash Flow Discounting-Based Methods (Part 5)
These methods seek to determine the company’s value by estimating the cash flows it will generate in the future and then discounting them at a discount rate matched to the flows' risk.
The mixed methods described previously have been used extensively in the past. However, they are currently used increasingly less and it can be said that, nowadays, the cash flow discounting method is generally used because it is the only conceptually correct valuation method. In these methods, the company is viewed as a cash flow generator and the company’s value is obtained by calculating these flows' present value using a suitable discount rate.
Cash flow discounting methods are based on the detailed, careful forecast, for each period, of each of the financial items related with the generation of the cash flows corresponding to the company’s operations, such as, for example, collection of sales, personnel, raw materials, administrative and sales expenses, loan repayments. Consequently, the conceptual approach is similar to that of the cash budget.
In cash flow discounting-based valuations, a suitable discount rate is determined for each type of cash flow. Determining the discount rate is one of the most important tasks and takes into account the risk, historic volatilities; in practice, the minimum discount rate is often set by the interested parties (the buyers or sellers are not prepared to invest or sell for less than a certain return, etc.).
1. General Method for Cash Flow Discounting
The different cash flow discounting-based methods start with the following expression:
V = CF1/(1+k)+CF2/(1+k)^{2} + CF3/(1+k)^{3}+…+ (CFn+ VRn)/(1+k)^{n},
where: CFi = cash flow generated by the company in the period i; Vn = residual value of the company in the year n; k = appropriate discount rate for the cash flows' risk.
Although at first sight it may appear that the above formula is considering a temporary duration of the flows, this is not necessarily so as the company’s residual value in the year n (Vn) can be calculated by discounting the future flows after that period. A simplified procedure for considering an indefinite duration of future flows after the year n is to assume a constant growth rate (g) of flows after that period.
Then the residual value in year n is VRn = CFn (1 + g)/(k — g).
Although the flows may have an indefinite duration, it may be acceptable to ignore their value after a certain period, as their present value decreases progressively with longer time horizons.
Furthermore, the competitive advantage of many businesses tends to disappear after a few years. Before looking in more detail at the different cash flow discounting-based valuation methods, we must first define the different types of cash flow that can be used in a valuation
2. Deciding the Appropriate Cash Flow for Discounting and the Company’s Economic Balance Sheet
There are three basic cash flows: the free cash flow, the equity cash flow, and the debt cash flow. The easiest one to understand is the debt cash flow, which is the sum of the interest to be paid on the debt plus principal repayments. In order to determine the present market value of the existing debt, this flow must be discounted at the required rate of return to debt (cost of the debt). In many cases, the debt’s market value shall be equivalent to its book value, which is why its book value is often taken as a sufficient approximation to the market value.
The free cash flow (FCF) enables the company’s total value (debt and equity: D + E) to be obtained. The equity cash flow (ECF) enables the value of the equity to be obtained, which, combined with the value of the debt, will also enable the company’s total value to be determined. The discount rates that must be used for the FCF and the ECF are explained in the following sections.
Figure 4 shows in simplified form the difference between the company’s full balance sheet and its economic balance sheet. When we refer to the company’s (financial) assets, we are not talking about its entire assets but about total assets less spontaneous financing (suppliers, creditors…). To put it another way, the company’s (financial) assets consist of the net fixed assets plus the working capital requirements. The company’s (financial) liabilities consist of the shareholders' equity (the shares) and its debt (short and long-term financial debt). In the rest of the paper, when we talk about the company’s value, we will be referring to the value of the debt plus the value of the shareholders' equity (shares).
Figure 4. Full and Economic Balance Sheet of a Company
The Free Cash Flow.
The free cash flow (FCF) is the operating cash flow, that is, the cash flow generated by operations, without taking into account borrowing (financial debt), after tax. It is the money that would be available in the company after covering fixed asset investments and working capital requirements, assuming that there is no debt and, therefore, there are no financial expenses. In order to calculate future free cash flows, we must forecast the cash we will receive and must pay in each period. This is basically the approach used to draw up a cash budget. However, in company valuation, this task requires forecasting cash flows further ahead in time than is normally done in any cash budget.
Accounting cannot give us this information directly as, on one hand, it uses the accrual approach and, on the other hand, it allocates its revenues, costs and expenses using basically arbitrary mechanisms. These two features of accounting distort our perception of the appropriate approach when calculating cash flows, which must be the «cash» approach, that is, cash actually received or paid (collections and payments). However, when the accounting is adjusted to this approach, we can calculate whatever cash flow we are interested in.
We will now try to identify the basic components of a free cash flow in the hypothetical example of the company XYZ. The information given in the accounting statements shown in Table 6 must be adjusted to give the cash flows for each period, that is, the sums of money actually received and paid in each period. Table 6 gives the income statement for the company XYZ, SA. Using this data, we shall determine the company’s free cash flow, which we know by definition must not include any payments to fund providers. Therefore, dividends and interest expenses must not be included in the free cash flow.
Table 7 shows how the free cash flow is obtained from earnings before interest and tax (EBIT). The tax payable on the EBIT must be calculated directly; this gives us the net income without subtracting interest payments, to which we must add the depreciation for the period because it is not a payment but merely an accounting entry. We must also consider the sums of money to be allocated to new investments in fixed assets and new working capital requirements (WCR), as these sums must be deducted in order to calculate the free cash flow.
Table 6. Income Statement for XYZ
2014 | 2015 | 2016 | |
Sales | 1,000.00 | 1,100.00 | 1,210.00 |
Cost of goods sold | -650.00 | -715.00 | -786.50 |
General expenses | -189.00 | -207.90 | -228.70 |
Depreciation | -20.00 | -20.00 | -20.00 |
Earnings before interest and tax (EBIT) | 141.00 | 157.10 | 174.80 |
Interest expenses | -10.00 | -10.00 | -10.00 |
Earnings before tax (EBT) | 131.00 | 147.10 | 164.80 |
Tax | -45.85 | -51.49 | -57.68 |
Net income (EAT) | 85.15 | 95.62 | 107.10 |
Dividends | -34.06 | -38.25 | -42.85 |
Retained earnings | 51.09 | 57.37 | 64.28 |
Table 7. Free Cash Flow of XYZ, SA
2014 | 2015 | 2016 | |
Earnings before interest and tax (EBIT) | 141.00 | 157.10 | 174.80 |
Tax paid on EBIT | -49.40 | -55.00 | -61.20 |
Net income without debt | 91.65 | -102.10 | -113.60 |
Depreciation | +20.00 | +20.00 | +20.00 |
Increase in fixed assets | -61.00 | -67.10 | -73.80 |
Increase in WCR | -11.00 | -12.10 | -13.30 |
Free cash flow | 39.65 | 42.92 | 46.51 |
In order to calculate the free cash flow, we must ignore financing for the company’s operations and concentrate on the financial return on the company’s assets after tax, viewed from the perspective of a going concern, taking into account in each period the investments required for the business’s continued existence.
Finally, if the company had no debt, the free cash flow would be identical to the equity cash flow, which is another cash flow variant used in valuations and will be analyzed below.
The Equity Cash Flow.
The equity cash flow (ECF) is calculated by subtracting from the free cash flow the interest and principal payments (after tax) made in each period to the debt holders and adding the new debt provided.
In short, it is the cash flow remaining available in the company after covering fixed asset investments and working capital requirements and after paying the financial charges and repaying the corresponding part of the debt’s principal (in the event that there exists debt). This can be represented in the following expression:
ECF = FCF — [interest payments x (1- T)] - principal repayments + new debt
When making projections, the dividends and other expected payments to shareholders must match the equity cash flows. This cash flow assumes the existence of a certain financing structure in each period, by which the interest corresponding to the existing debts is paid, the installments of the principal are paid at the corresponding maturity dates and funds from new debt are received. After that there remains a certain sum, which is the cash available to the shareholders, which will be allocated to paying dividends or buying back shares.
When we restate the equity cash flow, we are valuing the company’s equity (E), and, therefore, the appropriate discount rate will be the required return to equity (Ke). To find the company’s total value (D + E), we must add the value of the existing debt (D) to the value of the equity (E).
Capital Cash Flow
Capital cash flow (CCF) is the term given to the sum of the debt cash flow plus the equity cash flow. The debt cash flow is composed by the sum of interest payments plus principal repayments. Therefore:
CCF = ECF + DCF = ECF + I — ΔD
I = D Kd
It is important to not confuse the capital cash flow with the free cash flow.
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.
4. Calculating the Value of the Company as the Unlevered Value Plus the Discounted 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 shield 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
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 can be estimated using any of the following methods:
1. Gordon and Shapiro’s constant growth valuation model:
Ke = [Div1 / P0] + g, where 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 euro, it is expected to pay a dividend of 10 euro 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 beta, RM = expected market return, RM — RF = market risk premium or equity premium. 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 equity
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 (WACC_{BT}):
E + D = present value [CCF; WACC_{BT}]
WACC_{BT} = (E Ke + D Kd)/(E+D)
CCF = (ECF + DCF)
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Company Valuation Methods: Part1, Part2, Part3, Part4, Part5, Part6, Part7, Part8
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