Question

a stock analyst wants to use a dividend pricing model to value stock. the analyst believes will pay its first dividend in exactly 15 years, and she is guessing that the dividend will be $10.00 per share at that time. the analyst assumes that dividends will grow by 5% per year going forward after year 15. the required return to hold is estimated to be 12% per year. based on these assumptions, what is the intrinsic value of stock today

Answer 1

P0 = $27.4044 rounded off to $27.40

Step-by-step explanation:

The constant growth model of dividend discount model (DDM) can be used to calculate the price of the stock today. DDM calculates the price of a stock based on the present value of the expected future dividends from the stock. The formula for price today under constant growth DDM is,

P0 = D0 * (1+g) / (r - g)

Where,

• D0 * (1+g) is the dividend expected in Year 1 or next year

• g is the constant growth rate in dividends

• r is the discount rate or required rate of return

To calculate the price of the stock today, we firsts need to calculate the price of the stock in year 15 and discount it back to today's value.

As we can see that to calculate the price of the stock today, we use dividend that is expected for the next period or Year 1. Thus to calculate the price of the stock in Year 15, we will use the dividend that will be expected in Year 16.

P15 = D15 * (1+g) / (r - g)

P15 = 10 * (1+0.05) / (0.12 - 0.05)

P15 = $150 per share

To calculate the price of this stock today, we must discount the Year 15 price to today's price.

P0 = P15 / (1+r)^15

P0 = 150 / (1+0.12)^15

P0 = $27.4044 rounded off to $27.40