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## Hurdle rates for Firms

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Investment decision

- Firms should invest in projects that creates value for the firm’s shareholders
- These are projects that yield a return greater than the minimum acceptable hurdle rate with adjustments for project riskiness.

Investment decision

- Components of the investment decision making process
- Determine the appropriate hurdle rate for the firm (Ch. 7)
- Make adjustments for project riskiness (Ch. 8)
- Calculate the cash flows associated with the project (Ch. 9)
- Employ the appropriate decision tools (Ch. 10)
- Evaluate project interactions (ch 12)

What is a hurdle rate?

- The hurdle rate for the firm represents the minimum rate of return that the firm as a whole must generate on its investments to satisfy its investors.
- This is sometimes referred to as the weighted average cost of capital (WACC) or simply the cost of capital.
- This hurdle rate is a function of (among other things):
- Type and mix of investors (equity, debt, preferred stock)
- Riskiness of the firm

What is a hurdle rate?

- This hurdle will be higher for riskier projects than for safer projects.
- A simple representation of the hurdle rate is as follows:

Hurdle rate = Risk-free Rate + Risk Premium

- The two basic questions that every risk and return model in finance tries to answer are, for each type of security:
- How do you measure risk?
- How do you translate this risk measure into a risk premium?

Cost of equity

- Required rate of return for equity investors (or shareholders) is also referred to as the cost of equity
- For publicly traded firms, we initially assume that the these equity investors are diversified investors. Consequently,
- Only the firm’s risk relative to the market is relevant (systematic risk)
- Firm-specific risk is assumed to be diversified away
- We will later relax our diversified investor assumption

Cost of equity

- With our diversified investor assumption, the appropriate risk measure for a firm is beta (β) which measures the firm’s systematic risk
- Although it has its limitations, the appropriate model to estimate the cost of equity is the Capital Asset Pricing Model (CAPM)

where re is the cost of equity for a particular stock, rf is the risk free rate, and rm is the return on the market (S&P 500 index for our purposes)

Cost of equity

- To calculate the cost of equity for a firm, we need estimates for each of its components:
- Risk-free rate
- Market return, or alternatively the market risk premium, (rm-rf)
- Firm’s beta

Risk-free rate

- With the risk-free asset, the actual return and expected return do not vary.
- This asset assumes:
- No default risk
- No reinvestment risk
- Ideally, this means that you should use a risk-free asset whose maturity matches the timing of cash flows

Risk-free rate

- Realistically, using a long-term government bond (even with coupon), such as a 30-year Treasury bond return, is adequate for long-term analyses.
- For short-term analyses, short term government securities, such as the 3-month Treasury bill, are appropriate.
- The current rates for these instruments are available from the Yahoo (or other financial information sources) and are represented by the “yield”.

Market risk premium

- The market risk premium represents the extra returnbeyond that of a risk-free asset that an investor demands for moving their funds from the risk-free asset to the risky (market portfolio) asset.
- As a general proposition, this premium should be
- greater than zero
- increase with the risk aversion of the investors in that market
- increase with the riskiness of the “average” risky investment

What is your risk premium?

- Assume that stocks are the only risky assets and that you are offered two investment options:
- a riskless investment (say a Government Security), on which you can make 6%
- a mutual fund of all stocks, on which the returns are uncertain

How much of an expected return would you demand to shift your money from the riskless asset to the mutual fund?

- 6% or less
- 7%
- 8%
- 9%
- 10%
- 11% or more

Risk Aversion and Risk Premiums

- The risk premium is a weighted average of the risk premiums demanded by each and every investor.
- The weights will be determined by the magnitude of wealth that each investor has.
- As investors become more risk averse, you would expect the “equilibrium” premium to increase.

Risk Premiums do change..

Go back to the previous example. Assume now that you are making the same choice but that you are making it in the aftermath of losing your job. Would you change your answer?

- I would demand a larger premium
- I would demand a smaller premium
- I would demand the same premium

Estimating the market risk premium

- There are two methods to estimate the market risk premium.
- historical risk premium
- Implied risk premium
- The majority of analyses tend to employ the historical method or some form of weighted average between the two.

The historical premium approach

- In most cases, historical market risk premiums can be estimated as follows:
- define a time period for the estimation (1926-Present, 1962-Present....)
- calculate average returns on a stock index during the period; with longer-term analyses use geometric returns
- calculate average (geometric) returns on a risk-free security over the same period
- The market risk premium is then the difference between the two, i.e., rm - rf.

Historical premium limitations

- The limitations of this approach are:
- it assumes that the risk aversion of investors has not changed in a systematic way across time. (The risk aversion may change from year to year, but it reverts back to historical averages)
- it assumes that the riskiness of the “risky” portfolio (stock index) has not changed in a systematic way across time

Implied premium approach

- The implied risk premium approach estimates a risk premium based on current market values, dividends and growth rates.
- We can use a basic dividend discount model (DDM) to estimate the implied risk premium:

Index value = Expected index dividends

(RR on the index – growth rate in dividends)

- The implied risk premium would then be:

RR on index – current risk-free rate

Implied premium limitations

- The limitations of this approach are:
- It assumes that the DDM is correct to value the market.
- It assumes that the market is currently correctly valued

What should we use as a risk premium?

- The historical risk premium (4.91%) tends to be higher than the implied risk premium.
- An average of the two measures may serve as a good estimate for the risk premium because the historical risk premium is much too high to use in a market, where equities are currently priced with premiums that are closer to 3%.

Estimating betas

- A firm’s beta represents the level of systematic risk inherent in the firm.
- It can be measured in two ways:
- Historical measure (or top-down approach) – measured by regressing historical stock returns of the firm on index (or market) returns
- Bottom-up approach – estimated by measuring the average beta for firms within the same industry after adjusting for financial leverage

Historical betas

- The standard procedure for estimating historical betas is to regress stock returns (r) against market returns (rm) -

where a is the regression intercept and b is the slope of the regression.

- The slope of the regression (b) corresponds to the beta of the stock, and measures the riskiness of the stock.
- Note: Do not confuse this equation with the CAPM. This is simply a linear representation of the relationship between the return for the firm and the market return.

Setting up for the estimation

- Decide on an estimation period
- Services (such as Value-Line) use periods ranging from 2 to 5 years for the regression
- Longer estimation period provides more data, but firms change.
- Shorter periods can be affected more easily by significant firm-specific event that occurred during the period
- Decide on a return interval - daily, weekly, monthly
- Shorter intervals yield more observations, but suffer from more noise, monthly returns tend to work well.
- Noise is created by stocks not trading and biases all betas towards one.
- Estimate returns (including dividends) on stock
- Return = (PriceEnd - PriceBeginning + DividendsPeriod)/ PriceBeginning
- Included dividends only in ex-dividend month
- Choose a market index, and estimate returns (inclusive of dividends) on the index for each interval for the period.
- Run the regression

Applying the approach

- Data for periodic individual stock prices and market index values can be found on Yahoo and other financial websites
- In general, closing stock prices should be used.
- The S&P 500 serves as a good market index.
- Ensure that the returns are calculated including dividends.
- This would mean using the adjusted closing prices for the index and stock in Yahoo
- You should include the dividends paid by the company in the month in which it was paid (if monthly returns are calculated).

Forward looking beta adjustment

- The regression-estimated betas represent betas that are calculated using historical (or past) stock prices and index values.
- Since the purpose of calculating these betas is to provide us with a hurdle rate for future decisions, sometimes these values are adjusted to be forward-looking.
- When making the forward-looking adjustment, we assume that as firms mature, their betas tend towards 1 (market beta).

Forward-looking beta = Regression beta * 0.67 + 1 * 0.33

- Many financial reporting agencies, such as Value Line, use this adjustment

Estimating performance

- The regression output (intercept and slope)provides a simple measure of performance during the period of the regression, relative to the capital asset pricing model.
- CAPM provides an expected return for the stock:
- The regression model is a measure of the actual return for the stock:

Estimating performance

- If

a > rf (1-β) .... Stock did better than expected during regression period

a = rf (1-β).... Stock did as well as expected during regression period

a < rf (1-β).... Stock did worse than expected during regression period

- Alternatively, we can calculate Jensen’s alpha (α) :

α = a - rf(1-β)

If this measure is greater (less) than 0, the company performed better (worse) than investors expected during the period from which the regression data was obtained.

Firm-specific and market risk

- The R-squared (R2) of the regression provides an estimate of the proportion of the risk (variance) of a firm that can be attributed to market risk.
- The balance (1 - R2) can be attributed to firm-specific risk.
- Diversified investors are only concerned about market risk. Undiversified investors care about both market and firm-specific risks.
- For undiversified investors, a total beta measure which accounts for both risks is more appropriate.

The Relevance of R2

- You are a diversified investor trying to decide whether you should invest in Home Depot or Bed, Bath and Beyond. Both firms provide equal returns. They both have betas of 1.404, but Home Depot has an R2 of 40% while Bed Bath and Beyond’s R2 is only 15%. Which one would you invest in?
- BBB, because it has the lower R2
- HD, because it has the higher R2
- You would be indifferent
- Would your answer be different if you were an undiversified investor?

Bottom-up betas

- The bottom-up approach relies on the fundamental characteristics of the firm to determine the riskiness of the firm and thus the firm beta.
- These fundamental characteristics include:
- Type of Business: Firms in more cyclical businesses or that sell products that are more discretionary to their customers will have higher betas than firms that are in non-cyclical businesses or sell products that are necessities or staples.
- Operating Leverage: Firms with greater fixed costs (as a proportion of total costs) will have higher betas than firms with lower fixed costs (as a proportion of total costs)
- Financial Leverage: Firms that borrow more (higher debt, relative to equity) will have higher betas than firms that borrow less.

Bottom-up betas

- The critical assumption we make in using the bottom-up approach is that the riskiness associated with the type of business and operating leverage will be similar across firms that are in the same industry and are of similar size.
- This assumption implies that the only difference in riskiness between firms in a particular industry comes from differences in financial leverage, or debt/equity mix.

Bottom-up betas

- The first component of a firm’s risk is that associated with its operations:
- We can measure this risk by calculating the firm’s unlevered beta (βU), i.e., a beta that removes the effect of financial leverage.
- This unlevered beta is also referred to as an asset beta as it represents the riskiness of a firm’s assets.

Bottom-up betas

- The second component of a firm’s risk is that associated with its financial leverage
- The greater the debt/equity ratio, the greater the financial leverage, and therefore financial leverage risk
- The firm’s levered (or bottom-up) beta provides us with an estimate of both operating and financial leverage risks.
- This levered beta (βL), represents the firm’s risk and is equivalent (but not necessarily the same in value) to the historical beta calculated using the regression approach.

Bottom-up betas

- The levered beta can be estimated by doing the following:
- Find out the industry that a firm operates in
- Find the unlevered betas of other comparable firms in this industry
- Take a weighted (by sales or market value) average of these unlevered betas
- Lever up using the firm’s debt/equity ratio
- This method is best for beta estimation for non-traded (private) firms since stock prices are not available to measure a historical beta.

Equity betas and leverage

- The following equation provides us with the mathematical relationship between the unlevered and levered beta:

where

L = Levered Beta

u = Unlevered Beta

t = Corporate marginal tax rate

D = Debt Value

E = Equity Value

Betas are weighted averages

- The beta of a portfolio is always the market-value weighted average of the betas of the individual investments in that portfolio.
- Thus, for example,
- the beta of a firm is the weighted average of the betas of the firm’s distinct divisions
- the beta of a firm after a merger is the market-value weighted average of the betas of the companies involved in the merger.

Is beta an adequate measure of risk for a private firm?

- The owners of most private firms are not diversified. Beta measures the risk added on to a diversified portfolio. Therefore, using beta to arrive at a cost of equity for a private firm will…
- Over estimate the cost of equity for the private firm
- Under estimate the cost of equity for the private firm
- Could under or over estimate the cost of equity for the private firm

Total risk versus market (systematic) risk

- For private firms (or firms where owners are not diversified), it would be more appropriate to use the firm’s total risk rather than just market risk.
- The adjustment to account for total risk is a relatively simple one, since the R2 of the regression measures the proportion of the risk that is market risk.
- For private firms where we do not have stock returns to run a regression, the R2 of comparable firms will suffice.

Bottom-up or regression (top-down) beta: Which one should we use?

- The bottom-up beta will give you a better estimate of the true beta when
- the firm is not substantially different fundamentally (size, operational characteristics, etc.) from the other firms in the industry
- the firm has reorganized or restructured itself substantially during the period of the regression

Summary of cost of equity estimation

- Determine an appropriate risk-free rate (the 30-yr T-bond rate will usually suffice).
- Estimate an appropriate market risk premium
- Calculate firm beta either by:
- Using a top-down or regression approach
- Bottom-up approach
- Make adjustments if necessary to account for undiversified investors or to make the value forward looking
- Calculate the cost of equity using the CAPM

From cost of equity to cost of capital

- The cost of capital is a composite cost to the firm of raising financing to fund its projects.
- In addition to equity, firms can raise capital from debt or hybrid securities

What is debt?

- General Rule: Debt generally has the following characteristics:
- Commitment to make fixed payments in the future
- The fixed payments are tax deductible
- Failure to make the payments can lead to either default or loss of control of the firm to the party to whom payments are due.
- As a consequence, debt should include
- Any interest-bearing liability, whether short term or long term.
- Any lease obligation, whether operating or capital.

Cost of debt vs. required rate of return for debtholders

- The required rate of return for bondholders of a particular firm is a function of:
- Current interest rate for the risk-free asset (30-yr. T-bond yield)
- Default risk associated with the firm, i.e., how likely is the firm to go bankrupt (risk premium).
- Bondholders are compensated in interest payments (or coupon payments) for this required rate of return. This represents the before-tax cost of debt (BT rd)
- Because from the firm’s perspective interest expense is tax-deductible, the after-tax cost of debt (rd)is:

BT rd * (1 – tax rate)

Estimating the cost of debt

- Depending on whether or not the firm in question has bonds that are publicly traded and on available information, there are three ways (in order of preference) to estimate the before-tax cost of debt:
- Look for prices and yields of bonds outstanding
- Estimate the cost of debt from the firm’s credit rating
- Estimate the cost of debt by calculating a synthetic credit rating

Estimating the cost of debt

- If the firm has bonds outstanding, and the bonds are traded, the yield to maturity (YTM) on a long-term, straight (no special features) bond can be used as the before tax cost of debt.
- The YTM incorporates the risk-free rate and firm-specific default risk.
- Sources:
- Look at the Corporate Bond excerpt in the WSJ or other publications
- Yahoo may also have this information

rd = YTM * (1-t)

Estimating the cost of debt

- If the firm is rated, use the credit rating and a typical default spread on bonds with that rating to estimate the cost of debt.
- Standard & Poors, Moody’s and Fitch provide credit ratings for firms. The first of these ratings can be found at :

www.standardandpoors.com

- Default spreads can be found at www.bondsonline.com (premium service) OR inferred from bond spreads of other bonds with the same rating

rd = (30-yr. T-bond yield + spread) * (1-t)

Estimating the cost of debt

- If the firm is not rated,
- estimate a synthetic rating for the company, and use the synthetic rating to arrive at a default spread and a cost of debt

rd = (30-yr. T-bond yield + spread) * (1-t)

Estimating synthetic credit ratings

- The rating for a firm can be estimated using the financial characteristics of the firm. In its simplest form, the rating can be estimated from the interest coverage ratio

Interest Coverage Ratio = EBIT / Interest Expenses

Interest Coverage Ratio S&P Rating

> 8.5 AAA

6.50 - 8.50 AA

5.50 – 6.50 A+

4.25 – 5.50 A

3.00 – 4.25 A-

2.50 – 3.00 BBB

2.25 – 2.50 BB+

2.00 – 2.25 BB

1.75 - 2.00 B+

1.50 – 1.75 B

1.25 – 1.50 B-

0.80 – 1.25 CCC

0.65 – 0.80 CC

0.20 – 0.65 C

< 0.20 D

Cost of preferred stock

- The cost of preferred stock, which has some characteristics of debt and equity (specified dividend, not tax deductible, infinite life) is calculated as follows:

where rps, Dps, and Pps are the cost of preferred stock, dividend on preferred stock and current price per share of preferred stock, respectively.

- www.quantumonline.com has useful information about preferred stocks.

Estimating capital weights

- The firm’s cost of capital is a function of the cost of each type of financing the firm adopts and of the weights of each type of financing
- Book values (obtained from financial statements):
- Equity: includes common stock and retained earnings
- Debt: includes long term debt and the present value of leases
- Preferred Stock: includes preferred stock
- Convertible bond value should be apportioned to equity and debt.

Estimating capital weights

- Market Values:
- Market Value of Equity (E) and Preferred Stock (PS) should include the following:
- Market Value of Shares outstanding:

Shares outstanding * current stock price

- Market Value of Warrants outstanding
- 10-K filings (with the SEC) and annual reports should provide information about the shares outstanding, market value of warrants should be in the 10-Ks.
- Conversion option value of outstanding convertible bonds should be included in Equity.

Estimating capital weights

- Market value of debt (D) is more difficult to estimate because few firms have only publicly traded debt.
- Estimate the market value of debt from the book value by treating the entire debt as one coupon bond, with a coupon (C) set equal to interest expenses and maturity (n) equal to the average maturity of all debt outstanding and using the current before-tax cost of debt (BT rd).

Market value of bonds (D)

Converting leases to debt

- The “debt value” of leases is the present value of the lease payments, at a rate that reflects their risk.
- In general, this rate will be close to or equal to the rate at which the company can borrow, i.e., pre-tax cost of debt.
- Capital leases are included in the balance sheet, operating leases are not.

Accounting for convertible bonds

- A convertible bond is a bond that can be converted into equity at the option of the bondholder.
- To incorporate a firm’s outstanding convertible bond issues into our cost of capital calculations, we separate the bond

into 2 distinct components:

- Straight debt, whose value is
- Conversion option = Current bond price – straight debt value

Accounting for convertible bonds

- The straight debt component is included in debt.
- The conversion option component is included in equity.

Cost of Capital

- The weighted average cost of capital (or firm hurdle rate) is then just the weighted average of the individual sources of capital

*rd represents an after-tax cost of debt

- Divisional costs of capital may be calculated if firms have distinct major divisions of operation

Choosing a Hurdle Rate

- Either the cost of equity or the cost of capital can be used as a hurdle rate, depending upon whether the returns measured are to equity investors or to all claimholders on the firm (capital)
- If returns are measured to equity investors, the appropriate hurdle rate is the cost of equity.
- If returns are measured to capital (or the firm), the appropriate hurdle rate is the cost of capital.

Chapter 7 sections NOT covered

- Riskless Rates When There is Sovereign Risk
- Currency Choices and Real Rates
- Historical risk premiums for other countries (pg. 192-194) – this section does not have a separate title
- Accounting Betas

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