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Estimation of Risk-Free Rate As a Part of Financial Management ESTIMATION OF RISK-FREE RATE AS A PART OF FINANCIAL MANAGEMENT Petra Gavlaková, Veronika Kormaňáková, Martina Rypáková INTRODUCTION We can say that companies have constantly been trying to gain a competitive advantage in the particular market. It is a never ending process and there are plenty ways how to achieve this. One way that can be effective is the cost of capital management. Each company should, among other things of course, focus also on the estimation of cost of capital and on decreasing these costs. The risk-free rate is a very important part of this estimation. 1 RISK-FREE ASSET An expected return on risk-free asset is considered to be the risk-free rate (rF). Therefore it is very important to identify the risk-free asset. Firstly, it is necessary to say that there doesn’t really exist a risk-free investment. In the short term we can consider some returns on investments to be sure but in the long term each investment or asset faces some kind of risk [5]. The definition of the risk-free asset results from the risk measurement in the risk decision making. An investment risk depends on the difference between investor’s expected return on holding assets for some period of time and the actual yield from the investment (asset). The risk is then represented by the volatility of actual real return from the expected return. If an asset is risk-free then the actual return on this asset has to be always equal to the expected return. The probability distribution for risk-free investment is shown on the figure 1. Figure 1 Probability Distribution for Risk-free Investment Source: [5] Damodaran [5] says that the risk-free rate can be understood differently in context of the investment behaviour relatively to the other investments. Risk-free rate should generate the returns that aren’t correlated to the risky investments in the market. If the risk-free investment gives sure returns regardless of the circumstances these returns shouldn’t be correlated to the risky investment returns under different scenarios. 2 THE IMPORTANCE OF RISK-FREE RATE The risk-free return is a very important part of the cost of capital estimation. Business capital consists of two basic parts – Equity and Debt. Cost of equity is usually calculated as the sum of risk- free return and risk premium that is derived from an investment risk and systematic risk premium [6]. Cost of debt is estimated as the sum of risk-free return and default spread derived from the company credit risk. Therefore the growth of risk-free rate ceteris paribus causes the growth of discount rate and also the discounted cash flows present value reduction [1]. According to Damodaran the impact of risk-free rate depends on the investment potential. If an investment with high expected growth of return generates the cash flow in the distant future then the value of this investment, while risk-free rate is growing, will decrease more that the value of investment generating the significant cash flow in the near future. The value of a company with big growth potential is therefore much more sensitive to the risk-free rate changes than the stabilized companies. Figure 2: The impact of risk-free rate growth on the different types of assets Asset with big growth potential Stabilized asset If an investment If an investment The growth generates the cash flow generates the cash of risk-free in the distant future, the flow in the near rate impact of risk-free rate future the impact of growth is very risk-free rate growth significant, the value is little. will decrease. Source: [5] The risk-free rate is a very significant component of many financial models and also influences other parameters. These parameters are risk premiums that play an important role in cost of equity and cost of debt calculation. 2.1 THE CRITERIA FOR RISK-FREE RATE Pratt [8] says that the concept of risk-free investment lies on the assumption that investor can be sure that he gets certain amount of money at agreed date exactly like he was promised. However there are some conditions that have to be satisfied to meet this assumption. These conditions create the criteria for identification the risk-free asset and risk-free rate. Damodaran [5], Brigham [2] and Pratt [9] concur that the risk-free investment: - Can’t face any default risk of an issuer – it means that there can’t be used a security issued by private company for risk-free rate estimation because even the biggest and safest companies face some kind of default risk. The only securities that can be used for this purpose are the securities issued by governments because they control the money supply. - Can’t face reinvestment risk - The risk that future coupons from a bond will not be reinvested at the prevailing interest rate when the bond was initially purchased. Reinvestment risk is more likely when interest rates are declining. Brigham and Pratt also add the condition that the risk-free investment: - Can’t face liquidity risk – in case that investor decides to get back his money before the maturity of bonds, there has to exist the sufficiently liquid market where he could sell the investment again with the minimum commission cost. 2.2 BASIC APPROACHES TO RISK-FREE RATE ESTIMATION There doesn’t exist any unified way how to calculate the risk-free rate. However, a literature gives us several possible approaches [7]: - rF estimation according to the past bonds yields – it is based on the average yields of the selected bonds. This method is quite simple and requires the answers on the questions like the period length selection, which bonds to choose, what kind of average to use, etc. All of these can influence the result significantly. Some financial specialists criticize this approach because of the possibility to manipulate with results and also because of ignoring the current financial market conditions which means that it doesn’t support the forward-looking concept (that is a very important assumption of correct cost of capital estimation). Risk-free rate should be therefore derived from the values there are valid at the measurement date. - rF estimation according to the direct future prediction – this is the most accepted and most used approach which has several versions [7]: 1. Estimation of discount-rates of reputable companies – this method has been criticized almost as much as the rF estimation according to the past bonds yields. The source of the criticism is most often in the market conditions volatility which is proved for example by the variations in estimation among different institutions. This approach also doesn’t reflect the current economics and capital market conditions. 2. The real rates of return of government bonds (spot rates and other capital market rates of return) – a lot of financial experts agrees on using this method when calculating the risk-free rate. However, a very important assumption here is that the definition and criteria of risk-free investment have to be valid. 2.3 DETERMINANTS OF MARKET RISK-FREE RATE The risk-free rate should compensate investors for giving up the actual consumption and postponing it to the future [9]. This fact is observable in the market while the difference between risk- free investments is only in the term of the time to maturity. According to T. Cipra it is possible to decompose the market risk-free rate as follows [3]: * 1 i 1 r 1 iIP 1 iMRP 1 iDRP 1 iLP (1) Where: i - Market interest rate r* - Real risk-free interest rate iIP - Interest premium for inflation iMRP - Maturity risk premium iDRP - Default risk premium iLP - Liquidity premium Similar decomposition is offered by other authors (Pratt [9], Brigham [2]) who use additive decomposition form: i r* IP MRP DRP LP (2) Where: i - Market interest rate r* - Real risk-free interest rate IP - Inflation premium MRP - Maturity risk premium DRP - Default risk premium LP - Liquidity premium In accordance with risk-free investment criteria the risk-free interest rate shouldn’t include these components: DRP – Risk-free investment doesn’t face the default risk of issuer, that’s why the default risk premium should be close to zero (limDRP → 0). LP – There should always exist a sufficiently liquid market for the risk-free investment, therefore liquid premium should be close to zero (limLP → 0). MRP – consists of more parts. The part connected with interest rate risk is always the component of risk-free interest rate. The part connected with the reinvestment risk should be close to zero and MRP should therefore consist just of the interest rate risk. The decomposition of risk-free rate then looks like: * rF r IP MRP (3) The risk-free rate components are then: real risk-free interest rate (r*), inflation premium (IP) and interest-rate risk which is part of maturity risk premium. CONCLUSION Each company that wish to be successful and profitable should focus on the cost of capital management. A very important part of the cost of capital estimation is the risk-free rate calculation. There doesn’t exist a unified approach for this process, however, many experts and specialists in the field of financial management usually use government bonds’ rate of return. But the financial theory knows also other methods for risk-free rate estimation. The aim of this paper was to familiarize the reader with risk-free rate and with possible ways for its estimation. First part of paper describes the risk-free asset, risk-free rate, its importance and criteria, and the second part introduces the basic risk- free rate valuation methods and risk-free rate components.
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