Answer:
11.9981%( approx. 12.00% when rounded to 2 decimal places)
Step-by-step 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