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Sarah's Technologies has been growing quite rapidly in recent years, with earnings and dividends increasing at a rate of 30% per annum. This has been achieved by a relatively high level of retention in conjunction with high rates of return on investment. Retentions have been kept at a level of 60%. The company plans to continue with retentions at this level for another year, and then allow retentions to fall to 40% and 25% in the subsequent two years as good investment opportunities become more difficult to find. Earnings for the next year are expected to be $8,000,000. The expected rate of return on the investment to be undertaken next year is 30% and this is expected to fall to 25% the following year, and to 20% - which is the shareholder's required rate of return - the year after that.
Problem a. Provide an estimate of the firm's value today.
Problem b. Determine the rate of return the firm must have been earning to grow at 30% given the level of its retentions.
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