The Cost of Capital

Question 1

When talking about the “Cost of Capital”, we set ourselves in “Perfect Capital Markets”, what is meant by this?

Answer 1

• All shareholders share the same information
• All securities are fairly priced
• No taxes of transaction costs

Question 2

What is the formula for unlevered FCF?

Answer 2

EBIT*(1-T) + Non-cash expenses - ΔWCR - CAPEX

Question 3

What is the formula for levered FCF?

Answer 3

NI + Non-cash expenses - ΔWCR - CAPEX

Question 4

Why is risk of debt lower than the risk of equity?

Answer 4

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.

Question 5

In a world with no taxes, does an increase in debt impact the value of the company?

Answer 5

NO

Question 6

In a world with no taxes, does an increase in debt impact the cost of capital (WACC)?

Answer 6

NO

Question 7

In a world with no taxes, why doesn’t an increase of debt impact the value of the company?

Answer 7

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.

Question 8

What is the formula for WACC?

Answer 8

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.

Question 9

What are the 2 propositions of Modigliani & Miller?

Answer 9

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.

Question 10

Why do we assume that EBIT is equal to FCF_u?

Answer 10

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.

Question 11

What is the relationship between MM I and MM II?

Answer 11

1) EBIT = Int + DIV
2) E = DIV / r_e
3) D = Int / r_D

Question 12

Describe the relationship between the WACC and the value of a company?

Answer 12

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)

Question 13

What is the link between equity and debt?

Answer 13

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.

Question 14

Why does the cost of equity increase due to higher leverage?

Answer 14

Higher debt ratio –> higher risk of bankruptcy –> higher cost of equity for shareholders

Question 15

What is the formula for the Beta of the portfolio and what does it measure?

Answer 15

Beta of portfolio: Beta_portfolio = Beta_equity * X_equity + Beta_debt * X_debt

𝛽portfolio = 𝛽𝐴𝑠𝑠𝑒𝑡

Question 16

What is the formula for the 𝛽𝐸𝑞𝑢𝑖𝑡𝑦 and what does it measure?

Answer 16

𝛽𝐸𝑞𝑢𝑖𝑡𝑦 = 𝛽𝐴𝑠𝑠𝑒𝑡 + (𝛽𝐴𝑠𝑠𝑒𝑡 − 𝛽𝐷𝑒𝑏𝑡) ×𝐷/E

here we use CAPM

Question 17

What is the formula for the 𝛽𝐴𝑠𝑠𝑒𝑡 and what does it measure?

Answer 17

𝛽𝐴𝑠𝑠𝑒𝑡 = 𝛽𝐸𝑞𝑢𝑖𝑡𝑦 ×{𝐸 / (𝐸 + 𝐷)} + 𝛽𝐷𝑒𝑏𝑡 ×{D / (𝐸 + 𝐷)}

Question 18

In a world with taxes, does an increase in debt impact the company value?

Answer 18

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.

Question 19

In a world with taxes, does an increase in debt impact the cost of capital (WACC)?

Answer 19

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.

Question 20

How is the tax shield calculated?

Answer 20

Tax shield = Interest payment × Corporate Tax Rate
moreover,
(r_D * D) * T_c

Question 21

How is the PV of the tax shield calculated?

Answer 21

PV(Tax-shield) = { ((r_D * D) * T_c) / r_D }

Question 22

In a perfect world, with taxes AND Perpetual debt, how will the Value of the company be affected by an increase in debt?

Answer 22

It will increase the value of the company.

Higher debt –> higher tax shield –> Higher Present Value

Question 23

What is meant by NOPAT and how is it calculated?

Answer 23

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

Question 24

How do you calculate the value of a company with the help of WACC and NOPAT

Answer 24

Value of company = NOPAT / WACC

Question 25

With perpetual debt, what is the formula for WACC?

Answer 25

(1-T_c(D/V_L))r_A

Question 26

In theory, what is the optimal capital structure?

Answer 26

100% debt for the company in order for it to maximize its value.

Question 27

What happens with the WACC if the Leverage Ratio increases? (i.e, D/L) Why is that?

Answer 27

The WACC will decrease due to the tax shield becoming larger.

slide 27

Question 28

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?

Answer 28

r_A –> Unlevered value, due to being the cost of capital for an all equity firm.

WACC –> Levered value

Question 29

Why does the Beta of Equity increase when the firm acquires more debt?

Answer 29

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

Question 30

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?

Answer 30

PCM: value is unchanged

PCM + t: Value increases

Question 31

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?

Answer 31

PCM: value is unchanged

PCM + t: Value increases

Question 32

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?

Answer 32

PCM: value is unchanged

PCM + t: Value decreases

Question 33

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?

Answer 33

PCM: value increases

PCM + t: Value increases (but by a lesser amount, due to being multiplied by taxes)

Question 34

How is the Leverage Ratio calculated?

Answer 34

Net Debt / Leverage

Question 35

What are 3 explanations to why this theory doesn’t work out in real life?

Answer 35

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.

Question 36

What is the definition of Agency Costs?

Answer 36

Agency costs: is about conflicts that rises between the managers and the shareholders or debtholders (banks).

Question 37

What are the 2 ways to mitigate Agency costs?

Answer 37

1) Negative covenants: Prohibits actions that the company may take.
2) Positive covenants: specifies an action that the company agrees upon.

Question 38

In terms of negative covenants, there are 4 actions that could be issued, which ones?

Answer 38

1. Limitation of payout ratio
2. Firm may not pledge any of its assets to other lender
3. No sell or lease its major assets without approval
4. No issue of additional debt

Question 39

In terms of positive covenants, there are 2 actions that could be issued, which ones?

Answer 39

1. Maintain WCR at a minimum level

2. Periodical reporting