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 the price of $32.50. (Any stock that is not redeemed at the end of 10 years can be expected to be called by the comany in 15 years). 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?

18.92

To calculate the current market value of the preferred stock, we will use the discounted cash flow (DCF) valuation method. This method calculates the present value of the expected future cash flows from the stock, considering the investor's required rate of return.

First, let's calculate the present value of the dividend payments:

PV(dividends) = D / (1 + r)^n

Where:
PV(dividends) is the present value of the dividends
D is the annual dividend payment ($2.50)
r is the required rate of return (15% or 0.15)
n is the number of years until the dividends are received (10 years)

Using these values, we can calculate the present value of the dividend payments:

PV(dividends) = $2.50 / (1 + 0.15)^10
PV(dividends) = $2.50 / (1.15)^10
PV(dividends) ≈ $0.6522

Next, let's calculate the present value of the redemption value at year 10 (assuming the stockholder does not redeem the stock):

PV(redemption @ year 10) = R / (1 + r)^n

Where:
PV(redemption @ year 10) is the present value of the redemption value at year 10
R is the par value ($30)
r is the required rate of return (15% or 0.15)
n is the number of years until year 10 (10 years)

Using these values, we can calculate the present value of the redemption value at year 10:

PV(redemption @ year 10) = $30 / (1 + 0.15)^10
PV(redemption @ year 10) = $30 / (1.15)^10
PV(redemption @ year 10) ≈ $6.077

Finally, let's calculate the present value of the redemption value at year 15 (assuming the company calls the stock):

PV(redemption @ year 15) = R / (1 + r)^n

Where:
PV(redemption @ year 15) is the present value of the redemption value at year 15
R is the redemption price ($32.50)
r is the required rate of return (15% or 0.15)
n is the number of years until year 15 (15-10 = 5 years)

Using these values, we can calculate the present value of the redemption value at year 15:

PV(redemption @ year 15) = $32.50 / (1 + 0.15)^5
PV(redemption @ year 15) = $32.50 / (1.15)^5
PV(redemption @ year 15) ≈ $18.981

Now, we can calculate the current market value of the preferred stock by summing up the present values of the dividend payments and the two redemption values:

Current Market Value = PV(dividends) + PV(redemption @ year 10) + PV(redemption @ year 15)
Current Market Value ≈ $0.6522 + $6.077 + $18.981
Current Market Value ≈ $25.71

Therefore, the current market value of the preferred stock is approximately $25.71.