Question

A preferred stock (a perpetuity) pays an annual dividend of $4.80 forever. What is one share of this stock worth to you today if you require a rate of return of 11 percent?

Answer 1

Current Market Price of preferred stock = Annual Dividend/Required rate of return

Current market price of preferred stock = $4.80/11%

Current market price of preferred stock = $43.64

Answer 2

Given:

• Annual Dividend (D): $4.80 (paid forever)

• Required Rate of Return (r): 11% (or 0.11 in decimal form)

Formula for the Present Value (PV) of a Perpetuity:

$$PV=\frac{D}{r}$$

 

Calculation:

$$PV=\frac{4.80}{0.11}=\mathrm{43.6363...}$$

Final Value (rounded to two decimal places):

$$PV\approx \mathrm{\$}43.64$$

Interpretation:

• If you require an 11% return, you should be willing to pay $43.64 today for one share of this preferred stock.

• 
  

• This is because receiving $4.80 annually forever at an 11% return justifies the present value of $43.64.

Answer: One share of this stock is worth $43.64 today

Answer 3

Let's break down this problem step-by-step:

Understanding Perpetuity

A perpetuity is a stream of equal payments that continues forever. In this case, the preferred stock pays a fixed annual dividend of $4.80 indefinitely.

Present Value of a Perpetuity

The present value (PV) of a perpetuity is calculated using the following formula:

PV = Payment / Discount Rate

Where:

• PV is the present value of the perpetuity (the worth of the stock today).

• Payment is the fixed periodic payment (the annual dividend, $4.80).

• Discount Rate is the required rate of return (11% or 0.11).

Applying the Formula

Now, let's plug in the given values:

PV = $4.80 / 0.11

PV = $43.636363...

Rounding to Two Decimal Places

Since we're dealing with money, we round the result to two decimal places:

PV ≈ $43.64

Answer:

One share of this preferred stock is worth approximately $43.64 to you today if you require a rate of return of 11 percent.