Tranquility, Inc. has common shares with a price of $18.37 per share. The firm paid a dividend of $1.50 yesterday. If dividends are expected to grow at 9 percent for three years and then at 2 percent thereafter, what is the implied cost of common equity capital for Tranquility

11.9981%( approx. 12.00% when rounded to 2 decimal places)

Explanation:

Based on the fact that the current share price is the present value of future dividends and the terminal value of dividends beyond year 3, we can determine the implied cost of common equity capital for Tranquility  using the dividend discount model as shown thus:

Current dividend=$1.50

Years 1-3, dividend grows at 9% each year

Year 1 dividend=$1.50*(1+9%)=$1.635

Year 2 dividend=$1.635*(1+9%)=$1.78215

Year 3 dividend=$1.78215*(1+9%)=$1.942544

Terminal value=Year 3 dividend*(1+terminal growth rate)/(cost of equity-terminal growth rate)

terminal growth rate=2%

cost of equity is unknown, let us assume it is K

Terminal value=$1.942544*(1+2%)/K-2%

Terminal value=$1.981395/K-0.02

share price=$1.635/(1+K)^1+$1.78215/(1+K)^2+$1.942544/(1+K)^3+$1.981395/(K-0.02)/(1+K)^3

we need the value of K that gives the share price as $18.37

let us try try 11%

share price=$1.635/(1+11%)^1+$1.78215/(1+11%)^2+$1.942544/(1+11%)^3+$1.981395/(11%-0.02)/(1+11%)^3

share price=$20.44(close to $18.37, not exact)

After series of trials, I got 11.9981%

share price=$1.635/(1+11.9981%)^1+$1.78215/(1+11.9981%)^2+$1.942544/(1+11.9981%)^3+$1.981395/(11.9981%-0.02)/(1+11.9981%)^3

share price=$18.37

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