15/02
MN10500 Lecture 2: The Time Value of Money
Compare Values of Different 'Dimensions'
● We cannot add currencies without first converting into common currency.
● The same applies to cash flows (money) of different dates: Education Investment
(Current) VS Job Salary (Future)
Basis Problem (for understanding)
Your university education will cost you £30k pounds. Your parents set up an education
account 15 years ago with a bank to deposit £2k into the account each year. The bank pays
an interest of 3% annually. Also, assume that the opportunity cost of your capital is 5%.
● Will the saving be enough to cover the expense?
● Assume a bachelor's degree will increase your annual salary (without the degree) by
£1,800 for the next 30 years, will it be worth the investment?
● Further assume that the growth rate of your salary is 2%, will it be worth the
investment now?
Opportunity cost: second best return which you can get out of your money.
The Time Value of Money
● The time value of money
○ "A dollar today is worth more than a dollar tomorrow."
○ It concerns both the present value (PV) and the future value (FV).
● Interest rate (r) as a measure of time value of money
○ (Required) rate of return
○ Discount rate
○ Opportunity cost of money
○ Interest rate is the "exchange rate" that we use to transform the money at
different times to a unified dimension.
Future Value of a Single Cash Flow
● What is the future value of a £100 investment in a bank account paying 5% every
year for 2 years?
Future Value of a Single Cash Flow: Generalisation
, 15/02
Future Values with Compounding
Future Value of Annuities
● Annuity: a stream of equal cash flows that occurs yearly over a given period.
● A very important property is that at the same dimension of money, at a certain point
of time, all the cash flows can be added together.
Future Value of an Annuity: Generalisation
MN10500 Lecture 2: The Time Value of Money
Compare Values of Different 'Dimensions'
● We cannot add currencies without first converting into common currency.
● The same applies to cash flows (money) of different dates: Education Investment
(Current) VS Job Salary (Future)
Basis Problem (for understanding)
Your university education will cost you £30k pounds. Your parents set up an education
account 15 years ago with a bank to deposit £2k into the account each year. The bank pays
an interest of 3% annually. Also, assume that the opportunity cost of your capital is 5%.
● Will the saving be enough to cover the expense?
● Assume a bachelor's degree will increase your annual salary (without the degree) by
£1,800 for the next 30 years, will it be worth the investment?
● Further assume that the growth rate of your salary is 2%, will it be worth the
investment now?
Opportunity cost: second best return which you can get out of your money.
The Time Value of Money
● The time value of money
○ "A dollar today is worth more than a dollar tomorrow."
○ It concerns both the present value (PV) and the future value (FV).
● Interest rate (r) as a measure of time value of money
○ (Required) rate of return
○ Discount rate
○ Opportunity cost of money
○ Interest rate is the "exchange rate" that we use to transform the money at
different times to a unified dimension.
Future Value of a Single Cash Flow
● What is the future value of a £100 investment in a bank account paying 5% every
year for 2 years?
Future Value of a Single Cash Flow: Generalisation
, 15/02
Future Values with Compounding
Future Value of Annuities
● Annuity: a stream of equal cash flows that occurs yearly over a given period.
● A very important property is that at the same dimension of money, at a certain point
of time, all the cash flows can be added together.
Future Value of an Annuity: Generalisation
