Introductory Corporate Finance: Cost of Capital - Cost of Preferred Stock, rps = Dps / Pnet

What This Is

The cost of preferred stock (rps) is a crucial concept in corporate finance that represents the expected return on investment for preferred shareholders. It is calculated as the annual dividend per share (Dps) divided by the net proceeds per share (Pnet). For instance, if a company issues 1 million shares of preferred stock with a dividend of $5 per share and a net proceeds of $100 per share, the cost of preferred stock would be 5% (rps = 5 / 100 = 0.05).

Key Formulas & Models

• rps = Dps / Pnet – cost of preferred stock; represents the expected return on investment for preferred shareholders.
  • Dps: annual dividend per share
  • Pnet: net proceeds per share
• Pnet = Pissue - F – net proceeds per share; calculated by subtracting flotation costs (F) from the issue price (Pissue).
  • Pissue: issue price per share
  • F: flotation costs per share
• rps = Dps / (Pissue - F) – alternative formula for cost of preferred stock.
• Pissue = Pmarket + F – issue price per share; calculated by adding flotation costs (F) to the market price (Pmarket).
  • Pmarket: market price per share
  • F: flotation costs per share
• F = (Issue fees + Underwriting fees + Other costs) / Number of shares – flotation costs per share; calculated by dividing the total flotation costs by the number of shares issued.
• Dps = Annual dividend per share – annual dividend per share; represents the annual payment made to preferred shareholders.
• Pmarket = Market price per share – market price per share; represents the current market price of the preferred stock.

Step-by-Step Calculation

1. Determine the annual dividend per share (Dps) and the net proceeds per share (Pnet).
2. Calculate the cost of preferred stock (rps) using the formula rps = Dps / Pnet.
3. Verify the calculation by using the alternative formula rps = Dps / (Pissue - F).
4. Consider the impact of flotation costs (F) on the issue price (Pissue) and net proceeds (Pnet).
5. Analyze the relationship between the cost of preferred stock (rps) and the market price (Pmarket).

Common Mistakes

1. Mistake: Failing to account for flotation costs (F) when calculating the net proceeds per share (Pnet).
   • Correction: Include flotation costs in the calculation of Pnet to ensure accurate representation of the cost of preferred stock.
2. Mistake: Using the issue price (Pissue) instead of the market price (Pmarket) when calculating the cost of preferred stock (rps).
   • Correction: Use the market price (Pmarket) to reflect the current market value of the preferred stock.
3. Mistake: Ignoring the impact of flotation costs (F) on the issue price (Pissue) and net proceeds (Pnet).
   • Correction: Consider the effect of flotation costs on the issue price and net proceeds to ensure accurate calculation of the cost of preferred stock.

Exam / CFA Tips

1. Tip: Be prepared to calculate the cost of preferred stock (rps) using different formulas and scenarios.
2. Tip: Understand the impact of flotation costs (F) on the issue price (Pissue) and net proceeds (Pnet).
3. Tip: Distinguish between the cost of preferred stock (rps) and the cost of debt (rd) in capital structure decisions.

Quick Practice Problem

A company issues 1 million shares of preferred stock with a dividend of $5 per share and a net proceeds of $100 per share. Calculate the cost of preferred stock (rps).

Answer: rps = 5 / 100 = 0.05 Explanation: The cost of preferred stock is 5% (rps = 5 / 100 = 0.05).

Last-Minute Cram Sheet

1. rps = Dps / Pnet – cost of preferred stock; represents the expected return on investment for preferred shareholders.
2. Pnet = Pissue - F – net proceeds per share; calculated by subtracting flotation costs (F) from the issue price (Pissue).
3. F = (Issue fees + Underwriting fees + Other costs) / Number of shares – flotation costs per share; calculated by dividing the total flotation costs by the number of shares issued.
4. Dps = Annual dividend per share – annual dividend per share; represents the annual payment made to preferred shareholders.
5. Pmarket = Market price per share – market price per share; represents the current market price of the preferred stock.
6. rps = Dps / (Pissue - F) – alternative formula for cost of preferred stock.
7. In M&M Proposition I (no taxes), firm value is independent of capital structure – but with taxes, value increases with debt due to the interest tax shield.
8. Cost of preferred stock (rps) is higher than the cost of debt (rd) due to the priority of debt claims.
9. Flotation costs (F) reduce the net proceeds per share (Pnet) and increase the cost of preferred stock (rps).
10. Market price (Pmarket) reflects the current market value of the preferred stock and should be used in calculations.