## Cost of Capital at Ameritrade Day 1

- What factors should Ameritrade management consider when evaluating the proposed advertising program and technology upgrades? Why? -They should see how revenues have changed after adopting the new ad program and technology upgrades -They need to see ROI for their investments over time
- How can the Capital Asset Pricing Model be used to estimate the cost of capital (required return) for calculating the net present value of a project's cash flows? it will help us determine the Cost of capital or discount rate which we can use to calculate NPV, in other terms the numerator will never change (FCF), only the denominator will based on the cost of capital
- What is the estimate of the risk-free rate that should be employed in calculating the cost of capiual for Ameritrade's proposed investment? - the risk free rate should be the T-bills rate or the average annualized total annual returns on US government securities = 3. %. 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, 20-year rate is optimal. So it is 6,69% 4. What is the estimate of the market risk premium that should be employed in calculating the cost of capital for Ameritrade's proposed investment?

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## Market Risk Premium

Three distinct concepts are part of market risk premium:

- Required market risk premium: the return of a portfolio over the risk-free rate (such as that of treasury bonds ) required by an investor;
- Historical market risk premium: the historical differential return of the market over treasury bonds;
- Expected market risk premium: the expected differential return of the market over treasury bonds. Also called equity premium, market premium and risk premium.

Market Risk Premium = Expected Return of the Market – Risk-Free Rate The expected return of the market can be based on the S;P 500, for example, while the risk-free rate is often based on the current returns of treasury bonds. First to find the Expected Return of the market, from Exhibit 6, We take the aggregate stock market and multiply by 12: = 15. 71% The Risk-free rate is 3. 8% =;gt; The market risk premium= 15. 7 – 3. 8 = 11. 9% (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 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.

In principle, how would one go about determining beta for purposes of calculating the cost of capital for Ameritrade's proposed investment?

TO calculate Beta for cost of capital, or asset beta: We need to find first the Equity Beta = by regressing stock returns over market returns and it will then be the slope. We also need to calculate the market value of the equity of the firm which is the price per share multiplied by the total number of shares outstanding (see attached notes) 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). Ba = (D/D+E)BetaD+ (E/D+E)BetaE

It is common to assume that debt has no relationship to market risk; that BetaD=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. To get BetaE, 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 Note: An agent that mediates sales and exchanges between securities buyers and sellers at even lower commission rates than those offered by a regular discount broker . As one might expect, deep discount brokers also provide fewer services to clients than standard brokers; such brokers typically provide little more than the fulfillment of stock and option trades, charging a flat fee for each.

The problem that must be overcome in determining the implementation decision is the uncertainty of the cost of capital.

## Other Methods of Estimating Cost of Equity Capital

- The EP Method r = EPS / Stock Price
- The Constant Growth (Gordon) Model r = DIV1 / P 0 + g compute g from earnings, dividend, or cash flow growth or use the sustainable growth estimate

Equity Betas, the relationship of a given equity’s risk to that of the larger market, reflects two kinds of risk

- The risk of the business itself
- The risk that the debt a business has will prevent cash flow to equity
- We can de-lever these equity betas to strip out financial risk associated with leverage and find the implied beta for the business itself (asset beta)
- Asset beta measures the business risk only and does not change with capital structure

Often, the best way to estimate a forward looking asset beta for a company is to take a median of its industry peers asset betas (historically calculated) since one-time company events in the past will be averaged out? We can then find the equity beta for the company by re-levering the industry asset beta to the target debt / cap ratio of the company?

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, thereturn, compared to the previous period, is given by: 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 X for y stock split, use the formula: Copy the Return 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 with Beta D = 0 and once with 25. 0). 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

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