PhD Course in Cost Benefit Analysis

1

• PhD Course in Cost Benefit Analysis
• The Risk Free Cost of Capital,
• the CAPM, Systematic and Unsystematic Risk, and
• The Risk Adjusted Cost of Capital
• by
• Per Bjarte Solibakke
• Molde University College

2
PhD Course in Cost Benefit Analysis

• Overview
• Corporate Governance and Financial Goals
• The Foundation of the Discount Rate (risk-free
  Cost of Capital)
• 3. The Net Present Value (NPV) and Internal Rate
  of Return (IRR) with adjustment for Taxes (T)
• 4. Utility Theory and Risk Measures, Portfolio
  Theory and the CAPM
• 5. The Relevant Risk, Systematic and
  Unsystematic Risk and Risk Adjusted Cost of
  Capital for Corporate Decision Making
• 6. The implications of Debt (financial
  leverage), Taxes and the WACC

3
1. Corporate Governance and Financial Goals
The most widely accepted statement of good
corporate governance practices are established by
the Organisation for Economic Cooperation and
Development (OECD)

• The rights of shareholders The
  corporate governance framework should protect
  shareholders rights
• The equitable treatment for shareholders
  Equitable treatment of shareholders, including
  minority and foreign shareholders. Opportunity to
  obtain effective redress for violation of their
  rights
• The role of stakeholders in corporate governance
  Recognize the rights of stakeholders
  as established by law and encourage active
  cooperation between corporation and stakeholders
  in creating wealth and jobs, and the
  sustainability of financially sound enterprises.
• Disclosure and transparency
  Ensure timely and accurate disclosure on all
  relevant material, including financial situation,
  performance, ownership and governance of the
  company.
• The responsibility of the board
  Ensure strategic guidance of the company, the
  effective monitoring of management by the board,
  and the boards accountability to the company and
  the shareholders.

4
1. Corporate Governance and Financial Goals
Equity Markets Analysts and other market agents
evaluate the performance of the firm on a daily
basis
The Market Place (external)
The Corporation (internal)
Debt Markets Rating agencies and other analysts
review the ability of the firm to service debt
The Board of Directors The Chairman of the Board
and members are accountable for the organization
Auditors and Legal Advisors These contributors
provide an external opinion as to the legality
and fairness of the presentation and conformity
to standards of financial statements
Management The Chief Executive Officer (CEO) and
his team run the company
Regulators The SEC, the NYSE or other regulatory
bodies by country monitor corporate activities
for compliance with current laws and regulations
The Structure Corporate Governance represents
the relationships among stakeholders that is used
to determine and control the strategic direction
and performance of the organization.
5
Comparative Corporate Governance
1. Corporate Governance and Financial Goals

• Regime Basis Characteristics Examples
• Efficient equity markets USA, UK,
• Market based dispersed ownership Canada,
  Australia
• Management ownership is Hong Kong,
• Family based combined family/majority
  and Indonesia, France
• minority shareholders Singapore
• Government influence in bank Korea, Japan
• Bank based lending lack of transparency German
  y
• family control
• Government- State ownership of
  enterprise China
• affiliated lack of transparency no
  minority Russia
• influence

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Failures in Corporate Governance
1. Corporate Governance and Financial Goals

• Increasingly visible in recent years
• USA
• ENRON (Energy)
• Worldcom (telecommunications)
• Healthsouth
• Netherlands
• Ahold (grocer)
• Italy
• Parmalat (diary-products)
• Canada
• Hollinger International Inc.

• Norway
• Finance Credit

Solutions are clear transparency,
accountability, tough audits and criminal
penalties for those who cheat. Halfway measures
are an invitation to more cheating.
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Financial Management Goals
1. Corporate Governance and Financial Goals

• 1. Shareholder Wealth Maximization
• Maximize the returns to shareholders return
  risk
• Assumptions Stock Market efficient (right price,
  new information is absorbed quickly, share
  price best allocation mechanism in the macro
  economy).
• Risk The added risk the corporations shares add
  to a diversified portfolio.
• Unsystematic risk (operational risk) can be
  eliminated through diversification by investors.
• Systematic risk (market risk) the risk of the
  market in general, cannot be eliminated by
  diversification.
• Agent Theory Theory to motivate management to
  accept the prescriptions of the shareholder
  wealth model (JensenMeckling, 1986).
  Management should think as shareholders. If not,
  board of director should replace them. If board
  of directors too weak or in grown discipline of
  the stock market ? takeover.
• Impatient Capitalism from the SWM-model
• Impatience no problem Changes in ownership
  create values (recent Norwegian study).
• Still rooms for patient owners Warren Buffet,
  Kjell Inge Røkke, Olav Thon.

8
Financial Management Goals
1. Corporate Governance and Financial Goals

• 2. Stakeholder Capitalism Model
• Controlling shareholders are more constrained
  powerful other shareholders. Other stakeholders
  are labour unions, Governments, Banks and other
  financial institutions
• Attributes
• Markets No assumption of efficient/inefficient
  capital markets. Assumes long term loyal
  shareholders typically controlling - rather
  then the transient portfolio investor.
• Risk Total risk operation and financial counts.
  Risk measured more by product market variability
  rather than by short-term variation in earnings
  and share price.
• Multiple goals trade offs between multiple goals
  ? complex management compensation systems.

• For Financial Management Goals worldwide,
  although both models have their strength and
  weaknesses, two trends in recent years have led
  to an increasing focus on the shareholder wealth
  form
• Non Anglo-American markets have increasingly
  privatised their industries and
• Shareholder based MNEs are increasingly
  dominating their global industry segments.

9
PhD Course in Cost Benefit Analysis

• Overview
• Corporate Governance and Financial Goals
• 2. The Foundation of the Discount Rate (risk-free
  Cost of Capital)
• 3. The Net Present Value (NPV) and Internal Rate
  of Return (IRR) with adjustment for Taxes
• 4. Utility Theory and Risk Measures, Portfolio
  Theory and the CAPM
• 5. The Relevant Risk Systematic and
  Unsystematic Risk and Risk Adjusted Cost of
  Capital for Corporate Decision Making
• 6. The implications of Debt (financial
  leverage), Taxes and the WACC

10
Present and Future Consumption
2. The Foundation of the Discount Rate (risk-free
Cost of Capital)
Prospects as individuals Cash on hand kr.
50.000 Cash to be received 1
year from now kr. 75.000
Kroner in period 1
E
Only consumption in the future (1k)
1,03 Invest kr. 50.000 at 3 ? obtain 50.000
(1,03) kr 51.500 one year from now
with certainty ? 75.000 51.500 126.500 (point
E)
Only consumption in the Future kr. 126.500
B
Future Cash Flow kr. 75.000
Slope -(1k) Rate of exchange between periods
A
Kroner in period 0
F
Current Cash Flow kr. 50.000
11
Present and Future Consumption
2. The Foundation of the Discount Rate (risk-free
Cost of Capital)
Want to change consumption from Initial
t050.000 t175.000 to Period 0 kr. 75.000
Period 1 the rest
Kroner in period 1
E
Changing Consumption pattern between periods
Borrow kr. 25.000 at 1k1,03 ? obtain in
period 0 50.000 25,000 kr. 75.000 Next
period Repay 25.000 1,03 kr. 25.750
Consume 75.000 25.750 kr. 49.250 (point D)
B
D
Future CF - Repayment 75.000- 25.750 kr.
49.250
Slope -(1k) Rate of exchange between periods
A
C
Kroner in period 0
F
Current Cash Flow 50.00025.000kr. 75.000
12
Present and Future Consumption
2. The Foundation of the Discount Rate (risk-free
Cost of Capital)
Introducing Real Assets
Kroner in period 1
Initial resources H
G
Investment opportunities line (H-G) shows cash
flow from investing in Real Assets
Cash Flow 3rd Best Investment 7.500
Cash Flow 2nd Best Investment 15.000
Consumption t1
Cash Flow from Best Investment 25.000
H
Kroner in period 0
Consumption t0
Best Invest (10.000)
2nd Best (10.000)
3rd Best (10.000)
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Present and Future Consumption
2. The Foundation of the Discount Rate (risk-free
Cost of Capital)
Linking up the Physical and Financial Market
Kroner in period 1
Initial resources H (i.e. kr. 100.000) Only the
financial market Investing 0H result in 0I next
period. Physical Investments JH with cash flows
t0 0J t1 0K (optimal allocation Z).
Investment opportunities line (H-G)
E
Capital Market line (F-E)
M
S
G
Changing Consumption pattern (L) The
Prodigal Borrow against future CFLHConsume
period 0 0N Repay NJ(1k)KP Consume period 1
0P
Changing Consumption pattern (M) The
Miser LendRJConsume period 0 0R Receive
RJ(1k)KS Consume period 1 0S
I
Z
K
Cash Flow from Best Investment 25.000
L
P
Slope -(1k) Rate of exchange between periods
0
Kroner in period 0
H
F
J
N
R
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Present and Future Consumption
2. The Foundation of the Discount Rate (risk-free
Cost of Capital)
Results Real and Financial Assets 1. Maximum
amount realisation from the investment JH,
discounted future cash flow JF ? present value.
Net Present Value (NPV) JF - JH
2. Invest JH The physical investment line is
steeper than the financial market line from H to
Z (investment from H to J). The line represent
the return on the marginal investment ? Invest in
physical investment opportunities until the slope
is equal to the capital market line ? Internal
Rate of Return gt Capital market return (gt NPV
gt0)!
3. Borrow and/or lend in the capital market until
you have achieved the desired balance between
consumption to day and consumption to morrow.
In relation to the SWM-model The objectives
from the Shareholder Wealth maximization model is
fully satisfied using the Investment- Consumption
interpretation.
15
Present and Future Consumption
2. The Foundation of the Discount Rate (risk-free
Cost of Capital)
Separation Theorem (no. 1)
Maximize the present value their lifetime
consumption
The introduction of a capital market together
with a physical (real) project market, makes it
possible to analyse investments decisions in
companies with many small shareholders/investors/
owners, which is physically apart from the
management of the company.
Shareholders will be unanimous in there
preference (they use the capital market). The
management of the firm, acting as agents of the
shareholders, need not worry about making
decisions that reconcile differences in opinion
among shareholders. The managers will be
directed to undertake all projects that earn more
than the market rate of return (the cost of
capital/time value of money).
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PhD Course in Cost Benefit Analysis

• Overview
• Corporate Governance and Financial Goals
• The Foundation of the Discount Rate (risk-free
  Cost of Capital)
• 3. The Net Present Value (NPV) and Internal Rate
  of Return (IRR) with adjustment for Taxes
• 4. Utility Theory and Risk Measures, Portfolio
  Theory and the CAPM
• 5. The Relevant Risk Systematic and
  Unsystematic Risk and Risk Adjusted Cost of
  Capital for Corporate Decision Making
• 6. The implications of Debt (financial
  leverage), Taxes and the WACC

17
3. The Net Present Value (NPV) and Internal Rate
of Return (IRR) with adjustment for Taxes

• Net Present Value Criterion

where CF0 Investment/initial cash flow in year
0 CFt Net cash flow in year t Sn Salvage value
at end of life year n (N). N Maturity, number of
years k Cost of capital NPV Net Present Value r
/ IRR Internal rate of return
Decision criteria Accept all projects having a
positive NPV.
18
3. The Net Present Value (NPV) and Internal Rate
of Return (IRR) with adjustment for Taxes

• Internal Rate of Return

where CF0 Investment/initial cash flow in year
0 CFt Net cash flow in year t Sn Salvage value
at end of life year n (N). N Maturity, number of
years k Cost of capital NPV Net Present Value r
/ IRR Internal rate of return
Decision criteria Accept all projects having an
Internal Rate of return (r) greater than the Cost
of Capital (k).
19
3. The Net Present Value (NPV) and Internal Rate
of Return (IRR) with adjustment for Taxes

• Adjustment for Norwegian Tax Regime (added
  complexities)

Net Present Value NPV from salvage value
(SV) and from Cash Flows taxes (T) book
value year t (BVt) 1.The salvage value is taken
as income in year n 2. The salvage value is
writing off on existing assets
3. Writing off salvage book value
CFt Cash flow year t. DPt depreciation year
t. DPP depreciation percentage N number of
years k discount rate
20
PhD Course in Cost Benefit Analysis

• Overview
• Corporate Governance and Financial Goals
• The Foundation of the Discount Rate (risk-free
  Cost of Capital)
• 3. The Net Present Value (NPV) and Internal Rate
  of Return (IRR) with adjustment for Taxes
• 4. Utility Theory and Risk Measures, Portfolio
  Theory and the CAPM
• 5. The Relevant Risk Systematic and
  Unsystematic Risk and Risk Adjusted Cost of
  Capital for Corporate Decision making
• 6. The implications of Debt (financial
  leverage), Taxes and the WACC

21
4. Utility Theory and Risk Measures, Portfolio
Theory and the CAPM
A first and simple look at risk of any physical
project

• Many ks.
• One k for each risk level.

? A lower number of projects are accepted from
the NPV-rule and the IRR-rule.
A (k1)
-(1k1)
B (k2)
C (k3)
-(1k2)
Increasing interest rates Slowing down the
activity level in the economy
-(1k3)
where k1 lt k2 lt k3
22
4. Utility Theory and Risk Measures, Portfolio
Theory and the CAPM
Risk Classifications from Utility Theory
(xReward u(x)Utility measure
U(x)
x
1. EU(Project) lt UE(Project) ? Risk
aversion. 2. EU(Project) UE(Project) ?
Risk neutral. 3. EU(Project) gt
UE(Project) ? Risk preference.
General Assumption for our analysis Investors,
Management, Executives, Individuals are in
general risk averse.
23
4. Utility Theory and Risk Measures, Portfolio
Theory and the CAPM
Portfolio Theory
Result The variance of the returns from a
portfolio of assets is smaller than the
arithmetic average of the individual assets
variance. ? The risk is reduced depending on
portfolio diversification.
A portfolio consisting of two risky assets (A and
B) will have where aA - share in asset
A aB - share in asset B Variance is
defined as The Covariance is Cov (RA, RB)
The Correlation is
24
4. Utility Theory and Risk Measures, Portfolio
Theory and the CAPM
Portfolio Theory Example and Fundamental results
Assets Project A Project B
Returns E(RA) 25 E(RB) 18
Standard deviation ?A
8 ?B 4 A Fundamental Problem
Project A has both higher returns and standard
deviation! Construct a Portfolio consisting of
these two papers with share aA in asset A and
(aB1-aA) in asset B. Using an equally weighted
portfolio, i.e. aA til 0,5, we obtain while
the sP is dependent of the correlations between
the returns of A and B r(RA,RB).
We can therefore construct the following table
(holding aA constant at 0,5)  r(RA,RB) sP 1 6
0 4 -1 2
25
4. Utility Theory and Risk Measures, Portfolio
Theory and the CAPM
Portfolio Theory Examples and Fundamental results
----- 0,5 share in A and 0,5 share in B -----
0,8 share in A and 0,2 share in B.
26
4. Utility Theory and Risk Measures, Portfolio
Theory and the CAPM
Portfolio Theory Examples and Fundamental results
----- 0,5 share in A and 0,5 share in B -----
0,8 share in A and 0,2 share in B.
27
4. Utility Theory and Risk Measures, Portfolio
Theory and the CAPM
Portfolio Theory Examples and Fundamental results
----- 0,5 share in A and 0,5 share in B -----
0,8 share in A and 0,2 share in B. Z 1/3
share in A and 2/3 share in B ? zero risk only
when r(RA,RB) -1 (perfect negative)!
28
4. Utility Theory and Risk Measures, Portfolio
Theory and the CAPM
Portfolio Theory Examples and Fundamental results
Summary of findings (portfolio variance)
sP
Decreasing
Important finding The lower the correlation
(minimum -1) the higher the effects of
diversification.
29
4. Utility Theory and Risk Measures, Portfolio
Theory and the CAPM
The Capital Asset Pricing Model (CAPM) Increasing
the number of assets and introducing a risk free
alternative (RF)
D
C
30
4. Utility Theory and Risk Measures, Portfolio
Theory and the CAPM
The Capital Asset Pricing Model (CAPM) Investor
adaptations numerical example for three
different investors
Capital Market Line (CML) Example Point C E(RN)
16, sN 5 and RF 12. Initial resources
1.000 kroner. Portefolio ½ part risky project
and ½ part risk free. The implication
is a share in the risky portfolio aR 0,5
and the share in the risk-free asset is aRF 1
- aR 0,5 E(RP) 0,5 E(RN) (0,5) RF
0.5 16 0.5 12 14 and ?P a1 .
?N 0,5 5 2,5
Capital Market Line (CML) Example Point D E(RN)
16, sN 5 and RF 12. Initial resources
1.000 kroner. Portefolio 1/1 part risky project
and nothing (0) risk free. The
implication is a share in the risky portfolio
aR 1 and the share in the risk-free asset is
aRF 1 - aR 0 E(RP) 1 E(RN) (0) RF
1 16 0.5 12 16 and ?P a1 .
?N 1 5 5
Capital Market Line (CML) Example Point E E(RN)
16, sN 5 and RF 12. Initial resources
1.000 kroner. The investor wants to increase his
initial investment with 50, from 1000 to 1500,
suggesting a need to borrow 500 kroner. The
implication is a share in the risky portfolio
aR 1,5 and the share in the risk-free asset
is aRF 1 - aR -0,5 (?borrowing at RF) E(RP)
1,5 E(RN) (-0,5) RF 1,5 16 - 0.5
12 18 and ?P a1 . ?N 1,5 5 7,5
31
4. Utility Theory and Risk Measures, Portfolio
Theory and the CAPM
The Capital Asset Pricing Model (CAPM)
In general the Capital Market Line says for a
portfolio P
Note ?p is the standard deviation for a maximum
diversified investor.
Investor 3
Investor 2
Investor 1
32
4. Utility Theory and Risk Measures, Portfolio
Theory and the CAPM
The Capital Asset Pricing Model (CAPM) Separation
Theorem (no. 2)
Two fund Separation Principle Portfolios of all
risk-averse investors will consist of different
combinations only two portfolios. Each investor
will have utility maximization portfolio that is
combination of the risk-free asset (RF) and a
portfolio (or fund) of risky assets (M), that is
determined with the line drawn from the risk-free
rate of return tangent to the investors
efficient set of risky assets.
x - shares of the total capital in the risky
asset portfolio (M) (1 - x) - shares of the
total capital in the risk-free asset (RF) x lt 1
suggest that the investor borrows money and
place him to the right of M on the Capital
Market Line.
The two fund separation principle insight is that
investors are not important for risky projects.
The important factor is that all firms/projects
must be priced in equilibrium in M. Hence in the
point M, all projects priced in accordance with
attached risk.
33
4. Utility Theory and Risk Measures, Portfolio
Theory and the CAPM
The Capital Asset Pricing Model (CAPM)
The following relationships are therefore
important. For a maximum diversified investor (M
is the market portfolio) CML To make an
inefficient investment interesting for an
investor the asset must be priced so it is in the
market portfolio. To be in the market portfolio
the return/risk relation for an inefficient
investment must be MAL This relation is a
general expression for an inefficient investment
alternative. The name is the Market Return Line
and is derived from the intersection between the
CML and the efficient set of investment
alternatives.
Interpretation CML A risk premium only for
non-diversifiable risk. The market
portfolio. MAL A risk premium for a simple
investment s is made up of the premium for market
risk (?) and the individual investments s unique
risk (?s) together with the covariance investment
s has with the market (r(Rs,R m) ) ? ?
the part of investment s market portfolios
non-diversifiable risk!! ? only
compensation for non-diversifiable risk.
34
4. Utility Theory and Risk Measures, Portfolio
Theory and the CAPM
The Capital Asset Pricing Model (CAPM)
The expression now becomes
Defining
The CAPM expression is a fact
Graphical Representation of CAPM
Interpreting bs. ?s an index for asset s
systematic risk, relative to the market
portfolios systematic risk.
35
4. Utility Theory and Risk Measures, Portfolio
Theory and the CAPM
The Capital Asset Pricing Model (CAPM)
E(Rj)
Security Market Line
Project K required return
E(RK)
Project K expected return
RK
K
Decisions Reject project K
Company
ks E(Rj)
Accept project L
L
RL
E(RL)
RF
bj
bL
bj
bK
Project L required return
Project L expected return
36
4. Utility Theory and Risk Measures, Portfolio
Theory and the CAPM
The Capital Asset Pricing Model (CAPM)
Measuring b (beta) using regression analysis
37
PhD Course in Cost Benefit Analysis

• Overview
• Corporate Governance and Financial Goals
• The Foundation of the Discount Rate (risk-free
  Cost of Capital)
• 3. The Net Present Value (NPV) and Internal Rate
  of Return (IRR) with adjustment for Taxes
• 4. Utility Theory and Risk Measures, Portfolio
  Theory and the CAPM
• 5. The Relevant Risk Systematic and
  Unsystematic Risk and Risk Adjusted Cost of
  Capital for Corporate Decision making
• 6. The implications of Debt (financial
  leverage), Taxes and the WACC

38
5. The Relevant Risk Systematic and Unsystematic
Risk and Risk Adjusted Cost of Capital
Systematic versus Unsystematic Risk (relevant
risk)
A portfolio consisting of N risky
assets Returns where wi - weight asset
no. i E(Ri)- expected return asset no.
i Variance where sij - covariance between
asset i and j.
? Variance- Covariance Matrix (symmetric)
39
5. The Relevant Risk Systematic and Unsystematic
Risk and Risk Adjusted Cost of Capital
Systematic versus Unsystematic Risk (relevant
risk)
Note that the variance can be written as
The first term goes towards 0 (zero) as N ? 8.
The second term goes towards as N ? 8. ?
the average covariance
The average covariance as N ? 8 becomes
relatively more important.
40
5. The Relevant Risk Systematic and Unsystematic
Risk and Risk Adjusted Cost of Capital
Interpreting Systematic versus Unsystematic Risk

• CAPM provides the relationship between an
  investments systematic risk and expected return!
• Total risk Systematic Unsystematic risk.
• Possible scenarios according to CAPM
• Relatively high amount of total risk, but low
  expected returns
• Relatively low amount of total risk, but high
  expected returns.

• Degree of correlation dependence
• First have low market correlation Second have
  high market correlation

• Total risk (determined by the level of a firms
  cash flow
• Quality of management 5. Rate of growth of
  investments in the economy
• The state of its labour relations 6. the level
  of consumer demand
• The level of its advertising and 7. Movement
  in exchange Rates
• The effectiveness of its research and
  development. 8. Rates of corporation taxes
• 9. Level of Interest Rates

1-4 Company specific risk Determinants of
Unsystematic Risk 5-9 General factors that
effect all firms in the economy Determinants of
Market or Systematic Risk
41
5. The Relevant Risk Systematic and Unsystematic
Risk and Risk Adjusted Cost of Capital
Interpreting Systematic versus Unsystematic Risk

• Firms and Systematic Risk
• Three main determinants of systematic risk
  (relevant risk) exposure
• The sensitivity of the companys revenues to the
  general to the general level of economic activity
  in an economy and other macroeconomic factors.
• The proportion of fixed to variable costs (i.e.
  the degree of cost sensitivity).
• The level of financial gearing or leverage (i.e.
  the amount of interest bearing debt compared to
  shareholder equity).

Ship Building Company might be seen as an example
of high revenue sensitivity (Aker-Kværner) Food
retailers might be taken as an example of a
business with a low degree of revenue sensitivity
(ICA)

• High level of fixed cost relative to total costs.
  Company cash flows will be more volatile than
  would otherwise be the case (fixed interest
  payments). The debt to equity ratio is similar.
  Interest must be paid on interest whether or not
  it is generating positive cash flows before
  interest.
• Firms with high revenue sensitivity (1) minimize
  the proportion of both fixed financing (debt) and
• (2) fixed operating costs.

42
5. The Relevant Risk Systematic and Unsystematic
Risk and Risk Adjusted Cost of Capital
Systematic versus Unsystematic Risk (relevant
risk)
The single-price law of securities All
securities or combination of securities that have
the same joint distribution of returns, will have
the same price in equilibrium. Hence, no investor
will pay a premium to avoid diversifiable risk.
On the other hand, because covariance risk cannot
be diversified away, investors will pay a premium
to escape it.
43
5. The Relevant Risk Systematic and Unsystematic
Risk and Risk Adjusted Cost of Capital
Systematic versus Unsystematic Risk (relevant
risk)
Portfolio Risk
A construction of randomly selected portfolio of
shares consisting of only between 15 and 20
different securities results in elimination of
around 90 of the maximum amount of risk that it
would be possible to eliminate through
diversification.
Not all risk can be diversified away as indicated
above. There is an underlying rump of
non-diversifiable risk. Studies 65 of total
risk is diversifiable 35 is non-diversifiable.
Diversifiable Risk
Non- Diversifiable Risk
Number of Securities in Portfolio
20
44
5. The Relevant Risk Systematic and Unsystematic
Risk and Risk Adjusted Cost of Capital

• Net Present Value Criterion with adjustment for
  risk

where CF0 Investment/initial cash flow in year
0 CFt Net cash flow in year t Sn Salvage value
at end of life year n (N). N Maturity, number of
years RF Risk-free cost of capital NPV Net
Present Value E(RM) Expected Market Return b s
r(R,RM) /sM Systematic risk / relevant risk
Decision criteria Accept all projects having a
positive NPV.
45
5. The Relevant Risk Systematic and Unsystematic
Risk and Risk Adjusted Cost of Capital

• Internal Rate of Return with adjustment for risk

Decision criteria Accept all projects having
where CF0 Investment/initial cash flow in year
0 CFt Net cash flow in year t Sn salvage value
at end of life year n (N). N Maturity, number of
years RF Risk-free cost of capital NPV Net
Present Value E(RM) Expected Market
Return r Internal Rate of Return b sr(R,RM)/sM
Systematic risk / relevant risk
46
PhD Course in Cost Benefit Analysis

• Overview
• Corporate Governance and Financial Goals
• The Foundation of the Discount Rate (risk-free
  Cost of Capital)
• 3. The Net Present Value (NPV) and Internal Rate
  of Return (IRR) with adjustment for Taxes
• 4. Utility Theory and Risk Measures, Portfolio
  Theory and the CAPM
• 5. The Relevant Risk Systematic and
  Unsystematic Risk and Risk Adjusted Cost of
  Capital for Corporate decision making
• 6. The implications of Debt (financial
  leverage), Taxes and the WACC

47
6. The implications of Debt (financial leverage),
Taxes and the WACC
Financial leverage is the extent to which a firm
relies on debt and a levered firm is a firm with
some debt in its capital structure. Due to the
fact that interest payments must be undertaken
regardless of the firms sales, financial
leverage refers to the firms fixed costs of
finance.
As with any portfolio, the beta of this portfolio
is a weighted average of betas of the individual
items in the portfolio. For a levered firm, we
therefore have where bEquity - is the beta
of the levered firm bDebt - is the
beta of debt (very low in practice without
bankruptcy costs) bAsset - is the
beta of the assets of the firm If we make the
commonplace assumption that beta of debt is zero
(no bankruptcy costs)
48
6. The implications of Debt (financial leverage),
Taxes and the WACC
Financial leverage (debt and the equity risk)
b
bEquity
bAsset
Debt/Equity Ratio
Increasing financial leverage ?
49
6. The implications of Debt (financial leverage),
Taxes and the WACC
WACC with bankruptcy risk and no taxes
A firm using both equity and debt, the cost of
capital is a weighted average of each
If bDebt is 0 (zero no bankruptcy costs) the
debt term reduced to the risk-free cost of capital
50
6. The implications of Debt (financial leverage),
Taxes and the WACC
The Cost of Capital with Debt (weighted average
cost of capital (WACC))
A firm using both equity and debt but there are
no taxes, the cost of capital is a weighted
average of each Interest payments are
deductible at the corporate level. The after-tax
cost of debt is therefore where T is the
corporate tax rate (28). However, the value of
the firm is influenced by the tax shield, that
is VL VU TDebt that is, the nominal amount
of debt!
51
6. The implications of Debt (financial leverage),
Taxes and the WACC
Financial leverage (debt and the equity risk)
Cost of Capital ()
REquity
RAsset
Rwacc(without Taxes)
Rwacc(with Taxes)
RDebt
Debt-to-Equity Ratio (D/E)
Increasing financial leverage ?
52
6. The implications of Debt (financial leverage),
Taxes and the WACC
Finally, incorporating corporate taxes and
personal tax on dividends where TC -
Corporate tax rate TS - personal tax-rate on
dividend payments to Shareholders TB - personal
tax-rate on interest payments to
Bondholders/creditors
53
6. The implications of Debt (financial leverage),
Taxes and the WACC
Financial leverage (debt and the equity risk)
Value of the Firm (V)
VLVU TCD when TSTB
VLltVU TCD when TSltTB but (1-TB) gt (1-TC)(1-TS)
VLVU when (1-TB) gt (1-TC)(1-TS)
VU
VLltVU when (1-TB) lt (1-TC)(1-TS)
Debt (D)
Increasing debt ?
54
6. The implications of Debt (financial leverage),
Taxes and the WACC
Parameter values with an assumption of inflation
of 1,9 (last 12 months September 2006)
NHH Professor Thore Johnsen, april
2006Referanserenten