Estimating WACC and Capital Structure

Week 5: Estimating WACC and Capital Structure

• This week's focus includes estimating the Weighted Average Cost of Capital (WACC) and understanding optimal capital structure.
• The Modigliani-Miller (MM) Theorem suggests that in a perfect world, capital structure is irrelevant.

CAPM Recap

• Investors require compensation for bearing risk.
• The Capital Asset Pricing Model (CAPM) relates risk to expected return.
• Investors are only compensated for risks they cannot diversify, which is beta risk.
• The expected return on an asset A, according to CAPM, is E(rA) = rf + βA x [E(rm) - rf].
• rf is the risk-free rate, and [E(rm) - rf] represents the market risk premium.
• βA measures the non-diversifiable risk for asset A.

Estimating Cost of Equity with CAPM

• CAPM can be used to find the cost of equity (return).
• For this you can use the formula ri = rf + βi × (E[RMkt] - rf).

Risk-Free Rate

• The risk-free rate is determined by the yield on risk-free government securities, such as U.S. Treasury securities.
• Maturity should match cash flows that are being valued
• Most practitioners use 10 to 30 year treasuries when doing valuations

Market Risk Premium

• This represents the price of market risk, calculated as E[RMkt] - rf
• It reflects the return an investor requires above the risk-free rate for investing in a diversified portfolio.
• Estimating the premium should be forward looking
• A local stock market index (e.g., S&P 500 in the US) is used as the proxy for the market portfolio.

Approaches to Estimating Market Risk Premium

• Historical data extrapolation provides an unbiased estimate, assuming consistent market behavior.
• The future-oriented approach considers how risk tolerance and international diversification may have changed
• Consulting firms use market risk premia between 3% and 5% which is lower than historical averages.
• The implied market risk premium is a fundamental approach where the discount rate is consistent with the index.
• It is comparable to an IRR calculation in case of a bond, also known as YTM.

Estimating Equity Betas

• Beta of an asset is found with this formula: 𝛽𝛽𝑖𝑖 = 𝐶𝐶𝐶𝐶𝐶𝐶(𝑟𝑟𝑖𝑖 , 𝑟𝑟𝑚𝑚 ) / 𝜎𝜎𝑚𝑚 2
• The historical stock prices of Cisco and S&P500 are looked at and how they covary as an example.
• Beta corresponds to the slope of the best-fitting line in the plot of a security's excess returns versus the market excess return.
• (Ri - rf) = αi + βi (RMkt - rf) + εi where αi is the intercept term, βi is sensitivity to market risk and εi is the error term.
• If αi is positive, that means that the stock performed better than the CAPM predicted.
• If αi is negative, that means that the stock performed worse than the CAPM predicted.
• Using Ordinary Least Squares a regression for Cisco using monthly returns shows an average beta of 1.56.

Cost of Equity Example

• Risk-free rate: 3%
• Equity market risk premium: 5%
• Beta: 1.56
• ri = rf + βi × (E[RMkt] - rf)
• E(Ri) = 3% + 1.56 * 5% = 10.8%
• With 95% probability, the cost of equity is between 9.5% and 12%.

Cost of Debt

• Cost of debt is the opportunity cost of debtholder, equal to the expected rate of return on a comparable risky financial asset
• Can be estimated using CAPM, but beta debt is hard to estimate
• Promised Yield is not the expected rate of return

Three Approaches to Estimating Cost of Debt

• Expected (required) rate of return
• Current Yield on New Debt
• rD = rf + ßD[E(rM)-rf] for Accordings to CAPM but 0 < Beta debt < 0.4
• Ratings from credit agencies

Default Risk and Promised versus Expected Return

• If yield to maturity is the IRR an investor will earn from holding the bond to maturity to receiving its promised payments
• With little default risk YTM is a reasonable estimate of investors' expected rate of return
• With significant risk of default, YTM will overstate expected return
• Consider a one-year bond with YTM of y.
• Formula: rd = (1-p)y + p(y-L) = y – pL, also Yield to Maturity – Prob(default) * Expected Loss Rate
• Adjustment depends on the riskiness of the bond.
• The average loss rate for unsecured debt is 60%.
• During normal times annual default rate for B-rated bonds is 5.5%.
• Expected return to B-rated bondholders in normal times is 0.055 x 0.60 = 3.3% below the bond's quoted yield.

WACC in Capital Budgeting

• Imagine that you want to value an expansion project in a firm financed with both 1debt and equity
• The opportunity cost of capital in the case is the investors' rate of return.
• Use the WACC (Weighted Average Cost of Capital).

Calculating WACC

• WACC = rA = rE [E/(E+D)] + rD [D/(E+D)]
• rD = cost of debt
• rE = cost of equity
• E = market value of equity
• D = Market value of debt
• If including taxes: rwacc after-tax = rE [E/(D+E)]+ (1-tc )rD [D/(D+E)]
• The WACC is the discount rate in capital budgeting only when the risk of the new project is the same as that of the existing activities

Capital Structure Decisions

• Firms should choose the debt and equity mix that maximizes firm value.
• Capital structure considers the relative proportions of debt and equity.
• Leverage is D/E, where D is debt and E is equity.
• A firm with debt is levered, and an all-equity financed firm is unlevered.
• About 25% of US Public Companies in 2014, had negligible leverage. Summary of the Famous MM Theorem

MM Theorem

• If there are perfect capital markets, there is no effect of debt on a company's real decisions (EBIT unaffected)
• But imperfections change this, such as taxes, and the costs of financial distress, and manager's incentive
• There is no taxes and transaction or bankruptcy costs, frictionless borrowing or lending, with homogeneous expectations and no asymmetric information
• There is no effect of debt on company's real decisions (EBIT unaffected)

MM I

• Total cash flow paid out to all of a firm's security holders is equal to the total cash flow generated by the firm's assets
• By using the Law of One Price, the firm's securities and its assets must have the same total market value
• With no transaction cost, investors should be able to undo the financing decisions of the firm, can use homemade leverage

Financing strategy

• If 10% of firm "U" to total investment 0.1 VU is bought.
• Then it is equal total investment for 10% and equity in a levered firm: 0.1 EL + 0.1 DL = 0.1 VL
• Note that the returns (cash flows) of both strategies are identical

MM Proposition 1

• VU = VL

MM 1

• Note investors can mimic the financing decisions of the firm:
• Purchasing unlevered equity can be mimicked by purchasing equity and debt of a levered firm.
• Purchasing levered equity can be mimicked by purchasing unlevered equity and borrowing (since there's no friction).
• As a result, firm values must be equal.

all-equity example

• An all-equity financed firm has total shares that are $1000, with
• The projects have equal probabilities and have project returns = equity returns
• Shareholder’s returns are +40% or –10%
• The expected return of the unlevered equity is: ½ (40%) + ½(–10%) = 15%

Finance with debt and equity example

• Suppose the firm issues debt for $500 initially at the risk-free interest rate of 5%, buys back 25 shares at $20
• The debt obligation is $525
• The values, cash flows and deb and equity is demonstrated on the table on the slides

MM I cont’d: Homemade Leverage

• Investors can use leverage in their own portfolios to adjust the leverage choice made by the firm
• If investors would prefer an alternative capital structure, they can borrow or lend to achieve the same result.

Two cases:

• The firm is unlevered; the investor prefers to hold levered equity
• The firm is levered; the investor prefers to hold unlevered equity

Replicating Levered Equity vs Debt

• An investor can replicated levered equity can and unlevered debt
• By using Law of one Price, levered equity = unlevered equity - loan and that should all be equal

MM II and WACC

If a firm is unlevered, the cost of capital of the firm's assets and its equity coincide: rU = rA If a firm is levered, the cost of capital of the firm's assets is equal to the WACC

Modigliani & Miller I (Capital Structure Irrelevance)

• Leverage does not affect the total value of the firm; it only changes the allocations of cash flows (and risk) between debt and equity

Beta as a Measure of Risk when companies assume different ratios for debt

• Levered equity beta is higher because with levering up, risk has increase for the equity holder!

Explaining risk via Levered and Unlevered Betas

• The effect of leverage on the risk of a firm’s securities can also be expressed in terms of beta:
• Unlevered Beta ( βU ) is a measure of the risk of a firm as if it did not have leverage, which is equivalent to the beta of the firm’s assets (βA )
• Levered Beta: Leverage amplifies the market risk of a firm’s assets, βU, raising the market risk of its equity (βE)

WACC and Compensation for the Business Risk

• Why is WACC independent of the capital structure? -Beta risk is the only driver of the cost of capital -If the business risk does not change, WACC will remain constant regardless of the capital structure -An increase in the financial risk of the equity holder will compensate for the lower cost of debt

WACC, Cash and Net Debt

• When firms maintain high cash balances, there are some changes
• Since the the risk of the firm's enterprises is the foosic, then leverage should be measured in terms of net debt
• In the formulae above, D should be replaced by net debt!

Leverage and EPS Fallacy

-Firms indeed generate higher EPS with higher leverage -Equity investor receive higher return, but also need higher return to be compensated for higher risk -Therefor shareholders in perfect markets are no better off with more debt-financing!