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

To find the current share price for Gruber Corp, we use the present value of an annuity formula, considering a $8.75 constant dividend over 10 years and a 12% required return.

Step-by-step explanation:

To calculate the current share price of Gruber Corp stock when it pays a constant dividend for the next 10 years with no dividends afterwards, we need to use the present value of an annuity formula. Since the required return on the stock is 12 percent, we can discount the dividend of $8.75 for each of the next 10 years back to its present value.

The formula for the present value of an annuity is PV = D * ((1 - (1 + r)^-t) / r), where PV is the present value, D is the yearly dividend, r is the required rate of return, and t is the number of years. For Gruber Corp, D is $8.75, r is 0.12, and t is 10.

Using the formula, PV = $8.75 * ((1 - (1 + 0.12)^-10) / 0.12). This calculation will give the present value of all dividends over the next 10 years, which is equal to the stock's current price, since no dividends are paid after this period.

Answer 2

72,91

Step-by-step 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*(1-(1+i)^(-n) )/(i)+P*(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*(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*(1-(1+0.12)^(-10) )/(0.12)+8,75*(1)/(0.12)*(1+0.12)^(-10)`

`PV =72,91`