Practice Problems for Equity
valuation
A.IBX Stock Intrinsic-Value You
expect the price of IBX stock to
be INR 59.77 per share a year
from now.Its current market price
is INR 50, and you expect it to
pay a dividend 1 year from now
of INR 2.15 per share.
a.What is the stock's expected
dividend yield, rate of price
appreciation, and holding-period
return?
b.If the stock has a beta of 1.15,
the risk-free rate is 6% per year,
and the expected rate of return on
the market portfolio is 14% per
year, what is the required rate of
return on IBX stock?
c.What is the intrinsic value of
IBX stock, and how does it
compare to the current market
price?
a.Dividend yield = 2.15 /50 =
4.3%
Capital gains yield = (59.77 50) / 50 = 19.54%
Total return = 4.3% + 19.54% =
23.84% b.k = 6% + 1.15 (14% 6%) = 15.2% c.Po = (2.15 +
59.77) / 1.152 = INR 53.75,
which exceeds the market price.
This would indicate a
"buy"opportunity.
B.i) IBX's stock dividend at the
end of this year is expected to be
INR 2.15, and it is expected to
grow at 11.2% per year forever.If
the required rate of return on IBX
stock is 15.2% per year, what is
its intrinsic value?
ii) If IBX's current market price is
equal to this intrinsic value, what
is next year's expected price?
iii) If an investor were to buy
IBX stock now and sell it after
receiving the INR 2.15 dividend a
year from now, what is the
expected capital gain (i.e., price
appreciation) in percentage
terms? What is the dividend
yield, and what would be the
holding-period return?
i)D1 / (k - g) = INR 2.15 / (0.152
- 0.112) = INR 53.75
ii)P1 = Po (1 + g) = INR 53.75
(1.112) = INR 59.77
iii)The expected capital gain
equals INR 59.77 - INR 53.75 =
INR 6.02 for a percentage gain of
11.2%.The dividend yield is D1 /
Po = 2.15 / 53.75 = 4%, for a
holding-period return of 4% +
11.2% = 15.2%. C.ABC stock
has an expected ROE of 12% per
year, expected earnings per share
of INR 2.00, and expected
dividends of INR 1.50 per
share.Its market capitalization
rate is 10% per year.
a)What is its expected growth
rate, its price, and its P/E ratio?
b)If the plowback rate were 0.4,
what would be the expected
dividend per share, the growth
rate, price, and the P/E ratio?
a)ROE = 12%; b = INR 50 / INR
2.00 = 25 g = ROE x B = 12% x
0.25 = 3% Po = D1 / (k - g) =
INR 1.50 / (0.10 - 0.03) = INR
21.44
Po / E1 = INR 21.44 / INR 2.00 =
10.71 b)If b = 0.4, then 0.4 x INR
2.00 = INR 80.00 would be
reinvested and the remainder of
earnings, or INR 1.20, would be
paid as dividends. g = 12% x 0.4
= 4.8%
Po = D1 / (k - g) = INR 1.20 /
(0.10 - 0.048) = INR 23.08 Po /
E1 = INR 23.08 / INR 2.00 =
11.54 D.
2.Suppose that the risk premium
of the market portfolio is
estimated at 10% with a standard
deviation of 28%.What is the risk
premium on a portfolio invested
25% in Infosys and 75% in HUL,
if they have betas of 1.45 and
0.74 respectively? For these
investment proportions, Winfosys
and Whul, the portfolio beta is:
Beta(p) = [Winfosys x Beta
(Infosys)] + [Whul x Beta
(HUL)] = (0.25 x 1.45) + (0.75 x
0.74) = 0.9175 3.Stock XYZ has
an expected return of 12% and
risk of B = 1.Stock ABC has
expected return of 13% and B =
1.5.The market's expected return
is 11%, and Rf = 5%.
a.According to the CAPM, which
stock is a better buy? b.What is
the alpha if each stock?Plot the
SML and each stock's risk-return
point on one graph.Show the
alphas graphically. The alpha of a
stock is its expected return in
excess of that required by the
CAPM: Alpha (XYZ) = 12 - [5 +
1.0 (11 - 5)] = 1% Alpha (ABC)
= 13 - [5 + 1.5 (11 - 5)] = - 1%
1. Bobby read an analyst’s recommendation that WM shares are at least 30% undervalued based
on current market price. Which of these is the least valid reason that Bobby is unconvinced and
chooses not to buy WM shares?
a)
b)
Bobby feels that the assumptions used by the analyst are inaccurate.
Bobby feels that the difference between the intrinsic value of the stock and the market price
will eventually narrow
c) Bobby feels that insider trading is the reason why the stock price is currently so low
If the difference between the intrinsic value of the stock and the market price will eventually narrow,
Bobby will stand to profit if he buys the stock now when it is undervalued.
If the stock price is low due to insider trading, it means that the insiders know that there is something
wrong, and that the intrinsic value of the stock is actually lower.
2. Arrange chronologically the sequence of events for a typical dividend payout. (Drag and drop)
a)
b)
c)
d)
Declaration Date
Holder-of-Record Date
Payment Date
Ex-Dividend Date
Ans: a, d, b, c
3. Which of the following is equivalent to a company issuing a 10% stock dividend?
a) 1-for-10 stock split
b) 11-for-10 stock split
c) 10-for-1 stock split
A stock is currently priced at $25 and there are 3,000 outstanding shares. An analyst estimates that the
FCFE of the firm for the next 2 years will be $6,000 and $6,600 respectively. The analyst also expects the
share price to rise to $29 by the end of these 2 years.
4. Using the FCFE model with a required return of 8%, the intrinsic price of the stock today is
closest to:
a.
$26.76
b. $28.60
c. 32.74
Solution: FCFE per share for 1st year = 6000/3000 = $2
FCFE per share for 2nd year = 6600/3000 = $2.20
PV = PV(FCFE) + PV(terminal)
= 2/1.08 + 2.2/1.08^2 + 29/1.08^2
= $28.60
5. A preferred stock that is $100 par per share pays 7% dividend annually. The current market price
is $106.80.What is the intrinsic value of the preferred stock if the required return is 6.5%?
a)
$115.02
b.) $107.69
c) $106.80
Solution: Dividend per year = $100×0.07 = $7
PV(preferred) = Dividend / Required return = 7/0.065 = 107.69
6. A&C Corp is a tech company that is expected to experience a high growth of 14% for the next 2
years, slowing to a perpetual growth rate of 6% thereafter. The company just paid a dividend of
$3.
Using the Gordon Growth Model, estimate the intrinsic value of A&C’s shares in 2 years time.
Assume a required return of 11%.
a.
b.
c.
$82.68
$78
$67.10
Solution:
Dividend payout 2 years later = $3 x 1.14^2 = $3.90
Using GGM, PV2 = $3.90×1.06 / (0.11-0.06) = $82.68
7. A&C Corp is a tech company that is expected to experience a high growth of 14% for the next 2
years, slowing to a perpetual growth rate of 6% thereafter. The company just paid a dividend of
$3.
Using the terminal value of $82.68 at end of 2nd year (based on GGM), calculate the intrinsic
value of the A&C stock today. Required rate of return is 11%.
a.
b.
c.
$69.62
$73.35
$79.59
Solution:
D1 = $3×1.14 = $3.42
D2 = $3×1.14^2 = $3.90
PV = 3.42/1.11 + 3.9/1.11^2 + 82.68/1.11^2 = $73.35
8. A company had a net income of $1.5 million and the beginning owner’s equity on its books was
$12 million. The company paid $600,000 dividend to common stockholders and it does not have
any preference stockholders.
Calculate the sustainable growth rate of the company based on the information given.
a. 5%
b. 6.25%
c. 7.5%
Solution:
ROE = Net Income to common / Total Equity = $1.5M / $12M = 12.5%
Dividend payout ratio = Dividend paid / Net Income = 0.6/1.5 = 40%
g = ROE x (1-Div Payout Ratio) = 0.125 x (1-0.4) = 7.5%
9. Tangy Corp is a fast growing company and is expected to experience constant dividend growth
of 8%. The company is expected to pay a dividend of $4 next year, and the EPS is expected to be
$13 per share. Tangy’s shares currently trade at 12.4x P/E and have a required return of 11%.
Tangy’s shares are most likely _____________ based on its fundamentals.
a. Undervalued
b. Fairly valued
c. Overvalued
Justified P/E = (D1/E1) / (r-g) = (4/13) / (0.11-0.08) = 10.26x
Since market P/E (12.4x) > justified P/E (10.26x), shares are overvalued.
10. IMBD’s stock currently trades at $45 and there are 100,000 shares outstanding. Its current book
value of equity stands at $3 million. If the industry average P/B is 1.8x, determine the intrinsic
price of IMBD stock using the price multiples approach.
a.
$16.70
b. $45
c. $54
Solution:Intrinsic value of total equity = $3M x 1.8 = $5.4M
Intrinsic value per share = $5.4M/100000 = $54
11. IMBD’s EV/EBITDA stands at 9.8x, while the industry average EV/EBITDA is 14.2x. Rosa concludes
that IMBD’s common shares are undervalued solely based on the fact that IMBD’s EV/EBITDA is
lower than industry average. Which of the following statements is most accurate about Rosa’s
conclusion.
a.
A company's EV includes the value of its debt, preferred stock and common stock. Concluding
that the common stock is undervalued based on EV is not correct.
b. The ratios are too close for Rosa to make such a conclusion.
c. The enterprise value of a firm has nothing to do with its share price.
12. A company’s assets have recently been valued at $48 million by a professional valuator, and the
company’s debt are worth $13 million based on market value. The company does not have any
outstanding preferred shares, and has 400,000 outstanding common shares trading at $64.
Based on the asset-based valuation model, the company’s shares are most likely _________.
a. Undervalued
b. Fairly valued
c. Overvalued