What is the calculation to determine the end-of-quarter dividends for a share valued at $272.10 that pays quarterly dividends in perpetuity at a rate of return of 3.25% compounded semi-annually?
The calculation to determine the end-of-quarter dividends for a share valued at $272.10 that pays quarterly dividends in perpetuity at a rate of return of 3.25% compounded semi-annually involves using the formula for the present value of a perpetuity: PV = D / r. By rearranging the formula to solve for D and plugging in the given values, we can find the end-of-quarter dividends.
Calculating End-of-Quarter Dividends
To calculate the end-of-quarter dividends, the formula PV = D / r is utilized. Where PV represents the present value, D is the dividend payment, and r stands for the rate of return. Rearranging the formula, we get: D = PV * r.
In this scenario, the dividend payment D signifies the end-of-quarter dividend, the rate of return r equals 3.25% compounded semi-annually, and the present value PV refers to the share value of $272.10. By inserting these values into the formula, we can determine the end-of-quarter dividends.
Therefore, the calculation can be expressed as follows:
D = $272.10 * 3.25%
D = $272.10 * 0.0325
D = $8.84325
Rounding to the nearest cent, the end-of-quarter dividends for a share valued at $272.10 that pays quarterly dividends in perpetuity at a rate of return of 3.25% compounded semi-annually is approximately $8.84.