Corporate Finance

BBA 2- 2001/2 Semester 2.

1. Investment Appraisal.

2. Risk and Return/ Portfolio Management.

3. Cost of Capital.

4. Capital Structure and Firm Value.

5. Dividend Policy.

6. Financial Distress and Ratio Analysis.

7. Options.

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 => business risk.

Dep’n is not a cash flow – market Value of firm determined by cashflow.

Debt financing (fixed interest payments) => Financial Risk.

Net Income is the residual stream of earnings owned by shareholders => 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.

=> Net Income – Dividends = New Investment – New Equity = Retained Earnings

Management’s 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.

......)1()1(1 3

32

21

r

X

r

X

r

XINPV

r = discount Rate, cost of capital, or Investors’ Required Return.

X is net cashflow.

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.

......)1()1(1 3

32

21

r

X

r

X

r

XINPV

.r

XINPV

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?

$000 2000 2001 2002 2003 2004 2005 SALES 14000 16000 18000 20000 22000 90000

VARIABLE COSTS -9800 -11200 -12600 -14000 -15400 -63000

OPERATING EXPENSES -200 -200 -200 -200 -200 -1000

EQUIPMENT COSTS -15000 -15000

CASHFLOWS -15000 4000 4600 5200 5800 6400 11000

DF @ 12% 1.00 0.893 0.797 0.712 0.636 0.567

NPV -15000 3571 3667 3701 3686 3632 3257

19.75 1.00 0.84 0.70 0.58 0.49 0.41

IRR = 19.75% -15000 3340 3208 3028 2820 2599 -4

DO WE INVEST IN THIS NEW PROJECT?

NPV > 0.

COST OF CAPITAL (12%) < IRR (19.75%).

Note that if the NPV is positive, then the IRR exceeds the Cost of Capital.

NPV £m

Discount Rate %

12 %

3.3m

19.7%0

MUTUALLY EXCLUSIVE PROJECTS.YEAR A B C D DF: 10%

0 -1000 -1000 -1000 -1000 11 100 0 100 200 0.9092 900 0 200 300 0.8263 100 300 300 500 0.7514 -100 700 400 500 0.6835 -400 1300 1250 600 0.621

PAYBACK METHOD:

PROJECT A: 2 YEARS SELECT PROJECT APROJECT B: 4 YEARSPROJECT C: 4 YEARSPROJECT D: 3 YEARS

NPV:

PROJECT A: -407PROJECT B: 511PROJECT C: 531 SELECT PROJECT CPROJECT D: 519

IRR

PROJECT A: -200%PROJECT B: 20.9%PROJECT C: 22.8%PROJECT D: 25.4% SELECT PROJECT D

Discount Rate10% 22.8%

PROJ C

531

PROJ D

519

25.4%

COMPARING NPV AND IRR

Select Project with higher NPV: Project C.

NPV

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:

.117.111.1000,300

000,17512.1

000,300

000,125PVI

Project 1:

10.10.1300000

10000015.1

300000

200000PVI

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:-

.)1( depTNOINCF

Treatment of depreciation.

$000 2000 2001 2002 2003 2004 2005 SALES 14000 16000 18000 20000 22000 90000

VARIABLE COSTS -9800 -11200 -12600 -14000 -15400 -63000

OPERATING EXPENSES -200 -200 -200 -200 -200 -1000

EQUIPMENT COSTS -15000 -15000DEPRECIATION -3000 -3000 -3000 -3000 -3000NOI -15000 1000 1600 2200 2800 3400 11000NOI AFTER TAX 800 1280 1760 2240 2720 8800ADD BACK DEPN (= NCF) 3800 4280 4760 5240 5720 23800

DF @ 12% 1.00 0.893 0.797 0.712 0.636 0.567 -15000 3393 3412 3388 3330 3246 1769

NPV -15000 3266 3162 3022 2859 2683 -8 16.35 1.00 0.86 0.74 0.63 0.55 0.47

More Capital Budgeting Topics.

Projects with different lives.

-We assume that projects are replicated at constant scale.

]1)1(

)1()[(),(

N

N

k

kNNPVNNPV

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.

01 )1(

Ik

NCFPVN

N

ttt

K is the nominal cost of capital. We require real cost of capital, where

).1()1)(1( kInfr

Either add inflation to the cashflow estimates, or remove inflation from the nominal cost of capital.

Risk and Return.

An investor’s actual return is the percentage change in price:

100*1

t

tt

P

PPR

Risk = Variability or Volatility of Returns, Var (R).

We assume that Returns follow a Normal Distribution.

E(R)

Var(R).

./)....)( 21 TRRRAverageRE T

What do we mean by Risk?

The risk reflects the distribution (spread) of expected future returns.

Investors are assumed to be risk-averse (don’t like risk).

The higher the spread (risk), the higher the required return => current price adjusts to reflect this.

Risk.

A

B

B is riskier than A.

A

B

Time

Returns

Risk Aversion.

Investors prefer more certain returns to less certain returns.

Wealth

U

150100 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.

).()1()(.)( YXp REaREaRE

).,(.2)(.)1()(.)( 22 yxCovabYVaraXVaraRVar p

Combining the two assets in differing proportions.

E(R)

Portfolio of Many assets + Risk Free Asset.

E(R)

*

*

* * *

*fr

M.Efficiency Frontier.

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.

X

The Effect of Diversification on Portfolio Variance.

P

Number of Assets.

An asset’s 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 (Investor’s required return) should only reflect Market Risk – (Beta – CAPM).

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.

.])([)( fmf rrErrE

(beta) is a measure of risk.

CAPM shows the higher the risk, the higher the required return.

.])([)( fmf rrErrE CAPM.

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 Company’s point of view, cost of equity is the required return for the shareholders, given the company’s undiversifiable risk.

E(r)

1

E(rm)

Estimating Cost of Equity Using Regression Analysis.

We regress the firm’s past share price against the market.

.

.

i

imii

b

rbar

ir

mr

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.

.

.)1(

1

gK

DivV

gV

gDivK

ee

e

oe

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.

V

VTKVKWACC

WACC

TNCF

K

DK

K

NIVVV

ddee

d

d

ede

).1(.

)1(

where;

Miller- Modigliani Irrelevance Theorem.

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)1(

DEC

CUL

EC

U

VVWACC

TNCFBTVV

VTNCF

V

Irrelevance Theorem: Without Tax, Firm Value is independent of the Capital Structure.

Two firms, identical cashflows, same risk, but one firm is unlevered, the other is levered.

K

D/E

K

D/E

V

D/E D/E

V

Without Taxes With Taxes

Comparing MM and CAPM.

Type Of Capital CAPM Equation MM Equation

Debt

Unlevered Equity

Levered Equity

WACC

fd rK

Ufmf rrEr ])([

Lfmfe rrErK ])([

S

BTKK CbS )1)((

)1(SB

BTWACC C

V

VTKVK ddee ).1(.

UCL S

BT ])1(1[

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 => cost of levered equity = 13.2% => WACC = 11% => V = £909K.

.5.0L

Example:

Firm A: current capital structure: Debt/ TA = 20%.

Risk free rate = 7%.

Tax rate = 50%.

Systematic risk of firm’s equity, .5.0L

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 firm’s current WACC, and new WACC? Should it take new project?

3. Calculate unlevered cost of equity.

From MM: %44.11

4. Calculate new WACC using MM: New WACC = 9.44%.

Therefore, firm should not take new project, even at 35% debt.

Solution:

1. Calculate current cost of equity, using CAPM.

Ke = .07 + [0.17-.07]0.5 = 0.12.

2. Therefore, current WACC = 10.3%.

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% => NPV = £15.29.

Project 2: Cost of unlevered equity = 13%.

WACC at 20% debt, = 11.7% => NPV = £16.39.

Select Project 2.

2.1U

6.0U

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 firm’s financing decision is separate from its investment decision.

Pie Model of firm value.

DEBT DE

Equity

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).

D/E D/E

V

K

Trade-Off View of Optimal Capital Structure.

V

D/EK

D/E

Eg: Agency Costs/ signalling

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.

Agency Costs and signalling are beyond the scope of this course, and will be covered in the 4th Year Course.

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).

0

0

0

0

)1(

)1(

ttt

tt

INCFV

DivV

t

t

If everything not reinvested is paid out as dividends, then

Miller Modigliani’s Dividend Irrelevance.

NSDivINCF

DivINSNCF

tttt

tttt

Source of Funds = Application of Funds

MM used a source and application of funds argument to show thatDividend Policy is irrelevant:

11

0)1()1( tttt

tttt INCFNSDiv

V

1

0)1(tttt INCF

V

-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.

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0g

kNCFg

DivV

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.£K 19x5 19x6 19x7 19x8 19x9 Average Profits After Tax (NCF) 2500 2760 2635 2900 3100Retained Profit (NCF.K) 1550 1775 1600 1800 1900

Dividend (NCF(1-K)) 950 985 1035 1100 1200

Share Capital + retentionsB/F 30000 31550 33325 34925 36725C/F (= BF + Retained Profit) 31550 33325 34925 36725 38625

Retention Rate K 0.62 0.64 0.61 0.62 0.61 0.62r on opening capital 0.083 0.087 0.079 0.083 0.084 0.083

g = Kr = 0.05.

How do we use this past data for valuation?

Gordon Growth Model (Infinite Constant Growth Model).

Let

.1800005.12.0

1260

.1260)05.1(1200

.1200)1(

).1)(1()1()1(

0

1

00

0011

V

Div

KNCFDiv

gKNCFgDivKNCFDiv

%12

Finite Supernormal Growth.

-Rate of return on Investment > market required return for T years.

-After that, Rate of Return on Investment = Market required return.

)1(

)(.. 1

10

rTNCFK

NCFV

If T = 0, V = Value of assets in place (re-investment at zero NPV).

Same if r = .

Examples of Finite Supernormal Growth.

%.10

.1001

NCF

T = 10 years. K = 0.1.

A. Rate of return, r = 12% for 10 years,then 10% thereafter.

1018)1.01(1.0

)1.012.0(10).100.(1.0

1.0

1000

V

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

955)1.01(1.0

)1.005.0(10).100.(1.0

1.0

1000

V

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.

Ratio Analysis and Financial Distress.

-Uses financial data from the balance sheet (point in time) and income statements (flows).

Types of Financial ratios.

Liquidity => Short term solvency.

Gearing => firm’s reliance on debt finance.

Activity ratios => use of resources.

Profitability ratios.

Valuation ratios - ability of management to create market value in excess of investment cost.

Goal - maximise firm value and shareholder wealth.

Ratio Comparison.Walker Wilson and Industry.

WALKER INDUSTRYWILSON

Liquidty Ratios:

Current Ratio 2.3 2.5 SatisfactoryQuick Ratio 1.3 1 Good

Gearing Ratios:Debt/Assets 50% 33% PoorTimes Inerest Earned 3.9 8 Poor

Activity Ratios:Stock Turnover: 10 times 9 times SatisfactoryDebtor days 24 days 20 days Satisfactory

Profitability ratios:ROA 8.10% 11.40% Poor

Valuation Ratios:Price/earnings 1985 7.5 8 FairMarket/book 0.9 1 Poor

Uses and Limitations of Ratios.

-Useful to the financial manager and outside credit analysts.

-Useful in Security analysis - Valuation and long run profitability.

Limitations:

- Accounting data- interpretation and manipulation.

- Each ratio is analysed in isolation.

- judgements.

-profitability measures do not consider risk or timing of cashflows.

Predicting Corporate Bankruptcy: The Z score Model. Altman (1968).

-Altman’s model combines ratios into a meaningful predictive model of bankruptcy- Discriminant Analysis.

Discriminant Function:

XXXXXZ 54321 0.16.03.34.12.1

X= Working Capital/ Total Assets, Retained Earnings/ Total Assets, EBIT/Total Assets, Mkt value of equity/ book value of debt, Sales/Total Assets.

Use of the Z-Score in predicting bankruptcy.

Z < 2.675: firm has 95% probability of bankruptcy within 1 year.

However: 1.81 < Z < 2.99: Grey area.

Z < 1.81: Bankruptcy.

Z > 2.99: Non bankruptcy.Bankrupt Non-

Bankrupt

X1 -6.1% 41.4%X2 -62.6% 35.5%X3 -31.8% 15.4%X4 40.1% 247.7%X5 150% 190%

Z Score: -2.6 4.9

Examples of Use of Z Score Model.

1. RWJ: US Composite Corporation.

- Company trying to increase its credit from the Bank.

- Z Score Model => Z = 2.9.

- Bank concludes that Company is a good credit risk.

2. WC: Chrysler Corporation: 1979, Z = 1.512.

=> Likely to go bankrupt.

= However, Z value not too bad.

- fundamental analysis of Chrysler’s position required.

- Chrysler was having problems, but could be rescued.

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.

.0,0,0,02

T

cc

X

c

S

c

2

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.

S

WSelling a put option.

Selling a Call Option. Buying a Put Option.

S

WLong in Stock

Short in Stock

Buy a Bond

Sell a Bond

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.

=> 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.

DV

B-P

D

S

V

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.

S=20

q

1- q dS=13.40

uS=24.00

S = £20. q=0.5. u=1.2. 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 => 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.

cq

1- q

Cu = 3

Cd=0

Since hedge portfolio is riskless:

.))(1( uf mcuSmcSr

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 firm’s cashflows, and time to maturity.

-See CD exercise.

-more detailed analysis of convertible debt in 4th year advanced finance course.