IB 132: Foundations of Finance
Lecture 1: Introduction
- We will be considering public firms
Shares are traded at a stock exchange
Market value: share price x number of shares outstanding
Limited liability: at most, shareholders can lose the value of shares
This is why firms often have LLC after their name
- There is a separation between ownership and management
Shareholders elect of board of directors (each share gives 1 vote)
The BoD elects and monitors a CEO and sets executive remuneration
Managers are legally distinct from owners and pay their own taxes
- The management’s objective should be to maximize benefit for shareholders
Capital budgeting: how firms choose the best investments when they have multiple investment
opportunities
Different tools try to assign values to investments
For firms, investments generate cash flows
Capital structure: after deciding which investments to undertake, how should the firm pay for
the investments
Use a bank loan?
Sell a share to partners?
Payout decision: after investments have generated cash, how should we return the cash to the
shareholders?
Project: set of cash flows in the present and at different points in the future
- Usually entail immediate outflows (costs / expenses)
Followed by a series of future inflows (payoffs / revenues)
Valuation: assigning a project a monetary value today
- Valuation is relative to alternatives
Opportunity Cost of Capital: cost of foregoing alternative projects / investments
Law of One Price (LOP): identical projects have identical prices (or similar projects have similar
prices)
- Finance uses tools from other disciplines:
Economics: science of tradeoffs given limited resources
Statistics: science of dealing with uncertainty
Accounting: science of keeping financial accounts
,Lecture 2: Present Value
- You can always earn an interest rate (r) if you invest some money today, which will be paid at
some specified time in the future
Time value of money: the same amount of money today is more valuable today than in the
future because it can be invested and earn interest r
- Scarcity means investors cannot pursue every project
So, they must choose the most profitable
- We denote different time periods as:
0, today
1, next period (day, year, etc.)
t , some future time period
T , the final time period (if finite duration)
Cash flows: flows of money
- Outflows are negative and inflows are positive
C 0 is the cash amount today
C 1 is the cash amount in the next period
Rate of return: from investing C 0 and receiving C t
It is a percentage:
C t −C0 Ct
r 0,1 = = −1
C0 C0
- Do not confuse cash flows with rate of return!
- We begin with some unrealistic assumptions:
Perfect Capital Markets:
We pay no taxes, no transaction costs
No information asymmetries
Individual buyers and sellers are small
No Risk or Uncertainty:
Perfect foresight about the future
Know for certain the cash flow of each investment
Future value of this amount (C t ): the value of a certain amount of money in the future since it
can be invested and appreciate in value over time according to some rate of return
- For one time period, we know:
C 1−C 0
r 1=
C0
SO:
C 0 ( 1+r )=C1
- If we hold our investment for t periods, we compound it:
C t=C 0 ( 1+ r )t
Compounding produces an exponential graph
Holding period return: for a t -period project reflects compounding:
(1+r t )=( 1+ r ) (1+r ) … ( 1+r )=( 1+r )t
- If we are given the final interest and the holding period, we can find the rate of return for
each period:
, r =√1+r t−1
t
- The formula also works for fractional periods
Present Value of Money (PV): the value of a future amount of money today (Present value of
future cash flows???)
- Tells us what we should pay for a project and how it compares to alternatives
We must discount the amount tomorrow:
C1 C2 Ct
C 0= + +…
1+ r (1+ r)2
(1+r )
t
T
Ct
PV =∑ t
t =1 (1+r )
- The graph of the present value of a future $1 decreases exponentially the further in the
future the amount is
Opportunity cost of capital (OCC): rate at which money can grow if we invest in other similar
projects
- With no uncertainty, r is the risk-free rate
Discount factor: ( )
1 t
1+r 1
: translates future cashflows into money today
Bonds
- Zero-coupon government bonds cost C 0 today and pay C T =(1+r )C 0 at maturity
Since economy-wide interest rate is the cost of capital for bonds, the price of bonds
varies inversely with the interest rate
Cr
C 0=PV =
(1+r )
Net Present Value: present value of cash inflows minus present value of cash outflows
1. Translate inflows into today’s currency and sum to PV (inflows)
2. Translate outflows into today’s currency and sum to PV (outflows)
3. Subtract PV (outflows) form PV (inflows)
- Often, projects have one outflow at time 0 (C 0< 0)
T
Ct T
Ct
NPV =C 0+ ∑ t
=∑ t
t =1 (1+ r) (1+r ) t=0
Capital Budgeting Rule: we should undertake all projects with NPV > 0
- Increases wealth by more than other similar projects
Lecture 3: Perpetuities and Annuities
Perpetuity: asset that pays C per period forever
Lecture 1: Introduction
- We will be considering public firms
Shares are traded at a stock exchange
Market value: share price x number of shares outstanding
Limited liability: at most, shareholders can lose the value of shares
This is why firms often have LLC after their name
- There is a separation between ownership and management
Shareholders elect of board of directors (each share gives 1 vote)
The BoD elects and monitors a CEO and sets executive remuneration
Managers are legally distinct from owners and pay their own taxes
- The management’s objective should be to maximize benefit for shareholders
Capital budgeting: how firms choose the best investments when they have multiple investment
opportunities
Different tools try to assign values to investments
For firms, investments generate cash flows
Capital structure: after deciding which investments to undertake, how should the firm pay for
the investments
Use a bank loan?
Sell a share to partners?
Payout decision: after investments have generated cash, how should we return the cash to the
shareholders?
Project: set of cash flows in the present and at different points in the future
- Usually entail immediate outflows (costs / expenses)
Followed by a series of future inflows (payoffs / revenues)
Valuation: assigning a project a monetary value today
- Valuation is relative to alternatives
Opportunity Cost of Capital: cost of foregoing alternative projects / investments
Law of One Price (LOP): identical projects have identical prices (or similar projects have similar
prices)
- Finance uses tools from other disciplines:
Economics: science of tradeoffs given limited resources
Statistics: science of dealing with uncertainty
Accounting: science of keeping financial accounts
,Lecture 2: Present Value
- You can always earn an interest rate (r) if you invest some money today, which will be paid at
some specified time in the future
Time value of money: the same amount of money today is more valuable today than in the
future because it can be invested and earn interest r
- Scarcity means investors cannot pursue every project
So, they must choose the most profitable
- We denote different time periods as:
0, today
1, next period (day, year, etc.)
t , some future time period
T , the final time period (if finite duration)
Cash flows: flows of money
- Outflows are negative and inflows are positive
C 0 is the cash amount today
C 1 is the cash amount in the next period
Rate of return: from investing C 0 and receiving C t
It is a percentage:
C t −C0 Ct
r 0,1 = = −1
C0 C0
- Do not confuse cash flows with rate of return!
- We begin with some unrealistic assumptions:
Perfect Capital Markets:
We pay no taxes, no transaction costs
No information asymmetries
Individual buyers and sellers are small
No Risk or Uncertainty:
Perfect foresight about the future
Know for certain the cash flow of each investment
Future value of this amount (C t ): the value of a certain amount of money in the future since it
can be invested and appreciate in value over time according to some rate of return
- For one time period, we know:
C 1−C 0
r 1=
C0
SO:
C 0 ( 1+r )=C1
- If we hold our investment for t periods, we compound it:
C t=C 0 ( 1+ r )t
Compounding produces an exponential graph
Holding period return: for a t -period project reflects compounding:
(1+r t )=( 1+ r ) (1+r ) … ( 1+r )=( 1+r )t
- If we are given the final interest and the holding period, we can find the rate of return for
each period:
, r =√1+r t−1
t
- The formula also works for fractional periods
Present Value of Money (PV): the value of a future amount of money today (Present value of
future cash flows???)
- Tells us what we should pay for a project and how it compares to alternatives
We must discount the amount tomorrow:
C1 C2 Ct
C 0= + +…
1+ r (1+ r)2
(1+r )
t
T
Ct
PV =∑ t
t =1 (1+r )
- The graph of the present value of a future $1 decreases exponentially the further in the
future the amount is
Opportunity cost of capital (OCC): rate at which money can grow if we invest in other similar
projects
- With no uncertainty, r is the risk-free rate
Discount factor: ( )
1 t
1+r 1
: translates future cashflows into money today
Bonds
- Zero-coupon government bonds cost C 0 today and pay C T =(1+r )C 0 at maturity
Since economy-wide interest rate is the cost of capital for bonds, the price of bonds
varies inversely with the interest rate
Cr
C 0=PV =
(1+r )
Net Present Value: present value of cash inflows minus present value of cash outflows
1. Translate inflows into today’s currency and sum to PV (inflows)
2. Translate outflows into today’s currency and sum to PV (outflows)
3. Subtract PV (outflows) form PV (inflows)
- Often, projects have one outflow at time 0 (C 0< 0)
T
Ct T
Ct
NPV =C 0+ ∑ t
=∑ t
t =1 (1+ r) (1+r ) t=0
Capital Budgeting Rule: we should undertake all projects with NPV > 0
- Increases wealth by more than other similar projects
Lecture 3: Perpetuities and Annuities
Perpetuity: asset that pays C per period forever
