A prestigious investment bank designed a new security that pays a quarterly divi

Question

A prestigious investment bank designed a new security that pays a quarterly dividend of $5.00 in perpetuity. The first dividend occurs one quarter from today.

What is the price of the security if the stated annual interest rate is 8.5 percent, compounded quarterly?(Do not round intermediate calculations and round your final answer to 2 decimal places. (e.g., 32.16))

A prestigious investment bank designed a new security that pays a quarterly dividend of $5.00 in perpetuity. The first dividend occurs one quarter from today.

Explanation / Answer

The formula to calculate the PV of a perpetual cash flow = PMT / (I/Y)

Here, PMT = The periodic payment = $5

I/Y = Interest rate per period = 8.5% / 4 = 2.1250% (Interest is compounded quarterly and the payment is made quarterly hence we want a quarterly interest rate)

PV of the perpetuity = $5 / 0.021250

PV of perpetuity = $235.29$ is the PV or the price of the security.

I hope my solution solves your query.

Regards.

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