Hooks Athletics, Inc., has outstanding a preferred stock with a par value of $30 that pays a dividend of $2.50. The preferred stock is redeemable at the option of the stockholder in 10 years at a price equal to $30. The stock may be called for redemption by the company in 15 years at a price of $32.50. (Any stock that is not redeemed at the end of 10 years can
be expected to be called by the company in 15 years.)
(a). If you know that investors require a 15 percent pretax rate of return on this preferred stock, what is the current market value of this preferred stock?
(b). Would you advice investors to exercise thier redemption option? Why or why not?
To calculate the current market value of the preferred stock, we need to determine the present value of its future cash flows. Here's how you can do it:
(a). First, let's break down the cash flows associated with the preferred stock:
1. Annual dividend payments of $2.50 for the next 10 years.
2. A redemption value of $30 at the end of 10 years if the stockholder exercises their option.
3. If the stockholder does not exercise their option, the company will redeem the stock at $32.50 at the end of 15 years.
Next, let's calculate the present value of these cash flows. We'll use a financial calculator or a spreadsheet formula such as Excel's PV function to do this.
1. To calculate the present value of the dividends, we use the perpetuity formula for present value:
PV(dividends) = Dividend / Required Rate of Return
PV(dividends) = $2.50 / 0.15 = $16.67
2. To calculate the present value of the redemption price after 10 years, we can use the present value of a single sum formula:
PV(redemption at 10 years) = Redemption Price / (1 + Required Rate of Return)^n
PV(redemption at 10 years) = $30 / (1 + 0.15)^10 = $6.63
3. To calculate the present value of the redemption price after 15 years, we again use the present value of a single sum formula:
PV(redemption at 15 years) = Redemption Price / (1 + Required Rate of Return)^n
PV(redemption at 15 years) = $32.50 / (1 + 0.15)^15 = $6.05
Finally, we sum up all the present values to obtain the current market value of the preferred stock:
Current Market Value = PV(dividends) + PV(redemption at 10 years) + PV(redemption at 15 years)
Current Market Value = $16.67 + $6.63 + $6.05 = $29.35
Therefore, the current market value of this preferred stock is approximately $29.35.
(b). Whether or not investors should exercise their redemption option depends on the current market value of the stock. In this case, the current market value of the preferred stock is below its redemption price of $30 after 10 years.
Therefore, it would not be advisable for investors to exercise their redemption option, as they would receive less than the redemption price. They would be better off continuing to hold the stock and receive the annual dividend payments until the company calls it for redemption at the higher price of $32.50 after 15 years.