Question

North Pole Cruise Lines issued preferred stock many years ago. It carries a fixed dividend of $6 per share. With the passage of time, yields have soared from the original 6 percent to 14 percent (yield is the same as required rate of return).

a. What was the original issue price?

b. What is the current value of this preferred stock?

c. If the yield on the Standard & Poor’s Preferred Stock Index declines, how will the price of the preferred stock be affected?

Short answer

1. The original issue price is computed as $100.
2. The current price is $42.86.
3. The yields on the specified preferred stock will fall.

Step-by-step solution

Computation of the original price of preferred stock

$\begin{array}{rcl}\mathbf{Original}\mathbf{}\mathbf{Issue}\mathbf{}\mathbf{Price}& \mathbf{=}& \frac{\mathbf{Dividend}}{\mathbf{Rate}\mathbf{}\mathbf{of}\mathbf{}\mathbf{return}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{6}}{\mathbf{0}\mathbf{.}\mathbf{06}}\\ & \mathbf{=}& \mathbf{\$}\mathbf{100}\end{array}$

Computation of the current price of preferred stock

$\begin{array}{rcl}\mathbf{Current}\mathbf{}\mathbf{Price}\mathbf{}\mathbf{of}\mathbf{}\mathbf{Preferred}\mathbf{}\mathbf{Stock}& \mathbf{=}& \frac{\mathbf{Dividend}}{\mathbf{New}\mathbf{}\mathbf{Rate}\mathbf{}\mathbf{of}\mathbf{}\mathbf{return}}\\ & \mathbf{=}& \frac{\mathbf{\$}\mathbf{6}}{\mathbf{0}\mathbf{.}\mathbf{14}}\\ & \mathbf{=}& \mathbf{\$}\mathbf{42}\mathbf{.}\mathbf{86}\end{array}$

Effect on stock price

When the yield on the S&P preferred stock index falls, then the yields on the specified preferred stock will also fall because the yield on S&P preferred stock index on the given stock has a close correlation.