Julie's x-ray company paid $2.00 per share in common stock dividends last year. The company's policy is to allow its divident to grow at 5 percent for 4 years and then the rate of growth changes to 3 percnet per year from year 5 on. What is the value of the stock if the required rate of return is 8 percent
To find the value of the stock, we can use the Gordon Growth Model. The Gordon Growth Model equation is:
Value of Stock = Dividend / (Required Rate of Return - Growth Rate)
In this case, the dividend is $2.00, the required rate of return is 8 percent (0.08), and the growth rate changes from 5 percent to 3 percent after 4 years.
To calculate the value of the stock, let's break it down into two parts:
Part 1: Calculating the present value of dividends for the first 4 years
To calculate the present value of dividends for the first 4 years, we need to consider the growth rate of 5 percent. We can use the formula for the present value of a growing annuity:
Present Value of Growing Annuity = Dividend / (Required Rate of Return - Growth Rate) * (1 - (1 + Growth Rate)⁻ᴺ⁺¹) / (1 - (1 + Growth Rate)⁻¹)
In this case, the dividend ($2.00), required rate of return (8 percent), and the growth rate (5 percent) will be used in the formula. N will be 4 (years).
Part 2: Calculating the present value of dividends starting from the 5th year
From the 5th year onwards, the growth rate changes to 3 percent. We need to calculate the present value of dividends using the formula for a growing perpetuity:
Present Value of Growing Perpetuity = Dividend / (Required Rate of Return - Growth Rate)
In this case, the dividend ($2.00), required rate of return (8 percent), and the growth rate (3 percent) will be used in the formula.
After calculating both parts, we can sum them up to get the total value of the stock.
Now let's plug in the numbers and solve the equations.