1. Stock Valuation

2. What is Stock?
When a corporation wishes to raise money from public, it can issue shares in stock markets
A share of a stock represents a fraction of ownership in a business
Shareholders are owners of the firm that issues the stock
Bondholders are creditors of the firm that issues the bonds
Investors buy a share of stock in exchange for a share in the control of a corporation

3. Dividend
Dividend is a payment made by a corporation to its shareholders as a distribution of profits
Dividend is allocated as a fixed amount per share, so shareholders receiving dividends in proportion to their shares
Dividends are taxed at both corporate and individual shareholders level
A group of people start a business and they say let’s divide up the proceeds. This is very direct, isn’t it? If we are all working together, we divide up the proceeds. That means we are allocating shares. That is the basic idea of stock market.
Corporations that own stock in other corporations are permitted to exclude 70% of the dividend amounts they receive and are taxed only on the remaining 30%.

4. Zero Growth A stock that pays $0.50 as dividend per quarter
If investors require a return of 10% per year, how much would they like to pay to buy? 3 …
0.5 1 2
P=?

5. Zero Growth Investors require 10%/4 = 0.025 quarterly return
Stock price is the present value of all future dividends
𝑃= …
= =$20
Q: How can we estimate all future dividend payments?

6. Zero Growth
A stock pays dividend 𝐷 periodically and forever, so its price is
𝑷= 𝑫 𝒓
𝒓 is the periodical market rate of return

7. Zero Growth
Leslie's Unique Clothing Stores offers a common stock that pays an annual dividend of $2.70 a share. The company has promised to maintain a constant dividend. How much are you willing to pay for one share of this stock if you want to earn a 12.70% return on your equity investments?
2.70/0.127 = 21.26

8. Deferred Dividend with Zero Growth
Spiral Staircase is offering preferred stock which is commonly referred to as stock. This stock will pay an annual dividend of $10 a share starting 10 years from now. What is this stock worth to you today if you desire a 15% rate of return?
P9 = $10/0.15 = $66.67;
P0 = $66.67/1.159 = $18.95

9. Constant Growth
A stock has just paid dividend of $2. The dividend is expected to grow at a constant annual rate of 6%, how much is the dividend in year 1, 2, and 3?
Suppose you deposit $2 in a bank with annual interest rate of 6%, how much will you have in bank account in year 1, 2, and 3?
𝐷 1 =2×1.06=$2.12
𝐷 2 =2.12×1.06=2× =$2.2472
𝐷 3 =2.2472×1.06=2× =$2.3820

10. Constant Growth 𝐷 𝑡 = 𝐷 0 1+𝑔 𝑡
Dividend is expected to grow at a constant rate forever, 𝑔
𝐷 𝑡 = 𝐷 𝑔 𝑡
𝐷 0 = Dividend JUST PAID (time 0)
𝐷 𝑡 = Dividend paid at the end of period 𝑡

11. Constant Growth 𝑷 𝟎 = 𝑫 𝟏 𝒓−𝒈
Current price of stock with constant dividend growth at a rate 𝑔 is
𝑷 𝟎 = 𝑫 𝟏 𝒓−𝒈
𝐷 1 = Dividend in next period (time 1)
𝑃 0 = Current stock price (time 0)
𝑟= Market rate of return
Emphasis P0 meaning

12. TB Pirates, Inc.
Suppose TB Pirates, Inc. is expected to pay a $2 dividend in one year. If the dividend is expected to grow at 5% per year and the required return is 20%, what is the price?
𝐷 1 =$2.00, 𝑔=5%, 𝑟=20%
𝑃 0 = 𝐷 1 𝑟−𝑔 = 2 20%−5% =$𝟏𝟑.𝟑𝟑

13. Constant Growth 𝑷 𝟎 = 𝑫 𝟎 𝟏+𝒈 𝒓−𝒈
Current price of stock with constant dividend growth at a rate 𝑔 is
𝑷 𝟎 = 𝑫 𝟎 𝟏+𝒈 𝒓−𝒈
𝐷 0 = Dividend just paid (time 0)
𝑃 0 = Current stock price (time 0)
𝑟= Market rate of return
Emphasis P0 meaning

14. Big D, Inc.
Suppose Big D, Inc. just paid a dividend of $0.50. It is expected to increase its dividend by 2% per year. If the market requires a return of 15% on assets of this risk, how much should the stock be selling for?
𝐷 0 =$0.50, 𝑔 =2%, 𝑟=15%
𝑃 0 = 𝐷 0 1+𝑔 𝑟−𝑔 = 0.5×(1+2%) 15%−2% =$𝟑.𝟗𝟐

15. Problem 7-1 Stock Values
Anton, Inc., just paid a dividend of $3.30 per share on its stock. The dividends are expected to grow at a constant rate of 4.5% per year, indefinitely. Assume investors require a return of 10% on this stock. What is the current price?
P0 = D0 (1 + g) / (R – g) = $3.30 (1.0450) / (0.09 – ) = $76.63

16. Problem 7-4 Stock Values
Nofal Corporation will pay a $4.80 per share dividend next year. The company pledges to increase its dividend by 7.75% per year, indefinitely. If you require a return of 11% on your investment, how much will you pay for the company’s stock today?
P0 = D1 / (R – g) = $4.80 / (.11 – .0775) = $147.69

17. Gordon Growth Company
Gordon Growth Company is expected to pay a dividend of $4 next period and dividends are expected to grow at 6% per year. The required return is 16%.
What is the current price?
What is the price expected to be in year 4?

18. Gordon Growth Company (a) What is the current price?
𝐷 1 =$4.00, 𝑔=6%, 𝑟=16%
𝑃 0 = 𝐷 1 𝑟−𝑔 = 4 16%−6% =$40
(b) What is the price expected to be in year 4?
𝐷 5 = 𝐷 𝑔 4 =4× 1+6% 4 =$5.05
𝑃 4 = 𝐷 5 𝑟−𝑔 = $ %−6% =$50.50

19. Constant growth 𝑷 𝑻 = 𝑫 𝑻+𝟏 𝒓−𝒈
𝑇th period of stock with constant dividend growth at a rate 𝑔 is
𝑷 𝑻 = 𝑫 𝑻+𝟏 𝒓−𝒈
𝐷 𝑇+1 = Dividend in the 𝑇th period
𝑃 𝑇 = 𝑇th period price
𝑟= Market rate of return

20. Problem 7-1 Stock Values
Anton, Inc., just paid a dividend of $3.05 per share on its stock. The dividends are expected to grow at a constant rate of 5.5% per year, indefinitely. Assume investors require a return of 10% on this stock. What will the price be in five years and in fourteen years?
P5 = D0 (1 + g)6 / (R – g) = $3.05 (1.0550)6 / (0.10 – ) = $93.45 P14 = D0 (1 + g)15 / (R – g) = $3.05 (1.0550)15 / (0.10 – ) = $151.31

21. Problem 7-7 Stock Valuation
Bui Corp. pays a constant $14.40 dividend on its stock. The company will maintain this dividend for the next six years and will then cease paying dividends forever. If the required return on this stock is 12%, what is the current share price?
P0 = $14.40(PVIFA12%,6)
P0 = $59.20

22. Problem 7-10 Growth Rates
The stock price of Webber Co. is $ Investors require a return of 14% on similar stocks. If the company plans to pay a dividend of $3.65 next year, what growth rate is expected for the company’s stock price?
g = R – (D1 / P0) = .14 – ($3.65 / $54.00) = .0724

23. Problem 7-20 Finding the Dividend
Gontier Corporation stock currently sells for $64.83 per share. The market requires a return of 10% on the firm’s stock. If the company maintains a constant 4.75% growth rate in dividends, what was the most recent dividend per share paid on the stock?
P0 = D0 (1 + g) / (R – g)  
D0 = P0(R – g) / (1 + g) = $64.83(0.10 – ) / ( ) = $3.25

24. Nonconstant Growth
Dividend grows at “supernormal” rates over some finite length of time and eventually settles down at zero or constant growth rate
Two steps
Compute the price when dividend grows at zero or constant rate
Compute current price by discounting nonconstant dividends and the 1st step price back to now

25. Nonconstant Growth
Suppose a firm is expected to increase dividends by 20% in a year and by 15% in year two. After that dividends will increase at a rate of 5% per year indefinitely. If the dividend just paid was $1 and the required return is 20%, what is the price of the stock? 1 2 3
g = 20%
g = 15%
g = 5%
D D D3 …

26. Nonconstant Growth Find the 2nd year price 𝐷 1 =1× 1+0.2 =$1.20
𝐷 2 =1.20× =$1.38
𝐷 3 =1.38× =$1.449
𝑃 2 = 𝐷 3 𝑟−𝑔 = −0.05 =9.66 1 2 3
P D3
g = 5% …

27. Nonconstant Growth
1.0000
0.9583
6.7083
8.67 = P0
P2 = $9.66 1 2 3
R = 20%
Discount the 2nd year price, 1st and 2nd year dividends back to time 0
𝑃 0 = =$8.67

28. Problem 7-15 Nonconstant Growth
Metallica Bearings, Inc., is a young start-up company. No dividends will be paid on the stock over the next nine years, because the firm needs to plow back its earnings to fuel growth. The company will then pay a dividend of $13.25 per share 10 years from today and will increase the dividend by 5.00% per year thereafter. If the required return on this stock is 13.00%, what is the current share price?
P9 = D10 / (R – g) = $13.25 / (.1300 – .0500) P9 = $  
P0 = $ / = $55.13

29. Problem 7-18 Supernormal Growth
Yang Corp. is growing quickly. Dividends are expected to grow at a rate of 32% for the next three years, with the growth rate falling off to a constant 6.2% thereafter. The required return is 14% and the company just paid a $2.85 dividend. What are the dividends each year for the next four years? What is the share price in three years? What is the current share price?
3.76, 4.97, 6.55, 6.96
P3 = D3 (1 + g2) / (R – g2) = D0 (1 + g1)3 (1 + g2) / (R – g2) = $2.85(1.32)3(1.062) / (.14 – .062) = $89.25  
P0 = $2.85(1.32) / $2.85(1.32)2 / $2.85(1.32)3 / $89.25 / 1.143 = $71.79

30. Problem 7-19 Negative Growth
Antiques ‘R’ Us is a mature manufacturing firm. The company just paid a dividend of $11.10, but management expects to reduce the payout by 5% per year, indefinitely. If you require a return of 11% on this stock, what will you pay for a share today?
The constant growth model can be applied even if the dividends are declining by a constant percentage, just make sure to recognize the negative growth. So, the price of the stock today will be:
  P0 = D0 (1 + g) / (R – g) P0 = $11.10(1 – ) / [(.11 – (–.0500)] P0 = $65.91

31. If Stocks Don’t Pay Dividends…
If stocks don’t pay dividends or have erratic dividend growth rate, we can value them using the PE ratio
𝑷 𝑻 =𝑩𝒆𝒏𝒄𝒉𝒎𝒂𝒓𝒌 𝑷𝑬 𝒓𝒂𝒕𝒊𝒐×𝑬𝑷 𝑺 𝑻
Benchmark PE ratio
Similar companies
Industry average
Company’s historical values

32. Problem 7-13 PE Ratio
The Sleeping Flower Co. has earnings of $1.60 per share. If the benchmark PE for the company is 21, how much will you pay for the stock? If the benchmark PE for the company is 24, how much will you pay for the stock?
𝑃=21×$1.60=$33.60
𝑃=24×$1.60=$38.40
Mengying Wang – Introduction to Financial Management

33. Problem 7-26 PE Ratio
Sully Corp. currently has an EPS of $2.54, and the benchmark PE ratio for the company is 23. Earnings are expected to grow at 7% per year.
What is your estimate of the current stock price?
What is the target stock price in one year? 
Assuming that the company pays no dividends, what is the implied return on the company's stock over the next year?
P = Benchmark PE ratio × EPS = 23($2.54) = $ EPS1 = EPS0(1 + g) = $2.54( ) EPS1 = $2.72  
P1 = Benchmark PE ratio × EPS1 = 23($2.72) = $62.51
R = (P1 – P0) / P0 = ($62.51 – 58.42) / $58.42 = .07, or 7%
Assuming a stock pays no dividends and the PE ratio is constant, this will always be true when using price ratios to evaluate the price of a share of stock.
Mengying Wang – Introduction to Financial Management