Colgate-Palmolive Company has just paid an annual dividend of $ 1.09. Analysts are predicting dividends to grow by $ 0.19 per year over the next five years. After then, Colgate's earnings are expected to grow 5.3 % per year, and its dividend payout rate will remain constant. If Colgate's equity cost of capital is 7.5 % per year, what price does the dividend-discount model predict Colgate stock should sell for today?

$74.62

Explanation:

Div₀ = $1.09

expected growth $0.19 per year

Div₁ = $1.28

Div₂ = $1.47

Div₃ = $1.66

Div₄ = $1.85

Div₅ = $2.04

then constant growth rte of 5.3%

equity cost = 7.5%

first we need to determine the stock price in year 5 using the Gordon growth model:

stock price = [dividend x (1+g)] / (Re - g) = ($2.04 x 1.053) / (7.5% - 5.3%) = $97.64

now we can discount all the future cash flows:

stock price = $1.28/1.075 + $1.47/1.075² + $1.66/1.075³ + $1.85/1.075⁴ + $2.04/1.075⁵ + $97.64/1.075⁵ = $1.19 + $1.27 + $1.34 + $1.39 + $1.42 + $68.01 = $74.62

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