Answer:
Ans, The cost of the company’s cost of equity capital using the arithmetic average growth rate is 10.63% and using the geometric average of the growth rate is 10.60%
Explanation:
Hi, this is the equation we need to solve in order to find the company’s cost of equity capital.
![r=\frac{Dividend}{Price} +g](https://tex.z-dn.net/?f=r%3D%5Cfrac%7BDividend%7D%7BPrice%7D%20%2Bg)
As you can see, we almost have everything, the only problem here is "g", its growth rate, so let´s find "g" using the arithmetic average, but first, we need to find the growth rate for every period, the formula is
![g=\frac{(FinalDividend-PastDividend}{PastDividend}](https://tex.z-dn.net/?f=g%3D%5Cfrac%7B%28FinalDividend-PastDividend%7D%7BPastDividend%7D%20)
Therefore, we need to find 4 g´s, let´s call them g1, g2, g3 and g4:
![g1=\frac{(1.98-1.80)}{1.80} =0.10](https://tex.z-dn.net/?f=g1%3D%5Cfrac%7B%281.98-1.80%29%7D%7B1.80%7D%20%3D0.10)
![g2=\frac{(2.05-1.98)}{1.98} =0.0354](https://tex.z-dn.net/?f=g2%3D%5Cfrac%7B%282.05-1.98%29%7D%7B1.98%7D%20%3D0.0354)
![g3=\frac{(2.16-2.05)}{2.05} =0.0537](https://tex.z-dn.net/?f=g3%3D%5Cfrac%7B%282.16-2.05%29%7D%7B2.05%7D%20%3D0.0537)
![g4=\frac{(2.24-2.16)}{2.16} =0.0370](https://tex.z-dn.net/?f=g4%3D%5Cfrac%7B%282.24-2.16%29%7D%7B2.16%7D%20%3D0.0370)
So the average is:
![Average(g)=\frac{0.10+0.0354+0.0537+0.0370}{4} =0.0565](https://tex.z-dn.net/?f=Average%28g%29%3D%5Cfrac%7B0.10%2B0.0354%2B0.0537%2B0.0370%7D%7B4%7D%20%3D0.0565)
Therefore, the average growth rate is 5.65%
And the company’s cost of equity is:
![r=\frac{2.24}{45} +0.0565=0.1063](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B2.24%7D%7B45%7D%20%2B0.0565%3D0.1063)
so, if the average growth rate is found by using the arithmetic average is 10.63%.
Now, let´s find the geometric average
![g(average)=\sqrt[4]{(1+0.10)(1+0.0354)(1+0.0537)(1+0.0370)} -1=0.0562](https://tex.z-dn.net/?f=g%28average%29%3D%5Csqrt%5B4%5D%7B%281%2B0.10%29%281%2B0.0354%29%281%2B0.0537%29%281%2B0.0370%29%7D%20-1%3D0.0562)
therefore, using the geometric average to find the growth rate, the company’s cost of equity is:
![r=\frac{2.24}{45} +0.0562=0.1060](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B2.24%7D%7B45%7D%20%2B0.0562%3D0.1060)
using the geometric average, the company’s cost of equity is 10.60%
Best of luck.