What is the expected purchase at t? 3. Consider a common stock with the followin

Question

What is the expected purchase at t?

3. Consider a common stock with the following expected dividends: $2 in one year (i.e., at t=1), $3 in two years (at t=2), $0 in three years (at t=3), $2 in four years (at t=4) and $5 in five years (at t=5). After t=5, the dividends will grow at 10% per year for two years (i.e., t=6 and t=7). After t=7, dividends will grow at 2% per year, forever. The opportunity cost of capital is 12%. You plan to purchase the common stock in three years (i.e., at t=3). What is your expected purchase price at t=3?

Explanation / Answer

The present value of cash flows fromt he stock starting today is 41.72. If the purchase is intended after 3 years, the dividend for year 1 and 2 will have to be foregone. The third year has 0 dividend. Assuming that the buyeris not entitled to t3 dividend, the calculation is as follows

By consiedring t3 as 0, the discounted cash flow multiplied by PV factors will show the present value at t3 at $52.75. Inorder to bring that value down to todays value, the discount factor of t3 is used to discount it.

Year Dividend PV at 12% PV of cash flow t1 2 0.892857143 1.79 t2 3 0.797193878 2.39 t3 0 0.711780248 0.00 t4 2 0.635518078 1.27 t5 5 0.567426856 2.84 t6 5.5 0.506631121 2.79 t7 6.05 0.452349215 2.74 Terminal Value ((6.05+(6.05*2%))/(12%-2%) 61.71 0.452349215 27.91 Grand Total 41.72

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