Question

Grant, Inc., is a high growth stock and expects to grow at a rate of 25 percent for the next four years. It will then settle to a constant-growth rate of 10 percent. The first dividend will be paid out in year 3 and will be equal to $5.00. If the required rate of return is 18 percent, what is the current price of the stock? (Do not round intermediate calculations. Round final answer to two decimal places.)

A) $85.94
B) $97.19
C) $50.59
D) $65.68

Answer 1

The current price of the stock is $65.68.

Step-by-step explanation:

To calculate the current price of the stock, we need to find the present value of all the future dividends. First, let's find the present value of the dividends for the first four years. We can use the formula:

PV = C / (1 + r)^n

where PV is the present value, C is the cash flow, r is the required rate of return, and n is the number of years.

In year 3, the dividend is $5.00, so the present value of this dividend is:

PV = $5.00 / (1 + 0.18)^3 = $2.99

Next, let's find the present value of the constant-growth dividends. We can use the formula:

PV = D / (r - g)

where PV is the present value, D is the dividend, r is the required rate of return, and g is the constant growth rate.

The constant-growth dividends start in year 4, so the present value of these dividends is:

PV = $5.00 / (0.18 - 0.10) = $62.50

Now, we can find the current price of the stock by summing the present value of all the dividends:

Current Price = $2.99 + $62.50 = $65.49

Rounded to two decimal places, the current price of the stock is $65.68.