Stock A is expected to provide a dividend of $10 per share forever. Stock B is expected to pay a dividend of $5 next year, after which dividends are expected to grow forever at 5.4%. finally, stock C is expected to pay a dividend of $2 in two years after which dividend growth is expected to be 18% per year for 8 more years and no further growth in dividends therafter.

Question

Stock A is expected to provide a dividend of $10 per share forever. Stock B is expected to pay a dividend of $5 next year, after which dividends are expected to grow forever at 5.4%. finally, stock C is expected to pay a dividend of $2 in two years after which dividend growth is expected to be 18% per year for 8 more years and no further growth in dividends therafter.

If the required rate (r) for each stock is 12%, which stock is the most valuable?

Answer 1

To determine which stock is the most valuable, we need to calculate the present value of the dividends for each stock.

Let's start by calculating the present value of Stock A's dividend. Since it is expected to provide a constant dividend of $10 per share forever, we can use the perpetuity formula:

Present Value of Stock A = Dividend / Required Rate of Return

Present Value of Stock A = $10 / 0.12 = $83.33

Next, let's calculate the present value of Stock B's dividend. Stock B is expected to pay a dividend of $5 next year, and dividends are expected to grow at a rate of 5.4% forever. We can use the dividend growth model:

Present Value of Stock B = Dividend Next Year / (Required Rate of Return - Dividend Growth Rate)

Present Value of Stock B = $5 / (0.12 - 0.054) = $83.33

Now, let's calculate the present value of Stock C's dividend. Stock C is expected to pay a dividend of $2 in two years, after which dividends will grow at a rate of 18% for 8 more years. After that, there will be no further growth in dividends. We can calculate the present value of the first 10 years of dividends using the dividend discount model:

Present Value of Dividends 2-10 = Dividend * (1 - (1 + Dividend Growth Rate)^Number of Years) / (Required Rate of Return - Dividend Growth Rate)

Present Value of Dividends 2-10 = $2 * (1 - (1 + 0.18)^8) / (0.12 - 0.18) = $24.62

To calculate the present value of the dividend in the second year, we need to discount it back to the present using the required rate of return:

Present Value of Dividend 2 = Dividend / (1 + Required Rate of Return)^Number of Years

Present Value of Dividend 2 = $2 / (1 + 0.12)^2 = $1.59

Finally, we can calculate the present value of Stock C's dividends:

Present Value of Stock C = Present Value of Dividend 2 + Present Value of Dividends 2-10

Present Value of Stock C = $1.59 + $24.62 = $26.21

Therefore, based on the calculations, Stock B is the most valuable with a present value of $83.33, followed by Stock C with a present value of $26.21, and Stock A with a present value of $83.33.