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Cost of equity (discount rate in DD, DCF) Use the CAPM to find cost of equity
Cost of equity(discount rate in DD, DCF)
Use the CAPM to find cost of equity
CAPM
ππ ,π = π π + π½π(π π β π πΉ)
where: ππ ,π ππ π‘βπ πππ’ππ‘π¦ πππ£ππ π‘ππ
β²π ππππ’ππππ πππ‘π’ππ π€βππ πππ£ππ π‘πππ ππ πππππππ¦ πβ²π π π‘πππ
This will also be the discount rate used on the dividend discount models
π πΉ ππ π‘βπ πππ π β ππππ πππ‘ππ½π ππ πππππππ¦ π
β²π ππππ π’ππ ππ πππ β πππ£πππ πππππππ πππ ππ π ππ π‘βπ ππππππ‘ πππ‘π’ππ
Estimating betas
3 approaches to estimate beta
1. Using historical data on market prices
2. From fundamentals
3. Using accounting data
How to calculateBottom up
Beta
1.1. Find the median historical (regression) beta and the median D/E ratio for a
sample of comparable companies. Use the Damodaran link here:
http://pages.stern.nyu.edu/~adamodar/New_Home_Page/datafile/Betas.html
1.2. Calculate the median unlevered beta for the sample (cell G7 in bottom-up
beta file):
π½π =π½πΏ
(1 + 1 β π‘π·πΈ
)
2. Find the companyβs marginal tax rate and D/E ratio and use the formula for
levered beta to find the levered beta of the company where the unlevered beta is
the one from step 1.1. above:
π½πΏ = π½π 1 + 1 β π‘π·
πΈ
Bottom-up fundamental beta
Bottom-up beta is more precise than the historical beta because:
- averages across companies
- reflects current business mix
For AbbVie:
historical (regression) beta was 0.8827
bottom-up beta is 1.8631
Conclusion: using historical beta would severely understate the riskiness of the stock!
CAPM for calculating the cost of equity
ππ ,π = π π + π½π(π π β π πΉ)
where: ππ ,π ππ π‘βπ πππ’ππ‘π¦ πππ£ππ π‘ππ
β²π ππππ’ππππ πππ‘π’ππ π€βππ πππ£ππ π‘πππ ππ πππππππ¦ πβ²π π π‘πππ
This will also be the discount rate used on the dividend discount models
π πΉ ππ π‘βπ πππ π β ππππ πππ‘π π·πππΈπ½π ππ πππππππ¦ π
β²π ππππ π’ππ ππ πππ β πππ£πππ πππππππ πππ π π·πππΈπ π ππ π‘βπ ππππππ‘ πππ‘π’ππ
Estimating the risk premium (π π β π πΉ)
β’ Risk Premium - return demanded by investors for moving money from a riskless investment to a risky investment
β’ Depends on:
1. Risk aversion of investors
2. Riskiness of the investment
How to estimate in practice?
β’ using historical data
β’ using current market data
Estimating the risk premium (π π β π πΉ)
Historical Risk Premia
β’ Most common approach in CAPM: difference b/n avgreturns on stocks and avg returns on risk-free securities over an extended period of time
Process:
Step 1: Define time period (up to 1871 in U.S.*)
Step 2: Calculate avg. returns for a stock index over time
Step 3: Calculate avg. returns for a riskless security over time
Step 4: Historical RP = step 2 result β step 3 result
*NYSE opened on 3/8/1817 but data available after 1871
Historical Risk Premia
Causes of differences in practical estimation:
1. time period used: long is better
- Risk aversion is likely to change over time so using short period β estimation error
2. choice of risk-free security: long-term govβt bonds
3. method for calculating avg. returns: arithmetic vs. geometric
- Arithmetic average: sum/N
- Geometric average: compounded return= (π£πππ’π ππ ππππππ π)
(π£πππ’π ππ ππππππ 0)
1
πβ 1
Historical Risk Premia (%) for the U.S.1928-2017
Min = 3.04%Max = 12.48%
β’ Easier for U.S., more difficult for foreign
markets
β’ Little historical data and much volatility in
emerging markets
β’ Avg. for world = 3%
Stocks - T. Bills Stocks - T. Bonds Stocks - T. Bills Stocks - T. Bonds
1928-2018 7.93% 6.26% 6.11% 4.66%
Std Error 2.09% 2.22%
1969-2018 6.34% 4.00% 5.01% 3.04%
Std Error 2.38% 2.71%
2009-2018 13.00% 11.22% 12.48% 11.00%
Std Error 3.71% 5.50%Source: Damodaran
Arithmetic Average Geometric Average
How to estimate in practice?
β’ using historical data β this is based on past performance
β’ using current market data β based on current performance
Estimating the risk premium (π π β π πΉ)
Current Market Data for RP Estimation
Strong assumption: stock market is correctly priced
Simple valuation model for stocks:
ππππ’π =πΈπ₯ππππ‘ππ πππ£. ππ πππ₯π‘ ππππππ
π πππ’ππππ πππ‘π’ππ ππ πππ’ππ‘π¦ β ππ₯ππππ‘ππ ππππ€π‘β πππ‘π ππ πππ£.
Solve for required return on equity:
π πππ’ππππ πππ‘π’ππ ππ πππ’ππ‘π¦ =π·ππ£
ππππ’π+ ππ₯ππππ‘ππ ππππ€π‘β πππ‘π ππ πππ£.
πΌππππππ πΈπ π = π πππ’ππππ πππ‘π’ππ ππ πππ’ππ‘π¦ β π π
More realistic:
-market-driven
-forward-looking
-no need for hist.
data
Current Market Data for RP Estimation
On 9/25/2020 S&P500=3,257.32
Expected dividend yieldS&P500 = 1.83%
Expected growth rate of S&P500 dividends = 5.64%
π πππ’ππππ πππ‘π’ππ ππ πππ’ππ‘π¦ =3,257.32 β 0.0183
3,257.32+ 0.0564 = 7.47%
πΌππππππ πΈπ π = 7.47% β 0.68% = 6.79%
More realistic:
-market-driven
-forward-looking
-no need for hist.
data
To summarize ERP for U.S.
β’ Using historical data: 4.66%
β’ Using current market data and one growth rate of dividends and buybacks: 6.79% (we will use this one)
β’ Using current market data and two growth rates of dividends and buybacks: 4.37%
Calculate cost of equity
β’ Use CAPM:
ππ ,π = π π + π½π(π π β π πΉ)
β’ π π is the yield on the 10-year bond (in setup sheet)
β’ π½π is the bottom-up beta
β’ π π β π πΉ is the implied Equity Risk Premium for the U.S. = 6.79%
β’ Include the elements of CAPM on your setup sheet
β’ Then, go back and link your cost of equity in the dividend discount models (if you have dividends) to this newly calculated cost of equity
AbbVie CAPM:
ππ ,π΄π΅π΅π = 0.0068 + 1.8631 β 0.0679 = 13.33%
β’ π π is the yield on the 10-year bond (in setup sheet)
β’ π½π is the bottom-up beta
β’ π π β π πΉ is the implied Equity Risk Premium for the U.S. = 6.79%
β’ Include the elements of CAPM on your setup sheet
β’ Then, go back and link your cost of equity in the dividend discount models (if you have dividends) to this newly calculated cost of equity
Next step in DCF modelCalculate WACC for your company
β’ The weighted average cost of capital is equal to:
ππ΄πΆπΆ = ππ πππΈ
(πππΈ +πππ·πππ‘)+ ππ
πππ·πππ‘
(πππΈ +πππ·πππ‘)
ππ ππ π‘βπ πππ π‘ ππ πππ’ππ‘π¦ πππππ’πππ‘ππ π’π πππ πΆπ΄ππππ ππ π‘βπ πππ‘ππ β π‘ππ₯ πππ π‘ ππ ππππ‘ (ππ π¦ππ’π π ππ‘π’π π βπππ‘)
Calculate WACC on your setup sheet
