Hurdle rates for Firms (ch. 7)

10/04/05

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)

Firm hurdle rate: What is it? The hurdle rate for the firm represents the minimum rate of

return that the firm as a whole must generate to satisfy its investors.

This is sometimes referred to as the weighted average cost of capital (WACC) or simply the cost of capital.

This is equivalent to the required rate of return from the investors’ perspectives.

This hurdle rate is a function of (among other things): Type and mix of investors (equity, debt, preferred stock) Riskiness of the firm

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 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

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)

)( fmfe rrrr

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 WSJ and are represented by the “yield”.

Market risk premium The market risk premium represents the extra return

(beyond 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

Estimating the market risk premium

We will use the historical market risk premium as a proxy for the expected premium

The vast majority of analyses employ this method

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 in the U.S.

Geometric Average Risk Premium

Stocks T-bills T-bonds Stocks - T.Bills Stocks - T.Bonds

1928-2004 9.86% 3.84% 5.02% 6.02% 4.84%

1963-2004 10.54% 5.96% 7.06% 4.59% 3.47%

1993-2004 10.94% 4.09% 6.43% 6.85% 4.51%

Historial risk 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

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.

mbrar

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:

mf rrr )1(

mbrar

Estimating performance If

a > rf (1-β) .... Stock did better than expected during regression perioda = rf (1-β).... Stock did as well as expected during regression perioda < rf (1-β).... Stock did worse than expected during regression period

The difference between a and rf (1-β) is Jensen's alpha and provides an indication of whether the stock underperformed or overperformed during the regression period.

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.

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 will 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:

whereL = Levered Beta

u = Unlevered Beta

t = Corporate marginal tax rateD = Debt ValueE = Equity Value

EDtL

u /11

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 mutual fund is the weighted average of the

betas of the stocks and other investment in that portfolio

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.

2RL

T

Summary of cost of equity estimation

Determine an appropriate risk-free rate (the 30-yr T-bond rate will usually suffice).

Use a historical market risk premium – 4.84% is a good long-term estimate

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.

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 www.bondsonline.com 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

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 AAA6.50 - 8.50 AA5.50 – 6.50 A+4.25 – 5.50 A3.00 – 4.25 A-2.50 – 3.00 BBB2.25 – 2.50 BB+2.00 – 2.25 BB1.75 - 2.00 B+1.50 – 1.75 B1.25 – 1.50 B-0.80 – 1.25 CCC0.65 – 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.

ps

psps P

Dr

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, retained earnings, and

warrants (typically) 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

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) ndBTr

incipal)1(

PrBTr

)BTr+(11 - 1

C = d

nd

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

ndBTr

incipal)1(

PrBTr

)BTr+(11 - 1

C = d

nd

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

PSEDPSr

PSEDDr

PSEDErWACC psde

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.