Questions Covered

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 that should be employed in calculating the cost of capital for Ameritrade?

4. What is the estimate of the market risk premium that should be employed in calculating the cost of capital at Ameritrade?

5. 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?

6. Ameritrade does not have a beta estimate because 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?

7. Using the stock price and returns data in Exhibits 4 and 5, and the capital structure information in Exhibit 3, calculate the asset betas for the comparable firms.

8. How should Joe Ricketts, the CEO of Ameritrade, view the cost of capital you have calculated?

 Dear Andy! Sorry for my second delay with the case – it is all the preparation to universityexams. 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 thetime we do not have such companies as Ameritrade in Ukraine, because this kind of businessdoes not have it’s customers right now. This is a new thing to our country, and as usual, all thenew things are taken distrustfully.I can recall only one example : it is FOREX, but it actually deals with the currency exchangerates, buying and selling currency. The only same thing – all the processes are being held online.

1 . W h a t f a c t o r s s h o u l d A m e r i t r a d e c o n s i d e r w h e n e v a l u a t i n g t h e p r o p o s e d a d v e r t i s i n g  program and technology upgrades?Ameritrade needs a cost of capital to evaluate new projects. Firms maximize their value by taking all positive NPV projects.( )( )∑+=iiir CF  E  NPV 

*1 ...,2,1,0=i( )iCF  E is the expected cash flow in periodi*r  is the discount rateTo calculate an NPV, we need a discount rate. In the A-Rod case we used 8%. In theOcean Carriers case we used 9%. In this case we will learn how to determine anappropriate 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 ratewas 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%.Goodobservation.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 seethat Ameritrade has a cost of capital close to 22%. This high hurdle rate means thatAmeritrade should only accept projects with a very high potential rate of return (aslong as they are of similar risk levels).2 . H o w c a n t h e C a p i t a l A s s e t P r i c i n g M o d e l ( C A P M ) b e u s e d t o e s t i m a t e t h e c o s t o f c a p i t a l for a real investment decision? (Note: Areal investment decision here is contrastedfrom a financial investment decision. We are talking about real projects, with investmentin people and technologies, etc.)

Because we are talking about risks, we should think about systematic and versatilenon-systematic?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 iscomparatively 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 arisk premium

to account for the uncertaintyof the expected future cash flows in addition to reflecting the time value of money.Cost of capital =+= F  Rr *risk premium F  Ris the risk-free return, reflecting the time value of money. Textbook materialexplaining the CAPM is available on my website. The figure below may help tosummarize:The CAPM provides a useful framework for determining the discount rate by definingtherisk premiumabove. The diagram illustrates expected return for a stock,S  R. Wewant 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 Ain place of S.In slope-intercept form, the expected return, or appropriate discount rate, may be given as:( ) F M  Ameritrade A F R R Rr −+=β * Ameritrade Aβ 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.

Ris 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 . W h a t   i s   t h e   e s t i m a t e   o f   t h e   r i s k - f r e e  r a t e F  Rthat should be used in calculating the costof capital for Ameritrade?Since the projects being contemplated are long-term projects, we should use long-termrates. 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 governmentsecurities, because it is long-term capital investment. We may use 30-year rate, but weare investing in technology, and concerning the speed of technological enhancements, 20-year rate is optimal. So it is 6,69%.Sounds reasonable to me.

4 . W h a t i s t h e   e s t i m a t e o f t h e   m a r k e t r i s k   p r e m i u m , F M R R−, that should be used incalculating 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 thestock market will move in the future. Stock brokers have a conflict of interest; if they areoptimistic, and can persuade people of their optimism, then more funds should flow intothe stock market and their commissions and salaries increase. Thus we typically usehistorical spreads over a long period of time, covering many business cycles, and suggestthat with no better information, we anticipate the future to be like the past. Also, largestocks 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: during1950-96 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 marketeconomy, 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 quiteperceptive. The opposite side of this argument is that we don’t know what thefuture will bring. Perhaps we will have another period of world war, or terribleglobal market conditions. If such a scenario is not unreasonable, then we shouldn’texclude past data that relates to such times.  F M R R−=14%-6,69%=7,31%.

5 . I n   p r i n c i p l e , w h a t   a r e t h e s t e p s   f o r c o m p u t i n g t h e a s s e t b e t a i n t h e C A P M ?

 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 usemarket valueproportionsof debt and equity (see CAPM, p. 476). E  D A E  D E  E  D Dβ β β +++=It is common to assume that debt has no relationship to market risk; that.0

= Dβ  Empirical studies of corporate debt returns suggest it would be better to assign somemarket-related risk to corporate debt; and use estimates ranging from 0.20 to 0.30. Wewill compute both.To get E β , the equity beta for Ameritrade, we wouldnormallyrun a regression of equityreturns on stock market returns. That is, we would estimate the slope of the line that bestfits:Unfortunately, Ameritrade had their IPO (Initial Purchase Offer) in March of 1997, sothere is not enough data at the time of the case to calculate a reliable beta estimate. Soinstead, we will look at comparable firms. Firms in the same industry pursuing the sametypes of projects will have the same sorts of risks, thus their asset betaswill beapproximately the same. The returns we calculate for these firms, based on stock pricemovement, dividends, and stock splits, are their equity betas.These are influenced by thedegree 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 theamount 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.

 Therefore you should only use equity returns from the same period. 2) The returnfor the very first period is not a useful number, because you are implicitlysubtracting 0 as the previous price of the stock.

6 . E x h i b i t 4 p r o v i d e s v a r i o u s c h o i c e s o f   c o m p a r a b l e f i r m s .   W h i c h f i r m s d o   y o u r e c o m m e n d as the appropriate benchmarks for evaluating the risk of Ameritrade’s planned advertisingand 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, thereturn, compared to the previous period, is given by:11−−+−=t t t t t 

 P  D P  P  R. For example, if the price the previous period was $100, then wentup to $104, and in addition had a dividend of $8, the return would be +0.12, or 12%. In ashort time period, the returns will be much closer to 0.If there is an xfor  ystock split, use the formula:11−−+−=t t t t t  P  D y x P  P  y x R. To make calculating this efficient, we can set xand yequal to1 for those periods when there is not a stock split, then we can just use the secondformula. Here are the first few rows for Schwab

Copy the Rt values into Exhibit 6 alongside the appropriate dates, then regress theSchwab returns against the value-weighted NYSE returns for the same period. The slopeof the line is the equity beta.Do this for the other comparable firms. Calculate the asset betas using the formula inquestion 5 (twice, once with0= Dβ and once with25.0= Dβ ). 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 . W h a t   v a l u e ( s )   f o r  *r did you come up with? DONE!!r* for debt beta = 0 is 20,1%r* for debt beta = 0,25 is 20,4%.

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