Today’s Agenda
DCF 5 Steps
Risk-free Rates
Market risk premium
Country risk
Beta
Five Steps to Discounted Cash Flow Valuation
Before you start, choose asset to value. Recognize and identify as many preconceived biases and
assumptions that may influence your valuation.
1. Estimate the discount rate(s) to use in the valuation
a. Cost of equity or cost of capital
b. Discount rates can vary over time
2. Estimate current earnings and cash flows
3. Estimate future earnings and cash flows
4. Estimate when the firm will reach stable growth; and what will the firm’s risk and cash flows
look like at that time
5. Choose the ‘right’ DCF model to value the asset
Discount Rate
Critical input in all discounted cash flow models
 Discount rate should be consistent with both the riskiness and the type of cash flows being
discounted
• Cost of equity or cost of capital? (HINT: If using net income, use cost of equity)
• Which currency should I use?
• Nominal or real cash flows? (HINT: If using government bond rates or historical
growth rates, you are already using nominal flows)
Cost of Equity
The rate of return that equity investors need (expect) to make to invest in company
 Cost of equity should be higher for riskier investments; lower for safer investments
 Discount rate should reflect the perceived risk by the marginal investor in the investment
 Similar to many risk/return finance models, the discount rate should only consider risk that
is non-diversifiable by the marginal investor
Competing Models
Model
Expected Return
Inputs Needed
CAPM
E(R) = Rf + (Rm – Rf)
Risk-free rate; market beta; market risk
premium
APM
E(R) = Rf + j=1 j(Rj – Rf)
Risk-free rate; # of factors; factor betas; factor
risk premiums
Multifactor
E(R) = Rf + j=1,,N j(Rj – Rf)
Risk-free rate; macro factors; macro betas;
macroeconomic risk premiums
Proxy
E(R) = a + j=1,,N bj Yj
Proxies; regression coefficients
CAPM: Cost of Equity
Cost of Equity = Risk-free Rate + Equity Beta * (Equity Risk Premium)
In practice…
 Risk-free rates: usually use government security rates
 Risk premium: usually use historical risk premiums
 Beta: usually estimated by regressing stock returns against market returns
Risk-free Rate
•
On a risk-free asset, the actual return is equal to the expected return.
 NO variance around the expected return
•
For an investment to be risk-free, it has to have
 No default risk
 No reinvestment risk
Considerations:
 Time horizon
 Not all government securities are risk-free (HINT: remove default risk)
US Treasury Rates
Local Currency Government Bond Rates
Country CDS spreads
Risk-free Rate
In January 2012, the 10-year treasury bond in the US was 1.87%; a historical low. Assume
that you are valuing a company in US dollars at that time, but were concerned about the
risk-free rate being too low. What should you do?
A. Replace the current 10-year bond rate with a more reasonable normalized risk-free rate
(historical average was approximately 4%)
B. Use the current 10-year bond rate, but make sure other assumptions (about growth and
inflation) are consistent with the risk-free rate
C. Something else…
Historical Risk Premium
•
The historical risk premium is the difference between the realized annual return from investing in
stocks and the realized annual return from investing in a riskless security over a past time period.
 Premiums are sensitive to:
• Time horizon (how far back should you go?)
• Rates (T-bill or T-bond?)
• Assumptions (Arithmetic average or geometric average?)
Some problems with using historical premiums:
 Noisy estimates
 Survivorship bias
Assume that next year turns out to be a terrible year for stocks. What would happen to the historical
risk premium if that occurs?
A. Go up
B. Go down
Country Risk Premium
•
Historical risk premiums are nearly impossible to estimate with any precision in markets with
limited history
•
We can estimate a modified historical premium usually starting with U.S. premium as the base
 Country Bond approach (default spread)
• Country risk premium = Risk premiumUS + Country bond default spread
 Relative Equity Market approach (relative volatility)
• Country risk premium = Risk premiumUS * Country Equity / US Equity
Combined approach
*Country risk premium = Risk premiumUS + Country bond default spread * Country Equity / Country Bond
Country Risk Premium
Approach 1: Assume that every company in the country is equally exposed to country risk
E(Return) = Risk-free Rate + CRP + Beta (Mature ERP)
Approach 2: Assume that a company’s exposure to country risk is similar to its exposure to other
market risk
E(Return) = Risk-free Rate + Beta (Mature ERP + CRP)
Approach 3: Treat country risk as a separate risk factor and allow firms to have different exposures to
country risk
E(Return) = Risk-free Rate +  Mature ERP +  (CRP)
 = % of revenues domesticallyfirm / % of revenues domesticallyavg firm
ERP = Equity risk premium
CRP = Country risk premium
Country Risk Premium: Example
Consider the following information for Firm B:
Beta: 1.07
US Risk-free rate: 4%
US market risk premium: 5%
Country risk premium (Portugal): 7.89%
Firm B gets 3% of its revenues from Portugal; 97% from US
Average Portuguese firm gets 11% of revenues from Portugal
Estimate Cost of Equity for Firm B.
E(Return) = 4% + 1.07 (5%) + 7.89% = 17.24%
E(Return) = 4% + 1.07 (5%) + (0.03*7.89% + 0.97*0.0%) = 9.59%
E(Return) = 4% + 1.07 (5% + 7.89% )= 17.79%
E(Return) = 4% + 1.07 (5% + (0.03*7.89% + 0.97*0.0%)) = 9.60%
E(Return) = 4% + 1.07 (5%) + 0.27*7.89% = 11.48%
Approach 1
Approach 1a
Approach 2
Approach 2a
Approach 3
Estimating Beta
•
Standard procedure: regress stock returns against market returns:
•
The slope of the regression corresponds to the beta of the stock, thus measures the riskiness of the stock.
•
Considerations:
 Length of estimation period
 Return interval
 Benchmark
 Economic conditions
•
Some problems with this approach
 High standard error
 Reflects historical business mix; not current mix
 Reflects firms’ average leverage over the period; not current capital structure
•
Possible solutions
 Modify regression beta by changing the index or by using company fundamental
 Estimate beta using std. dev. of stock returns or adjusted earnings
 Estimate beta using bottom-up approach (business mix; financial leverage)
 Use alternate (non-regression-based) measure of market risk
Rj = a + b Rm
Estimating Beta: Yahoo! Finance example
Here is how you can calculate the beta provided by Yahoo! Finance:
1. Download monthly prices for your company and S&P 500 (Ticker: ^GSPC) for the past three
years (July 1, 2011 – July 31, 2011) from Yahoo! Finance (put them both in the same Excel
spreadsheet)
2. Calculate the monthly returns for your company and S&P 500 (use the Adjusted Close price and
use a simple return calculation (this month/last month – 1))
3. Use the ‘slope’ function to calculate Beta (use the monthly returns from your company for the
“known y’s” and the monthly returns from S&P 500 as the “known x’s”)
*You can also run a regression in Excel to get beta, along with other data. In Excel, go to options –
Add-Ins – Analysis ToolPak and click Go. Then in the Data tab, the button for Data Analysis should
appear. Click Data Analysis, and scroll to Regression. Input the same X and Y ranges, and you
should get the same beta coefficient as before.
** Alternatively, you can use the COVARIANCE.S formula and the VAR formula in Excel to
compute beta using the returns data for your company and a market index. Many resources are
available online to refresh your skills with using covariance and variance formulas.
Determinants of Beta
Product or Service
 A firm’s beta depends upon the sensitivity of the demand for its products and services and
of its costs to macroeconomic factors that affect the overall market.
• Cyclical companies have higher betas than non-cyclical firms
• Firms which sell more discretionary products will have higher betas than firms that sell
less discretionary products
Operating Leverage
 The greater the proportion of fixed costs in the cost structure of a business, the higher the
beta; because higher fixed costs increase your exposure to all risk (including market risk).
Financial Leverage
 The more debt a firm takes on, the higher the beta; because debt creates a fixed cost (interest
expense) that increases exposure to market risk.
Equity Betas and Leverage
•
Equity beta can be written as a function of the unlevered beta and the D/E ratio
L = u (1+((1-t)D/E))
where
L = Levered or Equity beta
u = Unlevered beta (Asset beta)
t = Corporate marginal tax rate
D = Market value of debt
E = Market value of equity
Bottom-up Beta
•
The bottom up beta can be estimated by :
 Taking a weighted (by sales or operating income) average of the unlevered betas of the
different businesses a firm is in.
j = 1,,k j [Operating Incomej / Operating IncomeFirm ]
(The unlevered beta of a business can be estimated by looking at other firms in the same business)
 Lever up using the firm’s debt/equity ratio
levered = unlevered[1+ (1- tax rate) (Current Debt/Equity Ratio)]
•
The bottom up beta will give you a better estimate of the true beta because:
 It has lower standard error (SEaverage = SEfirm / √n)
 It reflects the firm’s current business mix and financial leverage
 It can be estimated for divisions and private firms.
Bottom-up Beta: Example
Consider the following information for Firm A:
Segment
Division Revenues
EV / Sales
Unlevered Beta
Segment Weight
Media
12,411.72
2.43
0.91
70.39%
Consumer Products
6,784.76
1.87
0.80
29.61%
Assume:
• marginal tax rate is 35%
• MV Equity = $33,401
• MV Debt = $8,143
Compute Firm A’s Levered Beta.
Unlevered A = (0.91 * 70.39%) + (0.80 * 29.61%) = 0.88
Market D/E ratio = 8,143 / 33,401 = 24.38%
Levered A = 0.88 * (1 + (1-.35) * (24.38%)) = 1.02
Reminders
• Quiz 2 due by 10:00pm on Thursday (in HuskyCT)