Summary Corporate Finance
Week 1
Net present value
NPV = PV(benefits) – PV(costs)
Annuity that pays cash flow CF for t consecutive years
(
1
PV =CF × 1−
r
1
)
( 1+ r )t
,Perfect capital markets
- Investors and firms can trade the same set of securities at competitive market
prices equal to the present value of their future cash flows.
- There are no taxes, transaction costs, or issuance costs associated with
security trading.
- A firm’s financing decisions do not change the cash flows generated by its
investments, nor do they reveal new information about them.
MM proposition 1 (capital structure irrelevance)
In a perfect capital market, the total value of a firm is equal to the market value of the
total cash flows generated by its assets and is not affected by its choice of capital
structure.
- In the absence of taxes or other transaction costs, the total cash flow paid out
to all of a firm’s security holders is equal to the cash flows generated by the
firm’s assets.
o Therefore, by the law of one price, the firm’s securities and its assets
must have the same total market value.
o Leverage merely changes the allocation of cash flows between debt
and equity, without altering the total cash flows of the firm.
Initial value of the levered equity
By MM, the initial value of the levered equity is the difference between the equity
value of the unlevered firm and the debt value.
The expected return of levered equity
D
r E=r U + (r −r )
E U D
Return sensitivity
∆ Return=R ( situation A )−R ( Situation B )
¿ difference between two ❑' r ealise d ' returns
Risk premium
R p =return−rf rate
Equity β
D
β E =β A + ( β −β D )
E A
¿ business risk + financial risk
- Equity risk increases with leverage
- In all equity firm β E =β A
Asset β
E D
β A= βE+ β
E+ D E+ D D
MM proposition 2 (leverage and equity cost of capital)
D
r E=r A + ( r A −r D )
E
- Leverage increases the equity cost of capital because risky cash flows to
equity become more volatile.
, - Since risk requires a market premium, equity holders need to get
compensated.
- Any attempt to substitute ‘cheap’ debt for ‘expensive’ equity makes the
remaining equity in a way more expensive such that the overall cost of capital
remain constant.
Capital structure fallacies:
- EPS Fallacy: “Equity is more expensive than debt because equity issues
reduce expected earnings per share and drive down the stock price.”
- Dilution Fallacy: “Debt financing should be used because equity financing
dilutes existing shareholders. If new shares are issued, cash flows must be
divided among a larger number of shares leading to a lower share price.”
- WACC Fallacy: “Interest rates on debt are lower than investors’ required
return on equity. Thus, debt financing is preferred because it is cheaper than
equity.”
- Clientele Fallacy: “Investors have different preferences and desire different
cash flow streams. By issuing tailor-made securities, firms can attract
clienteles/investors who are willing to pay a premium.”
, Week 2
MM proposition 1 with taxes
The total value of the levered firm exceeds the value of the firm without leverage due
to the present value of the tax savings from debt.
L U
V =V + PV (interest tax shield)
The interest tax shield with permanent debt
Suppose a firm borrows debt D and keeps the debt permanently. If the firm’s
marginal tax rate is τ c, and if the debt is riskless with a risk-free interest rate r f ,
- Then the interest tax shield each year is τ c ×r f × D
- And the tax shield can be valued as a perpetuity:
τ c ×interest τ c × ( r f × D )
PV ( interest tax shield )= = =τ c × D
rf rf
Interest tax shield (not permanent)
D × Interest % × τ c
PV(interest tax shield)
Annual interest tax shield
rf
PV(interest tax shield) with growth
Annual interest tax shield
r−g
Tax savings
−τ c ×r × D
Effective after-tax cost of debt
r × ( 1−τ c ) × D
Week 1
Net present value
NPV = PV(benefits) – PV(costs)
Annuity that pays cash flow CF for t consecutive years
(
1
PV =CF × 1−
r
1
)
( 1+ r )t
,Perfect capital markets
- Investors and firms can trade the same set of securities at competitive market
prices equal to the present value of their future cash flows.
- There are no taxes, transaction costs, or issuance costs associated with
security trading.
- A firm’s financing decisions do not change the cash flows generated by its
investments, nor do they reveal new information about them.
MM proposition 1 (capital structure irrelevance)
In a perfect capital market, the total value of a firm is equal to the market value of the
total cash flows generated by its assets and is not affected by its choice of capital
structure.
- In the absence of taxes or other transaction costs, the total cash flow paid out
to all of a firm’s security holders is equal to the cash flows generated by the
firm’s assets.
o Therefore, by the law of one price, the firm’s securities and its assets
must have the same total market value.
o Leverage merely changes the allocation of cash flows between debt
and equity, without altering the total cash flows of the firm.
Initial value of the levered equity
By MM, the initial value of the levered equity is the difference between the equity
value of the unlevered firm and the debt value.
The expected return of levered equity
D
r E=r U + (r −r )
E U D
Return sensitivity
∆ Return=R ( situation A )−R ( Situation B )
¿ difference between two ❑' r ealise d ' returns
Risk premium
R p =return−rf rate
Equity β
D
β E =β A + ( β −β D )
E A
¿ business risk + financial risk
- Equity risk increases with leverage
- In all equity firm β E =β A
Asset β
E D
β A= βE+ β
E+ D E+ D D
MM proposition 2 (leverage and equity cost of capital)
D
r E=r A + ( r A −r D )
E
- Leverage increases the equity cost of capital because risky cash flows to
equity become more volatile.
, - Since risk requires a market premium, equity holders need to get
compensated.
- Any attempt to substitute ‘cheap’ debt for ‘expensive’ equity makes the
remaining equity in a way more expensive such that the overall cost of capital
remain constant.
Capital structure fallacies:
- EPS Fallacy: “Equity is more expensive than debt because equity issues
reduce expected earnings per share and drive down the stock price.”
- Dilution Fallacy: “Debt financing should be used because equity financing
dilutes existing shareholders. If new shares are issued, cash flows must be
divided among a larger number of shares leading to a lower share price.”
- WACC Fallacy: “Interest rates on debt are lower than investors’ required
return on equity. Thus, debt financing is preferred because it is cheaper than
equity.”
- Clientele Fallacy: “Investors have different preferences and desire different
cash flow streams. By issuing tailor-made securities, firms can attract
clienteles/investors who are willing to pay a premium.”
, Week 2
MM proposition 1 with taxes
The total value of the levered firm exceeds the value of the firm without leverage due
to the present value of the tax savings from debt.
L U
V =V + PV (interest tax shield)
The interest tax shield with permanent debt
Suppose a firm borrows debt D and keeps the debt permanently. If the firm’s
marginal tax rate is τ c, and if the debt is riskless with a risk-free interest rate r f ,
- Then the interest tax shield each year is τ c ×r f × D
- And the tax shield can be valued as a perpetuity:
τ c ×interest τ c × ( r f × D )
PV ( interest tax shield )= = =τ c × D
rf rf
Interest tax shield (not permanent)
D × Interest % × τ c
PV(interest tax shield)
Annual interest tax shield
rf
PV(interest tax shield) with growth
Annual interest tax shield
r−g
Tax savings
−τ c ×r × D
Effective after-tax cost of debt
r × ( 1−τ c ) × D
