I have a practice question that I have the answer to - I need someone to explain

Question

I have a practice question that I have the answer to - I need someone to explain step by step how I figure out the numbers so that I arrive at the answer please.

You observe that the Green Flash's common stock is selling for $40 per share. The next dividend is expected to be $4.00 and is expected to grow at a 4$ annual rate forever. If your required rate of is 12% should you purchase the stock?

The correct answer is - Yes, because the present value of the expected future cash flows is greater than $40.

Can you please walk me through how to figure this fact that the present value of the expected future cash flows is greater than $40? I am very new to this and not great with math so as elementary as possible will be so much appreciated.

Explanation / Answer

According to the given information, Current price of the stock (P0) = $40 Dividend in year-1(D1) = $4.00 Constant growth rate (g) = 4% Required return = 12% According to Dividend growth model, the expected return on the stock is calculated as                                R = (D1 / P0) + g Where D1 = $4.00            P0 = $40            g = 4% Substituting the values in the Dividend growth model formula, we get                                R = ($4.00 / $40) + 0.04                                   = 0.1 + 0.04                                   = 0.14 or 14% Therefore, the expected return on the stock is 14% If Expected return > Required return = Stock can be purchased If Expected return < Required return = Stock should not be purchased. The stock should be purchased because the expected return (14%) is more than the required return(12%). If the expected return is less than the required return, then the stock should not be purchased.

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