The Cost of Capital Flashcards
When talking about the “Cost of Capital”, we set ourselves in “Perfect Capital Markets”, what is meant by this?
- All shareholders share the same information
- All securities are fairly priced
- No taxes of transaction costs
What is the formula for unlevered FCF?
EBIT*(1-T) + Non-cash expenses - ΔWCR - CAPEX
What is the formula for levered FCF?
NI + Non-cash expenses - ΔWCR - CAPEX
Why is risk of debt lower than the risk of equity?
Answer:
1) Riskier to invest in stocks –> Can lose all of our money –> they, therefore, require a higher interest –> Higher cost of equity than debt
2) Stock vs bond - No guarantee of dividend with stocks, but that’s the case with bonds.
3) The higher the risk, the higher the return and the higher the cost of equity is.
In a world with no taxes, does an increase in debt impact the value of the company?
NO
In a world with no taxes, does an increase in debt impact the cost of capital (WACC)?
NO
In a world with no taxes, why doesn’t an increase of debt impact the value of the company?
Mentions M&M - pizza as a size of the firm - capital structure is the size of the firm - can divide it in different parts - doesn’t impact the value - not dependent on how we cut the pizza.
It’s all about restructuring.
What is the formula for WACC?
r_A = r_U = WACC = {r_E(E/V) + r_D(D/V)}
- where V = E + D, which functions as the weighted
market values of the firm.
What are the 2 propositions of Modigliani & Miller?
Proposition I:
- The market value of any firm is independent of its capital structure:V_L = E+D = Assets = V_U
Proposition II:
- The weighted average cost of capital is independent of its capital structure: r_wacc = r_A = r_U
- rA is the cost of capital of an all-equity firm (unlevered)
- NB: Whatever the capital structure, the total assets of the firm remain constant here.
Why do we assume that EBIT is equal to FCF_u?
Since; FCF_u=Non−Cash Expenses−ΔWCR−CAPEX
—> If there are no changes in depreciation, Fixed assets or the liquidity balance, then we assume that EBIT is equal to FCF.
What is the relationship between MM I and MM II?
1) EBIT = Int + DIV
2) E = DIV / r_e
3) D = Int / r_D
Describe the relationship between the WACC and the value of a company?
1) From the definition of the WACC:
r_wacc * V_L = r_equity * E + r_debt * D
2) As, r_equity * E = Div and r_debt * D = Int
- - -> r_wacc * V_L = EBIT
3) V_L = EBIT/r_wacc
This holds since,
i) EBIT = Int + DIV
ii) E = DIV / r_e
iii) D = Int / r_D
(See slide 14 & 15)
What is the link between equity and debt?
The link between the equity and the debt is that the higher (lower) the D/E-ratio is the higher (lower) the cost of equity will be.
Why does the cost of equity increase due to higher leverage?
Higher debt ratio –> higher risk of bankruptcy –> higher cost of equity for shareholders
What is the formula for the Beta of the portfolio and what does it measure?
Beta of portfolio: Beta_portfolio = Beta_equity * X_equity + Beta_debt * X_debt
𝛽portfolio = 𝛽𝐴𝑠𝑠𝑒𝑡
What is the formula for the 𝛽𝐸𝑞𝑢𝑖𝑡𝑦 and what does it measure?
𝛽𝐸𝑞𝑢𝑖𝑡𝑦 = 𝛽𝐴𝑠𝑠𝑒𝑡 + (𝛽𝐴𝑠𝑠𝑒𝑡 − 𝛽𝐷𝑒𝑏𝑡) ×𝐷/E
here we use CAPM
What is the formula for the 𝛽𝐴𝑠𝑠𝑒𝑡 and what does it measure?
𝛽𝐴𝑠𝑠𝑒𝑡 = 𝛽𝐸𝑞𝑢𝑖𝑡𝑦 ×{𝐸 / (𝐸 + 𝐷)} + 𝛽𝐷𝑒𝑏𝑡 ×{D / (𝐸 + 𝐷)}
In a world with taxes, does an increase in debt impact the company value?
Yes, the company value will increase
1) Why? More money –> more interest –> more cost –> less NI due to taxes –> higher value of the company
2) Also, there will be less to pay out in dividends, therefore saving more.
In a world with taxes, does an increase in debt impact the cost of capital (WACC)?
Yes, the WACC will decrease.
- The tax will work as a tax shield. If the company borrows money then they will pay less in tax.
How is the tax shield calculated?
Tax shield = Interest payment × Corporate Tax Rate
moreover,
(r_D * D) * T_c
How is the PV of the tax shield calculated?
PV(Tax-shield) = { ((r_D * D) * T_c) / r_D }
In a perfect world, with taxes AND Perpetual debt, how will the Value of the company be affected by an increase in debt?
It will increase the value of the company.
Higher debt –> higher tax shield –> Higher Present Value
What is meant by NOPAT and how is it calculated?
Net Operating Profit After Taxes = Unlevered Free Cash Flow
NOPAT = (EBIT -r_DD)(1-T_c)+r_DD-T_cr_D*D=EBIT(1-T-c)
see slide 25
How do you calculate the value of a company with the help of WACC and NOPAT
Value of company = NOPAT / WACC
With perpetual debt, what is the formula for WACC?
(1-T_c(D/V_L))r_A
In theory, what is the optimal capital structure?
100% debt for the company in order for it to maximize its value.
What happens with the WACC if the Leverage Ratio increases? (i.e, D/L) Why is that?
The WACC will decrease due to the tax shield becoming larger.
slide 27
In a single calculation, which rate of the cost of assets (r_A) and the WACC, will be able to calculate the unlevered company value and which one calculate the levered value of the company?
r_A –> Unlevered value, due to being the cost of capital for an all equity firm.
WACC –> Levered value
Why does the Beta of Equity increase when the firm acquires more debt?
It’s because a higher debt leads to a higher risk of bankruptcy and hence the risk of equity increases, I.e Beta equity.
slide 29
Based on the MM, what happens to the company’s FIRM value, when a company increases its leverage, in a Perfect Capital Market (PCM) and a PCM with taxes?
PCM: value is unchanged
PCM + t: Value increases
Based on the MM, what happens to a company’s EQUITY value, when a company increases its leverage, in a Perfect Capital Market (PCM) and a PCM with taxes?
PCM: value is unchanged
PCM + t: Value increases
Based on the MM, what happens to a company’s WACC, when a company increases its leverage, in a Perfect Capital Market (PCM) and a PCM with taxes?
PCM: value is unchanged
PCM + t: Value decreases
Based on the MM, what happens to a company’s Cost of equity (r_E), when a company increases its leverage, in a Perfect Capital Market (PCM) and a PCM with taxes?
PCM: value increases
PCM + t: Value increases (but by a lesser amount, due to being multiplied by taxes)
How is the Leverage Ratio calculated?
Net Debt / Leverage
What are 3 explanations to why this theory doesn’t work out in real life?
1) Start-up - if EBIT < 0 –> the company will pay no taxes –> no advantage of borrowing more money.
2) For unstable company’s they will, on average, borrow less money, due to the unstable conditions of profit. can’t borrow more.
3) Costs of financial distress: As debt increases the probability of financial problem increases as well. Direct costs, indirect costs and agency costs.
What is the definition of Agency Costs?
Agency costs: is about conflicts that rises between the managers and the shareholders or debtholders (banks).
What are the 2 ways to mitigate Agency costs?
1) Negative covenants: Prohibits actions that the company may take.
2) Positive covenants: specifies an action that the company agrees upon.
In terms of negative covenants, there are 4 actions that could be issued, which ones?
- Limitation of payout ratio
- Firm may not pledge any of its assets to other lender
- No sell or lease its major assets without approval
- No issue of additional debt
In terms of positive covenants, there are 2 actions that could be issued, which ones?
- Maintain WCR at a minimum level
2. Periodical reporting
