# Question

A firm’s dividends are expected to grow 20 percent a year for the next five years and then trend downward by 3 percent a year until they stabilize at a constant growth rate of 5 percent. The current dividend is $0.80 a share and the stock’s required rate of return is 13 percent. What should its current price be? If these growth expectations come to pass, what will its price be four years from now? Eight years from now?

Calculations for the current stock price follow (based on a spreadsheet, PV calculations could be rounded to the nearest penny or tenth of a penny).

The current price is the sum of the present values of the estimated dividends in years 1-10 plus the present value of the price in year 10; it equals $23.13.

The year 10 price is $3.342*(1.05)/(.13-.05) or $43.86. The present value of the stock price in year 10 is $43.86/(1.13)10 = 12.92. Adding this present value of the sum of the year 1-10 present values gives a current price of $23.13.

The spreadsheet can be adopted to estimate year 4 and year 8 prices. To estimate the price in year 4, we start with the year 5 dividend and discount it back one year, to year 4. Continuing this process and finding the present value of the year-10 price gives us

Similarly, the spreadsheet can be adapted to find the stock’s year-8 price, which equals the present value (as of year 8) of the year-9 dividend, the year-10 dividend, and the stock’s price in year 10: $2.82 + $2.62 + $34.35 = $39.79.

Calculations for the current stock price follow (based on a spreadsheet, PV calculations could be rounded to the nearest penny or tenth of a penny).

The current price is the sum of the present values of the estimated dividends in years 1-10 plus the present value of the price in year 10; it equals $23.13.

The year 10 price is $3.342*(1.05)/(.13-.05) or $43.86. The present value of the stock price in year 10 is $43.86/(1.13)10 = 12.92. Adding this present value of the sum of the year 1-10 present values gives a current price of $23.13.

The spreadsheet can be adopted to estimate year 4 and year 8 prices. To estimate the price in year 4, we start with the year 5 dividend and discount it back one year, to year 4. Continuing this process and finding the present value of the year-10 price gives us

Similarly, the spreadsheet can be adapted to find the stock’s year-8 price, which equals the present value (as of year 8) of the year-9 dividend, the year-10 dividend, and the stock’s price in year 10: $2.82 + $2.62 + $34.35 = $39.79.

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