A company recently paid out a $4 per share dividend on their stock. Dividends are projected to grow at a constant rate of 5% into the future, and the required return on investment is 8%. After one year, the holding period return to an investor who buys the stock right now will be:

In this question we need to find the holding period return for the stock, and for that we would need to know what is the stocks current price, what would the stocks price be in one year and how much dividend it will pay during the year. Their last dividend paid was $4 and their dividend is expected to grow at 5% in the future so the dividend paid in the current year would be 4*1.05= 4.2.

To find the current price of the stock we will use the DDM formula

DDM= D*(1+G)/R-G

(4*1.05)/(0.08-0.05)

Price = 140

Now we need to know what the stocks price would be in one year. For that we need to know the previous dividend which is 4.20, the growth rate which is 5% and the required rate of return which is 8%

DDM= (D*(1+G)/R-G

4.2*1.05/0.08-0.05

Price = 147

So now we know the current price, current year dividend and year end price we can calculate the holding period return.

Holding period return = (Dividend +(End of period price-Initial Price))/Initial Price

Dividend = 4.20

End Period Price = 147

Initial Price = 140

Holding period return = 4.20+(147-140)/140

=11.20/140

=0.08

=8%