17. Real is your boss and the treasurer of Free Cash Flow (FCF). She asked you to help her estimate the intrinsic value of the company's stock. FCF just paid a dividend of GHS 1.00, and the stock now sells for GHS 15.00 per share. Real asked a number of security analysts what they believe FCF's future dividends will be, based on their analysis of the company. The consensus is that the dividend will be increased by 10% during Years 1 to 3, and it will be increased at a rate of 5% per year in Year 4 and thereafter. Real asked you to use that information to estimate the required rate of return on the stock

The required rate of return is the rate of return that investors expect from the stock based on its current price GHS 15.00 per share and its forecast dividends.

The stock price is the present value of future dividends discounted at the required rate of return, the unknown

The dividends for the next 3 years would grow at the rate of 10%

Year 1 dividend=1.00*(1+10%)

Year 1 dividend=1.10

Year 2 dividend=1.10*(1+10%)

Year 2 dividend=1.21

Year 3 dividend=1.21*(1+10%)

Year 3 dividend=1.331

Dividend in year 4 and thereafter(forever, that the terminal value) would grow at the rate of 5%

Year 4 dividend=1.331*(1+5%)

Year 4 dividend=1.39755

Terminal value=Year 4 dividend*(1+g)/(r-g)

g=terminal growth rate=5%

r=unknown return

terminal value=1.39755*(1+5%)/(r-g)

share price=1.10/(1+r)^1+1.21/(1+r)^2+1.331/(1+r)^3+1.39755/(1+r)^4+1.39755*(1+5%)/(r-g)/(1+r)^4

we need the value of r such that share price 15.00

Using a trial and error approach, I got 12.97%

share price=1.10/(1+12.97%)^1+1.21/(1+12.97%)^2+1.331/(1+12.97%)^3+1.39755/(1+12.97%)^4+1.39755*(1+5%)/(r-12.97%)/(1+12.97%)^4

share price=15.01

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