Seminar Exercises – Session 5
Session 5: Valuing the Firm
Read: Chapter 9: Valuing Stocks
1. Consider the following three stocks:
a. Stock A is expected to provide a dividend of $10 a share forever. 10/r
b. Stock B is expected to pay a dividend of $5 at the end of first year. Thereafter, dividend
growth is expected to be 4 percent a year forever.5/(r-g)
c. Stock C is expected to pay a dividend of $5 at the end of first year. Thereafter, dividend
growth is expected to be 20 percent a year for 5 years and zero thereafter. After year 5
5.12^5/r; prima 1/(1+r)^6x(5.12^5)/r
If the market capitalization rate (in pratica è il tasso di sconto che uso) for each stock is 10
percent, which stock is the most valuable? What if the capitalization rate is 7 percent?
2. Crecimiento s.a. currently plows back (retain rate) 30 percent (so they distribute 70%) of its
earnings and earns a return of 25 percent on this investment. The dividend yield on the
stock is 5 percent. Assume price=100 an dividend 5
a. Assuming that Crecimiento can continue to plow back this proportion of earnings and
earn a return of 25 percent on the investment, how rapidly will earnings and dividends
grow? G=ROExplowback ; g=0,25x0,3 =75% It is growth rate both for dividends, and
EPS end Price What is the expected return on Crecimiento stock?r=DIV1/P0 +g =
dividend yeld + g and g=(P1-P0)/P0
b. Suppose that management suddenly announces that future investment opportunities
have dried up. Now Crecimiento intends to pay out all its earnings. How will the stock
price change? Paga perchè il tasso di sconto è > del ritorno sugli investimenti.
P0=EPS/r (Non ho più la parte di crescita legata agli investimenti). EPS/P0=rx(1-
PVGO/r) Prima dell’annuncio il 42% del prezzo dell’azione era dovuto alle opportunità di
crescita. Ora che questa nn c’è più il prezzo va giù del 42%
c. Suppose that management simply announces that the expected return on new
investment will in the future be the same as the cost of capital. Now what is
Crecimiento’s stock price? The same of before
3. Year
1 2 3 4
Book equity 10.00 12 14,4
Earnings per share, EPS 2,5 3
Return on equity, ROE .25 .25 .16 .16
Payout ratio .20 .20 .50 .50
Dividends per share 0,5 0,6 1,15 1,24
Growth rate of dividends -
a. Complete the table above. EPS=ROExBOOK Equity (EPS/BookEquity=ROE). First
year they distribute 0,5 and retain 2, which increments the book equity next year.
After, assuming ROE and payout ratio constant thereafter, b=0,5 and ROE=0,16 and
g=bxROE=0,08
b. Assume that the opportunity cost of capital is 12%. Calculate the value of the
company’s stock. = 0,5/1,12 + 0,6/1,12^2 poi alla terza e poi perpetuity 23,81
c. What part of that value reflects the discounted value of P3, the price forecasted for year
3? Just the perpetuity part of point 2
d. What part of P3 reflects the present value of growth opportunities (PVGO) after year
3?PVGO=10,25
