Equity Modeling and Valuation Problem

Hi everybody!

This is my first post in this forum after months of lurking. I need help with the logic behind the following problem:

An investor projects the price of a stock to be $16.00 in one year and expected the stock to pay a dividend at that time of $2.00. If the required rate of return on the shares is 11%, what is the current value of the shares?
A) $15.28.

B) $16.22.

C) $14.11.

The value of the shares = ($16.00 + $2.00) / (1 + 0.11) = $16.22

The answer is B. But I would like to know why are we adding the price and the dividend of year 1, and dividing it with the Required Rate of Return plus one. I understand this is a form of discounting, but I am trying to see the formula and/or logic behind this solution. My initial approach was to solve for it using the DDM model, but I am clearly missing the growth rate so that could not work. I do not think I can get the ROE (by using Dupont) nor the div. payout ratio.

Thank you so much to all the people who can answer :slight_smile:

Good luck with your studies!!!

It sounds like the holding period is only 1 year, since there is a projected terminal value.

I see, from what I can gather, it seems that this is just a regular Holding Period Yield, where the numerator (price+div) represents both the capital and div gains, and by dividing it with 1+Re we are able to get the price. We basically would be doing a HPY but just solving for price instead for the returns.

Thank you so much for your quick response!!