Case Study Guidelines
Students are required to read closely the assessment criteria
for both case study presentation and written report as listed
on the course outline (page 7 to 9).
Case Study Questions
Cost of Capital at Ameritrade
1) What factors should Ameritrade management consider when
evaluating the proposed advertising program and technology
upgrades? Why?
2) How can the Capital Asset Pricing Model be used to estimate
the cost of capital for a real (not financial) investment
decision?
3) What is the estimate of the risk-free rate and market risk
premium that should be employed in calculating the cost of
capital for Ameritrade?
4) In principle, what are the steps for computing the asset
beta in the CAPM for purposes of calculating the cost of
capital for a project?
5) Ameritrade does not have a beta estimate as the firm has
been publicly traded for only a short time period. Exhibit 4
provides various choices of comparable firms. What comparable
firms do you recommend as the appropriate benchmarks for
evaluating the risk of Ameritrade’s planned advertising and
technology investments?
6) Using the stock price and returns data in Exhibit 4 and 5,
and the capital structure information in Exhibit 3, calculate
the asset betas for the comparable firms.
7) How should Joe Ricketts, the CEO of Ameritrade, view the
cost of capital estimate you have calculated?
What factors Ameritrade should consider when evaluating the proposed advertising program and
technology upgrades?
–
–
–
–
–
–
–
–
–
–
–
–
Sustainability of the project- how long can Ameritrade maintain a cost leadership strategy before the
project becomes obsolete. This will assist in estimating the expected future cash flows necessary for
t
evaluating the project. V= ∑CF/(1+WACC)
The risk free rate
Market risk premium
Beta
Cost of debt- the cost of raising debt have an impact on the WACC equation
Financing mix- how you are going to fund the project. The financing mix should minimise the hurdle
rate and match the asset being financed. The proportion raised by debt and equity must maintain
their target capital structure or debt to equity ratio. This will affect the WACC equation.
State of the economy once the project is implemented. Ameritrade’s revenue is tied to the stock
market. Decision tree analysis can be used to determine the possible outcomes or value of the project
given the probability of different economic scenarios- high, average and low demand.
The risk of the project- the hurdle rate should be higher for riskier project than for safer projects.
The hurdle rate- invests in projects that yield a return greater than the minimum acceptable hurdle
rate. Since financial resources are finite, there is a hurdle that projects have to cross be being deemed
acceptable. In this case, the hurdle rate is the WACC of the project.
The unique risk
Previous advertising campaign success
Large initial outlay, strict and efficient cash flow management required
How can the CAPM be used to estimate the cost of capital for a real (not financial) investment decision?
The valuation models developed for financial investment such as CAPM are applicable for real asset
investment as well. Real assets and financial assets share several common characteristics: their value is
determined by the cash flows they generate, the uncertainty associated with these cash flows and the
expected growth in the cash flows.
The Capital Asset Pricing Model (CAPM) = E(r) = Rrf + β (Rm –Rrf)
The Capital Asset Pricing Model (CAPM) is traditionally used to determine the cost of equity (the return equity
investors’ demand from putting their funds into risky investments) which is a component of the cost of capital.
It represents the minimum return we need to achieve to satisfy our equity investors
Components of CAPM include:
– The risk-free rate (Rrf)
– Market risk premium (Rm –Rrf)
– Beta β
Most analysts use the rate on a long-term (10 to 20 years) government bond as an estimate for the risk-free
rate. The market risk premium used in the cost of equity equation is forward-looking. While the market risk
premium used in beta regression are historical realised for each stock return period.
The market risk component, beta, can be measured using the regression analysis between the stocks return
and the market portfolio. However, the short history of Ameritrade stock prices renders it inadequate. A more
appropriate method would be a bottom up beta method.
Steps to calculate bottom-up beta:
1.
2.
Identify the business the firm operates in.
Find other publicly traded firms in the same industry and obtain their betas, which are used to
compute the average beta of the industry.
3.
Utilising the Hamada equation, we need to obtain the unlevered beta, a proxy of Ameritrades risk if
the firm was entirely financed through equity.
Unlevered beta = beta comparable firms / [1+ (1-t) D/E comparable firms].
4. Finally, taking into account Ameritrade’s leverage, capital structure, use the Hamada equation to
compute its levered beta.
Further adjustment can be made for higher risk premium and compensation for liquidity for small firms.
CAPM assumes that marginal investors are well diversified and therefore are only rewarded for taking
additional risk that cannot be diversified away (systematic risk). Systematic risk is represented by the beta and
the market risk premium reflects the return required for taking risk above investments considered to be risk
free.
Alternatively, to apply the CAPM model to real investment decisions, assumptions for calculating beta and the
risk premium can be modified, mainly because of differences in liquidity across the two markets and in the
types of investors in each market.
Traditionally, regression analysis of stock returns to the market portfolio is used to obtain the beta of a stock
or financial asset. However, real asset investments are highly illiquid. The result is we do not observe the same
periodic price changes like that of financial assets. This leads us find an index, listed on the exchange,
containing comparable assets to the one being invested in.
Hence to estimate the beta, we must regress the market indexes return against the market portfolio.
Traditionally, the market portfolio used in calculating a stocks beta contains all stocks and financial asset only
and no real assets. A solution to this is to find an index indicative of all assets within the market which
comprises of real investments. That is, a consolidated market portfolio.
For the final adjustment, we must consider whether investing in real assets exposes an investor to additional
risks not experienced by financial investors and whether or not it is rewarded. An obvious distinction between
the two types of investors is their level of diversification. CAPM makes the fundamental assumption requiring
marginal investors be well diversified and hence only rewarded for the additional risk taken that is nondiversifiable. Since real assets tend to be large, expensive assets, real asset investors tend to possess little
diversification. Therefore, adjustments to the risk factor, beta, to a total beta reflect the fact most real
investors are not well-diversified.
Total beta = market beta/correlation between owners portfolio and the market.
What is the estimate of the risk‐free rate that should be employed in calculating the cost of capital for
Ameritrade?
In practice, we cannot find a truly riskless rate to base the CAPM as there is really no such thing as a truly
riskless asset in the economy. Therefore, most analysts use the rate on a long-term (10 to 20 years)
government or Treasury bonds as an estimate of the risk-free rate for the following reasons:
– Common stocks are long-term securities and thus it is reasonable to expect that stock returns embody
long-term inflation expectations similar to those reflected in bonds rather than the short-term
expectations in bills.
– Treasury bill rates are more volatile than are Treasury bond rates.
– In theory, the CAPM is supposed to measure the expected return over a particular holding period.
Substantial investments in technology to improve service and capacity and in advertising to increase
customer awareness are expected to be long term projects, so the holding period for the CAPM
should also be long. Therefore, the rate on a long-term T-bond appears to be a logical choice for the
risk-free rate.
Thus for the risk free rate component of CAPM, the rate of return for a government security is an adequate
proxy. Although not entirely risk free, government securities satisfy ‘the no default possibility’ criteria. The
company is of going concern, thus the rate on long term government bonds is an appropriate estimate of the
risk-free rate required in calculating the cost of capital. Since its formation in early 1971, Ameritrade has
maintained successful operation in the deep discount brokerage industry, earning 40% ROE for all but two
years.
In this case, we used the historic prices of long term bonds as the risk free rate parameter.
Prevailing Yields on U.S. Government Securities (August 31, 1997)
Annualized Yield to Maturity
3-Month T-Bills
1-Year Bonds
5-Year Bonds
10-Year Bonds
20-Year Bonds
30-Year Bonds
5.24%
5.59%
6.22%
6.34%
6.69%
6.61%
Hence this risk-free rate is 6.0%.
What is the estimate of the market risk premium that should be employed in calculating the cost of capital
for Ameritrade?
The market risk premium reflects the additional return required by risk adverse investors over and above what
investors deem as risk free. The excess return of the market portfolio over the risk free rate represents this
compensation. The market risk premium can be estimated as RM – RRF. The risk-free rate is observable and was
estimated to be 6.0%, so the key is to estimate the required return on the market.
Based on the extracts of exhibit 3, the large company stocks index serve as a sufficient proxy to the market
portfolio. Included in this index is S&P500 stock prices of the 500 largest firms in the US; satisfying CAPM’s
fundamental assumption that investors are well diversified.
Referring to the data above, the required return on the market is 14.0% for large company stocks, which is
based Standard and Poor’s 500 Stock Price Index. Therefore, using its annual average return of 14%, 6.0% risk
free rate of the 30 year govt bond, we yield a risk premium of 8.0%.
Historic Average Total Annual Returns on U.S. Government Securities and Common Stocks
(1950-1996)
T-Bills
a
Intermediate Bonds
b
Long-term Bonds
c
Large Company Stocks
d
Small Company Stocks
Average Annual Return
Standard Deviation
5.2%
6.4%
6.0%
14.0%
17.8%
3.0%
6.6%
10.8%
16.8%
25.6%
Historic Average Total Annual Returns on U.S. Government Securities and Common Stocks
(1929-1996)
T-Bills
a
Intermediate Bonds
b
Long-term Bonds
Average Annual Return
Standard Deviation
3.8%
5.4%
5.5%
3.3%
5.8%
9.2%
c
Large Company Stocks
d
Small Company Stocks
12.7%
17.7%
20.3%
34.1%
We choose to use historic average annual returns on US Government Securities and Common Stocks from the
period 1950-1996 over 1929-1996 since it has a lower standard deviation and standard error as seen in the
table below.
For the period 1950-1996
Estimation Period
5 Years
10 Years
25 Years
50 Years
Standard Error of risk premium estimate
16.8%/√5= 7.51%
16.8%/√10=5.31%
16.8%/√25=3.36%
16.8%/√50=2.38%
For the period 1926-1996
Estimation Period
5 Years
10 Years
25 Years
50 Years
Standard Error of risk premium estimate
20.3%/√5= 9.08%
20.3%/√10=6.41%
20.3%/√25=4.06%
20.3%/√50=2.87%
Theoretically, the further back in time, the smaller the standard error. However, in this case, the shorter
duration displayed lower standard error and hence was used as an estimate of market rate.
In principle, what are the steps for computing the asset beta in the CAPM for the purposes of calculating the
cost of capital for a project?
Beta is defined under CAPM as the amount of risk that a stock contributes to the market portfolio. In essence,
it is relevant risk of an individual stock.
𝑏𝑖 = (𝛿𝑖 |𝛿𝑀 )𝜌𝑖 𝑀
𝛿𝑖 is the standard deviation of the ith stock’s return
𝜌𝑖 is the correlation between the ith stock’s return and the return on the market
𝛿𝑀 is the standard deviation of the market’s return.
In principle, beta is usually estimated as the slope coefficient in a regression with the company’s stock returns
on the y-axis and market returns on the x-axis. This is known as the historical beta since it is based on historical
data.
a. Obtain daily or monthly price data on indices and stocks
b. Regress 60 monthly excess stock returns on excess market returns
c. Adjust for beta’s trend towards 1 over time
d. Further adjustment can be made for higher risk premium and compensation for liquidity for small
firms
Although this approach is simple, it is flawed in practice. Firstly, there is no theoretical guidance as to the
correct holding period over which to measure returns. The returns for a company can be calculated using daily,
weekly or monthly time periods and the resulting estimates of beta will differ. Beta is also sensitive to the
number of observations used in the regression. Secondly, the market return should theoretically reflect every
asset. In practice however, it is common to use only an index of common stocks such as the ASX, S&P 500 or
the NYSE Composite. Even though these indexes are highly correlated with one another, using different
indexes in the regression will often result in different estimates of beta.
This approach modifies the calculated historical beta in order to produce what they deem to be a more
accurate estimate of the true beta, when in fact the true beta should reflect the risk perceptions of the
marginal investor.
Some organisations modify the calculated historical beta in order to generate more accurate estimate of ‘true
beta’. The ‘adjusted beta’ attempts to correct a possible statistical bias by adjusting the historical beta to
make it closer to the average beta of 1.0. Furthermore, the ‘fundamental beta’ incorporates information about
the company such as changes in its product lines and capital structure.
In practice in computing the asset beta in the CAPM for the purposes of calculating the cost of capital for our
project, we used spreadsheet applications.
Two steps was involved in Excel’s regression function
Step 1
Compile the data
In order to calculate the standard deviations and correlations of stock and markets’ returns, we obtained
Standard and Poor’s 500 Stock Price Index returns which were consistent with the relevant periods of time.
The returns for a company can be calculated using daily, weekly, or monthly time periods. Stock prices are
downloaded from the Yahoo Finance! Most analysts use 4 to 5 years of monthly data or 1 to 2 years of weekly
returns, although some use 52 weeks of weekly data. But in this case, we used the monthly returns aligned
with available data of company’s stock return. The resulting estimates of beta will differ slightly due to
investor’s choice of time period.
Step 2
Once stock prices and index are obtained, transform stock data prices into return series (level to changes)
Rate of return =
Step 3
𝐴𝑚𝑜𝑢𝑛𝑡 𝑟𝑒𝑐𝑒𝑖𝑣𝑒𝑑−𝐴𝑚𝑜𝑢𝑛𝑡 𝑖𝑛𝑣𝑒𝑠𝑡𝑒𝑑
𝐴𝑚𝑜𝑢𝑛𝑡 𝑖𝑛𝑣𝑒𝑠𝑡𝑒𝑑
or ln 𝑃0 − ln 𝑃1
Perform regression analysis of stock returns against the market index return
Ameritrade does not have a beta estimate as the firm has been publicly traded for only a short time period.
Exhibit 4 provides various choices of comparable firms. What comparable firms do you recommend as the
appropriate benchmarks for evaluating the risk of Ameritrade's panned advertising and technology
investments?
Ameritrade belongs in the deep-discount brokerage sector. Ameritrade’s two primary sources of revenue were
from transaction and net interest. Virtually all of Ameritrade’s revenues were directly linked to the stock
market. Hence comparable firms are discount brokerages.
These firms focus in brokerage activity:
a. Charles Schwab Corp (Discount Brokerage)
b. E*Trade (Discount Brokerage)
c. Quick & Reilly (Discount Brokerage)
d. Waterhouse Investor Services (Discount Brokerage)
Using the stock price and returns data in Exhibit 4 and 5, and the capital structure information in Exhibit 3,
calculate the asset betas for the comparable firms.
How should Joe Ricketts, the CEO of Ameritrade, view the cost of capital estimate you have calculated?
Hence inserting all the calculated components into the CAPM equation, we estimate the cost of capital to be:
We should accept the project if the expected return exceeds the minimum hurdle rate (WACC).
Combine Wing-Yee, Percy, Lila
Questions
For estimating market risk premium, why did you use the forward risk premium and not the risk premium?
Other than the reason of volatility, why did you use Treasury bonds over Treasury bills as the estimate for the
risk-free rate?
Why did you 30 years Treasury bonds as opposed to 10 or 20 year bond?
Why did we leave out E*TRADE (not enough return history)
Maybe it’s not a brokerage firm?
Why we used the previous 5 years historical return? What years we used for regressing beta?
The company tax rates used? Why 35%
What we use for debt to equity for Ameritrade? Is there any debt in the current year?