HCS is currently retaining 100% of its earnings to finance future growth. Conseq
ID: 2705302 • Letter: H
Question
HCS is currently retaining 100% of its earnings to finance future growth. Consequently, no dividends will be paid on the stock during the next 3 years. Exactly 4 years from today, the firm expects to make an initial (first) dividend payment of $3.00 per share from earnings of $5.00 per share. The required rate of return on the company's stock is 14%. The current share price for HSC is $25.31. Assuming that HSC will continue to retain this constant fraction of earnings and to reinvest at the same incremental rate of return on equity from the end of year 4 through the end of eternity, determine the long-run incremental rate of return on equity ROE at which HSC is expected to reinvest future earnings from date 4 on.
Explanation / Answer
Price of share after 3 years is 25.31 * 1.14^3 = 37.5
Required growth of dividends to sustain this price be x
37.5 / ( 0.14 - x ) = 3
0.14 - x = 3/37.5
x = 0.14 - 3/37.5 = 0.06
Hence 6% growth is required
the dividends in 5th year is 3 * 1.06 = 3.18 and hence the earnings is 5/3 * 3.18 = 5.30
This extra 30 cents of earnings came from the extra $2 reinvested in year 4,
Hence the long run incremental rate of return is 0.3 / 2 = 0.15 = 15%
Hence the answer is 15%
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