18 Chapter 7 Stock Valuation

Conceptual Questions

•What is the difference between common stock and preferred stock? Provide an example of when an investor might prefer each type.

Common stock represents ownership in a company with voting rights and potential for capital appreciation, but dividends are not guaranteed. Preferred stock combines characteristics of debt and equity, offering fixed dividends with no voting rights but priority over common stock in bankruptcy.

Example: An investor seeking high growth might prefer common stock, while one desiring stable income might prefer preferred stock.

•Why is the dividend-discount model (DDM) less effective for valuing companies that do not pay dividends?

The DDM relies on dividends to calculate intrinsic value. For non-dividend-paying companies, the model cannot estimate value since no dividends are distributed, requiring alternative valuation methods like the discounted cash flow (DCF) model.

•How do share repurchases impact the value of remaining shares?

Share repurchases reduce the number of shares outstanding, increasing the earnings per share (EPS) and potentially boosting the stock price. This benefits remaining shareholders by consolidating ownership and enhancing the value of their shares.

•Explain why higher growth rates (g) in dividends lead to higher stock prices, assuming all other factors remain constant.

Higher growth rates increase the numerator in the dividend-discount model while reducing the effective discount rate (r – g). This results in a higher present value of expected future dividends, boosting stock prices.

•Describe the difference between the NYSE and Nasdaq in terms of how trades are executed.

The NYSE operates as an auction market where designated market makers facilitate trades. The Nasdaq is a dealer market, relying on market makers to provide liquidity and match buy/sell orders electronically.

Short Calculations

•A company’s stock is priced at $40 per share. It pays an annual dividend of $2 per share, and the stock price is expected to increase to $44 in one year.

What is the dividend yield? Dividend Yield = $2 / $40 = 5%.

What is the capital gains yield? Capital Gains Yield = ($44 – $40) / $40 = 10%.

What is the total return? Total Return = Dividend Yield + Capital Gains Yield = 5% + 10% = 15%.

•A company expects to pay a dividend of $5 next year, with dividends growing at 4% annually. The required rate of return is 10%. What is the stock’s current price based on the Dividend-Discount Model?

Stock Price = $5 / (0.10 – 0.04) = $83.33.

•A company has 1,000,000 shares outstanding, expects to pay $2 million in dividends next year, and plans to repurchase $500,000 worth of shares. The required return is 8%, and the growth rate of the total payout is 4%. What is the price per share using the Total Payout Model?

Total Payout = $2,000,000 + $500,000 = $2,500,000.

Total Equity Value = $2,500,000 / (0.08 – 0.04) = $62,500,000.

Price Per Share = $62,500,000 / 1,000,000 = $62.50.

Scenario-Based Problems

•An investor is deciding between two stocks: Stock A pays a consistent dividend of $3 per share annually, while Stock B reinvests all earnings into growth opportunities. Over five years, Stock A’s dividend yield is expected to remain at 6%, while Stock B’s price is projected to grow at an annualized rate of 9%. Based on total return, which stock should the investor choose, assuming equal risk?

Stock A Total Return = 6% (dividend yield) + 0% (capital gain) = 6%.

Stock B Total Return = 9% (capital gain).

Conclusion: The investor should choose Stock B due to its higher total return of 9%, assuming equal risk.

•A company currently pays an annual dividend of $4 per share, growing at a rate of 10% annually for the next three years, after which it will grow at a perpetual rate of 4%. The required return is 9%. Calculate the stock price today using a two-stage Dividend-Discount Model.

Dividend for the next three years:

D1 = $4 × (1 + 0.10) = $4.40

D2 = $4.40 × (1 + 0.10) = $4.84

D3 = $4.84 × (1 + 0.10) = $5.32

Terminal Value (P3): P3 = $5.32 × (1 + 0.04) / (0.09 – 0.04) = $110.74

Stock Price:

[latex]

P0 = $4.40 / (1 + 0.09) + $4.84 / (1 + 0.09)^2 + ($5.32 + $110.74) / (1 + 0.09)^3

[/latex]

P0 = $4.04 + $4.07 + $90.81 = $98.92

Conclusion: The stock is valued at $98.92 today.

Interactive Challenge

•You are evaluating two companies:

• • Company X pays a current dividend of $2.50 per share and is expected to grow dividends at 5% annually. The required rate of return is 8%.
  • Company Y does not pay dividends but plans to repurchase $1 million in shares next year. Its total payout is expected to grow at 6%, and it has 500,000 shares outstanding. The required return is 10%.

Tasks:

Calculate the price of Company X’s stock using the Dividend-Discount Model.

P0 = $2.50 × (1 + 0.05) / (0.08 – 0.05) = $2.625 / 0.03 = $87.50.

Calculate the price of Company Y’s stock using the Total Payout Model.

P0 = ($1,000,000 / (0.10 – 0.06)) / 500,000 = $1,000,000 / 0.04 = $25,000,000 / 500,000 = $50.

Which stock is a better investment based on the valuation?

Company X is priced at $87.50, and Company Y is priced at $50. The better choice depends on additional factors such as risk tolerance and growth potential.