Foundation of Finance:
Ameritrade
MFIN 210
Guo Chen, Rajan Grewal, Jiaming Hao, Fang Li, Jun Li,
Niddhi Rambhia, Haoming Wang, Junyu Zhu
12/08/2020
Factors to consider
When Ameritrade management evaluates the proposed advertising program and technology
upgrade, the main concern is whether the program will create value for the company and increase
revenue. Therefore, we need to consider the cost of capital and the return on investment, which is
measured by NPV and IRR. If the cost of capital exceeds the return on investment, the investment
should not be made.
Since we are considering NPV and IRR, we also need to verify that the projected cash flows are
forecasted accurately, as the cash flows, in addition to the cost of capital, will lead us to either
accept or reject an investment.
We also need to take into account the risk for the investment. More specifically, we need to
consider the systematic risk, which is beta, because this is a risk that cannot be diversified away.
Lastly, Ameritrade should consider any potential side effects that may occur as a result of the
proposed advertising program and technology upgrades.
CAPM and real investment decisions
The Capital Asset Pricing Model, or CAPM, defines the relationship between risk and return.
CAPM presents a framework that incorporates compensation for the time value and compensation
for systematic risk. The former is defined by the risk-free rate and the latter by the market risk
premium. The risk-free rate is the rate of return on an investment with absolutely no risk. The
market risk premium is the additional return that is expected by a capital provider for holding a
risky asset instead of the risk-free asset. Additionally, beta is used to measure the sensitivity of an
asset to market risk. By using the risk-free rate, market risk premium, and beta as inputs, CAPM
quantifies the return expected by an investment on the basis of the associated risk.
For a real investment decision, stockholders and creditors of the company provide capital. The
expected rate of return demanded by stockholders is assumed to be the firm’s cost of equity, which
is part of the weighted average cost of capital (WACC). WACC is determined by adding the
product of the cost of equity and the percentage of equity at market value and the product of the
cost of debt and the percentage of the debt at market value. Since CAPM derives the cost of equity,
we would then only need the yield to maturity on the outstanding bonds to find the cost of capital
for a real investment decision. The return on the investment must be larger than the cost of capital
to add value to the firm and therefore increase the wealth of the owners.
Risk-free rate
We consider the federal government treasury bond as a default-free bond, so we will use the federal
government bond yield as the risk-free rate. We need to match the expected market return and the
risk-free rate, so the risk-free rate must be historical. We will use the historic average from 1950
to 1996. The reason we don’t use the historic average from 1929-1996 is that the Great Depression,
which lasted from 1929 to the late 1930s, impacted the annual returns. We are assuming that the
economy will not enter another depression within the next 5 years.
Then, we need to match the investment horizon and maturity. Ameritrade is looking to adopt the
latest advances in technology and increase its advertising budget for 2 years. T-bills should not be
considered because the length of the investment is not short term. Also, since technology advances
relatively quickly, the long term bonds are not appropriate. Therefore, the risk-free rate that should
be employed in calculating the cost of capital for Ameritrade is the historic average annual return
for intermediate bonds from 1950 to 1996. Based on Exhibit 3, the risk-free rate is therefore 6.4%.
Market risk premium
The market risk premium is used to indicate the additional compensation that is required by riskaverse investors while they are doing risk-bearing investments. The market risk premium can be
calculated as the expected market return minus the risk-free rate. We know that the risk-free rate
is 6.4% from question 3. Therefore, we only need to estimate the expected market return.
To estimate the market return, we will use the annual returns of large company stocks, which is
the S&P 500 Index, from Exhibit 3 because it is the best proxy for the market return. Similar to
the risk-free rate, we will use the historic average annual return for large company stocks from
1950-1996 to get the expected market return of 14%. Therefore, the market risk premium is 14%
- 6.4% = 7.6%.
Comparable firms
Ameritrade’s strategy is mainly about reducing commissions per trade and providing low-cost
online brokerage services. Although Ameritrade is investing in technology to ensure its trading
reliability and execution speed, technology itself won’t be a revenue stream and therefore doesn’t
change Ameritrade’s business both functionally and operationally. Including companies that
operate in the internet industry would simply inflate the betas and consequently the cost of capital.
Therefore, we will only consider firms that specialize in brokerage services as the appropriate
benchmarks for evaluating the risk of Ameritrade’s planned advertising and technology
investments.
According to Exhibit 4, there are four firms that operate in the discount brokerage industry: Charles
Schwab Corp, E*Trade, Quick & Reilly Group, and Waterhouse Investor Services. These firms
have brokerage revenues of 82%, 95%, 81%, and 99%, respectively. From Exhibit 1, we calculated
Ameritrade’s brokerage revenues from 1995 to 1997 and found that it was approximately 91%
(Appendix 1). Ameritrade’s brokerage revenues as a percent of net revenues are similar to the
comparable firms we chose, which means that the comparables have similar firm risk as
Ameritrade, and can therefore be used as comparables.
However, out of these 4 firms, we will not use E*Trade. When doing the regression to calculate
the firms’ equity betas, it’s better to choose firms with more stock price data as it makes the sample
size larger, and thus increases the reliability of the regression results. As E*Trade has too little
stock price data compared to the other 3 firms, including it as one of the comparable firms can
cause the value of Ameritrade’s estimated asset beta to deviate largely from its true value.
Therefore, we will only use Charles Schwab, Quick & Reilly Group, and Waterhouse Investor
Services as our comparable firms.
Asset betas of comparables
The 3 comparables’ firm risk, which is similar to Ameritrade’s, is captured by the firms’ asset
betas. In order to estimate the asset betas of the comparables, we have four steps. See Appendix 2
for more detailed calculations and information.
1. We first have to identify the comparable firms, which we have already done in the previous
section.
2. We then calculate the comparable firms’ equity betas using regression analysis. We use the
data from Exhibit 5 for Charles Schwab Corp, Quick & Reilly Group, and Waterhouse
Investor Services from January 1992 to September 1996 to estimate equity beta.
3. To calculate the asset betas for the firms, we unlever the companies’ equity betas by
assuming that the companies’ debt does not have market risk.
4. We assume that the average of the three comparable firms’ asset betas is the asset beta of
Ameritrade.
Cost of capital
The cost of capital for Ameritrade is determined by the CAPM equation. We assume that
Ameritrade’s debt beta is 0. In other words, we assume that Ameritrade only uses equity financing,
which would make the weighted average cost of capital, or WACC, simply equal to the return on
equity which is calculated using CAPM.
To calculate the return on equity using CAPM, we use the risk-free rate of 6.4% and a market risk
premium of 7.6% from the earlier sections. To find Ameritrade’s asset beta, we take the average
of the asset betas for the three comparable firms and find it to be 2.2596 (Appendix 3).
Applying the CAPM equation, we found the cost of capital to be 23.573% (Appendix 4).
Appendix
1)
Transaction Income
Net Interest
Total Net
Revenues
Brokerage
Revenues
1995
$23,977,481
$8,434,584
$35,019,603
93%
1996
$36,469,561
$11,477,878
$54,338,753
88%
1997
$51,936,902
$18,193,946
$77,238,340
91%
Brokerage Revenues = (transaction income + net interest) / total net revenues
Average of 1995-1997 = (93 + 88 + 91) / 3 = 91%
2)
Company
BEquity (a) D/V (b) E/V (c) D/E (d)
Tax (e)
BAsset (f)
Charles Schwab
2.25861
0.08
0.92
0.0870
35%
2.13772
Quick & Reilly
2.35989
0
1
0
35%
2.35989
Waterhouse
3.18991
0.38
0.62
0.6129
35%
2.28115
Ameritrade
2.2596 (3)
a) Equity beta was calculated using the slope of the regression line between the
Exhibit 5 data of the company’s monthly excess returns and the market excess
return, which we assumed to be the VW NYSE, AMEX, and Nasdaq. See
Appendix 5 for details.
b) Since market values reflect the true economic claim of each type of financing
outstanding whereas book values may not, we assumed D/V to be the market
values of the average from 1992-1996 given in Exhibit 4.
c) E/V was calculated as 1 - (D/V)
d) D/E was calculated as (D/V) ÷ (E/V)
e) For the tax rate, we calculated Taxes/Income before Income Taxes for years 1995
to 1997 in Exhibit 1 and found that it was approximately 35%. We assumed that
this would be the tax rate for all firms.
f) For asset beta, we assumed debt had no market risk and therefore debt beta = 0.
Basset was therefore calculated as follows:
3) Ameritrade’s asset beta is the average of the comparable firm’s asset beta:
(2.13772 + 2.35989 + 2.28115) ÷ 3 = 2.2596
4) Cost of Capital = Rf + �(RM - RF)
= 6.4% + 2.2596(7.6%)
= 23.573%
5) We use the following equation to compute the monthly return of stock:
Monthly return of stocks and market can be found on the next page.
Month
Charles Schwab
Quick & Reilly
Waterhouse Investor Services
VW NYSE,
AMEX, and
NASDAQ
31-Jan-92
0.050700
(0.009009)
(0.036364)
(0.001650)
28-Feb-92
0.043137
0.042909
0.231132
0.013290
31-Mar-92
0.041353
0.004386
0.166667
(0.023680)
30-Apr-92
(0.175162)
(0.248908)
(0.187192)
0.013850
29-May-92
0.013158
0.003721
0.054545
0.006520
30-Jun-92
(0.186147)
(0.023256)
(0.212644)
(0.019240)
31-Jul-92
0.050426
(0.041667)
0.029197
0.039930
31-Aug-92
(0.086294)
(0.020870)
(0.208511)
(0.020760)
30-Sep-92
(0.200000)
0.025478
0.045455
0.012420
30-Oct-92
0.128333
0.043478
0.086957
0.010900
30-Nov-92
0.228395
0.212143
0.328000
0.040190
31-Dec-92
0.050251
(0.024631)
(0.012048)
0.017540
29-Jan-93
0.160191
0.090909
0.231707
0.012330
26-Feb-93
0.070248
(0.028889)
(0.034653)
0.005450
31-Mar-93
0.127413
0.043269
0.051282
0.025010
30-Apr-93
(0.100685)
(0.073733)
(0.097561)
(0.025510)
28-May-93
0.076336
0.043781
0.472973
0.029420
30-Jun-93
0.212766
0.160498
0.229358
0.005130
30-Jul-93
0.019298
0.064935
(0.014925)
(0.000760)
31-Aug-93
0.133621
0.141463
0.299242
0.039340
30-Sep-93
0.049430
0.035714
0.175953
0.000610
29-Oct-93
0.005072
(0.010345)
(0.057357)
0.018040
30-Nov-93
(0.079422)
(0.042509)
(0.182540)
(0.017350)
31-Dec-93
0.015686
0.096000
(0.174757)
0.019450
31-Jan-94
(0.086641)
(0.010490)
0.000000
0.031330
28-Feb-94
(0.067797)
(0.190247)
(0.035294)
(0.024090)
31-Mar-94
(0.022727)
(0.096916)
(0.140244)
(0.045740)
29-Apr-94
0.058419
0.029268
(0.092199)
0.009830
31-May-94
0.066079
0.023507
(0.046875)
0.009500
30-Jun-94
(0.181818)
(0.055814)
(0.122951)
(0.027380)
29-Jul-94
0.083636
(0.024631)
(0.028037)
0.030410
31-Aug-94
0.149533
0.186667
0.323077
0.042830
30-Sep-94
(0.036585)
(0.115385)
(0.169118)
(0.018650)
31-Oct-94
0.196456
(0.004831)
0.141593
0.014870
30-Nov-94
(0.098940)
(0.034175)
(0.116279)
(0.037070)
30-Dec-94
0.094118
0.146465
(0.140351)
0.012750
31-Jan-95
0.149534
0.088106
0.183673
0.020550
28-Feb-95
0.109375
0.142996
0.198276
0.039620
31-Mar-95
0.090141
0.014286
(0.071942)
0.026970
28-Apr-95
0.063876
0.144366
(0.031008)
0.024880
31-May-95
0.021898
0.156923
0.120000
0.034160
30-Jun-95
0.253571
0.173670
0.314286
0.030840
31-Jul-95
0.053105
0.051195
0.201087
0.040670
31-Aug-95
0.010840
(0.026623)
0.045249
0.009340
29-Sep-95
0.243968
0.227425
0.113537
0.036390
31-Oct-95
(0.209828)
(0.223433)
(0.225490)
(0.011150)
30-Nov-95
0.060109
0.071368
0.000000
0.042970
29-Dec-95
(0.170103)
(0.192118)
0.253165
0.015400
31-Jan-96
0.250435
0.134146
(0.045455)
0.028090
29-Feb-96
0.014925
0.132473
0.042328
0.016050
29-Mar-96
0.014706
0.123810
0.355330
0.011200
30-Apr-96
(0.051594)
0.033898
0.086142
0.025130
31-May-96
(0.010204)
0.112951
0.010345
0.026720
28-Jun-96
0.010309
(0.040590)
0.013652
(0.007660)
31-Jul-96
(0.013265)
(0.126923)
0.013468
(0.053390)
30-Aug-96
0.036269
0.033656
(0.000797)
0.032220
30-Sep-96
(0.080000)
(0.094017)
0.013378
0.052990