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Watch: Calculating Preferred Stock Price and Required Rate of Return

Run time: 12:41Covers: the price formula, the required return formula, and worked examplesTaught by: Dr. Paul Borosky, DBA, MBA

The Short Answer

What Is the Preferred Stock Price Formula?

Answer

Preferred stock price equals the annual dividend divided by the required rate of return. Because the dividend is fixed and has no end date, the stock is valued like a perpetuity. To find the required return instead, divide the dividend by the price.

The Formulas

Vp = D ÷ r   |   r = D ÷ Vp

Vp
Value or price of the preferred share
D
Annual preferred dividend in dollars (par value × dividend rate)
r
Required rate of return, written as a decimal (8% = 0.08)

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Step by Step

How Do You Calculate the Price of a Preferred Stock?

Here is a classic textbook setup: a preferred share has a $100 par value and pays a 6% dividend. Investors require a 9% return. What should the share sell for?

  1. 1

    Find the dollar dividend

    The 6% rate applies to par, not to price. D = $100 × 0.06 = $6.00 per year.

  2. 2

    Convert the required return to a decimal

    9% becomes 0.09.

  3. 3

    Divide the dividend by the required return

    Vp = $6.00 ÷ 0.09 = $66.67. That is what the share is worth to an investor who wants 9%.

  4. 4

    Sanity check it

    The required return (9%) is higher than the dividend rate (6%), so the price must land below the $100 par. It does. If investors only wanted 6%, the price would be exactly $100.

How Do You Solve for the Required Rate of Return?

Now flip it. A preferred share pays $3.00 a year and trades at $40.00. What return is the market asking for?

  1. 1

    Write down what you know

    D = $3.00. Vp = $40.00. You are solving for r.

  2. 2

    Divide the dividend by the price

    r = $3.00 ÷ $40.00 = 0.075, or 7.50%.

  3. 3

    Check it the other way

    $3.00 ÷ 0.075 = $40.00. The price formula returns the same number, so the answer holds.

Dr. Paul's Insight

Price and required return move in opposite directions. When the market demands more return, the price of a fixed dividend has to fall. Once that clicks, preferred stock, bonds, and even real estate cap rates start to make sense, because they all run on the same idea.

In Excel

How Do You Calculate Preferred Stock Price in Excel?

Excel has no special function for this. A simple division does the job. Put the dividend in one cell and the rate in another so you can change either one and watch the price move.

ProblemExcel formulaAnswer
$2.50 dividend, 8% required return=2.5/8%$31.25
$100 par, 6% dividend rate, 9% required return=(100*6%)/9%$66.67
$0.50 quarterly dividend, 8% required return=(0.5*4)/8%$25.00
Required return: $3.00 dividend, $40.00 price=3/407.50%

Format the return cell as a percentage, or Excel shows 0.075. In a template, use cell references like =B2/B3 so one sheet solves every homework problem.

Avoid These

What Are the Most Common Preferred Stock Mistakes?

  • Applying the dividend rate to the price. A 6% preferred pays 6% of par. On a $100 par share, that is $6.00, whatever the market price is.
  • Using a quarterly dividend as the annual number. A $0.50 quarterly dividend is $2.00 a year. Use the annual figure with an annual rate.
  • Typing the rate as a whole number. $6.00 ÷ 9 is $0.67, not $66.67. Use 0.09.
  • Adding a growth rate. Preferred dividends are fixed. Growth belongs in the constant growth model for common stock.
  • Confusing dividend rate and required return. The dividend rate is printed on the share. The required return is what investors demand today. They are rarely the same.

Real World Use

How a Student Uses the Preferred Stock Formula

Homework Problem

A $25 par preferred priced below par

The question: "A preferred stock has a $25 par value and a 7% dividend rate. It trades at $21.50. What is the required rate of return? What would the price be if investors required 9%?"

Step one, the dividend: $25 × 0.07 = $1.75. Step two, the return: $1.75 ÷ $21.50 = 8.14%. Step three, the new price: $1.75 ÷ 0.09 = $19.44.

The check is built in. A higher required return (9% versus 8.14%) produced a lower price ($19.44 versus $21.50). If the direction is wrong, the setup is wrong. In Excel, =1.75/21.5 and =1.75/9% confirm both answers.

Keep Going

More Videos in This Series

Constant Growth Formula for Stocks

Dr. Paul values common stock when the dividend grows every year. (7:56)

Dividend Yield Problem Solved in Excel and by Hand

Dr. Paul shows how to measure the cash return a dividend pays on today's price. (8:24)

Bond Valuation in Excel

Dr. Paul prices a bond and solves for yield to maturity with Excel functions. (7:06)

Questions

Preferred Stock Questions Students Ask

What is the formula for the price of preferred stock?
The formula is Vp = D ÷ r. D is the annual dividend in dollars and r is the required rate of return as a decimal. A $2.50 dividend with an 8% required return gives a price of $31.25.
How do you calculate the required rate of return on preferred stock?
Divide the annual dividend by the current price: r = D ÷ Vp. A share paying $3.00 a year and trading at $40.00 has a required return of 7.50%. Check it by plugging the answer back into the price formula.
Why is preferred stock valued as a perpetuity?
Preferred stock usually has no maturity date and pays a fixed dividend. A fixed payment that never ends is a perpetuity, and the present value of a perpetuity is simply the payment divided by the rate.
Do you use par value or market price to find the preferred dividend?
Use par value. The dividend rate is set as a percent of par when the share is issued. A $100 par, 6% preferred pays $6.00 a year no matter where the market price goes.
How do you find the price of preferred stock in Excel?
Divide the dividend by the rate, for example =2.5/8%, which returns $31.25. For the required return, divide the dividend by the price, such as =3/40, and format the cell as a percentage to see 7.50%.
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Written by Dr. Paul Borosky, DBA, MBA, current college professor, business consultant, and author with 14+ years and 1,000+ businesses served.

This page is for general educational purposes only. It is not financial, investment, legal, or tax advice.