Cashman Investments
Exam I In-Class Problems
1.
The margin requirement on a stock purchase is 15%. You fully use the margin allowed to
purchase 250 shares of MSFT at $22. If the price rises to $25, what is your percentage
gain or loss? The interest rate on your loan is 10%.
2.
Pagemaster Enterprises just paid a dividend of $4.50 per share (they pay dividends
annually). If Pagemaster’s reinvests 65% of its earnings at 20%, what is the price of a
share of Pagemaster? The market capitalization rate is 9%.
3.
Company Y plows back 20% of earnings at 15%. Its last dividend was $3. If the current
stock price is $50, what is the market capitalization rate?
4.
The Felix Corp. just paid a dividend of $0.50, which is expected to grow at 25% for the
next 3 years. Following this tremendous growth rate the company expects to grow at 15%
for the next 4 years. Then settle into a more conservative 5% grow rate in perpetuity. The
required rate of return is 10%. What is should the stock price be?
5.
You invested $150 dollars 5 years ago, and earned a rate of 12% on your investment. If inflation
was 2%, what was your real return?
6.
There are three possible states of the economy (Boom, Normal, and Recession)
Return: Boom=30%, Normal=12%, Recession= -9%
Probability: Boom=30%, Normal=50%, Recession= 20%
What is the Expected Return, Variance and Standard Deviation of the fund
7.
What is the Arithmetic and Geometric average of the historical data? What is the variance? Using
Blume’s Equation what is the expected yearly return over the next two years?
1995
12%
8.
1996
17%
1997
-9%
1998
3%
1999
-5%
2000
7%
Which of the following investments has performed “better”? The risk free rate is 4%.
Investment
Realized Risk
Premium
15%
20%
45%
A
B
C
Standard Deviation
0.09
0.14
0.35
Given Problems

What return do you require if you buy a stock for $25, which just paid its annual dividend of
$1.65. The company is expected to grow by 8% per year. What is the discount rate?
Div1 = 1.65 * (1.08) = 1.782
P0 = Div1/(r – g)
25 = 1.782 / (r – 0.08)
25 * (r – 0.08) = 1.782
r – 0.08 = 1.782 / 25 = 0.07128
r = 0.07128 + 0.08 = 0.15128 = 15.13%


Weisbro and Sons common stock sells for $21 a share and pays an annual dividend that
increases by 5% annually. The market rate of return on this stock is 9%. What is the amount
of the last dividend paid by Weisbro and Sons?
21= Div / (.09-.05)
Div = 21 * (.04) = 0.84
However this is the next dividend not the last one
Div1 = Div0 * (1 + g)
0.84 = Div0 * (1.05)
Div0 = 0.84 / 1.05 = 0.80
Can’t Hold Me Back, Inc. is preparing to pay its first dividends. It is going to pay $1.00,
$2.50, and $5.00 a share over the next three years, respectively. After that, the company has
stated that the annual dividend will be $1.25 per share indefinitely. What is this stock worth
to you per share if you demand a 7% rate of return?
First, we can get the value of the stock, when it is
acting like a perpetuity (year 4 and beyond)
1.25 / .07 = 17.86 @ year 3
Then discount back the four cash flows
1 / 1.07 + 2.50 / 1.07^2 + 5 / 1.07^3 + 17.86 / 1.07^3
21.78

Now or Later, Inc. recently paid $1.10 as an annual dividend. Future dividends are projected
at $1.14, $1.18, $1.22, and $1.25 over the next four years, respectively. After that, the
dividend is expected to increase by 2% annually. What is one share of this stock worth to you
if you require an 8% rate of return on similar investments?
First, we can get the value of the stock, when it is
acting like a perpetuity (year 5 and beyond)
(1.25*1.02) / (.08-.02) = 21.25 @ year 4
Then discount back the 5 cash flows
1.14 / 1.08 + 1.18 / 1.08^2 + 1.22 / 1.08^3 + 1.25 / 1.08^4 + 21.25 / 1.08^4
19.57

Mother and Daughter Enterprises is a relatively new firm that appears to be on the road to
great success. The company paid its first annual dividend yesterday in the amount of $.28 a
share. The company plans to double each annual dividend payment for the next three years.
After that time, it is planning on paying a constant $1.50 per share indefinitely. What is one
share of this stock worth today if the market rate of return on similar securities is 11.5%?
Part 1 is the Growing Annuity
(A) PV0 = 0.56/(0.115-1) * {1-(2/1.115)3} = 3.02
Part 2 is the Growing Perpetuity
1.5 / .115 = 13.04 @ year 3
(B) PV0 = 13.04/(1.1153) = 9.41
The price of the stock today is 12.43

Doctors-On-Call, a newly formed medical group, just paid a dividend of $.50. The
company’s dividend is expected to grow at a 20% rate for the next 5 years and at a 3% rate
thereafter. What is the value of the stock if the appropriate discount rate is 12%?
Part 1 is the Growing Annuity
PV0 = (0.5*1.2)/(0.12-0. 2) * {1-(1.2/1.12)5} = 3.089547
Part 2 is the Growing Perpetuity
Div6 = 0.5 * 1.25 * 1.03 = 1.281485
PV5 = 1.28/(0.12-0.03) = 14.23872
Part 3 Bring it back to time 0
PV0 = 14.24/(1.125) = 8.08
Part 4 Add them together
PV = 3.09 + 8.08 = 11.17

A stock had returns of 10%, -2%, 4% over the past three years. What is the expected return, the
variance, and the standard deviation of this stock over the past three years?
E(r) = (1/3)*0.10 + (1/3)*-0.02 + (1/3)*0.04 = 0.04
Var = 1/(3-1)*{(0.1-0.04)2 + (-0.02-0.04)2 + (0.04-0.04)2} = 0.0036
Std Dev = 0.06