1  Calculate returns
Your client is interested in buying a business. You help structure the transaction and draw up the appropriate dcouments. The client has been offered to ways to pay the $400,000 purchase price. One is for cash, which your client could finance by borrowing from the bank with a 9% loan payable over 10 years  annuial payments due on December 31 of each year. THe other is a strcutrued purchase as follows: $40,000.00/yr. for 10 years, payable by December 31 of each year, beginning next year plus each year accrued interest on the outstanding balance at an interest rate of 6%/year for the first five years, then 10% for years 6 through 10.
Which is the better deal for your client?
Assuming that past returns predict future returns,
what is the expected return for the following investments?

Investment
A 
Investment
B 
Market price (year
ago) 
$20,000 
$55,000 
Market price (present) 
21,000 
55,000 
Cash flow (current
year) 
1,500 
6,800 
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2  Required returns
You are considering buying a car for $8,500. You live
in the city and taking the bus costs you $1,700 in fares
and aggravation. You expect the car will cost about
$1,950 in annual maintenance and insurance costs. After
five years you expect to sell the car for $5,000. To
buy the car, you will dip into your savings account,
which earns 4.5% after taxes. You ask yourself whether
you should buy the car or keep on taking the bus.
 What are the cash flows and expected return applicable
to buying the car?
 Which is a better choice  buying the car (with
attendant costs and benefits) or keep on riding the
bus and investing the money?
 What if you plan to use money from your taxfree
municipal bond mutual fund, which has had steady aftertax
returns of 7.8%. How much should you spend on the
car given your alternative use of the purchase price?
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3  Return variation
You are considering three stock investments. You have
studied the stocks' historical returns over the last
five years.
Year 
Stock 1 
Stock 2 
Stock 3 
1996 
12% 
0% 
10% 
1997 
0% 
5% 
4% 
1998 
10% 
12% 
12% 
1999 
25% 
20% 
20% 
2000 
50% 
25% 
35% 
Assuming that historical returns are a measure of future
returns 
 Calculate the expected return, the standard deviation
(s) and coefficient of variation for each stock.
 Which stock has the highest expected return? the
highest risk?
 Which is the best combination of risk and return?
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4  Risk/return comparison
Portfolio A has an expected return of 8.4% and a standard
deviation of 12.1%. Portfolio B has an expected return
of 10.7% and a standard deviation of 15.8%. The risk
free rate of return is 5.1%.
 Assuming CAPM, what is the slope of the market line
if Portfolio A lies on the line? What about Portfolio
B?
 What do these slopes tell you? Which is the better
portfolio  that is, the better combination of risk
and return?
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5  Calculate beta
You want to calculate the betas for two companies.
You have the following return data:

Expected
return (%) 
Year 
Market 
Stock X 
Stock Y 
1991 
6 
11 
16 
1992 
2 
8 
11 
1993 
13 
4 
10 
1994 
4 
3 
3 
1995 
8 
0 
3 
1996 
16 
19 
30 
1997 
10 
14 
22 
1998 
15 
18 
29 
1999 
8 
12 
19 
2000 
13 
17 
26 
 How might you compute beta?
 Draw the characteristic line for each stock
and estimate slope.
 Use regression analysis to compute the line's
slope.
 Are the stocks riskier, less risky than the market?
 What is the beta of a portfolio containting
with equal amounts of Stock X and Stock Y? Is this
portfolio riskier than the market?
 You're not sure if the market will be up or down.
What will be the return on Stock X and Stock Y, assuming
either an up market next year with returns of +20.0%
or a down market with returns of 6.0%?
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6  Risk/return comparison
Assume the riskfree rate of return is 10%, and the
expected return on the market is 16%. An investment
manager can choose between two portfolios, A and B,
having the following properties:

A 
B 
Expected return 
.17 
.24 
Beta 
1.50 
2.00 
Under the CAPM, which portfolio should the investment
manager choose?
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7  Calculate E(r)
You compute the historical betas for various
investments and assume they are good predictors of expected
volatility  thus risk. You also assume various riskfree
rates and expected market returns. In each case calculate
the expected return for the investment.
Investment 
Beta 
Riskfree rate 
Market return 
A 
1.30 
5.2 
8.7 
B 
.90 
8.5 
13.4 
C 
.20 
9.1 
12.1 
D 
1.00 
10.9 
15.5 
E 
.60 
6.2 
10.8 
If the expected return is greater than the promised
return  what should you do? Buy or sell?
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8  With CAPM
Use the CAPM equation to compute the unknown variable

Investment 
Riskfree return 
Market return 
Beta 
Required return 
A 
4.2 
12.3 
.85 
? 
B 
? 
15.8 
1.35 
17.4 
C 
3.6 
? 
1.10 
16.1 
D 
5.2 
12.6 
? 
15.2 
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9  Problem
You compare two stocks, both traded on the stock exchange.
You are thinking of selling one. Which investment is
a better combination of risk and return? You look at
returns (cash flow and market appreciation) over the
last ten years. You predict that future returns will
be comparable.

Stock
X 
Stock
Y 
Year 
Cash flow 
Starting value 
Ending value 
Cash flow 
Starting value 
Ending value 
1 
1.0 
20.3 
22.5 
1.5 
20.8 
20.9 
2 
1.5 
22.5 
21.0 
4.2 
20.9 
22.4 
3 
1.8 
21.0 
24.8 
3.6 
22.4 
19.8 
4 
2.2 
24.8 
22.0 
5.1 
19.8 
22.1 
5 
2.4 
22.0 
28.5 
4.8 
22.1 
22.5 
6 
2.5 
28.5 
30.2 
3.2 
22.5 
19.3 
7 
2.5 
30.2 
26.4 
5.9 
19.3 
24.1 
8 
2.5 
26.4 
28.1 
4.6 
24.1 
22.7 
9 
1.8 
28.1 
27.7 
3.9 
22.7 
24.1 
10 
1.5 
27.7 
31.2 
5.7 
24.1 
25.6 
 Calculate the annual rate of return for each asset
for each year, and then compute the average return.
 Use these results to find standard deviation and
coefficient of variation for each investment.
 Based on these results, which investment offers
a better mix of risk and return?
 Assuming betas (X = 1.60, Y = .85) and
a riskfree rate of 4.8% and an expected market return
of 14.2%, use the CAPM to find the required return
for each investment.
 Using these CAPM results and comparing them to past
returns, which investment seems to offer a better
mix of risk and returns?
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