time value of money f f m

FINANCE FOR MANAGERS

COURSE LECTURER

Shumaila Paracha

Assistant Professor

Course Code: 0387

MBA Program

Academic Year

Fall 2010

Cash Flows

• 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 contract.

• 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

Interest Rate

• 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 lender)

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 today.

Time Line

• 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 431Time:

Time Line

• 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.

0 2

?

31Time:

Cashflow:

5%

-100

Time Line

• 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.

0 2

?

10%1Time:

Cashflow:

5%

-100

Future Value

• 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 called compounding.

Future Value

• 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 per year.

• 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

• 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 PV.

Present Value

• 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

• 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.

• 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 period:

Future Value of Ordinary (Deferred) Annuity

Future Value of Ordinary (Deferred) Annuity

C = Cash flow per period i = interest raten = number of payments

Present Value of Ordinary (Deferred) Annuity

• 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 together.


• 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.

Annuity Due

• When you are receiving or paying cash flows for an annuity due, your cash flow schedule would appear as follows:

Future Value of Annuity Due

Present Value of Annuity Due