Questions: Try Yourself - Question 2 Suppose a corporation's stock had a 2:1 split and that the price per share stayed the same over a 6 year period. What was the rate of return during this period? A. 12.0 % B. 12.2 % C. 12.4 % D. 12.6 % E. 12.8 % Recall that the rate of return is given by i=(FV / PV)^(1 / n)-1

Try Yourself - Question 2

Suppose a corporation's stock had a 2:1 split and that the price per share stayed the same over a 6 year period. What was the rate of return during this period?
A. 12.0 %
B. 12.2 %
C. 12.4 %
D. 12.6 %
E. 12.8 %

Recall that the rate of return is given by i=(FV / PV)^(1 / n)-1

Transcript text: Try Yourself - Question 2 Suppose a corporation's stock had a 2:1 split and that the price per share stayed the same over a 6 year period. What was the rate of return during this period? A. $12.0 \%$ B. $12.2 \%$ C. $12.4 \%$ D. $12.6 \%$ E. $12.8 \%$ Recall that the rate of return is given by $i=\left(\frac{F V}{P V}\right)^{1 / n}-1$

Solution

Solution Steps

To find the rate of return, we need to determine the future value (FV) and present value (PV) of the stock. Since the stock underwent a 2:1 split, the number of shares doubled, but the price per share remained the same. This means the total value of the investment remains unchanged, so FV = PV. Given that the period is 6 years, we can substitute these values into the rate of return formula to find the rate $ i $.

Step 1: Understanding the Problem

We are given that a corporation's stock had a 2:1 split, and the price per share remained the same over a 6-year period. We need to calculate the rate of return using the formula:

\[ i = \left(\frac{F V}{P V}\right)^{\frac{1}{n}} - 1 \]

where $ F V $ is the future value, $ P V $ is the present value, and $ n $ is the number of years.

Step 2: Setting Values

Since the stock price remained unchanged after the split, we can set $ F V = P V $. For simplicity, we can assign both values to 1:

\[ F V = 1, \quad P V = 1 \]

Step 3: Calculating the Rate of Return

Substituting the values into the formula, we have:

\[ i = \left(\frac{1}{1}\right)^{\frac{1}{6}} - 1 = 1^{\frac{1}{6}} - 1 = 1 - 1 = 0 \]

This indicates that the rate of return over the 6-year period is $ 0 $.