Estimating Discount Rates

In discount cash flow valuation approach, the future cash flow has to be discounted with the rates which reflect the riskiness of the cash flows. For debt issuer the risk is default risk and for equity investor the risk is of market thus we have to estimate the cost of debt and cost of equity separately and then we will take the weighted average of these two to evaluate the discount rate or in other terms cost of capital and it is also known as weighted average cost of capital (WACC).

For cost of equity there are three ways to measure it

Models that measure the risk in an investment and convert this risk measure into an expected return, which in turn becomes the cost of equity for that investment. This is called Risk and Return Model.

The second approach looks at differences in actual returns across stocks over long time periods and identifies the characteristics of companies that best explain the differences in returns. We then use this relationship to forecast expected equity returns for individual companies.

The third approach uses observed market prices on risky assets to back out the rate of return that investors are willing to accept on these investments.

Risk and Return Model

Measuring the risk – When the investor invests in any stock he expects some return over the holding period, there may be difference in actual return and the expected return. This difference in the two returns stems the risk. The spread of the actual returns around the expected return is measured by the variance or standard deviation of the distribution. The greater the difference higher the variance and higher the risk.

There are two types of risk one is firm specific risk and other is market risk. It is assumed that the investor has invested in many assets thus he is well diversified thus the firm specific risks will not have much effect on the portfolio but the market risk, which is a risk that impacts the entire market like increase in interest rate or slowing down of economy, will affect the portfolio returns. Firm specific risks can be reduced to almost zero if the investor is well diversified thus in finance we measure only the market risk.

Measuring Market Risk – Capital Asset Pricing Model (CAPM) is the most widely used model for measuring market risk. It is based on two key assumptions that there is no transaction cost and investors have no access to private information. If there is no transaction cost then investor will invest in almost all the stocks which he can buy with the money thus portfolio will be well diversified and that’s why it will have only market risk and not the firm specific risk. For any stock we measure how much risk it is adding to the portfolio risk (portfolio is market here) which is measured by the covariance of the stock return with the market return and we standardize this measure by dividing it by the variance of the market. Thus market risk contributed by any stock = covariance (return of stock, return of market)/Variance (Return of market). This ratio is called the beta of the stock which measures the market risk of the stock.

Beta of the market portfolio will be 1 and the stocks which are riskier than the market will have beta more than one and stocks that are safer than the market portfolio will have beta less than one. The riskless assets will have beta 0. Expected return on stock i = Risk free return + Beta (stock i) *( Market return –Risk free return)

Arbitrage Pricing Model (APM) – Expected return on stock i = Risk free return + Beta1 * (R(f1) – Risk free return) + Beat2 * (R(f2) – Risk free return) + ….Beta for different factors will be estimated and multiplied with the factor premium values to find the expected return on any stock but the main problem with this method is to identify the factors which will impact the return. We use statistical methods to identify the factors which impact the return. APM is a more general form of CAPM

Multi factor Model – Replace the unidentified statistical factors of APM with specific economic factors and the resultant model should have an economic basis while still retaining much of the strength of APM. Once the number of factors has been identified in the APM, their behavior over time can be extracted from data. This behavior can then be compared to the behavior of macroeconomic variables over that same period to see whether any of the variables is correlated, over time, with the identified factors

Estimating Parameters for Risk and Return Models – We need three inputs to calculate the expected rate of return by CAPM risk free rate, beta and market return (or market risk premium)

Risk free rate – The assets for which there is no uncertainty about the expected return are risk free assets. There should be no default risk and there should be no uncertainty about reinvestment rates i.e. there should not be any intermediate cash flows. The risk free rate is different for different periods but for valuations, where cash flows stretch out over long periods (or to infinity), the risk-free rates used should almost always be long-term rates. In most currencies, there is usually a 10-year government bond rate that offers a reasonable measure of the risk-free rate. The other point of contention for the companies which are operating in multiple countries is which country risk free rate should be taken. The point to note is that it is not where an asset or firm is domiciled that determines the choice of a risk-free rate, but the currency in which the cash flows on the project or firm are estimated. Thus, we can value a Mexican company in dollars, using a dollar discount rate, or in pesos, using a peso discount rate. For the former, we would use the U.S. Treasury bond rate as the risk-free rate, but for the latter we would need a peso risk-free rate.

The return on sovereign bond is taken as risk free return but the implicit assumption here is that governments do not default, at least on local currency borrowing but there are many cases where governments have defaulted on local currency borrowings as well in these cases we cannot take the return on 10 year government bond as risk free return, is such cases we have to make some adjustments to arrive at the risk free rates. We can adjust the local currency government borrowing rate by the estimated default spread on the bond to arrive at a riskless local currency rate. The default spread on the government bond can be estimated using the local currency ratings that are available for many countries

Risk Premium - The risk premium in the capital asset pricing model measures the extra return that would be demanded by investors for shifting their money from a riskless investment to an average-risk investment. There are three ways of estimating the risk premium in the capital asset pricing model: Large investors can be surveyed about their expectations for the future, the actual premiums earned over a past period can be obtained from historical data, and the implied premium can be extracted from current market data. The premium can be estimated only from historical data in the arbitrage pricing model and the multifactor models.

In many emerging markets, there is very little historical data and the data that exists is too volatile to yield a meaningful estimate of the risk premium. In such cases we use Equity Risk Premium = Base Premium for Mature Equity Market + Country Premium. Base premium for mature equity market is premium for US market which is 4.84% between 1928 and 2004. For country premium we use the ratings assigned to a country’s debt by rating agencies, these ratings measure default risk (rather than equity risk), but they are affected by many of the factors that drive equity risk—the stability of a country’s currency, its budget and trade balances, and its political standing, for instance. Analysts who use default spreads as measures of country risk typically add them on to both the cost of equity and debt of every company traded in that country.

The other method used is to calculate the relative riskiness of the specific country market. Relative Standard Deviation (Country X) = Standard deviation (Country X)/Standard deviation (US) and this relative SD is multiplied with the equity risk premium of the US so Equity Risk Premium (Country X) = Risk Premium (US) * Relative SD (Country X).

The country default spreads that come with country ratings provide an important first step, but still only measure the premium for default risk. Intuitively, we would expect the country equity risk premium to be larger than the country default risk spread. To address the issue of how much higher, we look at the volatility of the equity market in a country relative to the volatility of the country bond used to estimate the spread. This yields the following estimate for the country equity risk premium: Country Risk Premium = Country Default Spread * (SD of equity/SD of Country Bond)

Beta - There are three approaches available for estimating beta; one is to use historical data on market prices for individual assets, the second is to estimate the betas from fundamentals, and the third is to use accounting data. Most analysts who use betas obtain them from an estimation service; Barra, Value Line, Standard & Poor’s, Morningstar, and Bloomberg are some of the most widely used services. All these services begin with regression betas and make what they feel are necessary changes to make them better estimates for the future. In general, betas reported by different services for the same firm can be very different because they use different time periods (some use two years and others five years); different return intervals (daily, weekly, or monthly); different market indices; and different post regression adjustments.

Historical Data is used for calculating the beta of the stock. Return on Stock (i) = a + beta * Return on Market. Beta is the slope of this regression line.

Fundamental Betas - The beta of a firm is determined by three variables: (1) the type of business or businesses the firm is in, (2) the degree of operating leverage in the firm, and (3) the firm’s financial leverage. The degree of operating leverage is a function of the cost structure of a firm, and is usually defined in terms of the relationship between fixed costs and total costs. A firm that has high operating leverage (i.e., high fixed costs relative to total costs) will also have higher variability in operating income than would a firm producing a similar product with low operating leverage. This higher variance in operating income will lead to a higher beta for the firm with higher operating leverage. Other things remaining equal, an increase in financial leverage will increase the equity beta of a firm. Intuitively, we would expect the fixed interest payments on debt to increase earnings per share in good times and to push it down in bad times. Higher leverage increases the variance in earnings per share and makes equity investment in the firm riskier. If all of the firm’s market risk is borne by the stockholders (i.e., the beta of debt is zero), and debt creates a tax benefit to the firm, then Beta Levered = Beta Unlevered * [1+(1-t)D/E]. Intuitively, we expect that as leverage increases—as measured by the debt-to-equity (D/E) ratio—equity investors bear increasing amounts of market risk in the firm, leading to higher betas

Accounting Beta - A third approach is to estimate the market risk parameters from accounting earnings rather than from traded prices. Thus, changes in earnings at a division or a firm, on a quarterly or an annual basis, can be regressed against changes in earnings for the market, in the same periods, to arrive at an estimate of a market beta to use in the CAPM

Cost of Debt - The cost of debt measures the current cost to the firm of borrowing funds to finance its assets. In general terms, it should be a function of the default risk that lenders perceive in the firm. The default risk of a firm is a function of two variables. The first is the firm’s capacity to generate cash flows from operations and the extent of its financial obligations—including interest and principal payments. The simplest scenario for estimating the cost of debt occurs when a firm has long-term bonds outstanding that are widely traded. The market price of the bond, in conjunction with its coupon and maturity, can serve to compute a yield we can use as the cost of debt. This approach works for firms that have dozens of outstanding bonds that are liquid and trade frequently. Many firms have bonds outstanding that do not trade on a regular basis. Since these firms are usually rated, we can estimate their costs of debt by using their ratings and associated default spread, we will add the default spread to the Treasury bond rates to get the cost of debt. When there is no rating available to estimate the cost of debt, there are two alternatives: Recent borrowing history. Many firms that are not rated still borrow money from banks and other financial institutions. By looking at the most recent borrowings made by a firm, we can get a sense of the default spreads being charged the firm and use these spreads to come up with a cost of debt. The second approach is to estimate a synthetic rating and default spread. An alternative is to play the role of a ratings agency and assign a rating to a firm based on its financial ratios; this rating is called a synthetic rating. To make this assessment, we begin with rated firms and examine the financial characteristics shared by firms within each ratings class. After Tax Cost of Debt = (1-t) * Cost of Debt

Weights of equity and debt - In computing weights for debt, and equity, we have two choices. We can take the accounting estimates of the value of each funding source from the balance sheet and compute book value weights. Alternatively, we can use or estimate market values for each component and compute weights based on relative market value. As a general rule, the weights used in the cost of capital computation should be based on market values. This is because the cost of capital is a forward-looking measure and captures the cost of raising new funds to buy the firm today. Since new debt and equity have to be raised in the market at prevailing prices, the market value weights is more relevant. The market value of debt is usually more difficult to obtain directly since very few firms have all of their debt in the form of bonds outstanding trading in the market. Many firms have non traded debt, such as bank debt, which is specified in book value terms but not market value terms. To get around the problem, analysts make the simplifying assumption that the book value of debt is equal to its market value. A simple way to convert book value debt into market value debt is to treat the entire debt on the books as a coupon bond, with a coupon set equal to the interest expenses on all of the debt, and the maturity set equal to the face-value weighted average maturity of the debt, and to then value this coupon bond at the current cost of debt for the company

What Should Be Counted in Debt? All Interest-Bearing Liabilities, All Lease Commitments. The essential characteristic of debt is that it gives rise to a tax-deductible obligation that firms have to meet in both good times and bad, and the failure to meet this obligation can result in bankruptcy or loss of equity control over the firm. If we use this definition of debt, it is quite clear that what we see reported on the balance sheet as debt may not reflect the true borrowings of the firm. In particular, a firm that leases its assets and categorizes them as operating leases owes substantially more than is reported in the financial statements. After all, a firm that signs a lease commits to making the lease payment in future periods and risks the loss of assets if it fails to make the commitment. For financial analysis, we should treat all lease payments as financial expenses and convert future lease commitments into debt by discounting them back to the present, using the current pretax cost of borrowing for the firm as the discount rate. The resulting present value can be considered the debt value of operating leases and can be added on to the value of conventional debt to arrive at a total debt figure.

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