You expect that IBM will have earnings per share of $2.50 for the coming year. IBM plans to retain all of its earnings for years 1-3. For the subsequent two years (years 4 and 5), the firm plans on retaining 40% of its earnings. It will then retain only 10% of its earnings from that point forward. Retained earnings will be invested in projects with an expected return of 15% per year. If IBM's equity cost of capital is 12%, then what is the the price of a share of IBM's stock?
| Calculation of the price of a share of IBM's stock | |||||||||
| Price of a share of IBM's stock = Sum of Present values of all future dividends discounted at cost of capital i.e.12% | |||||||||
| Year | Dividend | Discount Factor @ 12% | Present Value | ||||||
| 1 | $0.00 | 0.892857 | $0.00 | ||||||
| 2 | $0.00 | 0.797194 | $0.00 | ||||||
| 3 | $0.00 | 0.71178 | $0.00 | ||||||
| 4 | $1.50 | 0.635518 | $0.95 | ||||||
| 5 | $1.50 | 0.567427 | $0.85 | ||||||
| Pertual (see working) | $12.50 | 0.567427 | $7.09 | ||||||
| Price of a share of IBM's stock | $8.90 | ||||||||
| Working | |||||||||
| Per Year Dividend from 3rd Year onwards = Earnings per share x (1 - retention %) = $2.5 x (1 - 0.40) = $1.50 | |||||||||
| Value of perpetual dividend = Dividend payable / equity cost of capital = $1.5 / 12% = $12.50 | |||||||||
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