Answer to Question #114162 in Finance for rita

Question

Moody Farms just paid a dividend of $3.75 on its stock. The growth rate in dividends is expected to be a constant 5 percent per year indefinitely. Investors require a return of 13 percent for the first three years, a return of 11 percent for the next three years, and a return of 9 percent thereafter. What is the current share price? (Do not round intermediate calculations and round your answer to 2 decimal places, e.g., 32.16.)

Answer 1

The procedure first involves the determination of price of stock in year 6 when both the rate of dividend growth and returns stabilizes to infinity. The price of the stock for the year 6 will be determined by the value of dividend in year 7 divided by the returns required less growth rate of dividends as follows:

$P6=$ $D0\frac{1+g}{R-g} =D0\frac{(1+g)^7}{R-g}$

= $3.75\times\frac{(1.05)^7}{0.09-0.05} =$ $ 131.91566462

The next step is to find the price in the third year. This year is very necessary for it this time where the returns change. The price value in year three is is the present value PV of dividends in the forth, fifth and sixth year in addition to the present value of stock in year 6. Thus in year 3;

$P3=$ $3.75\times\frac{(1.05)^4}{1.09}+ 3.75\times\frac{(1.05)^5}{(1.11^2)} +3.75\times\frac{(1.05)^6}{(1.11^3)} + \frac{131.91566462}{(1.11^3)}$

= $ 108.196355383

The present value is an expression of present value of dividends in the first , second and third year in addition the value of stork in year 3.

$P0=3.75\times\frac{(1.05)}{1.13}+ 3.75\times\frac{(1.05)^2}{(1.13^2)} +3.75\times\frac{(1.05)^3}{(1.13^3)} + \frac{108.19635382}{(1.13^3)}$

= $ 84.716431644

= $ 84.72