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- Corporate Finance
- BBA 2- 2007/8 Term 2.
- Investment Appraisal.
- Risk and Return/ Portfolio Analysis.
- 3. Cost of Capital.
- 4. Capital Structure and Firm Value.
- 5. Dividend Policy.
- 6. Options.

Connections throughout the course. Investment

Appraisal Net Present Value with discount rate

(cost of capital) given. Positive NPV increases

value of the firm.

Cost of Capital (discount rate) How do companies

derive the cost of capital? CAPM, DVM.

Capital Structure and effect on Firm Value and

WACC.

- Income Statement.
- Revenue
- Variable Costs
- Fixed costs
- Depreciation
- EBIT
- -rD
- EBT
- -tax
- Net Income
- -Dividends
- Retained earnings

Finance Topics. Revenue Risk. Operating

Leverage. Business Risk. Financial

Gearing. Shareholder Risk and Return Dividend

Policy.

Income Statement measures the flows of revenues

and expenses during the year. Future Revenues are

uncertain Revenue risk. Production technology

reflected in costs Variable costs and Fixed

Costs. Fixed Costs (operating leverage) affect

EBIT risk gt business risk. Depn is not a cash

flow market Value of firm determined by

cashflow. Debt financing (fixed interest

payments) gt Financial Risk. Net Income is the

residual stream of earnings owned by shareholders

gt affected by business risk and financial

risk. Dividend Policy how much of NI should

board pay as dividend- how much should it retain

to reinvest?

Balance Sheet. Liabilities Share Capital

Retained Earnings Equity Debt (eg loans

etc) Total Liabilities

Assets Fixed Assets Current Assets Total Assets

Balance Sheet is a snapshot. Total Assets

Total Liabilities. Book Value of Equity. Topic

Capital Structure (market values).

Source and Application of Funds.Net Income

New Equity Dividends New Investment.gt Net

Income Dividends New Investment New Equity

Retained Earnings

Managements aim is maximisation of market

value. Market Value of Equity Price Per Share

Number of Shares. Two management decisions

Investment and financing decisions. Capital

Budgeting Decision Select Projects which

maximise Shareholders wealth. Net Present Value

Rule Positive NPV increases shareholder

wealth.

r discount Rate, cost of capital, or Investors

Required Return. X is net cashflow.

Section 1 Investment Appraisal. 1. Net Present

Value. Internal Rate of Return (IRR).

Payback. Accounting Rate of Return. 2. Correct

Method NPV! We should only include relevant

costs. We should consider economic not accounting

costs. Cashflows- take costs when they occur.

Calculation of Net Present Value. Special Case

Perpetuities.

Example A firm is considering a new project

needs to invest 900, project will provide net

cashflow of 100 forever, the cost of capital is

10. The NPV of this project is 100. Since NPV

is Positive, it should be accepted.

Example Consider the following new

project- Initial capital investment of 15m. It

will generate sales for 5 years. Variable Costs

equal 70 of sales. Fixed cost of project 200m

P.A. A feasibility study, cost 5000, has already

been carried out. Discount rate 12. Should we

take the project?

DO WE INVEST IN THIS NEW PROJECT?

NPV gt 0. COST OF CAPITAL (12) lt IRR (19.75).

Note that if the NPV is positive, then the IRR

exceeds the Cost of Capital.

NPV m

3.3m

Discount Rate

0

12

19.7

MUTUALLY EXCLUSIVE PROJECTS.

COMPARING NPV AND IRR

NPV

531

519

Discount Rate

10

22.8

25.4

PROJ D

PROJ C

Select Project with higher NPV Project C.

- Mutually Exclusive Versus Independent Projects.
- -Mutually exclusive we can only select one

project- we choose the one with the highest NPV

(project 1). - Independent Projects select all positive NPV

projects (all projects). - Capital Rationing.

Project PV of Inflows Current Outflows PVI NPV

1 230,000 200,000 1.15 30,000

2 140,000 125,000 1.12 15,000

3 195,000 175,000 1.11 20,000

4 162,000 150,000 1.08 12,000

Capital Rationing And Independent Projects. The

firm is limited to a capital constraint of

300,000. Consider combinations of projects that

maximise weighted average PVI. Eg Projects 2 and

3

Project 1

Selecting Project 2 and 3 is superior to project

1.

Treatment of depreciation in NPV analysis. -We

only use cashflows in investment

appraisal. -Depreciation is not a

cashflow. -However, depreciation is allowable

against tax (see income statement), which affects

cashflow. For cashflow, add depreciation back-

Treatment of depreciation.

- More Capital Budgeting Topics.
- Projects with different lives.
- We assume that projects are replicated at

constant scale.

For Example Project A 2 years NPV (2)

10. Project B 3 years NPV(3) 14. K

10. Project A NPV(2, 10 ( 1.21/ .21)

57.6. Project B NPV (3, 14 (1.33 / .33)

56.4. Select Project A.

Capital Budgeting and Inflation.

K is the nominal cost of capital. We require real

cost of capital, where

Either add inflation to the cashflow estimates,

or remove inflation from the nominal cost of

capital.

Section 2 Risk and Return. An investors actual

return is the percentage change in price

Risk Variability or Volatility of Returns, Var

(R). We assume that Returns follow a Normal

Distribution.

Var(R).

E(R)

What do we mean by Risk? The risk reflects the

distribution (spread) of expected future

returns. Investors are assumed to be risk-averse

(dont like risk). The higher the spread (risk),

the higher the required return gt current price

adjusts to reflect this. Risk.

Returns

A

B

A

B

Time

B is riskier than A.

Risk Aversion. Investors prefer more certain

returns to less certain returns.

U

Wealth

150

100

200

Risk Averse Investor prefers 150 for sure than a

50/50 gamble giving 100 or 200.

Portfolio Analysis. Two Assets Investor has

proportion a of Asset X and (1-a) of Asset Y.

Combining the two assets in differing proportions.

E(R)

Portfolio of Many assets Risk Free Asset.

E(R)

Efficiency Frontier.

M

.

X

All rational investors have the same market

portfolio M of risky assets, and combine it with

the risk free asset. A portfolio like X is

inefficient, because diversification can give

higher expected return for the same risk, or the

same expected return for lower risk.

The Effect of Diversification on Portfolio

Variance.

Number of Assets.

An assets risk Undiversifiable Risk

Diversifiable Risk Market Risk Specific

Risk. Market portfolio consists of

Undiversifiable or Market Risk only.

Summary of Risk and Return Investors are assumed

to be risk averse. They combine assets to

diversify (reduce) risk. The more assets, the

lower the specific risk. The market portfolio

diversifies away all specific risk, and contains

all assets in the right proportions.

Implications for Investors. Current share prices

(which affect expected returns) are such that the

market only rewards investors for holding market

risk, not specific risk. Implications for

Individual Firms. Cost of Capital

(Investors required return) should only reflect

Market Risk (Beta CAPM).

- Section 3 Cost of Capital.
- Investors Required Return on their investment in

a company. - Cost Of Debt Coupon Rate.
- Cost of Equity.
- 2 methods to estimate cost of equity- Capital

Asset Pricing Model (CAPM), and Dividend

Valuation Model (DVM). - CAPM.

(beta) is a measure of risk.

CAPM shows the higher the risk, the higher the

required return.

What do we mean by Risk? The risk reflects the

distribution (spread) of expected future

returns. Investors are assumed to be risk-averse

(dont like risk). The higher the spread (risk),

the higher the required return. Risk.

A

B

A

B

Time

B is riskier than A.

Risk Aversion. Investors prefer more certain

returns to less certain returns.

U

Wealth

150

100

200

Risk Averse Investor prefers 150 for sure than a

50/50 gamble giving 100 or 200. He will require

a higher return to take the gamble Hence CAPM.

CAPM.

E(r)

E(rm)

1

Beta is a measure of Undiversifiable

Risk. Investors can hold a portfolio of shares-

this diversifies away some of the risk. What

remains is undiversifiable. From Companys point

of view, cost of equity is the required return

for the shareholders, given the companys

undiversifiable risk.

Estimating Cost of Equity Using Regression

Analysis. We regress the firms past share price

against the market.

Dividend Valuation Model.

The Cost of Equity is the Investors required

return, and affects current market

price. Interchangeability- Given current market

price and expected cashflows, we can estimate

cost of equity, or, given cost of equity and

expected cashflows, we can calculate market value

of equity.

Section 4 Capital Structure and Firm

Value. Value of the firm Discounted Value of

future cashflows available to the providers of

capital. Value of the firm Value of Equity

Value of debt.

where

Miller- Modigliani Irrelevance Theorem.

Two firms, identical cashflows, same risk, but

one firm is unlevered, the other is levered.

Irrelevance Theorem Without Tax, Firm Value is

independent of the Capital Structure.

K

K

Without Taxes

With Taxes

D/E

D/E

V

V

D/E

D/E

Comparing MM and CAPM.

Type Of Capital CAPM Equation MM Equation

Debt

Unlevered Equity

Levered Equity

WACC

Capital Structure Irrelevance without

taxes. Example A firm has annual NCF 100K.

(cashflow is a perpetuity.) Risk free rate rf

7. E(rm) 17. Debt/TA 20. Cost of levered

equity (from CAPM) 12. WACC 11. V

100/0.11 909K. Now it changes its capital

structure to Debt/TA 35. Levered Beta will

change, to 0.61 gt cost of levered equity 13.2

gt WACC 11 gt V 909K.

Example Firm A current capital structure Debt/

TA 20. Risk free rate 7. Tax rate 50.

Systematic risk of firms equity,

A. Change Capital Structure, and take on new

project of same operating risk as current

risk. new project has 9.25 expected return. What

is firms current WACC, and new WACC? Should it

take new project?

- Solution
- Calculate current cost of equity, using CAPM.
- Ke .07 0.17-.070.5 0.12.
- 2. Therefore, current WACC 10.3.

3. Calculate unlevered cost of equity. From MM

4. Calculate new WACC using MM New WACC

9.44. Therefore, firm should not take new

project, even at 35 debt.

B. Comparing projects with different

risks. Project 1 required date 0 investment

100, Expected NCF at date 1 135, Systematic

risk, Project 2 required date 0 investment

100, Expected NCF at date 1 130, Systematic

risk, Solution Project 1 Cost of Unlevered

Equity for the new project, using CAPM

19. WACC for the new project, at 20 debt, using

MM 17.1 gt NPV 15.29. Project 2 Cost of

unlevered equity 13. WACC at 20 debt, 11.7

gt NPV 16.39. Select Project 2.

- Although project 1 has a higher return than

project 2, it is also riskier. Investors require

a higher return for project 1. - So, project 2 is selected.
- Capital Budgeting- each project must be evaluated

at a cost of capital reflecting - Business Risk.
- And Financial Leverage.

Separability of Financing and Investment

Decisions. Implication of MM Irrelevance Theorem

A firms financing decision is separate from

its investment decision. Pie Model of firm value.

D

Equity

DEBT

E

MM said it does not matter how you slice the pie

between debtholders and equity holders- total

size of pie is the same.

Combining Tax Relief and Debt Capacity

(Traditional View).

K

V

D/E

D/E

Trade-Off View of Optimal Capital Structure.

V

Eg Agency Costs/ signalling

D/E

K

D/E

Optimal Capital Structure. Under MM irrelevance,

value of firm is independent of capital

structure. Capital structure does not

matter. Reasons for Optimal Capital

Structure. Taxes. Bankruptcy Costs. Debt Capacity

(traditional view). Agency Costs (Selfish

Manager). Signalling. We provide an overview of

Agency Costs and signalling - will be covered in

depth in the 4th Year Course.

- MM Irrelevance Theorem- Firm Value and WACC

independent of Capital Structure- Capital

Structure does not matter- Pie Model. - Problem No prescription to firms on how to

finance projects. - Introduce tax relief on debt gt 100 debt!
- Personal Taxes.
- Bankruptcy Costs.
- Traditional View.

- MM Irrelevance Theorem- Firm Value and WACC

independent of Capital Structure- Capital

Structure does not matter- Pie Model. - Problem No prescription to firms on how to

finance projects. - Introduce tax relief on debt gt 100 debt!
- Personal Taxes.
- Bankruptcy Costs.
- Traditional View.

Agency Costs (Selfish Manager). Jensen and

Meckling (1976). If firm issues equity (reduced

managerial ownership of firm value), Manager

pursues private benefits (private jet, plush

offices, time off to play golf), reducing firm

value. -If firm issues debt, manager has

incentive to take risky projects

(risk-shifting). Trade-off Optimal Capital

Structure.

V

D/E

D/E

Agency Costs (continued). Hart (1984)- Effort

Level. Equity holders are soft- Manager can

reduce effort. Debt holders can liquidate the

firmgt Bankruptcy gt manager losing job. This

threat may lead to manager working harder gt

Increasing firm value. Therefore, increasing debt

increases firm value.

Agency Costs- Continued. Free cashflow (Jensen

1986). -Managers may have pet negative NPV

projects. Equity gt free cashflow gt managers

can take these bad projects gt firm value

falling. Debt gt reduces free cashflow. Managers

cannot take the bad projects gt Firm value

rises. - Important in Mergers- See 4th year

course.

Asymmetric Information. Manager has inside

information. Issuing debt or equity may reveal

this information to the market. Myers-Majluf. -Fir

m has 50/50 chance of good or bad news. Market

values this firm at an average. Then Manager

observes this news market does not. If bad news

arrives, firm is currently overvalued in the

market manager will issue shares This signals

bad news, and share price falls. If Good news

arrives, firm is undervalued in the market, and

manager will not issue shares. Therefore, Issuing

equity signals bad news, firm value falls.

Asymmetric Information (continued). Ross (1977)-

Debt has bankruptcy threat. Manager has

compensation based on firm value, but is

penalised financially if firm goes

bankrupt. Market cannot observe whether manager

is good or bad. Good manager issues debt- signals

that he is not too worried about bankruptcy

therefore, firm value rises. Bad Manager is

worried about bankruptcy- does not issue debt.

Firm Value falls. Empirical Evidence- Issuing

equity causes firm value to fall- Debt causes

firm value to rise- contrary to MM. Agency Costs

and Signalling are explored in more detail in 4th

YR.

Section 5 Dividend

Policy. Assume All equity firm. Value of Firm

Value of Equity discounted value of future

cashflows available to equity holders

discounted value of dividends (if all available

cashflow is paid out).

If everything not reinvested is paid out as

dividends, then

Miller Modiglianis Dividend Irrelevance.

MM used a source and application of funds

argument to show that Dividend Policy is

irrelevant

Source of Funds Application of Funds

-Dividends do not appear in the equation. -If the

firm pays out too much dividend, it issues new

equity to be able to reinvest. If it pays out too

little dividend, it can use the balance to

repurchase shares. -Hence, dividend policy

irrelevant. -Key is the availability of finance

in the capital market.

Example of Dividend Irrelevance using Source and

Application of Funds. Firm invests in project

giving it NCF 100 every year, and it needs to

re-invest, I 50 every year. Cashflow available

to shareholders NCF I 50. Now, NCF I

Div NS 50. If firm pays dividend of 50, NS

0 (ie it pays out exactly the cashflow available

no new shares bought or sold). If firm pays

dividend of 80, NS -30 (ie it sells new shares

of 30 to cover dividend). If firm pays dividend

of 20, NS 30 (ie it uses cashflow not paid out

as dividend to buy new shares). In each case, Div

NS 50.

Gordon Growth Model. Where does growth come

from?- retaining cashflow to re-invest.

Constant fraction, K, of earnings retained for

reinvestment. Rest paid out as dividend. Average

rate of return on equity r. Growth rate in

cashflows (and dividends) is g Kr.

Example of Gordon Growth Model.

How do we use this past data for valuation?

Gordon Growth Model

(Infinite Constant Growth Model). Let

- Finite Supernormal Growth.
- Rate of return on Investment gt market required

return for T years. - After that, Rate of Return on Investment Market

required return.

If T 0, V Value of assets in place

(re-investment at zero NPV). Same if r

Examples of Finite Supernormal Growth.

T 10 years. K 0.1.

- Rate of return, r 12 for 10 years,then 10

thereafter.

B. Rate of return, r 5 for 10 years,then 10

thereafter.

Comparison of Gordon Growth and MM

Irrelevance. A. In MM irrelevance, NCF I is

fixed each period. Dividends and NS balance out.

Capital freely available. B. In Gordon Growth,

NCF (1-K) NCF I Divs. No New

shares. Dividends affect reinvestment I, which

affects growth and value. Another School of

Thought considers the signalling properties of

dividends this will be covered in the 4th year

course.

Section 6 Options as Financial Building

Blocks. A call option gives the holder the right

(but not the obligation) to buy shares at some

time in the future at an exercise price agreed

now. A put option gives the holder the right (but

not the obligation) to sell shares at some time

in the future at an exercise price agreed

now. European Option Exercised only at maturity

date. American Option Can be exercised at any

time up to maturity. For simplicity, we focus on

European Options.

- Factors Affecting Price of European Option (c).
- -Underlying Stock Price S.
- -Exercise Price X.
- Variance of of the returns of the underlying

asset , - Time to maturity, T.

The riskier the underlying returns, the greater

the probability that the stock price will exceed

the exercise price. The longer to maturity, the

greater the probability that the stock price will

exceed the exercise price.

Combining options, graphic presentation. Buying a

Call Option.

Selling a put option.

Selling a Call Option.

Buying a Put Option.

Long in Stock

Buy a Bond

Sell a Bond

Short in Stock

S P B C. S P C B.

Other Combinations Spread, Straddle, Straps and

strips. See Exercise.

Equity as a Call Option. Black and Scholes

pointed out that equity is a call option on the

value of the levered firm. If Value of firm

exceeds face value of debt (exercise price of

call option), equityholders pay the exercise

price, and gain the increase in value. If value

of firm is less than face value of debt, option

is not exercised. Risky debt risk-free debt

put option (B P).

Building Blocks. S P B C for Option. V

P B S for levered firm. gt V (B P)

S. S Max 0, V D . Equity call

option. B P Min V, D . Risky debt risk

free debt put option. Therefore, V ( B P )

S.

S

B-P

V

V

D

D

Important Implications for Firm. Equity is a call

option Value of Equity in creases with

risk. Value of Put option increases with risk

Therefore value of debt decreases with

risk. After all, Equity holders have limited

liability, and S Max 0, V D . B P

Min V, D . With (B P) S V. Therefore,

if S increases, ( B P) decreases. Equity

holders will want to choose riskier projects.

Pricing Call Options Binomial Approach.

Cu 3

uS24.00

q

q

c

S20

1- q

1- q

dS13.40

Cd0

- S 20. q0.5. u1.2. d.67. X 21.
- 1 rf 1.1.
- Risk free hedge Portfolio Buy One Share of Stock

and write m call options. - uS - mCu dS mCd gt 24 3m 13.40.
- M 3.53.
- By holding one share of stock, and selling 3.53

call options, your payoffs are the same in both

states of nature (13.40) Risk free.

Since hedge portfolio is riskless

1.1 ( 20 3.53C) 13.40. Therefore, C

2.21. This is the current price per call option.

The total present value of investment 12 .19,

and the rate of return on investment is 13.40 /

12.19 1.1.

- Application of Options- Convertible Debt.
- Convertible Debt gives the holder the right (but

not the obligation) to convert bonds into equity

at a future date. - Convertible debt is a combination of straight

debt plus a call option. - We saw that straight debt risky debt a put

option. - CD D C B P C .
- Implication Value of Convertible debt increases

with risk of firms cashflows, and time to

maturity. - -See CD exercise.
- more detailed analysis of convertible debt in 4th

year advanced finance course.