Vicky Robb is considering purchasing the common stock of Hawaii Industries, a rapidly growing boat manufacturer. She finds that the firm’s most recent (2020) annual dividend payment was $2.50 per share. Vicky estimates that these dividends will increase at a 20% annual rate, g1, over the next 3 years (2021, 2022, and 2023) because of the introduction of a hot new boat. At the end of the 3 years (the end of 2023), she expects the firm’s mature product line to result in a slowing of the dividend growth rate to 8% per year, g2, for the foreseeable future. Vicky’s required return, rs, is 15%. Required: What is the current (end-of-2020) value of Hawaii’s common stock, P0 = P2020.

P0 = $51.9956 rounded off to $52.00

Explanation:

The two stage growth model of DDM will be used to calculate the price of a stock whose dividends are expected to grow over time with two different growth rates. The DDM values a stock based on the present value of the expected future dividends from the stock.

The formula for price of the stock 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 = 2.5 * (1+0.2) / (1+0.15)  +  2.5 * (1+0.2)^2 / (1+0.15)^2  +  

2.5 * (1+0.2)^3 / (1+0.15)^3  +

[(2.5 * (1+0.2)^3 * (1+0.08) / (0.15 - 0.08) / (1+0.15)^3)

P0 = $51.9956 rounded off to $52.00

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