Advanced Corporate Finance

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1 Advanced Corporate Finance. Introduction r. Benjamin Lorent We thank rof. Kim OOSTERLINCK and rof. André FARBER for kindly sharing initial teaching material.

2 r. Benjamin Lorent Who am I? rofessor of Finance (SBS-EM/UMons/Luxembourg/Switzerland) Insurance (Vietnam) Research interests ) Insurance Regulation (Solvency II/hD) ) Asset Management Finance background SBS-EM + Actuarial Sciences Axa Consultant for Insurance & Financial Services Companies blorent@ulb.ac.be

3 Course Outline (/4) Theory (4h) + Exercises (h) + Textbooks and references Material available on rerequisites: Accounting, Microeconomics and Finance 0 => Familiar with V, Bonds and Stocks Valuation, NV, IRR rules, ortfolio theory, CAM and Option pricing (binomial model)

4 Course Outline (/4) Reference books: David Hillier, Stephen Ross, Randolph Westerfield, Jeffrey Jaffe, Bradford Jordan, Corporate Finance European edition, 3 rd edition, 03 Brealey, R., Myers, S. and Allen, F. (BMA), rinciple of Corporate Finance, th ed., McGraw-Hill, 04 (en français, rincipe de Gestion Financière). Berk, J. and. De Marzo, Corporate Finance et version française Finance d entreprise, 3 rd edition, earson, 04 Bodie Zvi, Kane Alex, Marcus Alan J., (0), Investments and ortfolio Management, Global Edition, McGraw Hill,

5 Course Outline (3/4) Second course in finance. Objectives, understand: How to move from accounting to cash flows The impact of capital structure on investment decisions Value of the firm (Modigliani-Miller) Optimal capital structure Raising capital and going public (IO, SEO) Risky debt

6 Course Outline (4/4) Wooclap Exercises Sessions ( hours): 3 teaching Assistants (groups will be provided later): Nicolas Degive, Nicolas Dhaene and Frederic van arijs Material on the website Exam Theory and Exercises Formula Sheet The Course is in ENGLISH => no dictionary Exam is HARD => be precise when answering and be sure that you master basic notions of finance! Examples are posted on the website

7 Roadmap. Introduction and Review of supposedly known concepts. From Accounting to Cash Flows 3. Capital Structure 4. roject Valuation using the Wacc 5. Financial Options (A review) 6. Real Options 7. Market Efficiency 8. Raising Capital and Going ublic 9. Long-Term Bonds 0. Insurance Business

8 Beware, Beware, Beware This session will provide a short wrap-up If you never had a finance class before (or not enough): WORK To help you here are the hillier et al. (03) chapters to be seen BEFORE this course: At least chapters:,, 4, 5, 6, 7, 0 and If not it is up to YOU to make up for this

9 A short review Financial valuation most of the time relies on the discounting concept Decisions to invest or not in a project are then made based on the NV rule (invest if NV > 0). Even though other methods exist (IRR, ayback, etc.) they do not always yield a proper result => stick to NV!!! Choosing the proper discount rate to use is not easy (more on this later). Besides one must take into account compounding intervals

10 A short review One may also wish to benefit from shortcut formulas to compute V Discounting future cash flows is also at the basis of bonds and equity valuation The discount rate should take risk into account Capital Asset ricing Model (CAM)

11 Discounting: Time value of Money 0 Case C ( 00) Capitalizing? 00 r Future value C ( 00) Case resent value 00 r 00 DF? Discounting

12 With Cash Flows 0 n- n C ( 00) time Case Future value C r C0 r r 0 C 0... r r C? 0 r n Case resent value C? C C n n n n r r r n n r r r C n... C n CF ( 00)

13 The discount factor How much would an investor pay today to receive C t in t years given market interest rate r t? We know that 0 (+r t ) t 0 in t = t Hence V (+r t ) t = C t V = C t /(+r t ) t = C t DF t The present value of a future cash flow is obtained by multiplying this cash flow by a discount factor (or present value factor) DF t The general formula for the t-year discount factor is: DF t ( r t ) t

14 Net resent Value (NV) Decide whether it is worth investing in a project Rule => it should bring value. To compare the cash flows arriving at dates => discount the cash flows Cash flows: C 0 C C C t C T t-year discount factor: DF t = /(+r t ) t NV = C 0 + C DF + + C t DF t + + C T DF T Usually C 0 < 0 since it often represents the investment made for the project

15 Example Suppose constant r = 0% t 0 3 Cash flow Discount Factor resentvalue NV 6.9 In this case the investment is worth undertaking NB: an alternative method could have been to compute the Net Future Value (NFV)

16 Net resent Value Internal Rate of Return The Internal Rate of Return is the discount rate that sets the NV equal to zero IRR 0% 5% 0% 5% 0% 5% 30% 35% 40% 45% 50% Discount rate

17 Internal Rate of Return Reinvestment assumption (in a multiple period setting): the IRR calculation assumes that all future cash flows are reinvested at the IRR Disadvantages: Does not distinguish between investing and financing projects IRR may not exist or there may be multiple IRR roblems with mutually exclusive investments Advantages: Easy to understand and communicate

18 Compounding Interval Up to now, interest paid annually If n payments per year, compounded value after year [+(r/n)] n where r = stated interest rate (without the compounding effect of interest rate). Example: Monthly payment : r = %, n = Compounded value after year : ( + 0./) =.68 Effective Annual Interest Rate :.68% Continuous compounding: [+(r/n)] n e rn (e=.783) Example : r = % e % =.75 Effective Annual Interest Rate :.75%

19 Shortcut Formulas Assuming constant r! Constant perpetuity: C t = C for all t r>0 V C r Growing perpetuity: C t = C t- (+g) r>g t = to V C r g Constant annuity: C t =C t= to T r>0 V C r ( ( r) T ) Growing annuity: C t = C t- (+g) r>g t = to T V C r g ( ( ( g ) r) T T )

20 Bond valuation Zero-Coupon one bullet payment (= face value or nominal value) at maturity T V ( r) T assuming face value = Level coupon bond, paying a yearly coupon C C C C 00 T 0 = T + T = C Ar r ( + r) ( + r) ( + r) DF T With A being the annuity factor = present value of to be received during T years. NB: Inverse relationship between interest rate r and Bond rice (measured by the duration)!

21 Stock (Equity) valuation Dividend Discount Model (DDM): -year horizon 0 = div + + r e Expected price r e = expected return on shareholders equity = Risk-free interest rate + risk premium Example: Assume r e = 0%, expected dividend = and expected price = Dividend yield = /47.7 = 4.3% Rate of capital gain = ( )/47.7 = 5.77%

22 DDM: where does the expected stock price come from? Expected price at forecasting horizon depends on expected dividends and expected prices beyond forecasting horizon To find, use -year valuation formula again: = div + + r e Current price can be expressed as: 0 = div + r e + div ( + r e ) + ( + r e ) General formula: 0 div div = + + re ( + re ) div ( + r T e ) T + ( + T r e ) T

23 DDM - general formula With infinite forecasting horizon: div div + ) ( + r ) div 3 + ( + r ) div t ( + r ) = 0 ( + 3 t re e e e +... Forecasting dividends up to infinity is not an easy task. So, in practice, simplified versions of this general formula are used. One widely used formula is the Gordon Growth Model based on the assumption that dividends grow at a constant rate. DDM with constant growth g Note: g < r e 0 = r div e - g

24 Risk-Return and diversification Risk linked to return Benefits from diversification, let us consider a portfolio of two stocks (A,B) Characteristics: Expected returns : Standard deviations : Covariance : R, A R B, ortfolio: defined by fractions invested in each stock X A, X B X A + X B = A AB B AB A B Expected return on portfolio: R X A R A X B R B Variance of the portfolio's return: X A A X A X B AB X B B

25 Covariance and correlation Covariance: Statistical measure of the degree to which random variables move together AB cov( R A, R B ) E[( R A R A )( R B R B )] Correlation AB Corr ( R, R ) A B Cov ( R A A, R B B ) Covariance divided by product of standard deviations Covariance and correlation have the same sign ositive : variables are positively correlated Zero : variables are uncorrelated Negative : variables are negatively correlated The correlation is always between and +

26 ortfolio with many assets ortfolio composition : (X, X,..., X i,..., X N ) X + X X i X N = Expected return: R X R X R... X N R N Risk: Note: N terms for variances N(N-) terms for covariances Covariances dominate j X j j i X X i j ij ji i j X i X j ij

27 Covariance domination Var Cov Cov Cov Cov Cov Var Cov Cov Cov Cov Cov Var Cov Cov Cov Cov Cov Var Cov Cov Cov Cov Cov Var

28 Equally weighted portfolio Consider the risk of an equally weighted portfolio of N identical stocks: R j R,, Cov ( R, R ) j i j cov Equally weighted: X j N Variance of portfolio: N ( N ) cov If we increase the number of securities? Variance of portfolio: cov N

29 In practice Diversification gains already close to maximum with n = 0 σ Unsystematic risk Systematic risk Diversification limit 0 n

30 Risk and CAM Discount rate should take risk into account Concept of opportunity cost Risk usually measured as the standard deviation of returns art of the risk may be reduced thanks to diversification (= unsystematic risk) The market only rewards the risk which cannot be diversified (= systematic risk) Capital-Asset ricing Model (CAM) R R R R ) F ( M F with i Cov ( R i ( R, R M M ) ) im M

31 This course Many questions remain unanswered How do we determine the Cash Flows to Discount? CAM provides some insights regarding the discount rate but how is it affected by the capital structure (% debt versus equity)? Is there such a thing as an optimal capital structure? How do we move from project valuation to company valuation? How do companies raise funds? Or go public? How do we value options in a broader setting? Are equity prices affected by behavioral elements? How do we deal with risky debt?

Advanced Corporate Finance Exercises Session 1 «Pre-requisites: a reminder»

Advanced Corporate Finance Exercises Session 1 «Pre-requisites: a reminder» Professor Kim Oosterlinck E-mail: koosterl@ulb.ac.be Teaching assistants: Nicolas Degive (ndegive@ulb.ac.be) Laurent Frisque