1 Objectives and functions of financial management
1.1 The role of the financial manager (CFO, finance director)
- Investment decisions (Azijde van BS)
o In which assets should the firm invest?
- Financing decisions (Pzijde van BS)
o How can/ should the firm finance these assets?
- Financial planning
o How should the financial flows be managed?
Trade off btw too much and too little money
1.2 The objective of financial management
- Maximisation of: Revenues? Profits? Profits per share? Value per share?
- VB: A company has a 20% profitability rate and a profit per share of € 2 (no debts).
The company can issue new equity and invest the proceeds in 10% bonds
Which objective?
- The creation of shareholder value
o Value is not determined by the current profit per share, but by the expected
future profits and the risk associated with these profits
o In an efficient market, the market price of a share will reflects its value
- BUT is value maximalisation really the objective of companies?
o Shouldn’t we also take into account the broader societal context?
- ESG (Environmental, Social and Governance) & CSR (Corporate Social Responsibility)
o Business practices that go beyond profit-making to positively impact society
Key areas: environment, community engagement, ethical labor
practices, corporate governance
Objectives: build trust, enhance brand reputation, ensure LT
sustainability
o FE: Reducing carbon footprint, fair trade sourcing, supporting local
communities
- = > Assumption: value maximization is the objective of the firm
Corporate governance:
- Concept: How can shareholders make sure that the management of the company will
maximise shareholder value?
- Often: conflicts of interest btw the management and the shareholders of a company
,- Agency-theorie:
o The ‘agent’ (= manager) acts in the interest of het ‘principal’ (= shareholder)
o In reality: the interest of the agent can be different from those of the principal
The agent may care more about his own interests than those of the
principal
The shareholder lacks info to have a full picture of what the manager
is doing
The manager can use the firm to pursue his own interests, at
the expense of shareholder value
- Other agency-relations in a company:
o Controlling shareholder vs minority shareholder
Family firms listed on a stock exchange
o Shareholders vs debtholders
Maximizing shareholder value may be at the expense of the value of
the debtholders
Shareholders want high dividends but debtholders want their
money back + interest on it
o Also customers, suppliers, employees and the state have interest in the firm
, PART 1: VALUATION PRINCIPLES
2 Basic valuation concepts
2.1 Present value (PV) and Future value (FV)
t
E=B ( 1+i )
E
⇔ B=
( 1+i )t
- E = endvalue = FV
- B = PV
- i = interest rate over the period
- t = number of periods
o ( 1+i )t = discount factor
Het principe van compound interest:
- = earning interest on interest -> every year more interest -> endvalue grows faster
and faster
- If you invest an amount B for 1y at an interest rate i, you will receive B (1+i ) back
after 1y. If you reinvest this amount for another year, you will receive
2
B (1+i ) ( 1+i )=B (1+i ) back in the second year
OEF:
- Assume you invest €1000 for 1y at 5%. What will be the value after 1y?
o Interest = 1000∗0,05=50
o Value after 1y = principle + interest = 1000+50=1050
o FV =1000 ( 1+0,05 )=1050
- If you invest thus sum again for 1y, what will be the value after 2y?
o FV =1000∗( 1,05 )∗( 1,05 )=1000∗ (1,05 )2=1102,50
OEF:
- Grandpa gives his granddaughter who was just born a sum of € 30000, which will be
invested at an annual interest rate of 7%
o How much money will the granddaughter have when she is 21y old? (~ FV)
En =B∗( 1+i )n=30.000∗( 1+0,07 )21=124.217
- Grandpa wants his grandson, who is now 10y old, to have the same capital as his
granddaughter when he’s 21 years old, this is € 124217
o What amount should grandpa invest if the annual interest rate is 7%? (~ PV)
, En 124.217
B= n
= =59.624,16
( 1+i ) ( 1+0,07 )11
2.2 Interest periodicity less than one year
FV and PV with an interest settlement shorter than 1y (per half year/ quarter/ …):
( )
m∗n
i
En =B∗ 1+
m
En
⇔ B=
( )
m∗n
i
1+
m
- m: number of periods in 1y/ interest settlement in 1y
NOTE: Higher number of interest settlements per year (m) and higher number of years
(n) -> higher end value (FV) because of compound interest
OEF:
- Investment of €100 with 8% annual interest
o Half-yearly interest settlement
( )
1
0,08
After half a year: E1 /2=100∗ 1+ =104
2
After 1y: E =100∗( 1+
2 )
2∗1
0,08
1 =108,16
o Interest settlement per quarter (4x/y)
( )
4∗3
0,08
After 3y: E3 =100∗ 1+ =126,82
4
FV and PV for continuous interest settlement:
En =B∗e i∗n
En
⇔ B=
ei∗n
OEF:
- End value (FV) of a €100 investment with 8% annual interest after 3y?
o In the case of continuous interest settlement:
E3 =100∗e0,08∗3 =127,12
o In the case of annual interest settlement:
E3 =100∗( 1+0,08 )3=125,97
2.3 FV and PV of a series of different cash flows
In most economic problems CF’s C t are received or paid at different points in time
, FV and PV of a series of different CF’s:
n
En =∑ ( 1+i ) ∗¿C t ¿
n−t
t=1
n
Ct
B0=∑
t =1 ( 1+i )t
2.4 The valuation of annuities and perpetuities
2.4.1 PV of an infinite series of equal cash flows (perpetuity)
∞ ∞
C 1 C
B=∑ =C∗∑ =
t =1 ( 1+i ) t
t =1 ( 1+i )
t
i
OEF:
- What is the PV of €1000 received annually forever, if the interest rate is 8%?
C 1000
o B= = =12500 €
i 0,08
2.4.2 PV of an infinite series of constantly growing cash flows
If the infinite series of CF’s is not constant but grows at a constant growth rate g, then:
C 1=C0∗( 1+ g )
C 2=C1∗( 1+ g )=C 0∗( 1+ g )2
n
⇒ C n=C 0∗( 1+ g )
The PV of an infinite series of constantly growing CF’s with growth rate lower than discount
rate ( g<i ), is:
∞ ∞
Ct ( 1+ g )t C 1
B=∑ =C 0∗∑ =
t =1 ( 1+i )
t
t =1 ( 1+i )
t
i−g
2.4.3 PV and FV of a finite series of equal cash flows (annuities)
If the series of equal CF’s is finite, ending in year n, the PV will be:
( )
1
( )
n ∞ ∞ n
C 1 1 1 i C∗( 1+ i ) −1
B=∑ =C∗ ∑ −∑ =C∗ − =
t =1 ( 1+i )
t
t=1 ( 1+i )
t
t=n+ 1 ( 1+i )
t
i ( 1+ i )n i∗( 1+i )
n
FV of an annuity flow: Annuity factor = AF
t
E=B∗( 1+i )
OEF:
- At the age of 40 you decide to save an equal amount each year, with the aim of
obtaining a capital of 250000 € when you retire at the age of 65. The financial
1.1 The role of the financial manager (CFO, finance director)
- Investment decisions (Azijde van BS)
o In which assets should the firm invest?
- Financing decisions (Pzijde van BS)
o How can/ should the firm finance these assets?
- Financial planning
o How should the financial flows be managed?
Trade off btw too much and too little money
1.2 The objective of financial management
- Maximisation of: Revenues? Profits? Profits per share? Value per share?
- VB: A company has a 20% profitability rate and a profit per share of € 2 (no debts).
The company can issue new equity and invest the proceeds in 10% bonds
Which objective?
- The creation of shareholder value
o Value is not determined by the current profit per share, but by the expected
future profits and the risk associated with these profits
o In an efficient market, the market price of a share will reflects its value
- BUT is value maximalisation really the objective of companies?
o Shouldn’t we also take into account the broader societal context?
- ESG (Environmental, Social and Governance) & CSR (Corporate Social Responsibility)
o Business practices that go beyond profit-making to positively impact society
Key areas: environment, community engagement, ethical labor
practices, corporate governance
Objectives: build trust, enhance brand reputation, ensure LT
sustainability
o FE: Reducing carbon footprint, fair trade sourcing, supporting local
communities
- = > Assumption: value maximization is the objective of the firm
Corporate governance:
- Concept: How can shareholders make sure that the management of the company will
maximise shareholder value?
- Often: conflicts of interest btw the management and the shareholders of a company
,- Agency-theorie:
o The ‘agent’ (= manager) acts in the interest of het ‘principal’ (= shareholder)
o In reality: the interest of the agent can be different from those of the principal
The agent may care more about his own interests than those of the
principal
The shareholder lacks info to have a full picture of what the manager
is doing
The manager can use the firm to pursue his own interests, at
the expense of shareholder value
- Other agency-relations in a company:
o Controlling shareholder vs minority shareholder
Family firms listed on a stock exchange
o Shareholders vs debtholders
Maximizing shareholder value may be at the expense of the value of
the debtholders
Shareholders want high dividends but debtholders want their
money back + interest on it
o Also customers, suppliers, employees and the state have interest in the firm
, PART 1: VALUATION PRINCIPLES
2 Basic valuation concepts
2.1 Present value (PV) and Future value (FV)
t
E=B ( 1+i )
E
⇔ B=
( 1+i )t
- E = endvalue = FV
- B = PV
- i = interest rate over the period
- t = number of periods
o ( 1+i )t = discount factor
Het principe van compound interest:
- = earning interest on interest -> every year more interest -> endvalue grows faster
and faster
- If you invest an amount B for 1y at an interest rate i, you will receive B (1+i ) back
after 1y. If you reinvest this amount for another year, you will receive
2
B (1+i ) ( 1+i )=B (1+i ) back in the second year
OEF:
- Assume you invest €1000 for 1y at 5%. What will be the value after 1y?
o Interest = 1000∗0,05=50
o Value after 1y = principle + interest = 1000+50=1050
o FV =1000 ( 1+0,05 )=1050
- If you invest thus sum again for 1y, what will be the value after 2y?
o FV =1000∗( 1,05 )∗( 1,05 )=1000∗ (1,05 )2=1102,50
OEF:
- Grandpa gives his granddaughter who was just born a sum of € 30000, which will be
invested at an annual interest rate of 7%
o How much money will the granddaughter have when she is 21y old? (~ FV)
En =B∗( 1+i )n=30.000∗( 1+0,07 )21=124.217
- Grandpa wants his grandson, who is now 10y old, to have the same capital as his
granddaughter when he’s 21 years old, this is € 124217
o What amount should grandpa invest if the annual interest rate is 7%? (~ PV)
, En 124.217
B= n
= =59.624,16
( 1+i ) ( 1+0,07 )11
2.2 Interest periodicity less than one year
FV and PV with an interest settlement shorter than 1y (per half year/ quarter/ …):
( )
m∗n
i
En =B∗ 1+
m
En
⇔ B=
( )
m∗n
i
1+
m
- m: number of periods in 1y/ interest settlement in 1y
NOTE: Higher number of interest settlements per year (m) and higher number of years
(n) -> higher end value (FV) because of compound interest
OEF:
- Investment of €100 with 8% annual interest
o Half-yearly interest settlement
( )
1
0,08
After half a year: E1 /2=100∗ 1+ =104
2
After 1y: E =100∗( 1+
2 )
2∗1
0,08
1 =108,16
o Interest settlement per quarter (4x/y)
( )
4∗3
0,08
After 3y: E3 =100∗ 1+ =126,82
4
FV and PV for continuous interest settlement:
En =B∗e i∗n
En
⇔ B=
ei∗n
OEF:
- End value (FV) of a €100 investment with 8% annual interest after 3y?
o In the case of continuous interest settlement:
E3 =100∗e0,08∗3 =127,12
o In the case of annual interest settlement:
E3 =100∗( 1+0,08 )3=125,97
2.3 FV and PV of a series of different cash flows
In most economic problems CF’s C t are received or paid at different points in time
, FV and PV of a series of different CF’s:
n
En =∑ ( 1+i ) ∗¿C t ¿
n−t
t=1
n
Ct
B0=∑
t =1 ( 1+i )t
2.4 The valuation of annuities and perpetuities
2.4.1 PV of an infinite series of equal cash flows (perpetuity)
∞ ∞
C 1 C
B=∑ =C∗∑ =
t =1 ( 1+i ) t
t =1 ( 1+i )
t
i
OEF:
- What is the PV of €1000 received annually forever, if the interest rate is 8%?
C 1000
o B= = =12500 €
i 0,08
2.4.2 PV of an infinite series of constantly growing cash flows
If the infinite series of CF’s is not constant but grows at a constant growth rate g, then:
C 1=C0∗( 1+ g )
C 2=C1∗( 1+ g )=C 0∗( 1+ g )2
n
⇒ C n=C 0∗( 1+ g )
The PV of an infinite series of constantly growing CF’s with growth rate lower than discount
rate ( g<i ), is:
∞ ∞
Ct ( 1+ g )t C 1
B=∑ =C 0∗∑ =
t =1 ( 1+i )
t
t =1 ( 1+i )
t
i−g
2.4.3 PV and FV of a finite series of equal cash flows (annuities)
If the series of equal CF’s is finite, ending in year n, the PV will be:
( )
1
( )
n ∞ ∞ n
C 1 1 1 i C∗( 1+ i ) −1
B=∑ =C∗ ∑ −∑ =C∗ − =
t =1 ( 1+i )
t
t=1 ( 1+i )
t
t=n+ 1 ( 1+i )
t
i ( 1+ i )n i∗( 1+i )
n
FV of an annuity flow: Annuity factor = AF
t
E=B∗( 1+i )
OEF:
- At the age of 40 you decide to save an equal amount each year, with the aim of
obtaining a capital of 250000 € when you retire at the age of 65. The financial
