1. Corporate Finance
BBA /2 Semester 2.
Investment Appraisal.
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.

2. 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.

3. 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?

4. 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).

5. Source and Application of Funds
Source and Application of Funds. Net Income + New Equity = Dividends + New Investment. => Net Income – Dividends = New Investment – New Equity = Retained Earnings

6. 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.
r = discount Rate, cost of capital, or Investors’ Required Return.
X is net cashflow.

7. 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.

8. 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.

9. 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?

10. DO WE INVEST IN THIS NEW PROJECT?
NPV > 0.
COST OF CAPITAL (12%) < IRR (19.75%).

11. Note that if the NPV is positive, then the IRR exceeds the Cost of Capital.
NPV £m
3.3m
Discount Rate %
12 %
19.7%

12. MUTUALLY EXCLUSIVE PROJECTS.

13. Select Project with higher NPV: Project C.
COMPARING NPV AND IRR
NPV
531
519
10%
22.8%
25.4%
Discount Rate
PROJ D
PROJ C
Select Project with higher NPV: Project C.

14. Project 1 2 3 4 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

15. 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.

16. 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:-

17. Treatment of depreciation.

18. 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.

19. 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.

20. Risk and Return.
An investor’s 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)

21. Investors are assumed to be risk-averse (don’t like risk).
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.
Returns A B A B
Time
B is riskier than A.

22. Investors prefer more certain returns to less certain returns.
Risk Aversion.
Investors prefer more certain returns to less certain returns. U
Wealth
100
150
200
Risk Averse Investor prefers £150 for sure than a 50/50 gamble giving £100 or £200.

23. Two Assets: Investor has proportion a of Asset X and (1-a) of Asset Y.
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)

24. 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.

25. The Effect of Diversification on Portfolio Variance.
Number of Assets.
An asset’s risk = Undiversifiable Risk + Diversifiable Risk
= Market Risk + Specific Risk.
Market portfolio consists of Undiversifiable or Market Risk only.

26. 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).

27. 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.

28. Beta is a measure of Undiversifiable Risk.
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 Company’s point of view, cost of equity is the required return for the shareholders, given the company’s undiversifiable risk.

29. Estimating Cost of Equity Using Regression Analysis.
We regress the firm’s past share price against the market.

30. 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.

31. 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;

32. 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.

33. K
Without Taxes K
With Taxes
D/E
D/E V V
D/E
D/E

34. Type Of Capital CAPM Equation MM Equation Debt Unlevered Equity
Comparing MM and CAPM.
Type Of Capital
CAPM Equation
MM Equation
Debt
Unlevered Equity
Levered Equity
WACC

35. 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.

36. Example:
Firm A: current capital structure: Debt/ TA = 20%.
Risk free rate = 7%.
Tax rate = 50%.
Systematic risk of firm’s 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 firm’s current WACC, and new WACC? Should it take new project?

37. Solution:
Calculate current cost of equity, using CAPM.
Ke = [ ]0.5 = 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.

38. 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.

39. 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.

40. 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. 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.

41. Combining Tax Relief and Debt Capacity (Traditional View).K V
D/E
D/E

42. Trade-Off View of Optimal Capital Structure.
Eg: Agency Costs/ signalling
D/E K
D/E

43. 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.

44. 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

45. Miller Modigliani’s Dividend Irrelevance.
MM used a source and application of funds argument to show that
Dividend Policy is irrelevant:
Source of Funds = Application of Funds

46. -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.

47. 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.

48. Where does growth come from?- retaining cashflow to re-invest.
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.

49. Example of Gordon Growth Model.
How do we use this past data for valuation?

50. Gordon Growth Model (Infinite Constant Growth Model).
Let

51. Finite Supernormal Growth.
Rate of return on Investment > 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 =

52. 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.

53. 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.

54. 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.

56. 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.

57. 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:
X= Working Capital/ Total Assets, Retained Earnings/ Total Assets, EBIT/Total Assets, Mkt value of equity/ book value of debt, Sales/Total Assets.

58. 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.
Z Score:

59. 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 =
=> 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.

60. 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.

61. 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.

62. Combining options, graphic presentation.
Buying a Call Option.
Selling a put option.
Selling a Call Option.
Buying a Put Option.

63. Other Combinations: Spread, Straddle, Straps and strips. See Exercise.
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.

64. 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).

65. V + P = B + S: for levered firm. => V = (B – P) + S.
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. S
B-P V V D D

66. 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.

67. Pricing Call Options – Binomial Approach.
Cu = 3
uS=24.00 q q c
S=20
1- q
1- q
dS=13.40
Cd=0
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 =
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.

68. Since hedge portfolio is riskless:
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 / = 1.1.

69. 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.