Ondernemingsfinanciering & Vermogensmarkten Samenvatting
Contents
Chapter 14 Capital structure in a perfect market ................................................................................... 5
Les 1 27-1 (14) ..................................................................................................................................... 9
Les 2 29-1 (14) ................................................................................................................................... 10
Chapter 15 Debt and taxes .................................................................................................................... 10
Les 3 3-2 (15) ..................................................................................................................................... 10
Tutorial 1 6-2 ......................................................................................................................................... 11
Chapter 16 Financial distress, managerial incentives, and information ............................................... 11
Les 4 10-2 (16) ................................................................................................................................... 12
Les 5 12-2........................................................................................................................................... 13
Les 6 17-2 (16) ................................................................................................................................... 13
Tutorial 2 20-2 ....................................................................................................................................... 14
Chapter 17 Payout Policy ...................................................................................................................... 15
Chapter 18 Capital budgeting and valuation with leverage .................................................................. 16
Les 7 2-3 (17) ..................................................................................................................................... 16
Les 8 4-3 (17 & 18)............................................................................................................................. 17
Les 9 9-3............................................................................................................................................. 17
Chapter 20 Financial Options ................................................................................................................ 17
Tutorial 3 13-3 ....................................................................................................................................... 18
Les 10 16-3......................................................................................................................................... 19
Les 11 18-3......................................................................................................................................... 19
Chapter 21 Option valuation ................................................................................................................. 20
Les 11 22-3......................................................................................................................................... 20
Chapter 23 Raising Equity Capital ......................................................................................................... 21
Les 12 6-4........................................................................................................................................... 23
Chapter 24 Debt financing..................................................................................................................... 24
Les 13 8-4........................................................................................................................................... 26
Les 14 20-4......................................................................................................................................... 26
Chapter 25 Leasing ................................................................................................................................ 27
Les 15 22-4......................................................................................................................................... 29
Chapter 26 Working capital management ............................................................................................ 29
Chapter 27 Short-term financial planning ............................................................................................. 30
Les 16 6-5........................................................................................................................................... 31
Chapter 28 Mergers and acquisitions ................................................................................................... 32
1
, Les 17 8-5........................................................................................................................................... 33
Les 18 11-5......................................................................................................................................... 33
Chapter 29 Corporate Governance (Not on exam) ............................................................................... 33
Chapter 30 Risk Management ............................................................................................................... 34
Les 19 ................................................................................................................................................. 35
Symbolen Betekenis
A Market value of the firm’s assets
A Pre-merger (equity) value of acquirer
B Bond
C Call option price
C0 The paid price (We assume that this is the ask price)
Ct Cash flow on date t
D Market value of debt in a levered firm
d Debt-to-value ratio
dis(K) The amount of the discount from face value to account for interest
Dp Duration of security or portfolio P
Ds Debt net of predetermined tax shields
E Market value of equity in a levered firm
Intt Interest expenses on t
k Interest coverage ratio (How many times the interest expenses are covered
with the FCF)
K Strike/exercise price
P Put option price / Price of a security
P’ New share price of increase in value
Pcum Cum-dividend stock price
Pex Ex-dividend stock price
Prep Stock price with share repurchase
Pretain Stock price if excess cash is retained
q Compounded, annualized dividend yield on the stock to the maturity of the
option
R Number of repurchased shares or Return
rA Expected return of firm assets
rD Market value returns on debt
rE Market value returns on levered equity
rU Market value return on unlevered equity
S Stock price
S Spot exchange rate
S (Present) value of the synergies created by the merger
SX De netto aandeelprijs (S-Pv(Div)) or S/(1+q)
T Time to maturity
T Pre-merger value of target
U Market value of unlevered equity
VU Unlevered value of the firm, so without debt. Only positive NPVs
x New shares issued by bidder in order to buy target
Δ Shares of stock in the replicating portfolio, thus representing the sensitivity of
option price to stock price
2
,ρ The probability of the chances in a risk-neutral two state model
σ Annualized volatility
τ*d Effective dividend tax rate
τc Corporate tax
τe Personal taxes on income from equity
τg Capital gains tax rate
τi Personal taxes on income from interest
Formule Betekenis
Chapter 14
A=U=E+D MM 1
𝐸 𝐷 Identity relationship (Pretax WACC). Only use this for multiple
𝑟
𝐸+𝐷 𝐸
+ 𝑟
𝐸+𝐷 𝐷
periods of time when D/E-ratio is constant for these periods
𝐷 MM Proposition II: Cost of levered equity, waarbij rU Cost of
rE = rU + (rU – rD)𝐸
unlevered equity is en rD de premium due to leverage is. re will
increase when D increases, if rU is larger then rD
𝐸 𝐷 Unlevered cost of capital
ru = 𝐸+𝐷 𝑟𝐸 + 𝐸+𝐷 𝑟𝐷
𝐸 𝐷 rwacc: verdisconteringsvoet van projecten
𝑟 + 𝐸+𝐷 𝑟𝐷 (1 − 𝜏𝑐 )
𝐸+𝐷 𝐸
𝐷 Number of repurchased shares
R = 𝑃′
𝐸 𝐷 A firm’s unlevered or asset beta
βU = 𝐸+𝐷 𝛽𝐸 + 𝐸+𝐷 𝛽𝐷
𝐷 The firm’s equity beta increases with leverage
𝛽𝐸 = 𝛽𝑈 + 𝐸 (𝛽𝑈 − 𝛽𝐷 )
𝐸𝑎𝑟𝑛𝑖𝑛𝑔𝑠 Earnings per share
EPS =
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠ℎ𝑎𝑟𝑒𝑠
R(strong economy)-R(weak Return sensitivity (Systematic Risk)
economy)
𝐸(𝐶𝑓) Expected return of equity. Don’t discount the CF or the Debt
E(r) = 𝐸𝑞𝑢𝑖𝑡𝑦 − 1
Chapter 15
VL = VU + τcD Value of a levered firm (With permanent debt)
VL = VU + τ*D
(1−𝜏𝑐 )(1−𝜏𝑒 ) Effective tax advantage of debt. Dit is lager dan het tax shield met
τ* = 1 - alleen corporate taxes. Dit komt van de vergelijking (1-τ*) (1-τi) = (1-
(1−𝜏𝑖 )
τc) (1-τe, waarbij τ* ervoor zorgt dat het gelijk maakt. Schets het
daadwerkelijke tax advantage
𝜏𝑒 −𝜏𝑖 Excess interest payments (τc = 0). Always negative
τex* =
(1−𝜏𝑖 )
𝑁𝑃𝑉 𝛽𝐷 𝐷 The shareholders will benefit from a new investment if this equation
> holds
𝐼 𝛽𝐸 𝐸
Chapter 17
Pcum – Pex = Div * (1-τ*d) Share price drop before and after dividend imbursement
𝜏𝑑 −𝜏𝑔
τ*d = ( 1−𝜏 ) Effective dividend tax rate
𝑔
1−𝜏 The share price before dividend is paid
Pcum = Pex + Div0 * (1−𝜏𝑑 )
𝑔
𝐷𝑖𝑣∗(1−𝜏𝑑 ) Share price if excess cash is retained
Pretain = 𝑟𝑓 ∗(1−𝜏𝑖 )
(1−𝜏𝑐 )(1−𝜏𝑔 ) Effective tax disadvantage of retaining cash
τ*retain = (1 −
(1−𝜏𝑖 )
Chapter 18
3
, 𝐿
VtL:
𝐹𝐶𝐹𝑡+1 +𝑉𝑡+1
. De waarde van het bedrijf op tijdstip t (Gebruik dit in de APV-
1+𝑟𝑤𝑎𝑐𝑐 methode)
Vu + PV(Interest Tax shield) Adjusted present value (APV)
rD * Dt-1 Interest paid in year t
Dt – Dt-1 Net borrowing at date t
FCFE = FCF – (1-τc) * Free cash flow to equity
(Interest Payments) + (Net
Borrowing)
Interest/FCF Interest Coverage Ratio
k * FCFt Interest paid in year t
VL = (1+τck)VU Levered value with a constant interest coverage ratio (Constant
interest coverage model)
𝑐 𝜏 ∗𝐼𝑛𝑡𝑡 The present value of interest tax shield
PV(τc * Intt) = (1+𝑟 𝑡 ∗
𝑈)
1+𝑟
(1+𝑟𝑈 )
𝐷
1+𝑟 Project-based WACC formula (Whereby the debt is adjusted
rwacc = ru – dτcrD1+𝑟𝑈
𝐷
annually rather than continuously to a target d)
1+𝑟𝑈 Value of a levered firm whereby the firm sets debt annually based
VL = (1+ τck ) * VU
1+𝑟𝐷
on its expected future free cash flow. This is still the constant
interest coverage model
𝐸 𝐷𝑠 Unlevered cost of capital with a fixed debt schedule
ru = 𝐸+𝐷𝑠 𝑟𝐸 + 𝐸+𝐷𝑠 𝑟𝐷
𝐸 𝐷𝑠 Unlevered cost of capital with personal taxes
ru = 𝐸+𝐷𝑠 𝑟𝐸 + 𝐸+𝐷𝑠 𝑟 ∗𝐷
r*D 1−𝜏𝑖
rD
1−𝜏𝑒
τ* * r*D * Dt-1 Interest tax shield in year t
Chapter 19
Debt -/- Cash Net debt
Chapter 20
C = P + S – PV(K) The price of a European call option (Put-call parity)
C = S – K + dis(K) + P
S–K Intrinsic value
dis(K) + P Time value
dis(K) + P – PV(Div)
Risk-free debt = Risky debt Removing risk by buying the same put option
+ Put option on firm assets
S+P=C+K Een aandeel met een put optie is altijd gelijk aan een call optie en
een zero-coupon bond
Chapter 21
𝑆 De beta van een call optie
𝛽𝑐 = 𝑐 𝛥𝛽𝑆
𝛽𝐸 De beta van een unlevered firm (Kun je herschrijven voor beta E)
𝛽𝑈 = 𝐷
𝛥(1+ )
𝐸
E=AΔ + B Equity in terms of a replicating portfolio of the firm’s assets and a
risk-free bond
𝐶 −𝐶 Delta. Het is de ‘beta’ van de opties
Δ = 𝑆𝑢−𝑆 𝑑
𝑢 𝑑
𝐶𝑑 −𝑆𝑑 Δ Risk free investment in replicating portfolio
B= 1+𝑟𝑓
𝑃𝑑 −𝑆𝑑 Δ
B=
1+𝑟𝑓
𝑆Δ Leverage ratio option
𝑆Δ+𝐵
4
, 𝜌∗𝐶𝑢 +(1−𝜌)∗𝐶𝑑 Prijs call option
C= 1+𝑟𝑓
Chapter 25
Purchase Price – PV(Lease Payments), if service/maintenance are non-existent
PV(Residual Value)
PV(Lease payments) + PV(Loan Payments
PV(Residual Value)
Chapter 26
Accounts receivable days + Cash Conversion Cycle (CCC)
Inventory Days – Accounts
payable days
Chapter 28
𝐴+𝑇+𝑆 𝐴 Post-merger share price > pre-merger share price
𝑁𝐴 +𝑥
>𝑁
𝐴
𝑥 𝑇+𝑆 𝑁𝐴 Exchange ratio
𝑛𝑇
< ( 𝐴 )𝑁
𝑇
𝑥 𝑃𝑇 𝑆 Exchange ratio in terms of target/acquirer prices
𝑛𝑇
< 𝑃 (1 + 𝑇)
𝐴
Chapter 30
𝑇
(1+ 𝑟 ) Covered Interest parity
F = S * (1+𝑟 $)𝑇
€
𝑆 Black-Scholes formula used to calculate the price of a call option on
C = (1+𝑟 𝑇 ∗ 𝑁(𝑑1 ) −
€)
𝐾 a currency
𝑇 𝑁(𝑑2 )
(1+𝑟$ )
𝑃𝑉(𝐶𝑡 ) Duration of a security
∑𝑡 ∗ 𝑡
𝑃
𝜀
-Duration * 𝑟 Percent change in value
1+
𝑘
𝐴 𝐵 Duration (D) of a portfolio with security A and B
DA+B = 𝐴+𝐵 𝐷𝐴 + 𝐴+𝐵 𝐷𝐵
𝐴 𝐿 Equity duration
DE = DA-L = 𝐴−𝐿 𝐷𝐴 − 𝐴−𝐿 𝐷𝐿
Short-term loan rate + Net borrowing cost
Fixed rate due on swap –
Floating rate received from
swap
(Expected payments)/(1+rL) AVIP
Stappenplan
Hoofdstuk 18
WACC methode om een project te waarden
1) Ga na of de aannames kloppen: Constante debt-to-equity ratio
𝐸 𝐷
2) Bereken de rwacc met de volgende formule: 𝑟 + 𝑟 (1 − 𝜏𝑐 )
𝐸+𝐷 𝐸 𝐸+𝐷 𝐷
3) Ga na wat de cashflows zijn (Zowel negatief als positief)
4) Verdisconteer alles met behulp van de rwacc
5) Resultaat: VL van het project
Adjusted Present Value (APV) methode om een project te waarderen
𝐸 𝐷
1) Reken de unlevered cost of capital uit: ru = 𝐸+𝐷 𝑟𝐸 + 𝐸+𝐷 𝑟𝐷
2) Reken de VU uit door alleen de positieve kasstromen te disconteren met de ru (Het gaat
namelijk niet om debt want het is unlevered)
𝐸 𝐷
3) Reken de WACC uit: 𝐸+𝐷 𝑟𝐸 + 𝐸+𝐷 𝑟𝐷 (1 − 𝜏𝑐 ).
5
Contents
Chapter 14 Capital structure in a perfect market ................................................................................... 5
Les 1 27-1 (14) ..................................................................................................................................... 9
Les 2 29-1 (14) ................................................................................................................................... 10
Chapter 15 Debt and taxes .................................................................................................................... 10
Les 3 3-2 (15) ..................................................................................................................................... 10
Tutorial 1 6-2 ......................................................................................................................................... 11
Chapter 16 Financial distress, managerial incentives, and information ............................................... 11
Les 4 10-2 (16) ................................................................................................................................... 12
Les 5 12-2........................................................................................................................................... 13
Les 6 17-2 (16) ................................................................................................................................... 13
Tutorial 2 20-2 ....................................................................................................................................... 14
Chapter 17 Payout Policy ...................................................................................................................... 15
Chapter 18 Capital budgeting and valuation with leverage .................................................................. 16
Les 7 2-3 (17) ..................................................................................................................................... 16
Les 8 4-3 (17 & 18)............................................................................................................................. 17
Les 9 9-3............................................................................................................................................. 17
Chapter 20 Financial Options ................................................................................................................ 17
Tutorial 3 13-3 ....................................................................................................................................... 18
Les 10 16-3......................................................................................................................................... 19
Les 11 18-3......................................................................................................................................... 19
Chapter 21 Option valuation ................................................................................................................. 20
Les 11 22-3......................................................................................................................................... 20
Chapter 23 Raising Equity Capital ......................................................................................................... 21
Les 12 6-4........................................................................................................................................... 23
Chapter 24 Debt financing..................................................................................................................... 24
Les 13 8-4........................................................................................................................................... 26
Les 14 20-4......................................................................................................................................... 26
Chapter 25 Leasing ................................................................................................................................ 27
Les 15 22-4......................................................................................................................................... 29
Chapter 26 Working capital management ............................................................................................ 29
Chapter 27 Short-term financial planning ............................................................................................. 30
Les 16 6-5........................................................................................................................................... 31
Chapter 28 Mergers and acquisitions ................................................................................................... 32
1
, Les 17 8-5........................................................................................................................................... 33
Les 18 11-5......................................................................................................................................... 33
Chapter 29 Corporate Governance (Not on exam) ............................................................................... 33
Chapter 30 Risk Management ............................................................................................................... 34
Les 19 ................................................................................................................................................. 35
Symbolen Betekenis
A Market value of the firm’s assets
A Pre-merger (equity) value of acquirer
B Bond
C Call option price
C0 The paid price (We assume that this is the ask price)
Ct Cash flow on date t
D Market value of debt in a levered firm
d Debt-to-value ratio
dis(K) The amount of the discount from face value to account for interest
Dp Duration of security or portfolio P
Ds Debt net of predetermined tax shields
E Market value of equity in a levered firm
Intt Interest expenses on t
k Interest coverage ratio (How many times the interest expenses are covered
with the FCF)
K Strike/exercise price
P Put option price / Price of a security
P’ New share price of increase in value
Pcum Cum-dividend stock price
Pex Ex-dividend stock price
Prep Stock price with share repurchase
Pretain Stock price if excess cash is retained
q Compounded, annualized dividend yield on the stock to the maturity of the
option
R Number of repurchased shares or Return
rA Expected return of firm assets
rD Market value returns on debt
rE Market value returns on levered equity
rU Market value return on unlevered equity
S Stock price
S Spot exchange rate
S (Present) value of the synergies created by the merger
SX De netto aandeelprijs (S-Pv(Div)) or S/(1+q)
T Time to maturity
T Pre-merger value of target
U Market value of unlevered equity
VU Unlevered value of the firm, so without debt. Only positive NPVs
x New shares issued by bidder in order to buy target
Δ Shares of stock in the replicating portfolio, thus representing the sensitivity of
option price to stock price
2
,ρ The probability of the chances in a risk-neutral two state model
σ Annualized volatility
τ*d Effective dividend tax rate
τc Corporate tax
τe Personal taxes on income from equity
τg Capital gains tax rate
τi Personal taxes on income from interest
Formule Betekenis
Chapter 14
A=U=E+D MM 1
𝐸 𝐷 Identity relationship (Pretax WACC). Only use this for multiple
𝑟
𝐸+𝐷 𝐸
+ 𝑟
𝐸+𝐷 𝐷
periods of time when D/E-ratio is constant for these periods
𝐷 MM Proposition II: Cost of levered equity, waarbij rU Cost of
rE = rU + (rU – rD)𝐸
unlevered equity is en rD de premium due to leverage is. re will
increase when D increases, if rU is larger then rD
𝐸 𝐷 Unlevered cost of capital
ru = 𝐸+𝐷 𝑟𝐸 + 𝐸+𝐷 𝑟𝐷
𝐸 𝐷 rwacc: verdisconteringsvoet van projecten
𝑟 + 𝐸+𝐷 𝑟𝐷 (1 − 𝜏𝑐 )
𝐸+𝐷 𝐸
𝐷 Number of repurchased shares
R = 𝑃′
𝐸 𝐷 A firm’s unlevered or asset beta
βU = 𝐸+𝐷 𝛽𝐸 + 𝐸+𝐷 𝛽𝐷
𝐷 The firm’s equity beta increases with leverage
𝛽𝐸 = 𝛽𝑈 + 𝐸 (𝛽𝑈 − 𝛽𝐷 )
𝐸𝑎𝑟𝑛𝑖𝑛𝑔𝑠 Earnings per share
EPS =
𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠ℎ𝑎𝑟𝑒𝑠
R(strong economy)-R(weak Return sensitivity (Systematic Risk)
economy)
𝐸(𝐶𝑓) Expected return of equity. Don’t discount the CF or the Debt
E(r) = 𝐸𝑞𝑢𝑖𝑡𝑦 − 1
Chapter 15
VL = VU + τcD Value of a levered firm (With permanent debt)
VL = VU + τ*D
(1−𝜏𝑐 )(1−𝜏𝑒 ) Effective tax advantage of debt. Dit is lager dan het tax shield met
τ* = 1 - alleen corporate taxes. Dit komt van de vergelijking (1-τ*) (1-τi) = (1-
(1−𝜏𝑖 )
τc) (1-τe, waarbij τ* ervoor zorgt dat het gelijk maakt. Schets het
daadwerkelijke tax advantage
𝜏𝑒 −𝜏𝑖 Excess interest payments (τc = 0). Always negative
τex* =
(1−𝜏𝑖 )
𝑁𝑃𝑉 𝛽𝐷 𝐷 The shareholders will benefit from a new investment if this equation
> holds
𝐼 𝛽𝐸 𝐸
Chapter 17
Pcum – Pex = Div * (1-τ*d) Share price drop before and after dividend imbursement
𝜏𝑑 −𝜏𝑔
τ*d = ( 1−𝜏 ) Effective dividend tax rate
𝑔
1−𝜏 The share price before dividend is paid
Pcum = Pex + Div0 * (1−𝜏𝑑 )
𝑔
𝐷𝑖𝑣∗(1−𝜏𝑑 ) Share price if excess cash is retained
Pretain = 𝑟𝑓 ∗(1−𝜏𝑖 )
(1−𝜏𝑐 )(1−𝜏𝑔 ) Effective tax disadvantage of retaining cash
τ*retain = (1 −
(1−𝜏𝑖 )
Chapter 18
3
, 𝐿
VtL:
𝐹𝐶𝐹𝑡+1 +𝑉𝑡+1
. De waarde van het bedrijf op tijdstip t (Gebruik dit in de APV-
1+𝑟𝑤𝑎𝑐𝑐 methode)
Vu + PV(Interest Tax shield) Adjusted present value (APV)
rD * Dt-1 Interest paid in year t
Dt – Dt-1 Net borrowing at date t
FCFE = FCF – (1-τc) * Free cash flow to equity
(Interest Payments) + (Net
Borrowing)
Interest/FCF Interest Coverage Ratio
k * FCFt Interest paid in year t
VL = (1+τck)VU Levered value with a constant interest coverage ratio (Constant
interest coverage model)
𝑐 𝜏 ∗𝐼𝑛𝑡𝑡 The present value of interest tax shield
PV(τc * Intt) = (1+𝑟 𝑡 ∗
𝑈)
1+𝑟
(1+𝑟𝑈 )
𝐷
1+𝑟 Project-based WACC formula (Whereby the debt is adjusted
rwacc = ru – dτcrD1+𝑟𝑈
𝐷
annually rather than continuously to a target d)
1+𝑟𝑈 Value of a levered firm whereby the firm sets debt annually based
VL = (1+ τck ) * VU
1+𝑟𝐷
on its expected future free cash flow. This is still the constant
interest coverage model
𝐸 𝐷𝑠 Unlevered cost of capital with a fixed debt schedule
ru = 𝐸+𝐷𝑠 𝑟𝐸 + 𝐸+𝐷𝑠 𝑟𝐷
𝐸 𝐷𝑠 Unlevered cost of capital with personal taxes
ru = 𝐸+𝐷𝑠 𝑟𝐸 + 𝐸+𝐷𝑠 𝑟 ∗𝐷
r*D 1−𝜏𝑖
rD
1−𝜏𝑒
τ* * r*D * Dt-1 Interest tax shield in year t
Chapter 19
Debt -/- Cash Net debt
Chapter 20
C = P + S – PV(K) The price of a European call option (Put-call parity)
C = S – K + dis(K) + P
S–K Intrinsic value
dis(K) + P Time value
dis(K) + P – PV(Div)
Risk-free debt = Risky debt Removing risk by buying the same put option
+ Put option on firm assets
S+P=C+K Een aandeel met een put optie is altijd gelijk aan een call optie en
een zero-coupon bond
Chapter 21
𝑆 De beta van een call optie
𝛽𝑐 = 𝑐 𝛥𝛽𝑆
𝛽𝐸 De beta van een unlevered firm (Kun je herschrijven voor beta E)
𝛽𝑈 = 𝐷
𝛥(1+ )
𝐸
E=AΔ + B Equity in terms of a replicating portfolio of the firm’s assets and a
risk-free bond
𝐶 −𝐶 Delta. Het is de ‘beta’ van de opties
Δ = 𝑆𝑢−𝑆 𝑑
𝑢 𝑑
𝐶𝑑 −𝑆𝑑 Δ Risk free investment in replicating portfolio
B= 1+𝑟𝑓
𝑃𝑑 −𝑆𝑑 Δ
B=
1+𝑟𝑓
𝑆Δ Leverage ratio option
𝑆Δ+𝐵
4
, 𝜌∗𝐶𝑢 +(1−𝜌)∗𝐶𝑑 Prijs call option
C= 1+𝑟𝑓
Chapter 25
Purchase Price – PV(Lease Payments), if service/maintenance are non-existent
PV(Residual Value)
PV(Lease payments) + PV(Loan Payments
PV(Residual Value)
Chapter 26
Accounts receivable days + Cash Conversion Cycle (CCC)
Inventory Days – Accounts
payable days
Chapter 28
𝐴+𝑇+𝑆 𝐴 Post-merger share price > pre-merger share price
𝑁𝐴 +𝑥
>𝑁
𝐴
𝑥 𝑇+𝑆 𝑁𝐴 Exchange ratio
𝑛𝑇
< ( 𝐴 )𝑁
𝑇
𝑥 𝑃𝑇 𝑆 Exchange ratio in terms of target/acquirer prices
𝑛𝑇
< 𝑃 (1 + 𝑇)
𝐴
Chapter 30
𝑇
(1+ 𝑟 ) Covered Interest parity
F = S * (1+𝑟 $)𝑇
€
𝑆 Black-Scholes formula used to calculate the price of a call option on
C = (1+𝑟 𝑇 ∗ 𝑁(𝑑1 ) −
€)
𝐾 a currency
𝑇 𝑁(𝑑2 )
(1+𝑟$ )
𝑃𝑉(𝐶𝑡 ) Duration of a security
∑𝑡 ∗ 𝑡
𝑃
𝜀
-Duration * 𝑟 Percent change in value
1+
𝑘
𝐴 𝐵 Duration (D) of a portfolio with security A and B
DA+B = 𝐴+𝐵 𝐷𝐴 + 𝐴+𝐵 𝐷𝐵
𝐴 𝐿 Equity duration
DE = DA-L = 𝐴−𝐿 𝐷𝐴 − 𝐴−𝐿 𝐷𝐿
Short-term loan rate + Net borrowing cost
Fixed rate due on swap –
Floating rate received from
swap
(Expected payments)/(1+rL) AVIP
Stappenplan
Hoofdstuk 18
WACC methode om een project te waarden
1) Ga na of de aannames kloppen: Constante debt-to-equity ratio
𝐸 𝐷
2) Bereken de rwacc met de volgende formule: 𝑟 + 𝑟 (1 − 𝜏𝑐 )
𝐸+𝐷 𝐸 𝐸+𝐷 𝐷
3) Ga na wat de cashflows zijn (Zowel negatief als positief)
4) Verdisconteer alles met behulp van de rwacc
5) Resultaat: VL van het project
Adjusted Present Value (APV) methode om een project te waarderen
𝐸 𝐷
1) Reken de unlevered cost of capital uit: ru = 𝐸+𝐷 𝑟𝐸 + 𝐸+𝐷 𝑟𝐷
2) Reken de VU uit door alleen de positieve kasstromen te disconteren met de ru (Het gaat
namelijk niet om debt want het is unlevered)
𝐸 𝐷
3) Reken de WACC uit: 𝐸+𝐷 𝑟𝐸 + 𝐸+𝐷 𝑟𝐷 (1 − 𝜏𝑐 ).
5
