HFT 4464

1. HFT 4464 Chapter 7 Common Stock

2. Chapter 7 Introduction • This chapter introduces common stocks including unique features that differentiate common stock from other securities and basic common stock valuation models.

3. Organization of Chapter 7 • Common stock as a residual ownership claim on a corporation • The difficulty in estimating the value of common stock relative to bonds and preferred stock. • Common stock features • Basic common stock valuation • Relationship between investor required rate of return, earnings and dividend growth, and common stock value

4. Common Stock as Residual Ownership • Common stock is quite different than bonds and preferred stock: • Return is dependent upon success of firm • Provides a residual claim on firm’s assets • Ownership rights to cash flows remaining after all other claims are paid • Not a contractual obligation and no stated maturity

5. Difficulty of Estimating Common Stock Value • The value of a security is the sum of the present values of its future expected cash flows. Common stock is difficult to value because future cash flows are uncertain. • Future common stock dividends are difficult to forecast accurately. • The future common stock selling price is difficult to forecast.

6. Common Stock Features • The defining features of common stock include: • A residual claim on assets and cash flow • Variable return • Voting rights • No set maturity

7. Common Stock Features • A corporation’s board of directors controls the firm. • Members are elected by stockholders. • Has the power to hire, fire, and set compensation for corporate executives • Determines corporate policy and strategy • Makes major corporate decisions

8. Common Stock Financing—Pros and Cons • Pros • It has lower risk than debt or preferred stock financing due to the lack of a fixed dividend. • Fewer restrictions than debt financing; a debt contract generally includes many restrictions on future corporate actions. • Expansion of a firm’s equity generally increases a firm’s debt capacity.

9. Common Stock Financing—Pros and Cons • Cons • The costs of issuing common stock are generally much higher than the costs of issuing debt and preferred stock. • Common stock is a riskier investment than bonds or preferred stock. Investors require a higher rate of return which translates into a higher cost of raising funds with common stock.

10. Valuing Common Stock • The value of common stock is the sum of the present values of its future expected cash flows. We will cover 4 basic models for valuing common stock: • General valuation model • Zero-growth model • Constant-growth model • Multiple growth rates ending in constant growth model

11. Valuing Common Stock • First we will introduce the concept of growth of a company’s earnings. • Earnings belong to the common stockholders: • They are paid back to the stockholders as dividends or • Invested back into the company and called additions to retained earnings.

12. Valuing Common Stock • When earnings are retained and invested into profitable projects, the company’s earnings grow. The pace of growth depends upon: • The amount of earnings retained • The returns earned on the projects

13. Valuing Common Stock • A firm’s earnings growth rate can be computed as follows: • Growth = retention ratio x ROE • Growth = earnings growth rate • Retention ratio = 1 – dividend payout ratio • ROE = Return on Stockholders Equity

14. Valuing Common Stock • For example, what is a firm’s earnings growth rate if it pays 40% of earnings as dividends and earns a 20% return on stockholders equity? • Growth = retention ratio x ROE • Growth = (1 – 40%) x 20% = 60% x 20% = 12%

15. General Dividend Valuation Model • The value of common stock is the PV of the expected dividends to be received plus the PV of the expected price the stock is sold for in the future: • For simplicity we will assume a firm pays out dividends just once a year.

16. General Dividend Valuation Model • Suppose an investor expects a common stock’s dividends to be $1.00, $1.05, and $1.10 at the end of each of the next 3 years and expects to sell the stock for $15 in 3 years. If the investor requires a 15% rate of return, what is the stock’s value today?

17. General Dividend Valuation Model • Or: Use the PVLS tables on p. 93 3 years @ 15% ($1.00 x .8696) +($1.05 x .7561) + ($1.10 x .6575) + ($15.00 x .6575) = $.8696 + .7939 + .7232 + 9.863 = $12.25

18. Zero-Growth Dividend Valuation Model • If a company’s dividends are not growing, but the company is paying out a constant dividend every year, this is similar to investing in preferred stock. The value of the common stock would be the PV of a perpetuity.

19. Zero-Growth Dividend Valuation Model • Suppose a company expects earnings of $5 per share and because they do not expect to grow, all earnings are paid out as dividends. Thus all future dividends are expected to be $5.00 per share. If investors require a 10% rate of return, the stock’s value today is:

20. Zero-Growth Dividend Valuation Model • Treating zero-growth common stock as a perpetuity seems to imply an investor will hold the stock forever! What if the investor just plans to hold the stock for 2 years and then sell it? • What would the stock’s selling price be in 2 years?

21. Zero-Growth Dividend Valuation Model • This investor expects to receive a $5 dividend for each of 2 years and then sell the stock for $50 in 2 years. The value of the stock today is: • The investor’s holding period does not affect the stock’s value!

22. Constant-Growth Dividend Valuation Model • A company with a constant dividend payout ratio and constant return on equity will have a constant growth rate. • For example, what is the growth rate for a company earning 12% on equity and a 40% dividend payout ratio? • Growth = (1 – 40%) x 12% = 60% x 12% = 7.2%

23. Constant-Growth Dividend Valuation Model • If we expect this company to have earnings of $5 per share in the coming year and the 7.2% growth rate is constant, we can compute the common stock value to an investor requiring a 10% return with the following constant growth model:

24. Constant-Growth Dividend Valuation Model • The company’s dividend in the coming year must be $2.00 per share: • d1 = $5.00 x 40% = $2.00 • And thus the value of the stock is:

25. Constant-Growth Dividend Valuation Model • Why is the value in this example higher than for the zero-growth example? Both examples assume earnings of $5 per share and a 10% rate of return. • The 7.2% growth rate makes the stock in the constant-growth example worth more!

26. Constant-Growth Dividend Valuation Model • Notice in the constant-growth example we made no assumptions about the investor’s holding period. • As we illustrated in the zero-growth valuation model, how long the investor plans to hold the stock should not affect the stock’s value today!

27. Constant-Growth Dividend Valuation Model • The constant-growth model provides good estimates of common stock value when a company’s future growth is expected to be stable. • The constant-growth model provides less accurate estimates when growth is difficult to estimate or large systematic differences year to year are expected in growth.

28. Valuing Stock with Multiple Growth Rates • Now we will consider how to estimate the value of common stock when several different growth rates are expected and the growth rates can be forecast with some degree of accuracy. • What if a company expects to pay a $2.15 dividend in a year and expects growth of 15% through the end of year 2? After year 2 growth is expected to decrease to 7.2% and stabilize at 7.2%.

29. Valuing Stock with Multiple Growth Rates • We can picture the growth rates and cash flows as follows: • 0 g = 15% 1 g = 15% 2 g = 7.2% |________|________|________________________ – $2.15 $2.47 • What is the value of this stock to an investor requiring a 10% rate of return?

30. Valuing Stock with Multiple Growth Rates • Remember, an investor’s holding period does not affect the value of common stock value. • Thus, in our example, we can use any holding period and it should not change the value of the stock! • To make the computation as easy as possible we will assume a 2-year holding period. The investor expects to receive 2 dividends (d1 and d2) and the selling price of the common stock in 2 years (P2).

31. Valuing Stock with Multiple Growth Rates • If we can estimate the common stock selling price in 2 years, then we can use the general dividend valuation model to compute the stock value as follows:

32. Valuing Stock with Multiple Growth Rates • Notice the growth rate in this example is constant at 7.2% annually after 2 years. This allows us to adapt the constant-growth model to estimate the price in 2 years. • The original constant-growth model is:

33. Valuing Stock with Multiple Growth Rates • The constant-growth model can be viewed more generally as: • Adapting this to our example, we can estimate the stock’s price at the end of 2 years:

34. Valuing Stock with Multiple Growth Rates • Estimate d3 by growing d2 at the 7.2% growth rate. • d3 = $2.47 x (1 + 7.2%) = $2.65 • Use this along with the 7.2% growth rate after year 2 to estimate the price in 2 years:

35. Valuing Stock with Multiple Growth Rates • Now use the selling price in year 2 ($94.64) along with the expected dividends in the first 2 years ($2.15 and $2.47) to estimate the value of the stock today:

36. Valuing Stock with Multiple Growth Rates • Holding Period Assumption • We assumed a 2-year holding period in our computations. Assuming any other holding period would not have changed the answer. It would just change the computations and made the estimation of the stock’s value an even more difficult process!

37. Valuing Stock with Multiple Growth Rates • Simplest Computation and Holding Period • When a stock is expected to have multiple growth rates, the easiest computation of the stock’s value is obtained by assuming a holding period exactly long enough to reach the point at which the growth rate becomes constant.

38. Value, Rate of Return, and Growth • What happens to a common stock’s value if the investor’s required rate of return increases but the future expected cash flows remain constant? • With the same expected future cash flows, the only way an investor can receive a higher rate of return is to pay less for the stock! Thus, higher rates of return cause stock values to decline!

39. Value, Rate of Return, and Growth • Let’s use the constant-growth example to illustrate this inverse relation between rates of return and common stock value. Previously we assumed a $2 dividend in 1 year, a 7.2% growth rate, and a 10% rate of return, and obtained a value of $71.43 as follows:

40. Value, Rate of Return, and Growth • What if the general level of interest rates rises and as a result investors now require a 12% return on this common stock? • The stock value declines to $41.67. This same relationship would hold for any of the common stock valuation models we have presented in this chapter.

41. Value, Rate of Return, and Growth • What happens to a common stock’s value if the earnings and dividends growth rate increases but the rate of return remains the same? • With a higher growth rate dividends are now expected to be greater. Of course with the same rate of return, the value of the common stock will increase to investors!

42. Value, Rate of Return, and Growth • Let’s use the constant-growth example to illustrate this direct relation between dividends and earnings growth and common stock value. Using the same beginning assumptions as before:

43. Value, Rate of Return, and Growth • What if the earnings and dividends growth rate rises from 7.2% to 8.0% and, as a result, future dividends are expected to be higher than before? • The stock value increases to $100.00. This same relationship would hold for any of the common stock valuation models we have presented in this chapter.

44. Summary of Chapter 7 Topics • Common stock as a residual ownership claim • Features of common stock • Pros and cons of common stock financing

45. Summary of Chapter 7 Topics • Valuing common stock — 4 models introduced: • General valuation model • Zero-growth model • Constant-growth model • Multiple growth rates ending in constant growth model • Relationship between common stock value, rates of return, and earnings and dividend growth rates

46. Homework • Problems: • See website