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Financiering

Jeroen E. Ligterinkjeroenl@fee.uva.nl

2001

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• onder: course material, first year finance

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• Alleen dan ben je goed voorbereid!

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BMM 8: Topics Covered

• How Firms Organize Their Investment Process

• Some “What If” Questions Sensitivity Analysis

Break Even Analysis

• Flexibility in Capital Budgeting Decision Trees

Options

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Capital Budgeting Process

• Capital Budgeting Problems Consistent forecasts

Conflict of interest

Forecast bias

Selection criteria (NPV and others)

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How To Handle Uncertainty

Sensitivity Analysis - Analysis of the effects of changes in sales, costs, etc. on a project.

Scenario Analysis - Project analysis given a particular combination of assumptions.

Simulation Analysis - Estimation of the probabilities of different possible outcomes.

Break Even Analysis - Analysis of the level of sales (or other variable) at which the company breaks even.

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Operating Leverage

Operating Leverage- The degree to which costs are fixed.

Degree of Operating Leverage (DOL) - Percentage change in profits given a 1 percent change in sales.

DOL = % change i n pr ofi t s% change i n sal es

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Operating Leverage

Example - A company has sales outcomes that range from $16mil to $19 mil, Depending on the economy. The same conditions can produce profits in the range from $550,000 to $1,112,000. What is the DOL?

DOL = = 5.45102.218.75

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Flexibility & Options

Decision Trees - Diagram of sequential decisions and possible outcomes.

• Decision trees help companies determine their Options by showing the various choices and outcomes.

• The Option to avoid a loss or produce extra profit has value.

• The ability to create an Option thus has value that can be bought or sold.

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Decision Trees

NPV=0

Don’t test

Test (Invest $200,000)

Success

Failure

Pursue project NPV=$2million

Stop project

NPV=0

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BMM 9: Topics Covered

• Rates of Return

• 73 Years of Capital Market History

• Measuring Risk

• Risk & Diversification

• Thinking About Risk

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Rates of Return

39.5%or .395=

= ReturnPercentage 741.25 + 28

P e rc e n ta g e R e tu rn = C a p i ta l G a in + D iv id e n d In i t ia l S h a re P r ic e

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Rates of Return

D iv id e n d Y ie ld = D iv id e n d In i t ia l S h a re P r ic e

C a p i t a l G a in Y ie ld = C a p i t a l G a inIn i t i a l S h a r e P r i c e

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Rates of Return

%01.7or 017.74

1.25= YieldDividend

%37.8or 378.74

28= YieldGain Capital

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Rates of Return

Nominal vs. Real

1+ real ror = 1 + nominal ror1 + inflation rate

37.3%ror real

373.1=ror real+1 .016 + 1.395 + 1

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Market Indexes

Dow Jones Industrial Average (The Dow)

Value of a portfolio holding one share in each of 30 large industrial firms.

Standard & Poor’s Composite Index (The S&P 500)

Value of a portfolio holding shares in 500 firms. Holdings are proportional to the number of shares in the issues.

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The Value of an Investment of $1 in 1926

Source: Ibbotson Associates

0.1

10

1000

Common Stocks

Long T-Bonds

T-Bills

Inde

x

Year End

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Rates of Return 1926-1998

Source: Ibbotson Associates

-60

-40

-20

0

20

40

60

26 30 35 40 45 50 55 60 65 70 75 80 85 90 95

Common Stocks

Long T-Bonds

T-Bills

Year

Per

cent

age

Ret

urn

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Expected Return

9.3+4.8=14.1% (1999)

9.3+14=23.3% (1981)

premium

risk normal+

billsTreasury

on rateinterest =

return

market Expected

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Measuring Risk

Variance - Average value of squared deviations from mean. A measure of volatility.

Standard Deviation - Average value of squared deviations from mean. A measure of volatility.

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Measuring RiskCoin Toss Game-calculating variance and standard deviation

(1) (2) (3)

Percent Rate of Return Deviation from Mean Squared Deviation

+ 40 + 30 900

+ 10 0 0

+ 10 0 0

- 20 - 30 900

Variance = average of squared deviations = 1800 / 4 = 450

Standard deviation = square of root variance = 450 = 21.2%

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Risk and Diversification

Diversification - Strategy designed to reduce risk by spreading the portfolio across many investments.

Unique Risk - Risk factors affecting only that firm. Also called “diversifiable risk.”

Market Risk - Economy-wide sources of risk that affect the overall stock market. Also called “systematic risk.”

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Risk and Diversification

Deviation from SquaredYear Rate of Return Average Return Deviation

1994 1.31 -23.44 549.431995 37.43 12.68 160.781996 23.07 -1.6 2.821997 33.36 8.61 74.131998 25.58 3.83 14.67Total 123.75 801.84

Average rate of return = 123.75/5 = 24.75Variance = average of squared deviations = 801.84/5=160.37Standard deviation = squared root of variance = 12.66%

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Risk and Diversification

Portfolio rate

of return=

fraction of portfolio

in first assetx

rate of return

on first asset

+fraction of portfolio

in second assetx

rate of return

on second asset

((

((

))

))

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Stock Market Volatility 1926-1998

0

10

20

30

40

50

60

Std

Dev

26

Risk and Diversification

0

5 10 15

Number of Securities

Po

rtfo

lio

sta

nd

ard

dev

iati

on

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Risk and Diversification

0

5 10 15

Number of Securities

Po

rtfo

lio

sta

nd

ard

dev

iati

on

Market risk

Uniquerisk