Capital Structure Theory & Applications

Capital Structure Theory & Applications Ruben D. Cohen ruben.cohen@citi.com 0207 500 5793 Risk Architecture Citigroup, London 1

1. Introduction Background, Scope and Outline 2

Background What is capital structuring? Process of interchanging debt, equity and assets Why is it important? Enables one to optimize the value of a firm or its WACC by finding the best mix for the amounts of debt and equity on the balance sheet. Provides a signal that the firm is following proper rules of corporate finance to improve its balance sheet. This signal is central to valuations provided by market investors and analysts. Who is interested in it? Academics, because it is controversial and open ended Practitioners, because they use it for valuation, advisory and development and marketing of financial products & strategies 3

Scope Capital Structure Corporate Firms Financial Institutions No Default Risk (Classical M&M) With Default Risk No Default Risk With Default Risk Unconstrained Constrained 4

Outline 1. Introduction 2. Modigliani & Miller (paper 1) Derivation Implementation 3. Beta (paper 3) Definition Implementation within M&M (Hamada Equation) 4. Default risk & credit rating models 5. Incorporating default risk to get the OCS (paper 2) 6. Incorporating default risk into beta (paper 3) 7. Extending the OCS methodology to more ratios 8. Application to different scenarios M&A s Divestitures Share and debt issues and buybacks 9. Applying constraints (paper 4) 10. Case studies 11. Depository institutions (paper 5) 5

End Part 1 6

2. The Modigliani-Miller (M&M) Theorems Motivation & Methodology 7

Motivation Key Observation 1 EBIT [ EBIT Operating Income R D D ](1 T ) = or R (1 T ) = R D D (1 T ) + To debt holders E E R E E To equity holders Balance Sheet Firm s Value, D+E Income Statement EBIT Debt, D Equity, E Tax EBIT x (1-T) What if T = 100%? Discounted value of cash flows to bond and equity holders will be zero. Therefore, value implicit within IS will be ZERO! Does not match the firm s value of E + D from the BS. 8

Motivation Key Observation 2 Income Statement EBIT (1 T ) = R D D (1 T ) + EBIT R E E Tax EBIT x (1-T) R D D(1-T) R E E D(1-T) E Total Discounted Value derived from Income Statement 80 x (1-40%) + 52 = 100 Effectively, a capital of 100 is being used to operate a firm that s worth 132! Notion of efficiency appears in the ratio 100/132 9

Theory Key observations create a need to: 1. Reconcile the difference in valuations between the IS and the BS 2. Exploit the notion of efficiency in capital structure M&M achieves the 2 objectives Main assumptions - Aside from the typical, there are 3: 1. Simple corporate firm able to freely exchange generic debt, equity and assets 2. EBIT & Tax rate held constant as firm exchanges debt, equity and assets 3. No default risk, so that credit spread = 0 at all levels of leverage 10

The M&M Methodology Simplistic Derivation Income Statement Expected EBIT 20 Interest (at 5%) 4 EBT 16 Tax (at 40%) 6.4 Expected profit 9.6 Balance Sheet Assets 132 Debt 80 Equity 52 Total Debt & Equity 132 Income Statement Tax Paid EBIT EBIT x (1-T) R D D(1-T) R E E Total Discounted Value derived from Income Statement D x (1-T) + E operating capital 11

The M&M Methodology Proposition I Value implicit in the IS = D x (1-T) + E ( operating capital ) Total Firm s Value (FV) = D + E Reconciling Difference = D x T This difference is attributed to tax and debt. Leads to M&M s Proposition I In the absence of taxes, there are no benefits, in terms of value, to increasing leverage. In the presence of taxes, such benefits, by way of the interest tax shield, do accrue when leverage is introduced and/or increased. Could be exploited to increase the efficiency of the firm e.g. increase Tax, Debt or the product DT. Tax is difficult to control, but debt could be increased. 12

Operating capital The M&M Methodology Proposition II If FV = D + E And the value added due to debt = D x T Then the remainder, D x (1-T) + E, must represent the unlevered value of the firm and is a constant, equal to E 0 = V U Recall: EBIT(1-T) = R D D(1-T) + R E E R U EBIT(1 T ) D(1 T ) + E = RDD(1 T ) D(1 T ) + E + REE D(1 T ) + E Defining φ = D/E & solving for R E gives M&M s Proposition II R E = R U + ( R R )(1 T )φ U D 13

The M&M Methodology in Practice Creating the FV Curve Step 1 Question: Consider the firm has D = 80 and E = 52. It wants to issue enough equity to buy back all debt and completely delever. How is this done according to M&M? Answer: We know ΔV = D x T = 80 x 40% = 32. Therefore to delever completely, the value of the allequity firm should be 132 32 = 100. Achieved by issuing 48 in equity and selling off 32 in assets, totalling 80 - enough to buy back all debt. 14

The M&M Methodology in Practice Creating the FV Curve Step 2 Question: The firm is now fully debt free. It wants to borrow 20 to buy back some of its shares and, at the same time, purchase some assets. How is this done according to M&M? Answer: We know ΔV = D x T = 20 x 40% = 8, which raises the firm s value from 100 to 108. Therefore, with additional debt of 20 buy back 12 in equity and purchase 8 in assets. 15

The M&M Methodology in Practice A More Methodical approach Begin with the original financial statement Create table similar to the one below 1. Insert debt in increments 2. Populate with information that s readily available 16

The M&M Methodology in Practice A More Methodical approach Define WACC EBIT (1 T ) D + E = EBIT (1 T ) V + DT U ROE = Profit E and populate relevant cells 17

The M&M Methodology in Practice A More Methodical approach Calculate parameters for D = 0 Recall: at D = 0, all equity firm value E 0 = E + D(1-T) = 52 + 80*(1-40%) = 100 Insert in the appropriate row 18

The M&M Methodology in Practice A More Methodical approach Recall E+(1-T)D = 100 across all debt levels i.e. at D=20, E = 100-(1-40%)*20 = 88; D=40, E = 100-(1-40%)*40 = 76, etc. Streamline and automate the process * to finally populate all cells at different increments of D * If preferred, this could be done using the beta approach (Hamada s Equation). Either way, the results must be identical 19

The M&M Methodology Graphical Representation 120 100 80 60 40 20 0 Equity, E Debt, D 0 40 80 120 160 170 160 150 140 130 120 110 100 Value, E + D Leverage, 0 10 20 30 40 200% 150% ROE 13% 12% 11% WACC 100% 10% 9% 50% 0% Leverage, 0 10 20 30 40 8% 7% 6% Leverage, 0 10 20 30 40 20

Spreadsheet Demo M&M Methodology Demo spreadsheet M&M 21

End of Part 2 22

3. Beta 23

What is Beta? Defined as: β It is a measure of relative risk It depends on leverage. This comes through R E To obtain beta, plot R E - R f vs R M - R f Slope of fitted straight line is the beta Beta turns out to be independent of R f L R R E M R R f f Market risk premium 24

What is Beta? Example with R f = 5% beta β L R R E M R f R f 25

What is Beta? Example with R f = 20% beta β L R R E M R f R f 26

What is Beta? Example with R f = 0 beta β L R R E M R f R f 27

Alternative Approach to Capital Structure Analysis Using the Beta Incorporating Hamada s Equation 28

Important Relationships β L Hamada Equation U [ 1+ (1 T )] = β φ Valid only when the cost of debt, R D, is constant, independent of leverage (see paper 3) CAPM R E R D β R L P Can be derived from definition of WACC WACC = RE RDφ(1 T ) + 1+ φ 1+ φ 29

Implementation D E D/E β ROE WACC 0 100 0.00 1.17 12.0% 12.0% 20 88 0.23 1.33 13.0% 11.1% 40 76 0.53 1.54 14.2% 10.3% 60 64 0.94 1.82 15.9% 9.7% 80 52 1.54 2.24 18.5% 9.1% 100 40 2.50 2.92 22.5% 8.6% 120 28 4.29 4.17 30.0% 8.1% 140 16 8.75 7.29 48.8% 7.7% 160 4 40.00 29.17 180.0% 7.3% 30

Implementation Populate E column using E = V U D(1-T) = 100 D(1-40%) D E D/E β ROE WACC 0 100 0.00 1.17 12.0% 12.0% 20 88 0.23 1.33 13.0% 11.1% 40 76 0.53 1.54 14.2% 10.3% 60 64 0.94 1.82 15.9% 9.7% 80 52 1.54 2.24 18.5% 9.1% 100 40 2.50 2.92 22.5% 8.6% 120 28 4.29 4.17 30.0% 8.1% 140 16 8.75 7.29 48.8% 7.7% 160 4 40.00 29.17 180.0% 7.3% 31

Implementation 1. Populate D/E column 2. Compute β U = β L 1+ φ(1 T ) = 2.24 1+ 1.54(1 40%) = 1.17 D E D/E β ROE WACC 0 100 0.00 1.17 12.0% 12.0% 20 88 0.23 1.33 13.0% 11.1% 40 76 0.53 1.54 14.2% 10.3% 60 64 0.94 1.82 15.9% 9.7% 80 52 1.54 2.24 18.5% 9.1% 100 40 2.50 2.92 22.5% 8.6% 120 28 4.29 4.17 30.0% 8.1% 140 16 8.75 7.29 48.8% 7.7% 160 4 40.00 29.17 180.0% 7.3% 32

Implementation Populate rest of beta: β = β [ 1+ φ(1 T )] L U D E D/E β ROE WACC 0 100 0.00 1.17 12.0% 12.0% 20 88 0.23 1.33 13.0% 11.1% 40 76 0.53 1.54 14.2% 10.3% 60 64 0.94 1.82 15.9% 9.7% 80 52 1.54 2.24 18.5% 9.1% 100 40 2.50 2.92 22.5% 8.6% 120 28 4.29 4.17 30.0% 8.1% 140 16 8.75 7.29 48.8% 7.7% 160 4 40.00 29.17 180.0% 7.3% 33

Implementation 1. Populate ROE: R E = R D + β R L P 2. Populate WACC: WACC = RE RDφ(1 T ) + 1+ φ 1+ φ D E D/E β ROE WACC 0 100 0.00 1.17 12.0% 12.0% 20 88 0.23 1.33 13.0% 11.1% 40 76 0.53 1.54 14.2% 10.3% 60 64 0.94 1.82 15.9% 9.7% 80 52 1.54 2.24 18.5% 9.1% 100 40 2.50 2.92 22.5% 8.6% 120 28 4.29 4.17 30.0% 8.1% 140 16 8.75 7.29 48.8% 7.7% 160 4 40.00 29.17 180.0% 7.3% 34

Comparison Beta approach D E D/E β ROE WACC 0 100 0.00 1.17 12.0% 12.0% 20 88 0.23 1.33 13.0% 11.1% 40 76 0.53 1.54 14.2% 10.3% 60 64 0.94 1.82 15.9% 9.7% 80 52 1.54 2.24 18.5% 9.1% 100 40 2.50 2.92 22.5% 8.6% 120 28 4.29 4.17 30.0% 8.1% 140 16 8.75 7.29 48.8% 7.7% 160 4 40.00 29.17 180.0% 7.3% Classical approach 35

Spreadsheet Demo M&M Methodology via Beta Demo spreadsheet M&M via beta 36

End of Part 3 37

4. Default Risk and Credit Rating Methodologies 38

Credit Risk and Credit Spread Some Facts The interest rate at which corporations can borrow money depends on the market s perception of the probability that they will not be able to pay back the debt. The premium for this rate above the risk-free interest rate is known as the credit spread. The credit spread, a direct measure of credit risk, is linked to the probability of default the recovery rate and The term of the loan The classification of credit risk into bands is known as credit rating. The banding follows AAA, AA, A, BBB, BB, B, CCC, CC, C and Default. Pluses and minuses are, in addition, used to add granularity within the different bands (i.e. A+, A-, etc.). 39

Credit Rating Models Credit agencies, the primary ones being S&P, Moody s and Fitch, use credit rating models to assess a firm s credit worthiness. These ratings are then binned into categories tabulated below: Rating Investment Grade Financial Capacity AAA Yes Extremely Strong AA Yes Very Strong A Yes Strong BBB Yes Adequate BB & No Weak CRM s are generally complex and inputs to them are both statistical and subjective, involving historical, as well as forward-looking, elements 40

Assessing the Risk of Default Different Credit Rating Methodologies There are three main classes of quantitative CRM s, which are used most widely. They are derivatives of: Ratio-driven models S&P Fitch Z Score Merton model There are also other types, which are hybrids 41

The S&P Model Key Ratios 42

The S&P Model Rating of the Key Ratios 43

The S&P Model How it works Interest Cover Rating 0.42 C 0.69 CC 1.02 CCC 1.62 B 2.25 BB 2.75 BBB 4.87 A 7.50 AA 10.50 AAA D/EBITDA Rating 0.00 AAA 0.60 AA 1.20 A 3.30 BBB 4.50 BB 5.60 B 6.20 CCC 7.50 CC 9.04 C D/E Rating 0.00 AAA 0.41 AA 0.63 A 1.60 BBB 2.50 BB 4.17 B 6.67 CCC 9.95 CC 14.28 C Income Statement EBITDA 23 D&A -3 EBIT (1) 20 Gross interest expense -4.0 EBT 16.0 Tax -6.4 Net profits 9.6 Balance Sheet Assets 132 Shareholders' equity 52 IB debt 80 Total liab. & equity 132 Ratios EBIT Interest cover 4.04 D/EBITDA 3.48 D/E 1.54 Convert to Credit Spread Ratios EBIT Interest cover A- D/EBITDA BBB D/E BBB+ Final Rating Average raw rating = BBB+ Subjective inputs Comprehensive description available at: http://www2.standardandpoors.com/spf/pdf/fixedinco me/corporateratings_2006.pdf?vregion=ap&vlang=en Rating Spread C 7.50% CC 6.00% CCC 5.00% B 3.25% BB 2.00% BBB 1.50% A 1.00% AA 0.50% AAA 0.20% 44

S&P Model Worked Example with One Ratio 45

S&P Model Worked Example with One Ratio Income Statement EBITDA 25 D&A -5.0 EBIT 20 Other income 0.0 Gross interest expense -5.0 EBT 15.0 Tax -6.0 Net profits 9.0 Balance Sheet Assets 132 Shareholders' equity 52 IB debt 80 Total liab. & equity 132 Assume the S&P CRM depends on a single ratio, i.e. interest coverage ratio = EBIT/interest expense, 1. Given current FS, we can calculate: Interest rate Interest cover Effective rating from table Credit Spread Risk-free rate 2. Evaluate interest rates, effective ratings, credit spreads at different values of leverage (this table is needed to create the WACC or FV curves) 46

Necessary Data http://www2.standardandpoors.com/spf/pdf/fixedincome/corporateratings_2006.pd f?vregion=ap&vlang=en 47

Necessary Data http://www.bonds-online.com/todays_market/corporate_bond_spreads.php 48

S&P Model Worked Example with One Ratio Cont d Curve Fit for Spread vs Rating Rating Spread 0 *** 1 CCC 13.75% 2 CCC+ 3 B- 7.75% 4 B 4.50% 5 B+ 3.75% 6 BB- 2.90% 7 BB 2.10% 8 BB+ 1.33% 9 BBB- 1.21% 10 BBB 1.49% 11 BBB+ 1.07% 12 A- 0.88% 13 A 0.75% 14 A+ 0.65% 15 AA- 0.55% 16 AA 0.50% 17 AA+ 0.40% 18 AAA- 19 AAA 0.30% Numerical Rating 100.0% 0 4 8 12 16 20 10.0% y = 1.0407E-01e -1.9904E-01x Spread 1.0% 0.1% 49

S&P Model Worked Example with One Ratio Cont d TABLE I Income Statement EBITDA 25 D&A -5.0 EBIT 20 Other income 0.0 Gross interest expense -5.0 EBT 15.0 Tax -6.0 Net profits 9.0 Balance Sheet Assets 132 Shareholders' equity 52 IB debt 80 Total liab. & equity 132 TABLE II Input/Output Parameters Effective tax rate 40% Pre-tax cost of debt 6.25% Implied spread 1.74% Implied risk-free rate 4.51% Curve fitted Assume the S&P CRM depends on a single ratio, i.e. interest coverage ratio = EBIT/interest expense, 1. Calculate: Interest rate = 5/80 = 6.25% Interest cover = 20/5 = 4.0 Effective rating from table = BBB- Credit Spread = 1.74% (from curve fit) Risk-free rate = 6.25%-1.74% = 4.51% 2. Evaluate interest rates, effective ratings, credit spreads at different values of leverage 50

S&P Model Worked Example with One Ratio Cont d ICR = 4.0, Interest rate = 6.25%, spread = 1.74% Create table (this table is needed to create the WACC or FV curves) D spread(1) ICR Rating spread(2) Interest rate Implied Rating 0 0.24% 10000.00 19 0.24% 4.75% AAA 8 0.24% 52.61 19 0.24% 4.75% AAA 16 0.24% 26.31 19 0.24% 4.75% AAA 24 0.53% 16.53 15 0.53% 5.04% AA- 32 0.78% 11.80 13 0.78% 5.30% A 40 0.78% 9.44 13 0.78% 5.30% A 48 0.95% 7.62 12 0.95% 5.47% A- 56 1.17% 6.29 11 1.17% 5.68% BBB+ 64 1.42% 5.26 10 1.42% 5.94% BBB 72 1.73% 4.44 9 1.73% 6.25% BBB- 80 1.74% 4.00 9 1.74% 6.25% BBB- 88 2.12% 3.43 8 2.12% 6.63% BB+ 96 2.12% 3.14 8 2.12% 6.63% BB+ 104 2.58% 2.71 7 2.58% 7.10% BB 112 3.15% 2.33 6 3.15% 7.67% BB- 51

S&P Model Worked Example with One Ratio Cont d Populate row D = 0 D spread(1) ICR Rating spread(2) Interest rate Implied Rating 0 0.24% 10000.00 19 0.24% 4.75% AAA 8 0.24% 52.61 19 0.24% 4.75% AAA 16 0.24% 26.31 19 0.24% 4.75% AAA 24 0.53% 16.53 15 0.53% 5.04% AA- 32 0.78% 11.80 13 0.78% 5.30% A 40 0.78% 9.44 13 0.78% 5.30% A 48 0.95% 7.62 12 0.95% 5.47% A- 56 1.17% 6.29 11 1.17% 5.68% BBB+ 64 1.42% 5.26 10 1.42% 5.94% BBB 72 1.73% 4.44 9 1.73% 6.25% BBB- 80 1.74% 4.00 9 1.74% 6.25% BBB- 88 2.12% 3.43 8 2.12% 6.63% BB+ 96 2.12% 3.14 8 2.12% 6.63% BB+ 104 2.58% 2.71 7 2.58% 7.10% BB 112 3.15% 2.33 6 3.15% 7.67% BB- 52

S&P Model Worked Example with One Ratio Cont d Use iterative procedure Debt Cost of debt Factors & Ratios CRM Spread Implied Rating Calculated cost of Debt = R f + spread to populate row D = 8 D spread(1) ICR Rating spread(2) Interest rate Implied Rating 0 0.24% 10000.00 19 0.24% 4.75% AAA 8 0.24% 52.61 19 0.24% 4.75% AAA 16 0.24% 26.31 19 0.24% 4.75% AAA 24 0.53% 16.53 15 0.53% 5.04% AA- 32 0.78% 11.80 13 0.78% 5.30% A 40 0.78% 9.44 13 0.78% 5.30% A 48 0.95% 7.62 12 0.95% 5.47% A- 56 1.17% 6.29 11 1.17% 5.68% BBB+ 64 1.42% 5.26 10 1.42% 5.94% BBB 72 1.73% 4.44 9 1.73% 6.25% BBB- 80 1.74% 4.00 9 1.74% 6.25% BBB- 88 2.12% 3.43 8 2.12% 6.63% BB+ 96 2.12% 3.14 8 2.12% 6.63% BB+ 104 2.58% 2.71 7 2.58% 7.10% BB 112 3.15% 2.33 6 3.15% 7.67% BB- 53

S&P Model Worked Example with One Ratio Cont d Populate remainder of table using the same iterative procedure: Debt Cost of debt Factors & Ratios CRM Spread Implied Rating Calculated cost of Debt = R f + spread D spread(1) ICR Rating spread(2) Interest rate Implied Rating 0 0.24% 10000.00 19 0.24% 4.75% AAA 8 0.24% 52.61 19 0.24% 4.75% AAA 16 0.24% 26.31 19 0.24% 4.75% AAA 24 0.53% 16.53 15 0.53% 5.04% AA- 32 0.78% 11.80 13 0.78% 5.30% A 40 0.78% 9.44 13 0.78% 5.30% A 48 0.95% 7.62 12 0.95% 5.47% A- 56 1.17% 6.29 11 1.17% 5.68% BBB+ 64 1.42% 5.26 10 1.42% 5.94% BBB 72 1.73% 4.44 9 1.73% 6.25% BBB- 80 1.74% 4.00 9 1.74% 6.25% BBB- 88 2.12% 3.43 8 2.12% 6.63% BB+ 96 2.12% 3.14 8 2.12% 6.63% BB+ 104 2.58% 2.71 7 2.58% 7.10% BB 112 3.15% 2.33 6 3.15% 7.67% BB- 54

Z-Score Model Based on regression analysis of ratios Define: 55

Z-Score Model Implementation Historical Statistics show that for manufacturers, non-manufacturer industrials, and emerging market credits the following relationship holds within reason: Z = 6.56X 1 + 3.26X 2 + 6.72X 3 + 1.05X 4 56

Z-Score Model US Bond Rating Equivalent Based on Z Score Model 57

Merton s Model Question: Borrow $D today to start a business. Interest is paid throughout the year and the loan is to be paid back at the end of one year. If the business were to sell its assets after one year to pay off the loan, would the amount be sufficient to cover it ( $D)? Portrayed as: Asset Volatility Today One year from today Similarity to option-pricing concept: Debt obligation strike price Asset market value & volatility Share price & volatility Probability of default Area under curve behind D 58

Comparison Ratios/Scoring Need calibration Incorporate more variables More dependent on historical information Probability of default computed indirectly Appear to involve more steps to get to the rating Heavy dependence on financial statement inputs More easily applied to private firms. Merton May not need calibration Incorporates less variables Less dependent on historical information Probability of default computed directly Less steps and more direct Involves primarily market variables Difficult to apply to private firms. 59

End of Part 4 60

5. Incorporating Default Risk 61

Impact of Default Risk on Capital Structure Incorporation into the Model and Optimization of Capital Structure 62

Impact of Default Risk 1. Leads to credit spread 2. Gives an optimal capital structure 3. Idea: tax benefits and default risk work against each other, taking FV-vs-leverage curve through a maximum or the WACC through a minimum 4. Approach identical to classical M&M, but must take into account the credit spread due to default risk 63

Optimization of the Capital Structure 1. Objective is to locate the optimal capital structure 2. By classical definition, minimum WACC is where the optimal capital structure occurs 3. Recall: WACC EBIT (1 T ) D + E 4. Since EBIT x (1-T) = constant by assumption, then max(e + D) and min(wacc) occur at exactly the same leverage 5. The rest is based on the principle of maximizing the firm s value rather than minimizing the WACC 64

Procedure Requirements 1. Need a credit-rating model to calculate credit spreads along the curve Can use any This work utilises the S&P approach, which is based on ratios 2. Important to recall that D * x (1-T) + E = constant was derived based on the default-free scenario (classical M&M), where D * is the default-free debt 3. Must accordingly adjust the BS debt when there is credit risk. Adjustment of the form: * R D = D D R * D 4. With this adjustment, procedure becomes identical to classical M&M s 65

Procedure Flowchart Original Financial Statement: With default risk Convert to no-default scenario Apply M&M methodology to obtain FV curve Convert back to default case Final Output FV curve with default Income Statement EBIT 20 Gross interest expense -5.0 EBT 15.0 Tax -6.0 Net profits 9.0 Balance Sheet Assets 132 Shareholders' equity 52 IB debt 80 Total liab. & equity 132 D * R R = D * D D D = 190 170 150 130 110 0.1 1.0 10.0 100.0 R R * D D D * 190 170 OCS 150 130 0.1 1.0 10.0 110 100.0 66

Procedure Begin with original financial statement: With default risk 67

Procedure Step-by-Step Produce table in the following form Fill in cells using the financial statement 68

Procedure cont d Need CRM Fill in remaining cells in the same row (Note: D* = 6.25%/4.51% 80 = 110.7) Ratio1 Rating Spread -100000 0 *** 0.4028584 1 CCC 13.75% 1.1885656 4 B 4.50% 2.5171402 7 BB 2.10% 4.68859 10 BBB 1.49% 7.999 13 A 0.75% 19.498 16 AA 0.50% 23.797 19 AAA 0.30% Or use curve-fitted 69

Procedure cont d Calculate V U = E 0 = D * x(1-t)+e = 110.7 (1 0.4) + 52 = 118.4 Populate first row at D = 0 70

Procedure cont d Populate next row via the following iteration scheme: Debt Cost of debt Factors & Ratios CRM Spread Implied Rating Calculated cost of Debt = R f + spread 71

Procedure cont d And so on... 72

Procedure Illustration Firm's Value (FV) 'Risk-Free' Value, V* Classical M&M Loss in value due to credit risk OCS 0.1 1.0 10.0 100.0 73

End of Part 5 74

6. Incorporating Default Risk into Beta Generating the WACC Curve via the Modified Hamada Equation 75

Important Relationships Recall β L R R * + β R D E Hamada Equation U [ 1 (1 )] * + T = β φ L P Valid only when interest rates are constant, independent of leverage. Therefore, must modify D/E to account for credit spread. WACC = RE RDφ(1 T ) + 1+ φ 1+ φ 76

Procedure Step-by-Step Create table with the following format Fill in cells using information from financial statement 77

Procedure Step-by-Step Calculate risk-free rate using earlier procedure Populate D*, D*/E, β, ROE, WACC using formulas (Note: D* = 6.25%/4.51% 80 = 110.7) 78

Compute βu using D*/E rather than D/E Procedure Step-by-Step L [ 1+ φ (1 T )] Compute V u = E + D*x(1-T) = 52+110.7x(1-40%) = 118.4 Populate row for D = 0 β U = β 2.13 = 110.7 1+ (1 40%) 52 * = 0.94 79

Procedure Step-by-Step Populate remaining rows using same methodology as before 80

Comparison WACC computed using beta WACC computed the direct way Shouldn t make any difference! 81

End of Part 6 82

7. Incorporating More Ratios 83

How It Works Interest Cover Rating 0.42 C 0.69 CC 1.02 CCC 1.62 B 2.25 BB 2.75 BBB 4.87 A 7.50 AA 10.50 AAA D/EBITDA Rating 0.00 AAA 0.60 AA 1.20 A 3.30 BBB 4.50 BB 5.60 B 6.20 CCC 7.50 CC 9.04 C D/E Rating 0.00 AAA 0.41 AA 0.63 A 1.60 BBB 2.50 BB 4.17 B 6.67 CCC 9.95 CC 14.28 C Income Statement EBITDA 23 D&A -3 EBIT (1) 20 Gross interest expense -4.0 EBT 16.0 Tax -6.4 Net profits 9.6 Balance Sheet Assets 132 Shareholders' equity 52 IB debt 80 Total liab. & equity 132 Ratios EBIT Interest cover 4.04 D/EBITDA 3.48 D/E 1.54 Convert to Credit Spread Ratios EBIT Interest cover A- D/EBITDA BBB D/E BBB+ Final Rating Average raw rating = BBB+ Subjective inputs Rating Spread C 7.50% CC 6.00% CCC 5.00% B 3.25% BB 2.00% BBB 1.50% A 1.00% AA 0.50% AAA 0.20% 84

Spreadsheet Example Note that the S&P CRM depends on 8 or 9 ratios. Previous example involved a single ratio - interest cover. A working spreadsheet with 3 ratios: ICR, Cash Flow and Leverage Demo spreadsheet 3 ratios 85

End of Part 7 86

8. Application to Scenarios M&A (acquisition) Divestiture Share and debt issues and buybacks 87

Extension to Other Scenarios 1. Spreadsheet Demo for M&A (Acquisition) M&A 88

Extension to Other Scenarios 2. Spreadsheet Demo for Divestiture Divestiture 89

Extension to Other Scenarios 3. Spreadsheet Demo for Share and Debt Issues and Buybacks Share & debt sale & buyback 90

End of Part 8 91

9. Applying Constraints 92

Applying Constraints To get to the OCS (max FV) from current, issue 43 units in E to buy back 32 units of debt and purchase an additional 11 of assets. Question: What if no suitable assets were available for purchase or there was a preference instead for a 1:1 share buy back? Constrains the firm to follow FV = const. This moves the firm on the FV curve, along which V U = const, towards the OCS. With no apparent maximum in the firm s value, how is the optimal capital structure determined??? 93

Finding the OCS under Constraints Every point along the E+D = const. line will have a unique V U associated with it (because V U varies with leverage) Obtain the locus of V U s and the OCS falls where the ratio V U /FV is minimised. 140 130 FV = constant 120 Vu min Vu 110 Unique unlevered values associated with each FV Leverage, D/E point. 100 0.0 0.4 0.8 1.2 1.6 2.0 94

Finding the OCS under Constraints OCS occurs at min V U /FV 140 1.02 130 FV = constant 1.00 0.98 120 110 FV = E + D OCS OCS Ratio Vu/FV 0.96 0.94 0.92 0.90 100 0.88 0.0 0.4 0.8 1.2 1.6 2.0 95

On the Side Recall From Part 2 (derivation of classical M&M) EBIT x (1-T) operating income R D D(1-T) R E E Total Discounted Value derived from Income Statement D x (1-T) + E operating capital = unlevered value = V u Outcome: operating income operating capital i.e. EBIT(1-T) = R u V u where R u is a proportionality constant (see Part 2) 96

On the Side Implications on the S&P CRM The S&P CRM contains ratios that involve the EBIT EBiT interest cover and D-to-EBITDA, among others Therefore in constrained cases, where V u varies with leverage, one must take into account the impact of this variation on the EBIT. Once this is accounted for, the ratios containing EBIT and EBITDA could subsequently be adjusted. Output EBITDA, EBIT, D, E, T, CRM spread V u Until convergence 97

Finding the OCS under Constraints Possible Scenarios 1 & 2 Scenario 1: Firm wants to follow Vu = const = 130, as per M&M s methodology. Scenario 2: The firm wants to keep the equity level constant at 52 and exchange debt with assets (raise debt to buy assets or sell assets to buy back debt. Current @ D/E=154% D E Vu V 0 130 130 130.3 8 125 130 133.2 16 120 130 136.0 24 114 130 138.5 32 108 130 140.5 40 102 130 142.0 48 95 130 143.2 56 86 130 142.5 64 74 130 138.5 72 62 130 133.6 80 52 130 132.0 88 37 130 124.8 96 15 130 110.9 OCS @ D/E=51% OCS @ D/E=92% 98

Finding the OCS under Constraints Possible Scenarios 3 & 4 Scenario 3: Firm wants to follow FV = const = 132 by exchanging debt for equity and vice versa at 1:1. Scenario 4: The firm wants to keep the debt level constant at 80 and exchange equity with assets (issue equity to buy assets or sell assets to buy back equity. OCS @ D/E=57% OCS @ D/E=51% 99

Finding the OCS under Constraints Results Summary Capital Structure Curve 1.02 1.00 0.98 All 3 cross here 0.96 0.94 0.92 0.90 0.88 Cosntant D Cosntant E Cosntant V 0.86 0.0 0.5 1.0 1.5 2.0 2.5 In general, any type of constraint could be created by combining the above. 100

Finding the OCS under Constraints Results Summary - Table Scenario Current leverage, D/E Leverage at OCS 1. Const V u at 130 (M&M) 1.54 51% 2. Const E at 52 1.54 92% 3. Const FV at 132 1.54 57% 4. Const D at 80 1.54 51% 101

Applying Constraints Spreadsheet Demonstration E = constant Const E 102

Applying Constraints Spreadsheet Demonstration FV = constant Const V 103

Applying Constraints Spreadsheet Demonstration D = constant Const D Const D - continuous 104

End of Part 9 105

10. Case Studies 106

Dealing with the Financial Statement I.S. B.S. Revenues Needed for M&M analysis Liabilities & Equity Non-IB liabilities Interest-bearing liabilities (IB debt) equity (Market value) Costs & Expenses EBITDA D&A EBIT Gross interest on IB debt EBT Tax Needed for CRM Needed for M&M analysis Profits 107

Case Studies by Company Procter & Gamble (USA) Coca-Cola (USA) Nestlé Group (Switzerland) Electrolux (Sweden) Walt Disney Company (USA) Telenor ASA (Norway) Henkel (Germany) 108

Company Analysis Procter & Gamble 109

Company Analysis Procter & Gamble Income Statement EBIT Interest* Other inc. Tax *Capital lease charge are generally to be included in gross interest. In this case, it is negligible. 110

Company Analysis Procter & Gamble Liabilities* ST IB Debt LT IB Debt *Capital leases are generally to be included in the balance sheet. In this case, they are negligible. 111

Company Analysis Procter & Gamble ME and BE BV of Equity Market cap = USD205B Ratio BV/MV = 0.33 112

Company Analysis Procter & Gamble Cash Flow Dep & Amort 113

Company Analysis Procter & Gamble Input into the Model EBITDA 16,014+3,130 = 19,144 D&A -3,130 EBIT+other income Interest EBT 15,274 Tax (Tax rate) Profit 10,906 15,450+564 = 16,014-1,304 (capital lease charge negligible) 4,370 4,370/15,274=28.6% IB Debt 23,375+12,039 = 35,414 (capital lease negligible) B Equity 66,760 BV/MV 0.33 Company name PG:US TABLE I Income Statement EBITDA 19,144 D&A -3,130 EBIT 16,014 Other income 564 Gross interest expense -1,304 EBT 15,274 Tax -4,368 Net profits 10,906 Balance Sheet Assets 240,829 IB debt 35,414 Book equity 66,760 Market equity 205,415 Total liab. & market equity 240,829 TABLE II Input/Output Parameters Effective tax rate 29% Book-to-Market Equity 0.33 114

Company Analysis Procter & Gamble Model Output 115

Application Spreadsheets PG case study (classical) PG const V PG const E 116

PG Comparison 1.20 1.15 1.10 Vu/V 1.05 1.00 0.95 D/E PG M&M PG Const. V PG Const. E 0.0 0.2 0.4 0.6 0.8 117

Company Analysis The Coca-Cola Company 118

Company Analysis Coca-Cola Income Statement EBIT Interest Other income *Capital lease charge are generally to be included in gross interest. In this case, it is negligible. 119

Company Analysis Coca-Cola Liabilities & Equity* ST IB Debt LT IB Debt Book Equity Market cap = USD137B Ratio BV/MV = 0.16 *Capital leases are generally to be included in the balance sheet. In this case, there are none. 120

Company Analysis Coca-Cola Cash Flow Dep & Amort 121

Company Analysis Coca-Cola Input into the Model EBITDA 7,252+1,163 = 8,415 D&A -1,163 EBIT+other income 7,252+ (236+668+173) Interest -456 EBT 7,873 Tax (Tax rate) 1,892 1,892/7,873 = 24% Profit 5,981 IB Debt 5,919+133+3,277 = 9,329 B Equity 21,744 BV/MV 0.16 122

Company Analysis Coca-Cola Model Output 123

Application Spreadsheets Coca-cola case study 124

Company Analysis Nestlé Group NESN-VX 125

Company Analysis Nestlé Group NESN-VX Income Statement EBIT Other Income See Notes 126

Company Analysis Nestlé Group NESN-VX Note 3 & 5 on Interest and Tax Interest* * Negligible capital lease charge. Tax 127

Company Analysis Nestlé Group NESN-VX Liabilities* ST IB Debt LT IB Debt *Capital leases negligible. 128

Company Analysis Nestlé Group NESN-VX Equity at Market Value MV of Equity Ratio BV/MV = 0.28 BV of Equity 129

Company Analysis Nestlé Group NESN-VX Cash Flow Dep & Amort Unusual 130

Company Analysis Nestlé Group NESN-VX Input into the Model Spreadsheet EBITDA 14,434+3,211 = 17,645 D&A 2,620+591= 3,211 EBIT+other income Interest -1,481 EBT 13,529 Tax (Tax rate) Profit 9,553 14434+576 = 15,010 3,400 3,400/13,529 = 25% IB Debt 24,541+6,129 = 30,670 MV Equity 195,661 BV/MV 54,234/195,086 = 0.28 Company name NESN-VX TABLE I Income Statement EBITDA 17,645 D&A -3,211 EBIT 14,434 Other income 576 Gross interest expense -1,481 EBT 13,529 Tax -3,398 Net profits 10,131 Balance Sheet Assets 225,757 IB debt 30,671 Book equity 54,234 Market equity 195,086 Total liab. & market equity 225,757 TABLE II Input/Output Parameters Effective tax rate 25% Book-to-Market Equity 0.28 131

Company Analysis Nestlé Group NESN-VX Model Output 132

Application Spreadsheet Nestle case study 133

Company Analysis Electrolux 134

Income Statement Electrolux - P. 7 All figures in SEKm EBIT+other income See notes for Interest EBT See notes for tax 135

Income Statement Electrolux - Note 9 Interest Expense Interest 136

Income Statement Electrolux - Note 10 Tax 137

Balance Sheet Liabilities Electrolux - P. 11 All figures in SEKm BE LT debt ST debt 138

Other Useful Information Electrolux Credit Rating (p. 37) Market Cap (p. 76) 139

Company Analysis Electrolux Input into the Model EBITDA 4,475+2,738= 7,213 D&A -2,738 EBIT+other income Interest -650 EBT 4,007 Tax rate 32.8% Profit 1,054 4,475 + 182 = 4,657 IB Debt 4,887+,701 = 10,588 B Equity 16,040 BV/MV 16,040/34,000=0.47 140

Company Analysis Electrolux Model Output Compare 141

Spreadsheet Demo Electrolux case study 142

Company Analysis The Walt Disney Company 143

Company Analysis Disney Income Statement For interest expense, see notes For tax see notes EBT 144

Company Analysis Disney D&A 145

Company Analysis Disney Gross Borrowings *Capital leases negligible 146

Company Analysis Disney Income Taxes EBT Total tax paid 147

Company Analysis Disney Gross Interest Expense *Capital lease charges, negligible 148

Company Analysis Disney Shareholders Equity BV of Equity MV of equity (market cap) = USD 65B 149

Company Analysis Disney Input into the Model EBITDA 9,962 D&A -1,491 EBIT+other income 7,725+746=8,471 Interest -746 EBT 7,725 Tax (Tax rate) 3,001 3,001/7725=39% Profit 4,724 IB Debt 15,172 B Equity 30,753 BV/MV = 30,753/65,000 = 0.473 150

Company Analysis Disney Model Output See p. 44 151

Application Spreadsheet Disney case study 152

Company Analysis Telenor ASA 153

Company Analysis Telenor Income Statement D&A For interest see notes EBT For tax see notes 154

Company Analysis Telenor Interest & Tax Interest Tax 155

Company Analysis Telenor Equity & IB Debt Market cap = NOK180,000 156

Company Analysis Telenor Input into the Model EBITDA 19,971+14,333+2650 = 36,954 D&A -14,333 EBIT+other income 22,621 Interest -2,650 EBT 19,971 Tax (Tax rate) 3,782 3,782/19,971=19% Profit 16,189 IB Debt 39,725+7,521 = 47,249 B Equity 74,655 BV/MV 74,655/180,000 = 0.41 157

Company Analysis Telenor Model Output See p. 44 158

Application Spreadsheet Telenor case study 159

Company Analysis Henkel 160

Company Analysis Henkel Input into the Model EBITDA 1,344+337=1,681 D&A 337 EBIT+other income 1,344+84+91=1,591 Interest -269 EBT 1,250 Tax (Tax rate) 309 309/1250=25% Profit 941 IB Debt 3,142 B Equity 5,643 BV/MV =5,643/5,010 =1.13 161

Company Analysis Henkel Model Output 162

Application Spreadsheet Henkel case study 163

Comparison Capital Structure & Rating 250,000 240,000 230,000 220,000 210,000 200,000 190,000 180,000 P&G 170,000 0.0 0.2 0.4 0.6 0.8 1.0 148,000 146,000 144,000 142,000 140,000 138,000 136,000 134,000 132,000 Coca-Cola 130,000 0.0 0.1 0.2 0.3 0.4 230,000 220,000 210,000 200,000 190,000 180,000 Nestlé 170,000 0.0 0.2 0.4 0.6 0.8 1.0 46,000 45,000 44,000 43,000 42,000 41,000 40,000 39,000 38,000 Electrolux 37,000 0.0 0.5 1.0 1.5 2.0 2.5 3.0 164

Comparison Capital Structure & Rating 82,000 80,000 78,000 76,000 Disney 74,000 0.0 0.2 0.4 0.6 0.8 1.0 8,300 8,200 8,100 8,000 7,900 7,800 7,700 7,600 7,500 Henkel 7,400 0.0 0.5 1.0 1.5 2.0 240,000 230,000 220,000 210,000 200,000 190,000 Telenor 180,000 0.0 0.5 1.0 1.5 Firm Model rating S&P rating P&G A AA- Coca Cola AA- A+ Nestlé A AA Electrolux A- BBB+ Disney A+ A Telenor A BBB+ Henkel A- A 165

End of Part 10 166

11. Depository Institutions 167

Depository Institutions Seeking the Optimal Capital Structure 168

Depository Institutions A depository (or lending) institution is a simple bank that generates revenues from lending the assets on its BS. Tax Step1: R D D Step2:R E E Depositor/ Bond Investor D Depository Institution E Equity Investor D+E R T [D+E] Counterparty (Borrower) Income Statement Operating Income (at 5% of assets) 10 Interest paid (at 4%) -6 EBT 4 Tax (at 40%) -1.6 Net Profit 2.4 Balance Sheet Total Assets 200 Debt 150 Equity 50 Debt + Equity 200 Ratios Leverage, D/E 3 ROE, Net Profit/Equity 5% 169

Depository Institutions Main Differences with Corporate Firms Significantly more complicated than corporate firms because: Two entities, rather than one, are subject to credit/default Risk The Bank (as borrower from investors/depositors) and the Counterparty (as borrower from the Bank). The operating income (EBIT) of the bank is not constant, but varies with the size of its BS There are limits to lending In order to protect depositors and investors, banks cannot lend to the third party only what they borrow. A pre-determined amount of the money lent out must be equity. This amount of equity is dictated by certain regulatory capital ratios, determined by the borrower s risk rating and the size of the bank s BS. Above limitations create strong interdependence between bank and borrower 170

Depository Institutions M&M Treatment of a Simplified Financial Statement Income Statement Operating Income (at 5% of assets) 10 Interest paid (at 4%) -6 EBT 4 Tax (at 40%) -1.6 Net Profit 2.4 Balance Sheet Total Assets 200 Debt 150 Equity 50 Debt + Equity 200 Ratios Leverage, D/E 3 ROE, Net Profit/Equity 5% Operating income EBIT = R T (D+E) Interest expense = R D D Profit = R E E = [R T (D+E) - R D D] (1-T) EBIT(1 T) WACC = RT (1 T) = const. E + D IS Value = = R ( 1 T) + [ R R ] (1 T) φ R R T E T ( D + E)(1 T ) RDD(1 T ) = α R T D D REE + R E 171

Depository Institutions Fundamental Relationships R E = R ( 1 T ) + [ R R ] (1 T ) φ T T D Form of M&M s proposition II is preserved. EBIT (1 T ) WACC = RT (1 T ) = const E + D Inverse proportionality relation between WACC & FV is lost. R ( D + E)(1 T ) RDD(1 T ) RE E T = + = D(1 T ) E α R R + R T ( 1 T ) D(1 T ) E Tφ = const = + = 1 α D + E D + E 1+ φ D E Fundamental constant in this case is D/E, instead of D(1-T)+E 172

Depository Institutions Limitations To protect depositors/bond investors from borrowers risk, a bank s BS must adhere to certain limitations imposed on some of its financial ratios. Limitations are known as Regulatory Capital and the ratios involved are called Tier 1, Tier 2, etc., going down in order of importance. These are used to describe the capital adequacy of the bank and ensure that capital allocation is risk sensitive. Tier 1 capital is the core capital, which includes equity capital and disclosed reserves. Tier 2 capital is the secondary bank capital. It includes items such as undisclosed reserves, general loss reserves, subordinated debt, and more. These restrictions make the bank and borrower highly interdependent on each other and, thus, significantly complicate the analysis. 173

Depository Institutions Possible Cases Recall: EBIT (1 T ) WACC = RT (1 T ) = E + D const R E = R ( 1 T ) + [ R R ] (1 T ) φ T T D Case R T R D I Constant Constant Out: R D II III Constant Variable Variable Constant Depository Institution In: R T IV Variable Variable 174

Depository Institutions Case I - R T & R D constant R D Depository Institution R T 20% Ideal - Case i 10% R E 0% Leverage, φ = D/E WACC 0 5 10 15-10% 175

Depository Institutions Case II R T constant, R D variable with φ R D Depository Institution R T 20% 10% 0% -10% Return on Equity, RE Leverage, φ = D/E 0 5 10 15 176

Depository Institutions Impact of the Tier 1 Capital Restriction Definition - Tier 1 capital is the core capital. It includes equity capital and disclosed reserves. This is assigned a maximum limit of typically 8%. Applied to the simplified financial statement of a lender, lending assets E + D to a single borrower: T 1 E RWA = E r ( E + D) = 1 r (1 +φ) RWA = risk weighted assets r = risk weighting of borrower 177

Depository Institutions Relationship Between r and R T With T 1 = constant, above may be written as: r = 1 as φ T (1 + φ), r 1 Recall: r is the borrower s risk weighting. Therefore, as r, R T Combining: as φ, R T 178

Depository Institutions Case III R D constant, R T variable as φ R D Depository Institution R T 20% 10% (III) (I) (II) 0% -10% Return on Equity, RE Leverage, φ = D/E 0 5 10 15 179

Depository Institutions Case IV R D variable as φ, R T variable as φ R D Depository Institution R T 20% 10% (III) (I) (II) (IV ) 0% Return on Equity Leverage, φ = D/E 0 5 10 15-10% 180

Depository Institutions Case IV Impact of T 1 20% 4% Tier 1 = 4% Tier 1 = 8% Tier 1 = 12% 10% 8% 12% 0% -10% Return on Equity, RE Leverage, φ = D/E 0 5 10 15 181

Depository Institutions Where is the Optimal? Consider the most realistic case, being Case IV, where R D as φ and R T as φ : WACC is a decreasing function of leverage, φ. Note that not all T 1 s have a max at some finite leverage. Note that max R E does not coincide with min WACC. Etc., etc.,... 8% 6% R E 4% WACC 2% 0% Leverage, φ = D/E 0 2 4 6 8 10 182

Conclusions Reasons for complications Lender s risk Borrower s risk Interdependence between the two Discussed different scenarios Concluded that there is no straightforward way to define the OCS 183

End of Part 11 184