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Corporate Finance Cheatsheet

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Population Variance (σ2) and Standard Deviation (σ): When using all the members of the population, denominator is the number of members (T) (as in previous slide)  Sample Variance (σ2) and Standard Deviation (σ): When using a sample of the population, denominator is the number of members of the sample minus 1 (T-1)

CML: The CML does not permit the assessment of the risk-return relationship of assets or portfolios which are not a combination of the market portfolio and the risk-free asset. This is achieved through the CAPM // Slope =(Er(M)- rf) / σM)[pic 7][pic 8][pic 9]

Std of a portfolio of 2 assets (dont one rf)[pic 10]

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Beta (Systematic risk) varies proportionally with correlation. However, it also depends on the ratio between the asset’s volatility and the volatility of the market portfolio

CAPM (Rate of return (equilibrium) of a portfolio efficiently priced, if the expected return is higher than the CAPM the portfolio is under-priced). EX: The market (CAPM) expects a return of 10.6%. You expect a lower return. If you are right the price should fall. Thus, the stock must be sold.[pic 14]

2/ WACC (After a decision on leverage, if WACC↓ the decision is value increasing!)

Return on debt and equity w/ or w/out taxes:

1/Keeping leverage constant, as the return on debt rises the return on equity falls and WACC stays the same (both cases)

2/Keeping the return on debt constant (not realistic), as D/V increases, return on equity goes up and WACC falls (w/ taxes), does not vary (w/out taxes).[pic 15]

An Unlevered Beta (Beta Assets vs Normal or Levered Beta) paints a more accurate picture of a company’s operating stability, and the risk that an investor could be taking on by purchasing its stock. Higher debt (↑Leverage) = ↑ BetaL. Lower or Zero Debt (↓Leverage or Unlvered) = ↓BetaL[pic 16][pic 17][pic 18]

Class ex: 1. Estimate equity betas from stock price series of comparable firms. 2. Convert leverage ratios to D/E basis. 3. Calculate unlevered betas for comparable firms. 4. Average unlevered betas. 5. Estimate levered beta for target firm. 6. Levered beta for the target is used to calculate rE with the CAPM formula.

Unlevered Free Cash Flow: The cash flow produced by the asset side. It is equal to the cash flow to shareholders if there is no debt Levered Free Cash Flow: The cash flow received by the shareholders. It is different from the unlevered free cash flow when there is debt.

IMPORTANT: The value of a levered firm after taxes equals the PV of the unlevered free cash flows after taxes discounted at WACC. Taxes are overestimated in the free cash flows but this is compensated with a lower discount rate (WACC). In consequence, when there are corporate taxes, the value of the firm rises with the leverage ratio. Tax Shield: Tax savings as a consequence of the deductibility of interest payments.

Bankruptcy: The MM formula tells us that the higher the leverage ratio the more valuable the firm is.  However, this is unrealistic since the costs associated with bankruptcy are ignored. Bankruptcy costs, also called Costs of Financial Distress, will be discussed later on

Project Risk Vs Firm Risk: Every WACC valuation incorporates the tax shield. The tax shield adds value whenever the debt is inseparable from the investment as is the case with firms and some specific projects (Ex. Project Finance, mortgages). WACC is the right discount rate to value firms. Specific projects must be discounted at the unlevered discount rate corresponding to their own risk – If there is an attached debt the corresponding tax shield must be added to unlevered present value   US evidence shows that, remarkably, most firms use a single company- wide discount rate to evaluate a project even though the project might have different risk characteristics. Of course, this is wrong.

Cost of financial Distress:  When leverage rises a larger proportion of cash flows must be targeted for servicing the debt. Given that the cash flows are volatile; the probability of default also increases with leverage. When interested parties perceive significant risk of default expected costs of financial distress (or expected bankruptcy costs) arise. The expected costs of financial distress increase with leverage.

Cost of Financial Distress: Types Direct Costs incurred if bankruptcy takes place (legal, audits, indemnizations etc.) Generally less important than indirect costs Indirect → Managerial difficulties (focus on short-term crisis), loss of customers and key employees, stricter supply terms etc. Agency Costs: Stem from unresolved conflicts among interested parties (managers, employees, debtholders, equityholders, etc.). Moral Risk (unethical behavior by management) Asymmetric Information.

CFD: Implications The expected cost of going bankrupt is a product of the probability and the cost of going bankrupt – The latter includes both direct and indirect costs. The probability of going bankrupt will be higher in businesses with more volatile earnings and the cost of bankruptcy will also vary across businesses according to the complexity of the contracts among interested parties

Practical WACC: A practical way to (approximately) account for the costs of financial distress is by making the discount rate of debt equal to the cost of debt when computing WACC and using a beta based return on equity – This is actually a deviation from the formal WACC formula where rD becomes an independent variable. As leverage increases, on the one hand the tax shield lowers WACC and on the other hand the increasing costs of debt and equity rise WACC. This approach also offers a practical (approximate) way to estimate the optimal capital structure: The optimal capital structure is attained where WACC is minimized – However, in practice the optimal capital structure is affected by other factors (more about this later). Although useful from a practical standpoint this approach is inconsistent with the CAPM since the full cost of debt (and not just its systematic part) is accounted for.



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