This summary consists out of 5 of 19 chapters of the book. At the end of the summary you will find all the calculations and explanations of every step.
Principles of Managerial Finance
Lawrence J. Gitman and Chad J. Zutter
Chapter 5: Time value of Money
5.1 The role of time value in Finance
The time value of money refers to the fact that it is better to receive money sooner than later.
A dollar today is worth more than a dollar tomorrow. Managers need to compare cash inflows
and outflows that occur at different times.
5.1.1 Future value versus present value
Future value = the value at a given future date of an amount placed on deposit today and
earning interest at a specific rate. Can be found by applying compound interest over a specific
period of time.
Present value = the current value of a future amount. The amount of money that would have
to be invested today at a given interest rate over a specific period to equal the future amount.
To make a right investment decision, mangers need to compare cash flows at a single point in
time, usually the beginning or the end of a period.
The future value technique uses compounding to find the future value of each cash flow at the
end of the investment’s life and then sums these values to find the investment’s future value.
Compounding = adding up interest that is earned on a given deposit to the principle, which
becomes the new principle for the next period. (Principle + interest = new principle)
Principle = The amount of money on which interest is paid.
The present value technique uses discounting to find the present value of each cash flow at
time zero and then sums these values to find the investment’s value today.
Discounting = the opposite of compounding. Deducting the interest of the principle at a
certain point in time to find the present value of a future amount.
5.1.2 Basic patterns of cash flow
The cash flow of a firm can be described by its general pattern:
Single amount = A lump-sum amount either currently held or expected at some future date.
Annuity = A level of periodic stream of cash flows. Usually annual.
Mixed stream = A stream of cash flow that is not an annuity, it’s a stream of unequal
periodic cash flows which have no specific pattern.
5.2 Single amounts
5.2.1 Future value of a single amount
The future value of a current amount depends on the rate of interest earned and the length of
time the money is left on deposit.
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, Every period the amount is on deposit the interest will be added up and will become part of
the principle. The period can be annual, semi-annually, quarterly, monthly, weekly, daily or
even continuously.
To find the future value of a single amount we use the following formula:
= Future value at the end of period n
PV = Initial principle, or present value
r = Annual rate of interest paid
n = Number of periods that the money is left on deposit
Important:
- We measure future value at the end of the given period.
- The higher the interest rate, the higher the future amount
- The longer the period of time, the higher the future amount
- With an interest percentage of 0, the future value always equals the present value.
5.2.2 Present value of a single amount
Finding out what should be placed on deposit today to earn a certain amount in the future.
This is done by discounting cash flows, which is dependent on the annual rate of return
(interest rate), which is also referred to as discount rate, required return, cost of capital and
opportunity cost.
To find the present value of a single amount we use the following formula:
Note the similarity between this equation and the one for the future value of a single amount.
PV and FVn are swapped. And here we use a division instead of times at the same point
during the calculation.
5.3 Annuities
Annuity = a stream of equal periodic cash flows over a specific time period. These cash flows
can be inflows of returns earned on investments or outflows of funds invested to earn future
returns.
5.3.1 Types of annuities
Ordinary annuity = an annuity for which the cash flow occurs at the end of each period.
Annuity due = an annuity for which the cash flow occurs at the beginning of each period.
The value of an annuity due is always greater than the value of an ordinary annuity.
When an annuity is not further specified it always concerns an ordinary annuity.
5.3.2 Finding the future value of an ordinary annuity
One way to find the future value of an ordinary annuity is to calculate the future value of each
cash flow and then add up those numbers, but fortunately there is a formula shortcut:
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