Preferred products has issued preferred stock with an

DDM
Discount Dividend Model.
Q1. Gentleman Gym just paid its annual dividend of $3 per share, and it is widely expected that the dividend will increase by 5% per year indefinitely.
a. What price should the stock sell at if the discount rate is 15%?
Current Price $31.50 =3*(1+5%)/(15%-5%)
b. What price should the stock sell at if the discount rate is 12%.
Current Price $45.00 =3*(1+5%)/(12%-5%)
Q2. Arts and Crafts, Inc., will pay a dividend of $5 per share in 1 year. It sells at $50 a share, and firms in the same industry provide an expected rate of return of 14%. What must be the expected growth rate of the company’s dividends?
Expected growth rate 4.00% =14%-5/50
Yields
Yields. Income Gain and Capital Gain in DDM Model
Horse and Buggy Inc. is in a declining industry. Sales, earnings, and dividends will be all shrinking at a rate of 10% per year with the following financial data.
Input data.
Annual growth rate -10.00%
Required return 15%
DIV1 $3
a. what is the value of a share today?
Value of a share $12.00 =3/(15%+10%)
b. What price do you forecast for the stock next year?
Stock price 10.800 =3*(1-10%)/(15%+10%)
c. What rate of return should you expect if you buy the stock today and sell it in one year?
Expected rate of return 15.00% =15%
c-1. What is the income gain and the capital gain if you buy the stock today and sell it in one year?
Income gain (Dividend Yield) 25.00% =3/12
Capital gain (Investment Yield, g) -10.00% =-10%
Growth
Growth
Here are the forcasted data on two stocks of the year 1, both of which have discount rates of 15%:
a. What are the dividend payout ratios for each firm?
b. What are the expected dividend growth rates for each firm?
c. What is the proper stock price for each firm?
Stock A Stock B
Discount rate 15% 15%
Return on equity at year 1 15% 10%
Earnings per share at year 1 $2.00 $1.50
Dividends per share at year 1 $1.00 $1.00
a. Dividend payout ratio 50.00% 66.67% =1/1.5
b. Expected dividend growth 7.50% 3.33% =10%*(1-66.67%)
c. Stock price today $13.33 $8.57 = 1/(15%-3.33%)
PS valuation
Preferred Stock Valuation.
Preferred Products has issued preferred stock with an annual dividend of $8 that will be paid in perpetuity.
Input variables:
Annual dividend $8.00
Discount rate 12.00%
a. If the discount rate is 12%, at what price should the preferred sell?
Price0 $66.67 =8/12%
b. At what price should the stock sell 1 year from now?
Price1 $66.67 =8/12%
c. What is the dividend yield, the capital gains yield, and the expected rate of return of the stock?
Dividend yield 12% =8/66.67
Capital gains yield 0% =(66.67-66.67)/66.67
Rate of return 12% =12% - 0%
PE ratio
Price Earning (P/E) Ratio
Favorita Candy’s stock is expected to earn $2.40 per share this year. Its P/E ratio is 18. What is the stock price?
Data.
EPS $2.40 =2.4
P/E Ratio 18 =18
Price $43.20 =C5*C6
Growth & Multiples
Return on Equity & P/E, P/B ratio
Start-Up Industries is a new firm that has raised $200 million by selling shares of stock. Management plans to earn a 24% rate of return on equity, which is more than the 15% rate of return available on comparable-risk investments. 40% of all earnings will be reinvested in the firm.
a. when ROE 24% b. when ROE 12%
Book value ($, million) 200 =200 Book value ($, million) 200 =200
Return on equity (%) 24% =24% Return on equity (%) 12% =12%
Earnings ($, million) 48 =200*24% Earnings ($, million) 24 =200*12%
Plowback(Retention) ratio (%) 40% =40% Plowback(Retention) ratio (%) 40% =40%
Dividends ($, million) 29 =48*(1-40%) Dividends ($, million) 14 =24*(1-40%)
g (%) 10% =24%*40% g (%) 5% =12%*40%
Discount rate (%) 15% =15% Discount rate (%) 15% =15%
Market value ($, million) 533 =C10/(C12-C11) Market value ($, million) 141 =F10/(F12-F11)
P/E ratio 11.11 =C13/C8 P/E ratio 5.88 =F13/F8
P/B ratio 2.67 =C13/C6 P/B ratio 0.71 =F13/F6
Permanent value
Stock Price with Permanent Value
Q. Tattletale News Corp. has been growing at a rate of 20% per year, and you expect this growth rate in earnings and
dividends to continue for another 3 years. If the last dividend paid was $2, the discount rate is 15% and
the steady growth rate after 3 years is 4%, what should the stock price be today?
Data.
Growth rate for Years 1-3 20%
Last dividend paid $2
Discount rate 15%
Growth rate after 3 years 4%
Stock price PV0 DIV1 DIV2 DIV3
28.02 2.40 2.88 3.46 =D15*(1+C9)
28.02 =C10*(1+C9) =C15*(1+C9) 32.67 PV3
Short-cut of PV0 =(E15*(1+C12))/(C11-C12)
=C15/(1+C11)^1+D15/(1+C11)^2+(E15+E16)/(1+C11)^3 =D15*(1+C9)
=NPV(C11,C15,D15,E15+E16)
Holding Return
Expected Holding Period Rate of Return
Better Mousetraps has come out with an improved product, and the world is beating a path to its door. As a result, the firm projects growth of 20% per year for 4 years. By then, other firms will have copycat technology, competition will drive down profit margins, and the sustainable growth rate will fall to 5%. The most recent annual dividend was DIV0 = $1 per share.
Input variables:
Initial growth rate 20%
Initial growth rate years 4
Sustainable growth rate 5%
DIV0 $1.00
Discount Rate 10%
a. What are the expected values of DIV1, DIV2, DIV3, and DIV4?
DIV1 $1.2000 =C9*(1+C6)
DIV2 $1.4400 =C13*(1+$C$6)
DIV3 $1.7280 =C14*(1+$C$6)
DIV4 $2.0736 =C15*(1+$C$6)
b. If the discount rate is 10%, what is the expected stock price 4 years from now?
Stock Price in 4 yrs (HV4) $43.5456 =C16*(1+C8)/(C10-C8)
c. What is the stock price today?
Stock price today $34.738 =NPV(C10,C13,C14,C15,C16+C19)
d. Find the dividend yield, DIV1 / P0.
Dividend yield year 1 3.45% =1.2/C22
e. What will next year's stock price, P1, be?
Expected Stock price at year 1 $37.012 =NPV(C10,C14,C15,C16+C19)
f. What is the expected rate of return to an investor who buys the stock now and sells it in 1 year?
Expected Return at year 1 10.00% =(37.012-34.738+1.2)/34.738
PVGO
Present Value of Growth Opportunities (PVGO)
Web Cites Research projects a rate of return of 20% on new projects. Management plans to pay back 70% of all earnings into the firm. Earnings this year will be $3 per share, and investors expect a 12% rate of return on stocks facing the same risks as Web Cites.
Input variables:
Return on Equity 20%
Payback ratio 70%
Earnings per share $3
Required return 12%
a. What is the sustainable growth rate?
Sustainable growth rate 6.00% =C6*(1-C7)
b. What is the stock price?
Stock price $35.00 =3*70%/(12%-6%)
c. What is the P/E ratio?
P/E ratio 11.67 =C15/C8
d. What would the price and P/E ratio be if the firm paid out all earnings as dividends?
Stock price $25.00 =C8/C9
P/E ratio 8.33 =C21/C8
e. What is the present value of growth opportunities (PVGO)?
PVGO $10.00 =C15-C21