When a company is looking to raise funds, they can issue preferred shares.  A preferred share has no maturity date (no expiration date or fixed term) but will stop regular payments if the company stops making a profit or goes out of business.  Because we usually have no way of knowing when a business will end or stop making profits, we will treat preferred shares like perpetuities and assume the profits (and therefore regular payments) will continue indefinitely (forever).

Let us first understand some of the terminology:

• Dividend: The regular payment (PMT) paid by the issuer of the preferred share.  The value of this dividend remains fixed and does not change through the lifetime of the share.
• Price: The selling price of the share (PV). This is the fair market value (ie: what you are willing to pay for the share).
• Market Rate: The current interest rate (I/Y).

See the sections below for the key formulas, tips and examples related to calculating values for preferred shares.

Calculating Fair Market Values using the Formulas

To calculate any values for preferred shares, you can use the same formulas as for perpetuities. If the dividend is awarded at the end of the each payment interval, and if you would like to know the fair market value of the share, use the following formula:

[latex]PV = \frac{PV}{i}[/latex]

If you would like to know the fair market value of the preferred share and the dividends are awarded at the start of each payment interval, use the following formula:

[latex]PV_{due} = \frac{PMT}{i} + PMT[/latex]

Let us now look at Kiana’s purchase of preferred shares and determine how much she should be willing to pay to purchase the preferred shares.

Example 5.9.1

Kiana purchases 100 Koodo preferred shares. Koodo pays a dividend of $0.80 every quarter on their preferred shares.  The next dividend will be paid out in 3 months.  If Kiana wants to earn a minimum of 5% compounded quarterly on her investment, how much should she be willing to pay for the 100 shares?

Let us first calculate the periodic rate (i) using the nominal rate (j₄ = 2.75%):

[latex]i = \frac{5%}{4} = \frac{0.05}{4} = 0.0125[/latex]

Because the first payment will be paid out at the end of the first interval (in 3 months), we use the following formula to calculate PV (the price per share):

[latex]PV = \frac{PMT}{i}[/latex]

Inputting i = 0.0125 and PMT = $0.80 into the formula gives the following price per share:

[latex]PV = \frac{\$0.80}{0.0125}= \$64[/latex]

Kiana should be willing to pay $64 per share. To calculate the price she should pay for all 100 shares, multiply by the 100 shares:

[latex]\textrm{Price for 100 Shares} = \$64\times100= \$6,400[/latex]

Conclusion: Kiana should pay $6,400 for the 100 Koodo preferred shares.

Example 5.9.2

Let us again look at Kiana’s purchase of 100 Koodo preferred shares (from Example 1). What if the first dividend were paid immediately instead of in 3 months? How much should Kiana be willing to pay for the 100 shares?

Because the first payment will be paid out immediately, we use the following formula to calculate PV (the price per share):

[latex]PV = \frac{PMT}{i}+PMT[/latex]

Inputting i = 0.0125 and PMT = $0.80 into the formula gives:

[latex]PV = \frac{\$0.80}{0.0125}+\$0.80= \$64.80[/latex]

Kiana should be willing to pay $64.80 per share. To calculate the price she should pay for all 100 shares, multiply by the 100 shares:

[latex]\textrm{Price for 100 Shares} = \$64.80\times100= \$6,480[/latex]

Conclusion: Kiana should pay $6,480 for the 100 Koodo preferred shares.

Calculating Fair Market Values using the BAII Plus

We can also use your BAII Plus calculator to calculate the fair market value of preferred shares. We use the same ‘tricks’ as for perpetuities:

• N = 1000×P/Y. Use 1000 years when calculating the number of payments (N)^[1].
• I/Y = Nominal Interest Rate (the current interest rate).
• FV = 0. You can never take the principal out. You only ever get paid the regular dividends.
• PMT = Regular Dividend Amount. We will enter this amount as positive because it is the amount the share holder receives^[2].
• CPT PV. Calculate the fair market value of the share (PV).

Example 5.9.3

Calculate Kiana’s price per share for shares from Example 1 using the BAII Plus:

Conclusion: Kiana should pay $64 per share the Koodo preferred shares (the same prices as in Example 1).

Example 5.9.4

Calculate Kiana’s price per share for shares from Example 2 using the BAII Plus:

Conclusion: Kiana should pay $64.80 per share the Koodo preferred shares (the same prices as in Example 2).

Calculating the Gain or Loss from Preferred Shares

We calculate the gain or loss from the sale of preferred ways in the same way as for bonds:

[latex]\textrm{Gain (or Loss)} = \textrm{Selling Price} - \textrm{Purchase Price}[/latex]

When the selling price is higher than the purchase price, we gain money on the sale of the shares. When the selling price is lower than the purchase price, we loose money on the sale.

Example 5.9.5

Kiana paid $64.00 per share when she bought 100 Koodo shares. Kiana would like the sell the shares several years later when interest rates have risen to 6.4%. Assume the next dividend of $0.80 will be paid in 3 months. Calculate Kiana’s gain (or loss) on the sale of the 100 shares.

Key Takeaways for Preferred Shares

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