The aim of this paper is to present a framework to bank valuation based on two generally acceptable valuation models that are not specific to banks: the model of discounted Equity Cash Flow to Equity (ECF) and the model of discounted Residual Income (RI). As emphasized by Koller, Goedhart and Wessels (pp. 663, 2005) [1] in a bestselling book on the valuation of firms, the valuation process of a financial institution is characterized by fundamental difficulties because of the peculiarities that characterize the function of banking business and also the lack of information on critical bank financial data, such as the quality of the loan portfolio. This means that estimates based on assumptions must be created for these data and in this direction this paper provides an analytical guideline. For carrying out the valuation of a financial institution, specific templates of banking accounting statements ( i.e. a Balance Sheet and a Profit and Loss statement) proposed by Dermine (2009) [2] are used. The paper shows that both ECF and RI produce equivalent equity bank values. Given the recent financial crisis that has elevated the concern of banking institutions’ soundness, it is important to illustrate in practice the existing bank accepted valuation methodologies in order to form a clear framework for measuring the value of a bank and assess bank performance. The proposed framework can be applied by bank practitioners.
In building a cash flow model of a bank from the outside, the Equity Cash Flow (ECF) method rather the enterprise Discounted Cash Flow (DCF) method should be used. The reason is that for banks, the operating and financing decisions cannot be separated since interest income and expense (components of financing decisions) are important elements of the bank’s operating income. Therefore, in the proposed framework for valuing banks, the study uses the ECF method. Additionally, the paper utilizes a Residual Income (RI) method in order to confirm the theoretical justification of Koller, Goedhart and Wessels (2005) [
Both valuation models are based on discounting either future cash flows (ECF) or the periodic residual income (RI). To estimate future values of these variables is a prerequisite to predict the account figures of the bank’s financial statements. Thus, a full income statement and a balance sheet along with an abbreviated schedule of changes in shareholder’s equity which then lead to the equity cash flow, are utilized. Also, information about the Risk Weighted Assets (RWA) and Basel Tier 1 capital (equity and other capital that provides the most cushion for depositors and creditors) are used in order to incorporate some estimates of capital adequacy into the analysis. It is worth noting that the purpose of the current study is not to provide a comprehensive provisioning procedure, but to illustrate the various steps in the estimation of a bank’s value.
The methodological procedure the study follows is the below: initially, a full income statement and a balance sheet, along with an abbreviated schedule of changes in shareholder’s equity, are created. Then, forecasted financial statements are formed, based on specific assumptions. Thereafter, the future cash flows attributable to shareholders along with the terminal value of the bank are calculated. In the same manner, the residual income, created each year for shareholders along with the terminal value of the bank, is estimated. Then, through the use of the Capital Asset Pricing Model (CAPM) for the derivation of cost of equity, the cash flows and the terminal value are discounted and subsequently the equity value for the bank is derived. Also, the residual income and the terminal value are discounted and the sum of these components derives the equity value for the bank.
The main contribution of this tutorial paper is that presents analytically through an example a framework to bank valuation using the ECF and RI model. In addition, the paper explains the concept behind ECF and RI model as the appropriate valuation tools in banking and verifies the equivalence of both models. Moreover, the paper highlights in the conclusion section some important shareholder value determinants.
The paper is structured as follows: Section 2 presents the procedure for the preparation of primary financial statements for valuing purposes along with the assumptions that study hypotheses. Section 3 derives the equity value through the use of the discounted ECF model. Section 4 explains the discounted RI model and the final section concludes the paper.
The below financial accounting statement templates (
Assets | Liabilities |
---|---|
Cash Balances with BoG Due from Banks Securities & Investments Loans (net) PPE Accrued Income Other Assets | Due to Banks Deposits Bonds Issued Deferred Tax Liability Other Liabilities Total Shareholders’ Equity |
Total Assets | Total liabilities and Shareholder Equity |
(+) | Interest & Similar Income |
---|---|
(−) | Interest Expense & Similar Charges |
Net Interest Income | |
(+) | Fee & Commission Income |
(−) | Fee & Commission Expense |
Net Fee & Commission Income | |
(+) | Other Operating Income |
Total Operating Income | |
(+) | Depreciation |
(+) | Other General Administrative Expenses |
(−) | Operating Expenses |
(−) | Provision for Impairment |
Profit Before Tax | |
(−) | Income Tax |
Net Profit |
The projection of the accounting data included in the financial statements, which form the future annual cash flow and the residual income, is a critical task in a bank valuation process (Gross, 2006) [
The total forecasted period is divided into two phases: In the first phase the accounting data included on the financial statements are estimated, while in the second phase the terminal value of the bank is calculated. The first phase typically covers a five to ten-year period for industrial companies (Rappaport, 1986 [
As it is explained in the introduction, the priority is not to focus on the provision of balance sheet accounts. The literature mentions both qualitative and quantitative methods for predicting future financial performance of banks. Usually, the quantitative methods (due to available data) are used through a time series analysis, where the future performance based on historical accounting data is formed (Damodaran, 2009 [
Tables 3-8 present in detail the employed accounting statements for valuing purposes covering the analytical eight-year period: The Balance Sheet, the calculation of RWA and the required regulatory capital, the statement of change of the bank’s equity, the Profit and Loss statement, the calculation of ECF and RI respectively.
As regards the balance sheet (
Assets | 0 (today) | 1˚ year | 2˚ year | 3˚ year | 4˚ year | 5˚ year | 6˚ year | 7˚ year | 8˚ year | 9˚ year |
---|---|---|---|---|---|---|---|---|---|---|
Cash | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 | 100 |
Balances with Central Bank | 63 | 65 | 67 | 69 | 71 | 73 | 75 | 77 | 80 | 82 |
Due from Banks | 350 | 360 | 370 | 380 | 390 | 400 | 410 | 420 | 430 | 450 |
Securities and Investments | 350 | 360 | 370 | 380 | 390 | 400 | 410 | 420 | 430 | 450 |
Loans (net) | 3500 | 3605 | 3713 | 3825 | 3939 | 4057 | 4179 | 4305 | 4434 | 4567 |
Fixed Tangible Assets | 175 | 180 | 186 | 191 | 197 | 203 | 209 | 215 | 222 | 228 |
TOTAL Assets | 4538 | 4670 | 4806 | 4945 | 5087 | 5233 | 5383 | 5537 | 5695 | 5877 |
LIABILITIES | ||||||||||
Due to Banks | 1059 | 1094 | 1122 | 1151 | 1180 | 1209 | 1239 | 1268 | 1299 | 1348 |
Customer Deposits | 3150 | 3245 | 3342 | 3442 | 3545 | 3652 | 3761 | 3874 | 3990 | 4110 |
Bonds Issued | - | - | - | - | - | - | - | - | - | - |
Other Liabilities | - | - | - | - | - | - | - | - | - | - |
Total Shareholder Equity | 329 | 332 | 341 | 352 | 362 | 373 | 384 | 395 | 406 | 419 |
Total Liabilities and Equity | 4538 | 4670 | 4806 | 4945 | 5087 | 5233 | 5383 | 5537 | 5695 | 5877 |
1˚ year | 2˚ year | 3˚ year | 4˚ year | 5˚ year | 6˚ year | 7˚ year | 8˚ year | 9˚ year | |
---|---|---|---|---|---|---|---|---|---|
Risk Weighted Assets (RWA)* | 3316 | 3415 | 3516 | 3619 | 3726 | 3835 | 3948 | 4063 | 4193 |
Tier 1 (8%) for the Minimum Required Capital and Additional Capital (2%) for Growth Purposes | 10% | 10% | 10% | 10% | 10% | 10% | 10% | 10% | 10% |
Total Regulatory Capital | 332 | 341 | 352 | 362 | 373 | 384 | 395 | 406 | 419 |
*Due for banks are weighted with 20%, loans with 75%, securities and investments and tangible assets with 100% and cash-balances with Central Banks with 0%.
Years | 1˚ year | 2˚ year | 3˚ year | 4˚ year | 5˚ year | 6˚ year | 7˚ year | 8˚ year | 9˚ year |
---|---|---|---|---|---|---|---|---|---|
Equity (Beginning of the Year) | 329 | 332 | 341 | 352 | 362 | 373 | 384 | 395 | 406 |
(+) Share Capital Increase | - | - | - | - | - | - | - | - | - |
(+) Profit for the Period (from | 112 | 115 | 119 | 122 | 126 | 130 | 134 | 138 | 142 |
(-) Dividends and Potential Dividends | 109 | 106 | 109 | 112 | 115 | 119 | 122 | 126 | 129 |
Equity (End of Year) (as It Is Derived from the Above Table) | 332 | 341 | 352 | 362 | 373 | 384 | 395 | 406 | 419 |
0 (present) | 1˚ year | 2˚ year | 3˚ year | 4˚ year | 5˚ year | 6˚ year | 7˚ year | 8˚ year | 9˚ year | |
---|---|---|---|---|---|---|---|---|---|---|
Interest and Similar Income | 77 | 79 | 82 | 84 | 87 | 89 | 92 | 94 | 97 | 101 |
(+) Fee and Commissions Income | 15 | 16 | 16 | 17 | 17 | 18 | 18 | 19 | 19 | 20 |
(+) Other Operating Income | 8 | 8 | 8 | 8 | 9 | 9 | 9 | 9 | 10 | 10 |
Total Operating Income | 100 | 103 | 106 | 109 | 113 | 116 | 119 | 123 | 126 | 130 |
(−) Depreciation | 9 | 9 | 9 | 10 | 10 | 10 | 10 | 11 | 11 | 11 |
(−) Other General Administrative Expenses | 61 | 63 | 65 | 67 | 69 | 71 | 73 | 75 | 77 | 80 |
(−) Provision for Impairment | 25 | 26 | 27 | 27 | 28 | 29 | 30 | 31 | 32 | 33 |
Profit before Tax | 145 | 149 | 154 | 159 | 163 | 168 | 173 | 178 | 183 | 189 |
(−) Income Tax | 36 | 37 | 38 | 40 | 41 | 42 | 43 | 45 | 46 | 47 |
Net Profit | 109 | 112 | 115 | 119 | 122 | 126 | 130 | 134 | 138 | 142 |
that the customer loan balances increase at an annual growth rate of 3% (its increase is in line with the annual growth rate of nominal GDP). Loans to other credit institutions and the value of securities and investments are predicted to increase by 10 units per year, while for the year after the analytical eight years’ period, by 20 points. Deposit balances at the central bank are calculated as a proportion of 2% of the annual amounts of the total deposits (following the ECB guidelines) while the bank’s own cash balance is considered fixed over time. Also, the value of property is assumed to correspond every year to 5% of the loan balances.
Regarding liabilities, it is considered that the bank maintains throughout the analytical period a fixed ratio of loans to deposits equal to 90%. For the calculation of the annual equity the minimum bank capital required defined by Basel rules (the Basel I ratio) is used, which corresponds to at least 8% of the RWA. At the regulatory rate of 8%, two percentage points are added. This is justified by the fact that the bank must have additional funds (beyond the minimum requirement for capital) in order to exploit possible future investment opportunities. So, for each year the RWA are calculated (
In the paper’s example, the weights below are applied: 75% for customer loan balances, 20% for loans to financial institutions, 0% for cash equivalents and 100% for all other assets. Then, the sum of RWA for each year is multiplied by 10% and thus the capital required by the bank at the end of each year is derived. Then (
1˚ year | 2˚ year | 3˚ year | 4˚ year | 5˚ year | 6˚ year | 7˚ year | 8˚ year | 9˚ year | |
---|---|---|---|---|---|---|---|---|---|
Net Income | 112 | 115 | 119 | 122 | 126 | 130 | 134 | 138 | 142 |
(+) Depreciation | 9 | 9 | 10 | 10 | 10 | 10 | 11 | 11 | 11 |
(−) Net Increase in Loans | 105 | 108 | 111 | 115 | 118 | 122 | 125 | 129 | 133 |
(−) Net Increase in Securities and Investments | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 20 |
(−) Net Increase in Amounts due from Banks | 12 | 12 | 12 | 12 | 12 | 12 | 12 | 12 | 22 |
(−) Net Capital Expenditure | 14 | 15 | 15 | 16 | 16 | 17 | 17 | 18 | 18 |
(+) Net Increase in Deposits | 95 | 97 | 100 | 103 | 106 | 110 | 113 | 116 | 120 |
(+) Net Increase in Interbank Funds | 35 | 28 | 29 | 29 | 29 | 30 | 30 | 30 | 49 |
Equity Cash Flow | 109 | 106 | 109 | 112 | 115 | 119 | 122 | 126 | 129 |
Robustness check for the calculation of FCFE (second method, Koller Goedhart and Wessels, 2005 [ | |||||||||
(+) Dividends and Potential divIdends | 109 | 106 | 109 | 112 | 115 | 119 | 122 | 126 | 129 |
(−) Share Capital Issue (Repurchase) | - | - | - | - | - | - | - | - | - |
Equity Cash Flow (ECF) | 109 | 106 | 109 | 112 | 115 | 119 | 122 | 126 | 129 |
Present Value of ECF | 99* (0.909)** | 87 (0.826) | 82 (0.751) | 77 (0.683) | 72 (0.621) | 67 (0.565) | 63 (0.513) | 59 (0.466) | |
Terminal Value | - | - | - | - | - | - | - | - | 1420*** |
Present value of Terminal Value | - | - | - | - | - | - | - | - | 662**** (0.424)** |
EQUITY VALUE: Present Value of ECF + Present Value of terminal value = 605 + 662 = 1267 |
*The PV of ECF with a discounting rate of 10% according to CAPM. **Is the PV of 1 monetary unit. ***The terminal value of the bank is derived if we divide the net profit of year 9 (142) to the cost of equity (10%). ****Is the PV of terminal value with a discounting rate of 10%.
1˚ year | 2˚ year | 3˚ year | 4˚ year | 5˚ year | 6˚ year | 7˚ year | 8˚ year | 9˚ year | |
---|---|---|---|---|---|---|---|---|---|
Net Income | 112 | 115 | 119 | 122 | 126 | 130 | 134 | 138 | 142 |
(−) Cost of the Capital Employed (Equity b.o.y. * Cost of Equity 10%) | 33 | 33 | 34 | 35 | 36 | 38 | 39 | 40 | 41 |
Residual Income | 79 | 82 | 85 | 87 | 90 | 92 | 95 | 98 | 101 |
Present Value of Residual Income | 72* (0.909)** | 68 (0.826) | 64 (0.751) | 60 (0.683) | 56 (0.621) | 52 (0.565) | 49 (0.513) | 46 (0.466) | - |
Terminal Value | - | - | - | - | - | - | - | - | 1010*** |
Present Value of Terminal Value | - | - | - | - | - | - | - | - | 471**** (0.4241)** |
Equity Value: Equity (b.o.y) + Present Value of Residual Income + Present Value of Terminal Value = 329 + 467 + 471 = 1267 |
*Is the PV of Residual Income with a discounting rate of 10% according to CAPM. **Is the PV of 1 monetary unit. ***The terminal value of the bank is derived if we divide residual income of year 9 (101) to the cost of equity (10%). ****Is the PV of terminal value with a discounting rate of 10%.
takes place, if the required capital each year is covered by the annual profits and if an excess amount arises that is distributed to shareholders as dividend. Otherwise, an equity increase should take place in order to ensure the required capital level. Finally, liabilities to credit institutions each year are derived from the difference between total equity and total assets (i.e. an assumption is made that the capital structure does not vary over time).
For the income statement (
According to the previous section, one of the most appropriate models for valuing financial institutions is that of discounted ECF. The bank’s equity cash flows can be calculated either directly (direct approach) or indirectly (indirect approach), where both approaches lead to the same result. According to Gross (p. 49, 2006 [
The methodological steps for the derivation of the bank’s equity value are described below: First, the cash flows with the indirect method are calculated (
The second step is to determine the terminal value of the bank, for the period after the analytical calculations. For its calculation, the formula proposed by Copeland, Koller and Murrin (2000) [
where:
beta = Systematic risk of the bank.
The cost of equity is equal to the yield of a risk-free debt instrument plus the systematic risk of the bank, where the latter previously has been multiplied by the market risk premium. In banking literature, the yield on ten-year government bonds is used as an indicator of risk free rate (Copeland, Koller and Murrin, 2000 [
The final step, after the calculation of the analytical cash flows and the terminal value of the bank, is to discount these cash flows and the terminal value in present values using as a discount rate the cost of equity, as shown above through the usage of CAPM (assume 10% in our example). The sum of the present value of cash flows and terminal value of the bank, gives the ECF value (
In order to verify the derived bank equity (ECF model), an alternative bank valuation model is utilized based on discounted residual income (
The methodological steps for the derivation of the bank’s equity value are described below: First, the residual income (RI) for the analytical period of eight years is calculated. RI is the difference between operating profits after taxes and the cost of equity capital employed. The latter equals the previous year’s total equity multiplied by the cost of equity according to CAPM. Second, the terminal value of the bank in perpetuity is estimated by dividing the residual income of the year following the analytical period with the cost of equity (Gross, 2006) [
The purpose of this tutorial paper is to propose an analytical guideline to bank valuation. The occurrence of recent banking crisis with contagion effects to the real economy has demonstrated the importance of valuing and assessing correctly the bank performance and in this direction this paper attempts to illustrate in practice the existing bank accepted valuation. The paper employs two valuation methods appropriate for valuing financial institutions based on discounted equity cash flows and residual incomes respectively.
The study finds that both models lead to the same equity value (1267 monetary units) thus verifying the theoretical justification of Koller, Goedhart and Wessels, (2005) [
In memory of Professor Vasilios Spiropoulos, Department of Accounting, Technological Institute of Patras, Greece.
Aggelopoulos, E. (2017) Understanding Bank Valuation: An Application of the Equity Cash Flow and the Residual Income Approach in Bank Financial Accounting Statements. Open Journal of Accounting, 6, 1-10. http://dx.doi.org/10.4236/ojacct.2017.61001