Final answer:
To calculate the price of the stock today, we need to find the present value of the expected future dividends. Using the formula for present value and perpetuity, we can calculate the present value of the dividends from year 1 to year 7 and the perpetual dividend starting from year 7. Adding these present values will give us the price of the stock today.
Step-by-step explanation:
To calculate the price of the stock today, we need to find the present value of the expected future dividends. Since the company will not pay a dividend for the next 5 years, we need to calculate the present value of these zero dividends. We can then add the present value of the perpetual dividend stream starting from year 7.
The present value of the dividends from year 1 to year 7 can be calculated using the formula:
PV = D / (1 + r)^n
Where, PV is the present value, D is the dividend, r is the required return, and n is the number of years. Once we have the present value of the dividends, we can sum them up to get the price of the stock today.
Let's calculate the present value of the dividend in year 7 using the perpetuity formula:
PV = D / r
Substituting the values, we get:
(1.60 / 0.111) = 14.41
Now, let's calculate the present value of the dividends from year 1 to year 7:
(3.50 / 1.111) + (3.50 / 1.111^2) + (3.50 / 1.111^3) + (3.50 / 1.111^4) + (3.50 / 1.111^5) + (3.50 / 1.111^6) + (14.41 / 1.111^7) = 19.47
So, the price of the stock today is the present value of the expected future dividends, which is $19.47.