Exciting Calculation of End-of-Quarter Dividends!
What is the value of a share that pays quarterly dividends in perpetuity at a rate of return of 3.25% compounded semi-annually?
How can we calculate the end-of-quarter dividends for this scenario?
Calculation of End-of-Quarter Dividends
To calculate the end-of-quarter dividends, we use the formula for present value of a perpetuity. The share value, rate of return, and dividend frequency are given.
In this exciting scenario, we have a share valued at $272.10 that pays quarterly dividends in perpetuity at a rate of return of 3.25% compounded semi-annually. Let's dive into the calculation process to find the end-of-quarter dividends!
First, we need to determine the quarterly rate based on the given semi-annual rate. By taking the square root of 1 plus the semi-annual rate and subtracting 1, we can find the quarterly rate which turns out to be 0.0159.
Next, using the formula P = D/r where P is the share value, D is the annual dividend payment, and r is the rate of return, we can solve for D to find the end-of-quarter dividends. Plugging in the values, we get:
272.10 = D / 0.0159
D = 272.10 * 0.0159 = 4.3283 (rounded to $4.33)
Therefore, the end-of-quarter dividends for this share is $4.33. What an exciting calculation to determine the dividends for this scenario!