The course material covered in weeks 4 and 5 should be suﬃcient for doing this problem set. The questions below are for the Cost of Capital at Ameritrade case in your course packet. You can ﬁnd the data for this case on the course website in a spreadsheet named Ameritrade.xls.
Please turn in your problem set solutions by posting them to bSpace as an Excel ﬁle or pdf ﬁle. Upload a single solution for each group, with all group members listed on the ﬁrst page. If you turn in an Excel ﬁle, make sure the grader can understand what you did without clicking on any cells. To make that possible, please include cells with appropriate explanations of what you did.
This problem set is due by 9:00 a.m. on Wednesday, 11/28. No late assignments will be accepted.
Questions: Assume that the investments under consideration will be ﬁnanced with equity only (i.e., no debt ﬁnancing).
1. What estimate of the risk-free rate should be employed in calculating the cost of capital for Ameritrade?
2. What estimate of the market risk premium should be employed in calculating the cost of capital for Ameritrade?
3. Ameritrade does not have a beta estimate since 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? Hints for #3:
• It does not matter what Ameritrade spends its investments on up-front (advertising and technology investments) since these costs are known numbers, and you are calculating the cost of capital to ﬁgure out the present value of the projected cash ﬂows from later years. What matters is what beta the ﬁrm’s assets will have, where the assets are the subsequent cash ﬂows that Ameritrade gets out of making the up-front investments.
• It is probably not useful to use a comparable that has very little data (less than 2 years, say) since the equity beta you estimate based on very little data will be very noisy (you can try it—look at the standard error on your estimated equity beta).
Hints for #4:
βE : To estimate the equity betas, here are some hints:
• Please regress (raw) stock returns on (raw) market returns—you are not given a time series for the riskless rate, so you cannot run the regression using excess stock returns and excess market returns (over the riskless rate).
• You use the market returns from Exhibit 6, but you’ll have to discuss with your group members whether you should use value-weighted or equal-weighted market returns. (The equal-weighted market return sets all the xi ’s to be equal.) • For some of the stocks you are given data for stock prices and dividends rather than being given the stock return directly. Some of the stocks have undergone stock splits.