FINANCE FOR MANAGERS
Course Code: 0387
• Payment is cash outflow and receipt is cash
inflow of money.
• Financial contract-agreement or investment that
produces cash flows.
• We are concerned with the cash flow
consequences of a decision or a contract.
• How much cash flow b/w the parties?
• When will this cash flow occur?
• These basic questions must be answered when
analyzing financial contract.
Rate of Return
• Calculation that expresses the ratio of net cash
inflows to cash outflows produced by a financial
• Where there are only 2 cash flows in the contract
i.e one at the start and another at the end the
rate of return is usually measured by:
• r = (C1-C0)/C0
• C1 : cash inflow at time 1
• C0: cash outflow at time 0
• r: rate of return per period
• It is rate of return on debt.
• Debt-financial contract in which the receiver
of the initial cash (the borrower) promises a
particular cash flow, usually calculated using
an interest, to the provider of the funds ( the
Time Value of Money
• Time value of money principle that a dollar is
worth more (less), the sooner (later) it is to be
received, all other things being equal.
• Money has a time value.
• Suppose you have a choice to receive $100
either today or 1 years time. As a rational
person you will chose to take the money
• Time Lines
– An important tool used in TVM analysis.
– It is a graphical representation used to show the
timing of cash flows.
– Time 0 is today; Time 1 is one period from today,
or end of period 1 and so on.
0 2 431
• The interest rate for each of the three periods is 5%; a
single amount cash outflow is made at time 0; and
time 3 value is unknown cash inflow. Since the initial
$100 is an outflow (an investment), it has a minus sign.
• The interest rate is 5% during the first period, but it
rises to 10% during the second period. If the interest
rate is constant in all periods, we show it only in the
first period, but if it changes, we show all the relevant
rates on the time line.
Q.) Setup a time line to illustrate following situation: You currently have
$2000 on hand and would like to invest it in 3 year certificate of deposit
that pays 4% annually.
• A $ in hand today is worth more than a $ to be
received in the future because, if you had a
now, you could invest it, earn interest, and
end up with more than one $ in the future.
• The process of going from today's value, or
present values (PVs), to future values (FVs) is
• Formula: FVn=PV(1+i)n
• PV : present value, or beginning amount, in
your account. It is the value now.
• i : interest rate the bank pays on the account
• n : number of period involved in the analysis.
• FVn : future value or ending amount of your
account at the end of n periods.
• Present value – the value today of a future cash flow
or series of cash flows.
• Opportunity Cost Rate – the rate of return on the
best available alternative investment of equal risk.
• Discounting -the process of finding the present value
of a cash flow or a series of cash flows; discounting is
the reverse of compounding.
• If you know the PV you can compound to find FV,
while if you know the FV you can discount to find the
• Formula : PV=FVn / (1+i)n
• At this point one should realize that
compounding and discounting are related and
we are dealing with one equation. There are
four variables in this equation and if you know
the value of any three variables you can easily
find the value of fourth variable.
• Annuity – a series of payments of an equal
amount at fixed intervals for a specified
number of periods.
• Example: $100 at the end of each of the next
3 years is a 3 year annuity.
• PMT (or C-cash flow per period) - is the fixed
payment and they occur at either the
beginning or end of each period.
Types of Annuity
• Ordinary (Deferred) Annuity
– An annuity whose payments occur at the end of
each period. Payments on mortgages, car loans,
and student loans are typically set up as ordinary
• Annuity Due
– An annuity whose payments occur at the
beginning of each period. Rental payments of an
apartment, life insurance premiums are typically
set up as annuity due.
Ordinary (Deferred) Annuity
Consider the following annuity cash flow schedule
In order to calculate the future value of the annuity, we have to calculate the
future value of each cash flow. Let's assume that you are receiving $1,000 every
year for the next five years, and you invested each payment at 5%. The
following diagram shows how much you would have at the end of the five-year
Future Value of Ordinary
C = Cash flow per period
i = interest rate
n = number of payments
Present Value of Ordinary
• If you would like to determine today's value of
a series of future payments, you need to use
the formula that calculates the present value
of an ordinary annuity.
• To obtain the total discounted value, we need
to take the present value of each future
payment and than add the cash flows
Present Value of Ordinary
• calculating and adding all these values will
take a considerable amount of time, especially
if we expect many future payments. As such,
there is a mathematical shortcut we can use
for PV of ordinary annuity.
• When you are receiving or paying cash flows
for an annuity due, your cash flow schedule
would appear as follows: