Finance
Chapter 5
The time value of money refers to the observation that it’s better to receive money sooner than
later. You can invest money you have in hand today to earn a positive rate of return, producing
more money tomorrow. A dollar today is worth more than a dollar in the future.
There are several basic cash flow patterns:
- Single amount: an amount either currently held or expected. For example, someone
might want to know how much a $1,000 investment today might be worth in 5 years or
how much money you have to set aside today to cover some specific one-time payment
in the future.
- Annuity: a level periodic stream of cash flow. Many financial arrangements involve
making or receiving a fixed payment each month or each year for several years. Home
mortgage for example. You can use time-value-of-money techniques to determine what
the monthly mortgage payment will be given the size of the loan required to buy a home.
- Mixed stream: a stream of cash flow that is not an annuity; a stream of unequal periodic
cash flows that don’t reflect a particular pattern. Business investments for example.
Future value of a single amount (lump sum):
- Future value is the value on some future date of money that you invest today.
- Compound interest is interest that is earned on a given deposit and has become part of
the principal at the end of a specific period. The term principal may refer to the original
amount of money placed into an investment or to the balance on which an investment
pays interest. Example:
If Fred places $100 in an account paying 7% interest compounded annually, after 1 year he will
have $108 in the account. The future value at the end of the first year is:
- Future value at the end of year 1 = $100 * (1+0.08) = $108
If Fred were to leave his money in the account for another yearm he would be paid 8% interest
on the new principal of $108.
- Future value after 2 years = $108 * (1+0.08) = $116.64
- Or:
- Future value after 2 years = $100 * (1+0.08)^2 = $116.64
Simple interest is interest that is earned only on an investment’s original principal and not on
interest that accumulated over time.
Money accumulates faster on compound interest.
, Discounting cash flows is the process of finding present values: the inverse of compounding
interest.
Fred has an opportunity to receive $300 1 year from now. He can earn a return of 2% on money
he has on hand today. To determine how much he would be willing to pay to receive $300 one
year from now, Fred can think of how much of his own money he would have to set aside right
now to earn $300 by next year.
● PV0 * (1+0.02) = $300
● PV0 = $300 / (1+0.02) = $294.12
The present value of $300 received 1 year from today, using a 2% interest rate is $294.12.
- Present value today (today = 0) = future value n / (1+r)^n
Fred has been offered an investment opportunity that will pay him $1,700 8 years from now. He
requires a 4% return on this opportunity. He should pay:
● PV0 = $1,700 / (1+0.04)^8 = $1,242.17 for now.
Compounding = calculating sums today into the future.
Discounting = calculating future funds to today's value (the opposite of compounding).
Chapter 10
Capital budgeting describes the process of evaluating and selecting investment projects.
The net present value method has become the gold standard for analyzing investments. Other
methods are payback and the internal rate of return.
Capital budgeting is the process of evaluating and selecting long-term investments that
contribute to the firm’s goal of maximizing owners’ wealth. Companies usually make a variety of
long-term investments: fixed assets such as property, plant and equipment but also research
and development (earning assets).
- Does the investment create value for shareholders?
- Where will the money to pay for the investment come from?
Chapter 5
The time value of money refers to the observation that it’s better to receive money sooner than
later. You can invest money you have in hand today to earn a positive rate of return, producing
more money tomorrow. A dollar today is worth more than a dollar in the future.
There are several basic cash flow patterns:
- Single amount: an amount either currently held or expected. For example, someone
might want to know how much a $1,000 investment today might be worth in 5 years or
how much money you have to set aside today to cover some specific one-time payment
in the future.
- Annuity: a level periodic stream of cash flow. Many financial arrangements involve
making or receiving a fixed payment each month or each year for several years. Home
mortgage for example. You can use time-value-of-money techniques to determine what
the monthly mortgage payment will be given the size of the loan required to buy a home.
- Mixed stream: a stream of cash flow that is not an annuity; a stream of unequal periodic
cash flows that don’t reflect a particular pattern. Business investments for example.
Future value of a single amount (lump sum):
- Future value is the value on some future date of money that you invest today.
- Compound interest is interest that is earned on a given deposit and has become part of
the principal at the end of a specific period. The term principal may refer to the original
amount of money placed into an investment or to the balance on which an investment
pays interest. Example:
If Fred places $100 in an account paying 7% interest compounded annually, after 1 year he will
have $108 in the account. The future value at the end of the first year is:
- Future value at the end of year 1 = $100 * (1+0.08) = $108
If Fred were to leave his money in the account for another yearm he would be paid 8% interest
on the new principal of $108.
- Future value after 2 years = $108 * (1+0.08) = $116.64
- Or:
- Future value after 2 years = $100 * (1+0.08)^2 = $116.64
Simple interest is interest that is earned only on an investment’s original principal and not on
interest that accumulated over time.
Money accumulates faster on compound interest.
, Discounting cash flows is the process of finding present values: the inverse of compounding
interest.
Fred has an opportunity to receive $300 1 year from now. He can earn a return of 2% on money
he has on hand today. To determine how much he would be willing to pay to receive $300 one
year from now, Fred can think of how much of his own money he would have to set aside right
now to earn $300 by next year.
● PV0 * (1+0.02) = $300
● PV0 = $300 / (1+0.02) = $294.12
The present value of $300 received 1 year from today, using a 2% interest rate is $294.12.
- Present value today (today = 0) = future value n / (1+r)^n
Fred has been offered an investment opportunity that will pay him $1,700 8 years from now. He
requires a 4% return on this opportunity. He should pay:
● PV0 = $1,700 / (1+0.04)^8 = $1,242.17 for now.
Compounding = calculating sums today into the future.
Discounting = calculating future funds to today's value (the opposite of compounding).
Chapter 10
Capital budgeting describes the process of evaluating and selecting investment projects.
The net present value method has become the gold standard for analyzing investments. Other
methods are payback and the internal rate of return.
Capital budgeting is the process of evaluating and selecting long-term investments that
contribute to the firm’s goal of maximizing owners’ wealth. Companies usually make a variety of
long-term investments: fixed assets such as property, plant and equipment but also research
and development (earning assets).
- Does the investment create value for shareholders?
- Where will the money to pay for the investment come from?
