Apple Inc. is starting a new project. It plans to manufacture new type of i-Phones that have a 3D screen effect. It expects these phones to be a great success and bring rapidly growing profits in the first few years. After that, it expects the competition from other phone companies to kick in which will reduce the growth of annual profits. The dividends on Apple's shares will be growing accordingly. Here is the exact schedule of expected future dividends: Most recently paid dividend is $3. Expected annual growth rate of dividends for the first 3 years is 50%. Expected annual growth rate of dividends after that is 14%. Discount rate for this company is 16%. Calculate the price per share of stock of Apple Inc. (Increase decimal places for any intermediate calculations, from the default 2 to 6 or higher. Only round your final answer to TWO decimal places: for example, 100.23. DO NOT put "$" in your answer.)

P0 = 385.121878 rounded off to 385.12

Explanation:

To calculate the market price of the stock today, we will use the two stage growth model of DDM. The two stage growth model calculates the values of the stock today based on the present value of the expected future dividends from the stock. The formula for price today under this model is,

P0 = D0 * (1+g1) / (1+r)  +  D0 * (1+g1)^2 / (1+r)^2  +  ...  +  D0 * (1+g1)^n / (1+r)^n  +  [(D0 * (1+g1)^n * (1+g2))  /  (r - g2)] / (1+r)^n

Where,

P0 = 3 * (1+0.50) / (1+0.16)  +  3 * (1+0.50)^2 / (1+0.16)^2  +  3 * (1+0.50)^3 / (1+0.16)^3    +  [(3 * (1+0.50)^3 * (1+0.14)) / (0.16 - 0.14)] / (1+0.16)^3

P0 = $385.121878 rounded off to $385.12

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the answer is a.

by: nicholas dooley