Question

The National Bank of Columbia has issued perpetual preferred stock with a $100 par value. The bank pays a quarterly dividend of $3.10 on this stock. What is the current price of this preferred stock given a required rate of return of 8.2 percent

Answer 1

The current price of the National Bank of Columbia's perpetual preferred stock, which pays a quarterly dividend of $3.10, is $151.22, calculated using the present discounted value formula and the required annual rate of return of 8.2%.

Step-by-step explanation:

The question deals with calculating the current price of preferred stock issued by the National Bank of Columbia, given a fixed quarterly dividend and a required rate of return. To find the current price of the perpetual preferred stock, which pays a consistent dividend over time without a maturity date, we need to use the formula for the present value of a perpetuity. The formula is:

Current Price = Dividend per Period / Required Rate of Return

Since the required rate of return is given as an annual rate, we need to adjust it to a quarterly rate, as dividends are paid quarterly. Thus, the quarterly rate is 8.2 percent divided by 4, which equals 2.05 percent or 0.0205 in decimal form. Now we can calculate as follows:

Current Price = $3.10 / 0.0205 = $151.22

As present discounted value principles suggest, an investor should be willing to pay $151.22 today for a perpetual dividend stream from the bank’s preferred stock at a quarterly rate, assuming an 8.2% required annual rate of return.