Answer to Question #223412 in Financial Math for Ratul

Question

You are planning for long term investment in a stock. After specific analysis you have two options i.e., Stocks of Company A and Stocks of Company B. You have following data on the stock prices of both companies;

Time Line

Share A

Share B

2010

15

125

2020

41

320

 

Please select the share that is more likely give you better return in the long run. Also, show your selection process. 

Answer 1

Solution:

The share price is the current market price of the share. It is the price of the share at any individual can purchase such share from the secondary market.

Now, let's compute the growth rate of share A, using the equation as shown below:

$\begin{aligned} \ 41 &=\ 15 \times(1+\text { Growth rate })^{10} \\ 2.73333333333 &=(1+\text { Growth rate })^{10} \end{aligned}$

Rearrange the above-mentioned equation to determine the growth rate as follows:

$1+ Growth\ rate =\sqrt[10]{2.73333333333}$

$\begin{aligned} \text { Growth rate } &=1.105781-1 \\ &=10.5781 \% \end{aligned}$

Hence, the growth rate of share A is 10.58 %.

Next, let's compute the growth rate of share B, using the equation as shown below:

Share price in year 2020= Share price in 2010 $\times(1+\text { Growth rate })^{\text {Time }}$

$\begin{aligned} &\ 320=\ 125 \times(1+\text { Growth rate })^{10} \\ &2.56=(1+\text { Growth rate })^{10} \end{aligned}$

Rearrange the above-mentioned equation to determine the growth rate as follows:

1+ Growth rate $=\sqrt[10]{2.56}$

$\begin{aligned} \text { Growth rate } &=1.09856-1 \\ &=9.856 \% \end{aligned}$

Hence, the growth rate of share B is 9.86%.

The growth rate of share A is 10.58% and the growth rate of share B is 9.86%. Share A provides better growth in the last 10 years and thus, Share A is likely to provide a better return in long run. 

Thus, Share A is likely to provide a better return in long run.