ACCA_F9 03

• If the NPV of an investment > = 0, go with the investment (or project • NPV < 0, reject the investment (or project)
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The problem is that, where we to find the “discount rate”
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Distribution of return and Risk
Investment’s Rate of Return If state occurs (%)
State of the economy Possibility of occurance
T-Bill 8 8 8 8
Bond 12 9 8.5 9.45
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During the previous session, we learnt that the role of the financial manager is to make financial decisions:
– – – – – Identify future cash flows Discount them into present values Add PVs, minus Investment cost This is NPV NPV decision rule
Stock -15 20 35 17.5
Recession Stay as normal booming
0.2 0.5 0.3
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E represents Expectation Risk of return We use both variance and standard deviation as measure of risk The variance of returns = σ2 =
Netherlands
Germany (ex 1922/3)
Denmark
Spain
Canada
Belgium
S Africa
Average
Norway
Sweden
France
Japan
USDow Jones Risk
Annualized Standard Deviation of the DJIA over the preceding 52 weeks (1900 – 2006)
Denmark
South Africa
Australia
Spain
Germany
Belgium
Norway
Canada
Sweden
Country
Average
France
Japan
USA
Italy
UK
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Dividend Yield (1900-2006)
10.00 9.00 8.00 7.00 Dividend Yield, % 6.00 5.00 4.00 3.00 2.00 1.00 0.00 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000
r = n (1 + r1 )(1 + r2 )(1 + r3 )...(1 + rn ) −1
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Example:
The returns of security A over the past five years can be listed as below, calculate arithmetic and geometric return. 12% 14% -10% -5% 19%
20
00
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Measuring Risk
Histogram of Annual Stock Market Returns (1900(1900-2006)
# of Years
24 20 16 12 8 4 0
24 20 17 10 4 12 13
3
-20 to -10 -10 to 0 10 to 20 20 to 30 30 to 40 40 to 50 0 to 10
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Because the future returns will be only one of the possible events, the returns become uncertain. When future returns are not determined, our prediction on the future is only estimation of all the possible outcomes by their possibility”
– You cannot find it by looking at the bank’s interest rate table – If you choose a wrong discount rate, you will make a wrong financial decision
Finance is a study to find the right discount rate
40 35 30 25 20 15 10 5 0
18.93 19.79 16.64 17.88
33.66 34.17 27.91 29.24 23.58 23.64 23.8 24.93 21.51 21.64 22.28 22.71 22.71 23.35
Switzerland
Australia
Ireland
possibility 0.5 0.3 0.2
Expected return 40 15 -30
Arithmetic return = Geometric return = The results are different.
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The Value of an Investment of $1 in 1900
$100,000
Common Stock US Govt Bonds T-Bills
Risk premium, %
11 10 9 8 7 6 5 4 3 2 1 0
7.62 6.88 7.52 5.95 6.06 6.17 6.45 6.5 4.85 5.33 5.5
10.2910.97 9.39 9.71 8.58 8.81 8.85
Switzerland
Ireland
Netherlands
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We need scientific definitions of return and risk
Any cash payments received + Price change over the periods Price at which the asset is purchased any cash payments received = + Price at which the asset is purchased Price change of the asset Price at which the asset is purchased = asset yield + capital gain r=
Project Expected return Expected risk
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A
12%
23%
B
12%
15%
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then we look at the third case
Project Expected return Expected risk
A
12%
22%
B
8%
15%
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Our question is how to compromise between the risk and the return
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Rates of Return 1900-2006
Stock Market Index Returns
80%
Percentage Return
60% 40% 20% 0% -20%
00 20 40 60 80 19 19 19 19 19
-40% -60%
Year
Source: Ibbotson Associates
– Arithmetic return: simply average returns (usually at a particular time point)
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r1 + r2 + r3 + ... + rn r= n
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– Geometric return: the average return over a certain periods
$10,000
21,536
Dollars
$1,000 176 66
$100
$10
$1
19
19
19
19
19
Start of Year
19
19
19
19
19
20
2007
00
10
20
30
50
60
40
70
80
90
00
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The Value of an Investment of $1 in 1900
Real Returns
1
-50 to -40
1
-40 to -30 -30 to -20
2
Return %
50 to 60
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Equity Market Risk (by country)