Dear Andy! Sorry for my second delay with the case – it is all the preparation to university exams. I shall try to finish Friendly Cards in time. So I used to make parallels from cases to our real life and economic situation in Ukraine. At the time we do not have such companies as Ameritrade in Ukraine, because this kind of business does not have it’s customers right now. This is a new thing to our country, and as usual, all the new things are taken distrustfully. I can recall only one example : it is FOREX, but it actually deals with the currency exchange rates, buying and selling currency. The only same thing – all the processes are being held online. 1.
What factors should Ameritrade consider when evaluating the proposed advertising program and technology upgrades? Ameritrade needs a cost of capital to evaluate new projects. Firms maximize their value by taking all positive NPV projects.
NPV = ∑ i
E ( CFi )
(1 + r )
* i
i =0,1, 2, ...
E ( CFi ) is the expected cash flow in period i r * is the discount rate
To calculate an NPV, we need a discount rate. In the A-Rod case we used 8%. In the Ocean Carriers case we used 9%. In this case we will learn how to determine an appropriate rate. If Ameritrade analysts use a discount rate that is too high, good projects may be rejected. If they use a discount rate that is too low, bad projects may be accepted. Also the Ameritrade analysts should consider, that their company’s internal discount rate was often used as 15%, but some managers felt appropriate the rate of 8-9%. At this time, the external discount rate, used by Credit Swiss First Boston was 12%. Good observation. So actually computing the NPV earlier, Ameritrade analysts accepted only the best projects which fitted their high requirements. Now at the end of your analysis, we see that Ameritrade has a cost of capital close to 22%. This high hurdle rate means that Ameritrade should only accept projects with a very high potential rate of return (as long as they are of similar risk levels). 2.
How can the Capital Asset Pricing Model (CAPM) be used to estimate the cost of capital for a real investment decision? (Note: A real investment decision here is contrasted from a financial investment decision. We are talking about real projects, with investment in people and technologies, etc.)
Because we are talking about risks, we should think about systematic and versatile nonsystematic? risks. Systematic risks usually depend on overall economical situation, government steps, state economic policy and law base risks. In the US this kind of risk is comparatively low. But in Ukraine it will be much higher because of unstable economy, government policy and laws. That is why computed cost of capital would be higher, if this company was situated in Ukraine. That seems reasonable to me. Ameritrade’s cost of capital should reflect a risk premium to account for the uncertainty of the expected future cash flows in addition to reflecting the time value of money. Cost of capital = r * = RF + risk premium RF is the risk-free return, reflecting the time value of money. Textbook material
explaining the CAPM is available on my website. The figure below may help to summarize:
The CAPM provides a useful framework for determining the discount rate by defining the risk premium above. The diagram illustrates expected return for a stock, RS . We want the expected return (the appropriate discount rate) for investments in various assets, which are financed by a combination of equity and debt, so we use the subscript A in place of S. In slope-intercept form, the expected return, or appropriate discount rate, may be given as:
r * = RF + β AAmeritrade ( RM − RF )
βAAmeritrade is called beta of the assets of Ameritrade, and represents the risk of Ameritrade. A company of average risk gets a beta of 1.0.
RM is the return of the average-risk company, or equivalently, the return of a broad-
based portfolio of companies, like those listed on the New York Stock Exchange (NYSE). 3.
What is the estimate of the risk-free rate RF that should be used in calculating the cost of capital for Ameritrade? Since the projects being contemplated are long-term projects, we should use long-term rates. Since the projects are in the future, we should use current (at the time of the case) yields, not historical rates. In my opinion, we should use the risk-free rate equal to yield of 20-year US government securities, because it is long-term capital investment. We may use 30-year rate, but we are investing in technology, and concerning the speed of technological enhancements, 20year rate is optimal. So it is 6,69%. Sounds reasonable to me.
4.
What is the estimate of the market risk premium, RM − RF , that should be used in calculating the cost of capital for Ameritrade? Typically analysts use the stock market return minus U.S. government bond returns. Unlike the bond market, where the current yields are the unbiased market prices for bonds whose cash flows are in the future, we don’t have a reliable estimate of where the stock market will move in the future. Stock brokers have a conflict of interest; if they are optimistic, and can persuade people of their optimism, then more funds should flow into the stock market and their commissions and salaries increase. Thus we typically use historical spreads over a long period of time, covering many business cycles, and suggest that with no better information, we anticipate the future to be like the past. Also, large stocks tend to better estimate the market than small stocks. That is why we may use the difference between US Government Securities rate (6,69%) and historical Large Company Stocks annual returns. But we have 2 numbers: during 1950-96 and 1929-96. The difference between them is 1,3%. I think that we should use “younger” value of 14%, because the years 1930-1949, of course, were under market economy, but at the same time there were not so stable laws, a Second World War passed, many companies at that time worked for government orders, so this number may be a bit out of overall tendencies. I appreciate your thoughtfulness. You are quite perceptive. The opposite side of this argument is that we don’t know what the future will bring. Perhaps we will have another period of world war, or terrible global market conditions. If such a scenario is not unreasonable, then we shouldn’t exclude past data that relates to such times. RM − RF =14%-6,69%=7,31%.
5.
In principle, what are the steps for computing the asset beta in the CAPM?
A cost of capital is a weighted average of the cost of debt and equity. Likewise, the asset beta is the weighted average betas of debt and equity. We use market value proportions of debt and equity (see CAPM, p. 476). βA =
D E βD + βE D+E D+E
It is common to assume that debt has no relationship to market risk; that βD = 0. Empirical studies of corporate debt returns suggest it would be better to assign some market-related risk to corporate debt; and use estimates ranging from 0.20 to 0.30. We will compute both. To get βE , the equity beta for Ameritrade, we would normally run a regression of equity returns on stock market returns. That is, we would estimate the slope of the line that best fits:
Unfortunately, Ameritrade had their IPO (Initial Purchase Offer) in March of 1997, so there is not enough data at the time of the case to calculate a reliable beta estimate. So instead, we will look at comparable firms. Firms in the same industry pursuing the same types of projects will have the same sorts of risks, thus their asset betas will be approximately the same. The returns we calculate for these firms, based on stock price movement, dividends, and stock splits, are their equity betas. These are influenced by the degree of leverage each company is using (recall that higher leverage leads to higher ROE, EPS and DPS, but also leads to greater variability in earnings). Knowing the amount of debt in their capital structures (at market values), we can calculate the asset beta for each comparable firm. Then we will average these to use as a proxy for Ameritrade’s asset beta. Please see spreadsheet work. This is very good. I would just make two observations, however: 1) the debt to total capital ratios in Exhibit 4 are for the period 1992-1996.
6.
Therefore you should only use equity returns from the same period. 2) The return for the very first period is not a useful number, because you are implicitly subtracting 0 as the previous price of the stock. Exhibit 4 provides various choices of comparable firms. Which firms do you recommend as the appropriate benchmarks for evaluating the risk of Ameritrade’s planned advertising and technology investments? Determine the betas for these firms. Let us agree that Charles Schwab is a comparable firm. Their price changes, dividends, and stock split information for 1992-1996 is in Exhibit 5. If there were no stock split, the return, compared to the previous period, is given by: Pt − Pt −1 + Dt . For example, if the price the previous period was $100, then went Pt −1 up to $104, and in addition had a dividend of $8, the return would be +0.12, or 12%. In a short time period, the returns will be much closer to 0. If there is an x for y stock split, use the formula: Rt =
x x Pt − Pt −1 + Dt y y . To make calculating this efficient, we can set x and y equal to Rt = Pt −1
1 for those periods when there is not a stock split, then we can just use the second formula. Here are the first few rows for Schwab Shares
Price
31-Jan-92
38,394
31.875
28-Feb-92
38,394
33.250
31-Mar-92
38,479
34.625
30-Apr-92
38,479
28.500
x
y
Rt
1
1
0.051
-
1
1
0.043
-
1
1
0.041
1
1
-0.175
Dividends
Split
0.040
0.060
Copy the Rt values into Exhibit 6 alongside the appropriate dates, then regress the Schwab returns against the value-weighted NYSE returns for the same period. The slope of the line is the equity beta. Do this for the other comparable firms. Calculate the asset betas using the formula in question 5 (twice, once with βD = 0 and once with βD = 0.25 ). Average the results. This should be a good estimate of Ameritrade’s asset beta. Finally, put these results back into the equation in #2 to estimate Ameritrade’s cost of capital. Please see spreadsheet calculations. 7.
What value(s) for r * did you come up with? DONE!! r* for debt beta = 0 is 20,1% r* for debt beta = 0,25 is 20,4%.
It is higher than usually used rate, but this is long-term project and we need to be sure that we would not accept a bad project. DONE!!!! Very good! 98 – 5 late
