Cost of equity(discount rate in DD, DCF)

Use the CAPM to find cost of equity

CAPM

𝑟𝑠,𝑖 = 𝑅𝑓 + 𝛽𝑖(𝑅𝑚 − 𝑅𝐹)

where: 𝑟𝑠,𝑖 𝑖𝑠 𝑡ℎ𝑒 𝑒𝑞𝑢𝑖𝑡𝑦 𝑖𝑛𝑣𝑒𝑠𝑡𝑜𝑟

′𝑠 𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑑 𝑟𝑒𝑡𝑢𝑟𝑛 𝑤ℎ𝑒𝑛 𝑖𝑛𝑣𝑒𝑠𝑡𝑖𝑛𝑔 𝑖𝑛 𝑐𝑜𝑚𝑝𝑎𝑛𝑦 𝑖′𝑠 𝑠𝑡𝑜𝑐𝑘

This will also be the discount rate used on the dividend discount models

𝑅𝐹 𝑖𝑠 𝑡ℎ𝑒 𝑟𝑖𝑠𝑘 − 𝑓𝑟𝑒𝑒 𝑟𝑎𝑡𝑒𝛽𝑖 𝑖𝑠 𝑐𝑜𝑚𝑝𝑎𝑛𝑦 𝑖

′𝑠 𝑚𝑒𝑎𝑠𝑢𝑟𝑒 𝑜𝑓 𝑛𝑜𝑛 − 𝑑𝑖𝑣𝑒𝑟𝑠𝑖𝑓𝑖𝑎𝑏𝑙𝑒 𝑟𝑖𝑠𝑘𝑅𝑚 𝑖𝑠 𝑡ℎ𝑒 𝑚𝑎𝑟𝑘𝑒𝑡 𝑟𝑒𝑡𝑢𝑟𝑛

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):

𝛽𝑈 =𝛽𝐿

(1 + 1 − 𝑡𝐷𝐸

)

2. Find the company’s 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:

𝛽𝐿 = 𝛽𝑈 1 + 1 − 𝑡𝐷

𝐸

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

𝑟𝑠,𝑖 = 𝑅𝑓 + 𝛽𝑖(𝑅𝑚 − 𝑅𝐹)

where: 𝑟𝑠,𝑖 𝑖𝑠 𝑡ℎ𝑒 𝑒𝑞𝑢𝑖𝑡𝑦 𝑖𝑛𝑣𝑒𝑠𝑡𝑜𝑟

′𝑠 𝑟𝑒𝑞𝑢𝑖𝑟𝑒𝑑 𝑟𝑒𝑡𝑢𝑟𝑛 𝑤ℎ𝑒𝑛 𝑖𝑛𝑣𝑒𝑠𝑡𝑖𝑛𝑔 𝑖𝑛 𝑐𝑜𝑚𝑝𝑎𝑛𝑦 𝑖′𝑠 𝑠𝑡𝑜𝑐𝑘

This will also be the discount rate used on the dividend discount models

𝑅𝐹 𝑖𝑠 𝑡ℎ𝑒 𝑟𝑖𝑠𝑘 − 𝑓𝑟𝑒𝑒 𝑟𝑎𝑡𝑒 𝐷𝑂𝑁𝐸𝛽𝑖 𝑖𝑠 𝑐𝑜𝑚𝑝𝑎𝑛𝑦 𝑖

′𝑠 𝑚𝑒𝑎𝑠𝑢𝑟𝑒 𝑜𝑓 𝑛𝑜𝑛 − 𝑑𝑖𝑣𝑒𝑟𝑠𝑖𝑓𝑖𝑎𝑏𝑙𝑒 𝑟𝑖𝑠𝑘 𝐷𝑂𝑁𝐸𝑅𝑚 𝑖𝑠 𝑡ℎ𝑒 𝑚𝑎𝑟𝑘𝑒𝑡 𝑟𝑒𝑡𝑢𝑟𝑛

Estimating the risk premium (𝑅𝑚 − 𝑅𝐹)

• Risk Premium - return demanded by investors for moving money from a riskless investment to a risky investment

• Depends on:

1. Risk aversion of investors

2. Riskiness of the investment

How to estimate in practice?

• using historical data

• using current market data

Estimating the risk premium (𝑅𝑚 − 𝑅𝐹)

Historical Risk Premia

• 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 – 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 → estimation error

2. choice of risk-free security: long-term gov’t bonds

3. method for calculating avg. returns: arithmetic vs. geometric

- Arithmetic average: sum/N

- Geometric average: compounded return= (𝑣𝑎𝑙𝑢𝑒 𝑖𝑛 𝑝𝑒𝑟𝑖𝑜𝑑 𝑁)

(𝑣𝑎𝑙𝑢𝑒 𝑖𝑛 𝑝𝑒𝑟𝑖𝑜𝑑 0)

1

𝑁− 1

Historical Risk Premia (%) for the U.S.1928-2017

Min = 3.04%Max = 12.48%

• Easier for U.S., more difficult for foreign

markets

• Little historical data and much volatility in

emerging markets

• 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?

• using historical data – this is based on past performance

• using current market data – based on current performance

Estimating the risk premium (𝑅𝑚 − 𝑅𝐹)

Current Market Data for RP Estimation

Strong assumption: stock market is correctly priced

Simple valuation model for stocks:

𝑉𝑎𝑙𝑢𝑒 =𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑑𝑖𝑣. 𝑖𝑛 𝑛𝑒𝑥𝑡 𝑝𝑒𝑟𝑖𝑜𝑑

𝑅𝑒𝑞𝑢𝑖𝑟𝑒𝑑 𝑟𝑒𝑡𝑢𝑟𝑛 𝑜𝑛 𝑒𝑞𝑢𝑖𝑡𝑦 − 𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑔𝑟𝑜𝑤𝑡ℎ 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑑𝑖𝑣.

Solve for required return on equity:

𝑅𝑒𝑞𝑢𝑖𝑟𝑒𝑑 𝑟𝑒𝑡𝑢𝑟𝑛 𝑜𝑛 𝑒𝑞𝑢𝑖𝑡𝑦 =𝐷𝑖𝑣

𝑉𝑎𝑙𝑢𝑒+ 𝑒𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑔𝑟𝑜𝑤𝑡ℎ 𝑟𝑎𝑡𝑒 𝑜𝑓 𝑑𝑖𝑣.

𝐼𝑚𝑝𝑙𝑖𝑒𝑑 𝐸𝑅𝑃 = 𝑅𝑒𝑞𝑢𝑖𝑟𝑒𝑑 𝑟𝑒𝑡𝑢𝑟𝑛 𝑜𝑛 𝑒𝑞𝑢𝑖𝑡𝑦 − 𝑅𝑓

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%

𝑅𝑒𝑞𝑢𝑖𝑟𝑒𝑑 𝑟𝑒𝑡𝑢𝑟𝑛 𝑜𝑛 𝑒𝑞𝑢𝑖𝑡𝑦 =3,257.32 ∗ 0.0183

3,257.32+ 0.0564 = 7.47%

𝐼𝑚𝑝𝑙𝑖𝑒𝑑 𝐸𝑅𝑃 = 7.47% − 0.68% = 6.79%

More realistic:

-market-driven

-forward-looking

-no need for hist.

data

To summarize ERP for U.S.

• Using historical data: 4.66%

• Using current market data and one growth rate of dividends and buybacks: 6.79% (we will use this one)

• Using current market data and two growth rates of dividends and buybacks: 4.37%

Calculate cost of equity

• Use CAPM:

𝑟𝑠,𝑖 = 𝑅𝑓 + 𝛽𝑖(𝑅𝑚 − 𝑅𝐹)

• 𝑅𝑓 is the yield on the 10-year bond (in setup sheet)

• 𝛽𝑖 is the bottom-up beta

• 𝑅𝑚 − 𝑅𝐹 is the implied Equity Risk Premium for the U.S. = 6.79%

• Include the elements of CAPM on your setup sheet

• 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:

𝑟𝑠,𝐴𝐵𝐵𝑉 = 0.0068 + 1.8631 ∗ 0.0679 = 13.33%

• 𝑅𝑓 is the yield on the 10-year bond (in setup sheet)

• 𝛽𝑖 is the bottom-up beta

• 𝑅𝑚 − 𝑅𝐹 is the implied Equity Risk Premium for the U.S. = 6.79%

• Include the elements of CAPM on your setup sheet

• 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

• The weighted average cost of capital is equal to:

𝑊𝐴𝐶𝐶 = 𝑟𝑠𝑀𝑉𝐸

(𝑀𝑉𝐸 +𝑀𝑉𝐷𝑒𝑏𝑡)+ 𝑟𝑖

𝑀𝑉𝐷𝑒𝑏𝑡

(𝑀𝑉𝐸 +𝑀𝑉𝐷𝑒𝑏𝑡)

𝑟𝑠 𝑖𝑠 𝑡ℎ𝑒 𝑐𝑜𝑠𝑡 𝑜𝑓 𝑒𝑞𝑢𝑖𝑡𝑦 𝑐𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒𝑑 𝑢𝑠𝑖𝑛𝑔 𝐶𝐴𝑃𝑀𝑟𝑖 𝑖𝑠 𝑡ℎ𝑒 𝑎𝑓𝑡𝑒𝑟 − 𝑡𝑎𝑥 𝑐𝑜𝑠𝑡 𝑜𝑓 𝑑𝑒𝑏𝑡 (𝑜𝑛 𝑦𝑜𝑢𝑟 𝑠𝑒𝑡𝑢𝑝 𝑠ℎ𝑒𝑒𝑡)

Calculate WACC on your setup sheet