Name:........................................................................
ECO 4368— Fall 2014
Midterm 2
There are 3 problems and 6 short answer questions.
TOTAL POINTS: 100
Question 1 (20 points): A company with a stock price P0 = $103 had
a constant dividend growth rate last estimated to be g = 3%. Suppose now
that the market updates its beliefs on the constant dividend growth rate, and
it is now estimated to be g new = 6%. After this new estimate, the stock price
went down to P0new = $132:5. The required rate of return on the market
portfolio is rm = 6% and the risk-free rate is 2% and did not change: The
company’s beta also remained the same.
a) (10 points) What is the last dividend D0 of the company?
Answer: Since rm ; rRF and
s
did not change; we have
rsbef ore
D0 (1 + g)
+g
P0
D0 (1 + 0:03)
+ 0:03
103
(0:10)D0 + 0:03
(0:002)D0
D0
= rsaf ter
D0 (1 + g new )
=
P0new
D0 (1 + 0:06)
=
+ 0:06
132:5
= (0:008)D0 + 0:06
= 0:03
0:03
=
= 15
(0:002)
1
b) (10 points) What is the beta of the company?
D0 (1 + 0:03)
+ 0:03
103
15(1 + 0:03)
=
+ 0:03 = 18%
103
rsbef ore =
rsbef ore
Hence we have
rsbef ore = 18% = rRF + s (rM
18% = 2% + s (6% 2%)
s = 4
2
rRF )
Question 2 (25 points): A company paid a recent dividend of $1 per
share. (D0 = $1) and it had an expected constant dividend growth rate
of g = 5% before a reevaluation of company’s dividend policy. Before this
reevaluation, company’s stock price was P0 = $35.
After the revaluation, the stock price increased to P0new = $25 due to a
change in its g. The beta of the company stock remained the same after
reevaluation. The return on the market is rM = 11% and the risk-free rate
is rRF = 6%:
a) (15 points) What is the new estimated gnew that caused the
price DECREASE?
Answer: Since rm ; rRF and
s
rsbef ore
D0 (1 + g)
+g
P0
1(1 + 0:05)
+ 0:05
35
0:08
0:04
g new
did not change; we have
= rsaf ter
D0 (1 + g new )
=
+ g new
new
P0
1(1 + g new )
=
+ g new
25
= 0:04(1 + g new ) + g new
= 1:04g new
= 3:84%
3
b) (10 points) What is the beta of the company?
Answer: We have
1(1 + 0:05)
+ 0:05 = 8%
35
8% = 6% + s (11% 6%)
2%
= 0:4
s =
5%
rsbef ore =
4
Question 3 (25 points): A company recently paid a dividend of D0 =
$3 per share. The company has a constant dividend growth rate of g = 5%
and a beta equal to 1:5. The required rate of return on the market is rM = 8%
and the risk-free rate is rRF = 2%.
a) (15 points) What should be the company’s stock price according to
the constant dividend growth rate model?
Answer: We have
D0 (1 + g)
rs g
= 2% + 1:5(8% 2%) = 11%
3(1 + 0:05)
=
= 52:5
0:11 0:05
P0 =
rs
P0
5
b) (10 points) The company is considering a change of policy which will
reduce its g to 3%. If market conditions remain unchanged, what new beta
will cause the stock price of the company to remain unchanged?
Answer: Let’s …rst …nd the required return on the stock when we have
g new = 3%
rsnew =
3(1 + 0:03)
+ 0:03 = 8:88%
52:5
Hence we can write
rsnew = rRF + new
s (rM
new
8:88% = 2% + s (8%
6:88%
new
= 1:14
=
s
6%
6
rRF )
2%)
Short Answer Questions (5 points each, 30 points total)
Explain what happens to the dividend return on a stock, if the stock’s
beta, the dividend growth rate g; risk free rate (rRF ) all remain the
same, but return on market portfolio (rM ) goes down.
Explain if the following statement is True or False: "Suppose, the company beta decreases, the risk free rate and return on market portfolio
remain the same. For the stock price to remain constant, the dividend
growth rate estimate g must go down".
7
Suppose the required return rM on the market portfolio and the risk
free rate (rRF ) both decrease, the dividend growth rate estimate g
increases, and company beta remains constant. Does this imply that
the dividend return on the stock must INCREASE?
Suppose the required return rM on the market portfolio, risk free rate
(rRF ) and the dividend growth rate estimate g remain the same, and
company beta decreases. Does this imply that the dividend return on
the stock must INCREASE?
8
If the market lowers its estimate of a company’s beta and also increases
its dividend growth estimate g, does this mean the stock price should
go up if everything else remains constant?
Explain if the following statement is true or false. "If the dividend
growth estimate g on a stock goes up and the risk free rate (rRF ) and
return on the market portfolio rM both go down, then the stock price
should increase unless beta of the stock goes up".
9
SOME FORMULAS:
CAPM Equation:
rs = rRF +
s (rM
rRF )
Constant Dividend Growth Stock Valuation
P0 =
D0 (1 + g)
D1
D1
or P0 =
) rs =
+g
rs g
rs g
P0
The required return on equity (stock) can be computed in two ways.
rs =
D1
+ g or rs = rRF +
P0
10
s (rM
rRF )