Chapter 5. Time Value of Money

 Time line
 Future value (FV) and present value (PV)
 Future value annuity (FVA) and present value annuity (PVA)
 Perpetuity
 Uneven cash flows
 Semiannual and other compounding periods
 Amortization
 Applications


Now everyone knows that people can deposit money in banks and banks pay interest on the deposits. Hence if one invests $1000 in a deposit and goes after 90 days he gets a higher amount. Thus value of deposit appreciates with time. This phenomenon of appreciation in the value of principal with passage of time due to payment of interest is known as time value of money. Hence, the amount deposited and amount received back reflect the time value of money.


 Time line
Time line: an important tool used to show timing of cash flows
  Cash outflows vs. cash inflows: cash outflows are negative and cash inflows are
positive

 Future value (FV) and present value (PV)

FV: the amount to which a cash flow will grow over a given number of periods

Compounding: an arithmetic process of determining the final value of a cash flow or a series of cash flows when compound interest is applied


The relationship among future value, interest rate, and time


PV: the value today of a future cash flow
Discounting: a process of finding the present value of a cash flow or a series of  cash flows from the future


The relationship among present value, interest rate, and time


 Future value annuity (FVA) and present value annuity (PVA)
Annuity: a series of equal payments for a number of specified periods
Ordinary annuity: an annuity with payments made at the end of each period
FVA: the future value of an annuity for a number of specified periods


Annuity due: an annuity with payments made at the beginning of each period

Each payment in annuity due earns one period of additional interest



PVA: the present value of an annuity over a number of periods


Rule of 72: Number of years  to double your money(N)   Interest per year * N = 72 (approximation)

 Perpetuity
Annuity that lasts forever
Present value of a perpetuity = payment / interest rate = PMT / (I/YR)
 Uneven cash flows
A series of cash flows that varies in amount from one period to the other
(1) Annuity plus additional final payment
(2) Irregular cash flows
Looking for patents or treat each cash flow separately
Naïve way to deal with uneven cash flows: deal with one cash flow at a time

 Semiannual and other compounding periods
Annual compounding: interest payment is calculated once a year
Semiannual compounding: interest payment is calculated twice a year
Other compounding periods: quarterly, monthly, daily, and continuously, etc.
Effective rate = (1 + i / m)m
- 1, where i is the nominal annual rate and m is the
number of compounding (for example, for quarterly compounding, m = 4)



 Amortization
Amortized loan: a loan that is repaid in equal payments over its duration.


 Applications of Time Value of Money

Bond and stock valuations use time value of money mathematics.
Project appraisal or investment proposal appraisal uses time value of money ideas.