Question

Gruber Corp. pays a constant $8.75 dividend on its stock. The company will maintain this dividend for the next 10 years and will then cease paying dividends forever. The required return on this stock is 12 percent. What is the current share price?

Answer 1

Answer:

72,91

Explanation:

the key to answer this question is to see that we can calculate the present value as a series of future payments valuated today, so there are two stages, the first one i going until 10 years and from ther is to infinity, so the present value can be solved as:

$PV =P*\frac{1-(1+i)^{-n} }{i}+P*\frac{1}{i}*(1+i)^{-n}$

where $a_{n}$ is the present value of the annuity, $i$ is the interest rate for every period payment, n is the number of payments, and P is the regular amount paid. so applying to this particular problem.

keep in mind that $P*\frac{1}{i}*(1+i)^{-n}$ is the formula for calculating a perpeuity, it means the present value of a infinite future payments but look carefully at the expresion $(1+i)^{-n}$  it means we are calculating a perpeuity which is located in the future and we compute it as money of today, so we have:

$PV =8,75*\frac{1-(1+0.12)^{-10} }{0.12}+8,75*\frac{1}{0.12}*(1+0.12)^{-10}$

$PV =72,91$