Question

Frazier Inc. paid a dividend of $4 last year (D0). The firm is expecting dividends to grow at 21% in years 1-2 and 10% in Year 3. After that growth will be constant at 8% per year. Similar investments return 14%. Calculate the value of the stock today.

Answer 1

The value of the stock today can be calculated using the constant growth model, also known as the Gordon Growth Model. The dividends for each year are identified and the present value of each dividend is calculated. The sum of the present values of all the dividends gives the value of the stock today.

Step-by-step explanation:

To calculate the value of the stock today, we will use the constant growth model, also known as the Gordon Growth Model. This model calculates the present value of all future dividends, taking into account the growth rate and the required rate of return. Here are the steps to calculate the value of the stock:

1. Identify the dividends for each year. In this case, we have D0 = $4, D1 = $4 * 1.21 = $4.84, D2 = $4.84 * 1.21 = $5.85, and D3 = $5.85 * 1.10 = $6.42.
2. Calculate the present value of each dividend using the formula: PV = D / (1 + r)^n, where PV is the present value, D is the dividend, r is the required rate of return, and n is the number of years.
3. Sum up the present values of all the dividends to get the value of the stock today. In this case, it would be: PV0 = PV(D0) + PV(D1) + PV(D2) + PV(D3).

Using the given information, the required rate of return is 14%.

Let's calculate the value of the stock:

1. PV(D0) = $4 / (1.14)^0 = $4
2. PV(D1) = $4.84 / (1.14)^1 = $4.25
3. PV(D2) = $5.85 / (1.14)^2 = $4.41
4. PV(D3) = $6.42 / (1.14)^3 = $4.47
5. PV0 = $4 + $4.25 + $4.41 + $4.47 = $17.13

Therefore, the value of the stock today is $17.13.