Lecture 1: Introduction to the three decisions & time value of money
Teaching plan
Introduction to corporate finance
● A corporation is a legal entity. In the view of the law it is a legal person that is owned by its
shareholders
● Corporations invest in real assets, which generate income. Some of these assets, such as plant and
machinery, are tangible, while others such as brand names and patents are intangible
● Corporations finance their investments by:
○ borrowing
○ retaining and reinvesting cash flow
○ selling additional shares of stock to the corporation’s shareholders
● There is a trade-off for a firm when making investments and paying out dividends to shareholders.
The more cash is used to invest in a project, the less cash the corporation has to pay out dividends
● A corporation’s financial manager faces two broad financial questions:
○ What investments should the corporation make?
○ How should the corporation pay for these investments?
● The secret to success of financial management is how to increase the value of the corporation and its
current stock price (ethically). Each stockholder wants three things:
1
, ○ To be as rich as possible, that is, to maximize his or her current wealth
○ To transform that wealth into the most desirable time pattern of consumption either by
borrowing to spend now or investing to spend later
○ To manage the risk
● A public limited company is usually owned by shareholders
● The main objective of the financial management of an organization is to maximize shareholders’
wealth
Financial decisions
There are two (or three) main types of financial decisions:
1. Investment appraisal → what kind of investments are we going to make?
2. Corporate finance → are we going to pay excess cash as dividends and how?
Time value of money
● It is essential that cash flows have an amount and a time, cash flows at different times are not the
same
● The concept of the time value of money states that “a dollar today is worth more than a dollar
tomorrow.”
○ This is because you can invest the full amount and receive an additional return over the
following years
● You cannot add two different currencies together because cash flows at different points in time are
not compatible → bring them back to present value, converting to common currency
● If the interest rate of a year is greater than the inflation rate of that year, then net interest is
positive
● If the interest of a year is lower than the inflation rate of that year, then net interest is negative
● The second basic financial principle is that “a safe dollar is worth more than a risky dollar”
○ Most investors dislike risky ventures and won’t invest in them unless they see the prospect of
higher return
○ If you invest in stocks which are expected to provide you with a 12% return then that is the
opportunity cost of not investing in a project, for instance
○ If you are expected to receive a 14.3% return when investing in an office building and the
opportunity cost is 12%, you should go ahead with the project
Money/nominal vs real rate of return
Money/nominal rate of return — measures the return of money in terms of the unit currency that is
2
, (due to inflation), usually falling
Real rate of return — measures the return of money in constant price level terms
● The two rates of return are linked by the equation: (1 + r-nominal) = (1 + r-real)*(1 + inflation rate)
● Prior to discounting, it is important to figure out which rate to use
○ Money/nominal rate of return: use if cash flows are expressed in terms of actual pounds that
will be received or paid in the future
○ Real rate of return: used if cash flows are expressed in terms of the value of the pound at
time 0 (that is constant price level terms)
Compounding & discounting
● We account for the time differences this way, it is the equivalent of “exchange rates”
● Compounding — present value to future value
● Discounting — future value to present value
Present value — the value today of a future cash flow
Future value — the amount to which an investment will grow after earning interest
Compounding formula
𝑡
𝐹𝑉 = 𝑃𝑉 · (1 + 𝑟)
Where r = interest rate, and t = number of years
* FV can also be abbreviated as 𝐶 𝑡
Example
“Find the value in two years time of £1.00 if the interest rate is 10%”
2
𝐹𝑉 = 1 · (1 + 0. 1)
FV = 1.21
3
, Discounting formula
1
𝑃𝑉 = 𝐹𝑉 · 𝑡
(1 + 𝑟)
𝐹𝑉
𝑃𝑉 = 𝑡
(1 + 𝑟)
● To find the discounting formula you just have to rearrange the compounding formula and solve for PV
1
As 𝑡 is known as the discount factor we can rewrite the formula as:
(1 + 𝑟)
𝑃𝑉 = 𝐹𝑉 · 𝐷𝐹
𝑃𝑉 = (𝐶 1
· 𝐷𝐹 1) + (𝐶 2
· 𝐷𝐹 2
) ...
Where DF = discount factor
● The discount factor can be calculated as above, but often in an exam there will be a present values
table of discount rates and you have to pick the correct one based on the discount rate and time
1
○ E.g. for 8% discount rate and time = 3, 𝐷𝐹 = 3
(1.08)
Discount rate
Discount rate — the reward investors demand for accepting a delayed payment
● Investors demand what they could have received from risk-equivalent investment alternatives
● Thus the discount rate of a particular project is also called the opportunity cost of capital because
it is the return forgone by investing in that particular capital project rather than in other projects
4
Teaching plan
Introduction to corporate finance
● A corporation is a legal entity. In the view of the law it is a legal person that is owned by its
shareholders
● Corporations invest in real assets, which generate income. Some of these assets, such as plant and
machinery, are tangible, while others such as brand names and patents are intangible
● Corporations finance their investments by:
○ borrowing
○ retaining and reinvesting cash flow
○ selling additional shares of stock to the corporation’s shareholders
● There is a trade-off for a firm when making investments and paying out dividends to shareholders.
The more cash is used to invest in a project, the less cash the corporation has to pay out dividends
● A corporation’s financial manager faces two broad financial questions:
○ What investments should the corporation make?
○ How should the corporation pay for these investments?
● The secret to success of financial management is how to increase the value of the corporation and its
current stock price (ethically). Each stockholder wants three things:
1
, ○ To be as rich as possible, that is, to maximize his or her current wealth
○ To transform that wealth into the most desirable time pattern of consumption either by
borrowing to spend now or investing to spend later
○ To manage the risk
● A public limited company is usually owned by shareholders
● The main objective of the financial management of an organization is to maximize shareholders’
wealth
Financial decisions
There are two (or three) main types of financial decisions:
1. Investment appraisal → what kind of investments are we going to make?
2. Corporate finance → are we going to pay excess cash as dividends and how?
Time value of money
● It is essential that cash flows have an amount and a time, cash flows at different times are not the
same
● The concept of the time value of money states that “a dollar today is worth more than a dollar
tomorrow.”
○ This is because you can invest the full amount and receive an additional return over the
following years
● You cannot add two different currencies together because cash flows at different points in time are
not compatible → bring them back to present value, converting to common currency
● If the interest rate of a year is greater than the inflation rate of that year, then net interest is
positive
● If the interest of a year is lower than the inflation rate of that year, then net interest is negative
● The second basic financial principle is that “a safe dollar is worth more than a risky dollar”
○ Most investors dislike risky ventures and won’t invest in them unless they see the prospect of
higher return
○ If you invest in stocks which are expected to provide you with a 12% return then that is the
opportunity cost of not investing in a project, for instance
○ If you are expected to receive a 14.3% return when investing in an office building and the
opportunity cost is 12%, you should go ahead with the project
Money/nominal vs real rate of return
Money/nominal rate of return — measures the return of money in terms of the unit currency that is
2
, (due to inflation), usually falling
Real rate of return — measures the return of money in constant price level terms
● The two rates of return are linked by the equation: (1 + r-nominal) = (1 + r-real)*(1 + inflation rate)
● Prior to discounting, it is important to figure out which rate to use
○ Money/nominal rate of return: use if cash flows are expressed in terms of actual pounds that
will be received or paid in the future
○ Real rate of return: used if cash flows are expressed in terms of the value of the pound at
time 0 (that is constant price level terms)
Compounding & discounting
● We account for the time differences this way, it is the equivalent of “exchange rates”
● Compounding — present value to future value
● Discounting — future value to present value
Present value — the value today of a future cash flow
Future value — the amount to which an investment will grow after earning interest
Compounding formula
𝑡
𝐹𝑉 = 𝑃𝑉 · (1 + 𝑟)
Where r = interest rate, and t = number of years
* FV can also be abbreviated as 𝐶 𝑡
Example
“Find the value in two years time of £1.00 if the interest rate is 10%”
2
𝐹𝑉 = 1 · (1 + 0. 1)
FV = 1.21
3
, Discounting formula
1
𝑃𝑉 = 𝐹𝑉 · 𝑡
(1 + 𝑟)
𝐹𝑉
𝑃𝑉 = 𝑡
(1 + 𝑟)
● To find the discounting formula you just have to rearrange the compounding formula and solve for PV
1
As 𝑡 is known as the discount factor we can rewrite the formula as:
(1 + 𝑟)
𝑃𝑉 = 𝐹𝑉 · 𝐷𝐹
𝑃𝑉 = (𝐶 1
· 𝐷𝐹 1) + (𝐶 2
· 𝐷𝐹 2
) ...
Where DF = discount factor
● The discount factor can be calculated as above, but often in an exam there will be a present values
table of discount rates and you have to pick the correct one based on the discount rate and time
1
○ E.g. for 8% discount rate and time = 3, 𝐷𝐹 = 3
(1.08)
Discount rate
Discount rate — the reward investors demand for accepting a delayed payment
● Investors demand what they could have received from risk-equivalent investment alternatives
● Thus the discount rate of a particular project is also called the opportunity cost of capital because
it is the return forgone by investing in that particular capital project rather than in other projects
4
