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Business Finance(MGT 232)

Lecture 4

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Time Value of MoneyTime Value of MoneyTime Value of MoneyTime Value of Money

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Overview of the Last Lecture• Financial Market• Types of Financial Markets

– Physical Vs Financial asset– Money Vs Capital– Primary Vs. Secondary– Spot Vs. Future– Public Vs. Private– Mortgage Vs Consumer Credit

• Types of Capital transfer• Types of Financial Intermediaries

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The Time Value of MoneyThe Time Value of Money

• The Interest Rate• Simple Interest• Compound Interest• Annuity• Uneven Cash flow• Amortizing a Loan

• The Interest Rate• Simple Interest• Compound Interest• Annuity• Uneven Cash flow• Amortizing a Loan

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Obviously, Rs. 10,000 todayRs. 10,000 today.

You already recognize that there is TIME TIME VALUE TO MONEYVALUE TO MONEY!!

The Interest RateThe Interest Rate

Which would you prefer – Rs. 10,000 Rs. 10,000 todaytoday or Rs. 10,000 in 5 yearsRs. 10,000 in 5 years?

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The worth or value of MONEY at different The worth or value of MONEY at different points in time ispoints in time is “Time value of Money” “Time value of Money”

Time Value of MoneyTime Value of Money

Why is TIMETIME such an important element in your decision?

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Types of InterestTypes of Interest

• Compound InterestCompound InterestInterest paid (earned) on any previous interest

earned, as well as on the principal borrowed (lent).

Simple InterestSimple Interest

Interest paid (earned) on only the original amount, or principal borrowed (lent).

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Simple InterestSimple Interest

We require: Value:Simple InterestPV: Deposit today (t=0)i: Interest Rate per Periodn: Number of Time Periods

Two types of Values:• Present Value• Future Value

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Future Value (FV)Future Value (FV)

• FV is the value at some future time of a present amount of money, or a series of payments, evaluated at a given interest rate.

• The process of going from today’s value to future values is called CompoundingCompounding

FV = PV (1 + i)ⁿFV = PV (1 + i)ⁿFV = Future ValueFV = Future ValuePV= Present ValuePV= Present Valuei= interest ratei= interest raten = No of yearsn = No of years

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FV ExampleFV Example

• Assume that you deposit Rs.1,000 in an account earning 7% simple interest for 2 years. What is the accumulated interest at the end of the 2nd year?

FV = PV (1 + i)ⁿFV = PV (1 + i)ⁿ

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Assume that you deposit Rs.1,000Rs.1,000 at a compound interest rate of 7% for 2 years2 years.

Future ValueSingle Deposit (Graphic)

Future ValueSingle Deposit (Graphic)

0 1 22

Rs.1,000Rs.1,000FVFV22

7%

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0

5000

10000

15000

20000

1st Year 10thYear

20thYear

30thYear

Future Value of a Single $1,000 Deposit

10% SimpleInterest

7% CompoundInterest

10% CompoundInterest

Why Compound Interest?Why Compound Interest?Fu

ture

Valu

e (

U.S

. D

olla

rs)

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FVFV11 = PVPV(1+i)1 = Rs.1,000Rs.1,000 (1.07) = Rs.1,070Rs.1,070

Compound InterestYou earned Rs.70 interest on your Rs.1,000

deposit over the first year.This is the same amount of interest you would

earn under simple interest.

Future ValueSingle Deposit (Formula)

Future ValueSingle Deposit (Formula)

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FVFV11 = PVPV(1+i)1 = Rs.1,000Rs.1,000 (1.07) = Rs.1,070Rs.1,070

FVFV22 = FV1 (1+i)1 = PVPV (1+i)(1+i) = Rs.1,000Rs.1,000(1.07)(1.07)= PVPV(1+i)2 = Rs.1,000Rs.1,000(1.07)2

= Rs.1,144.90Rs.1,144.90You earned an EXTRA Rs.4.90Rs.4.90 in Year 2 with

compound over simple interest.

Future ValueFuture ValueSingle Deposit (Formula)Single Deposit (Formula)Future ValueFuture ValueSingle Deposit (Formula)Single Deposit (Formula)

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FVFV11 = PV(1+i)1

FVFV22 = PV(1+i)2

General Future Value Future Value Formula:FVFVnn = PV(1+i)n

or FVFVnn = PV(FVIFFVIFi,n)

General Future Value Formula

General Future Value Formula

etc.

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FVIFFVIFi,n

Valuation Using TableValuation Using Table

Period 6% 7% 8%1 1.060 1.070 1.0802 1.124 1.145 1.1663 1.191 1.225 1.2604 1.262 1.311 1.3605 1.338 1.403 1.469

1.145

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FVFV22 = Rs.1,000 (FVIFFVIF7%,2)= Rs.1,000 (1.145)

= Rs.1,145Rs.1,145 [Due to Rounding]

Using Future Value TablesUsing Future Value Tables

Period 6% 7% 8%1 1.060 1.070 1.0802 1.124 1.145 1.1663 1.191 1.225 1.2604 1.262 1.311 1.3605 1.338 1.403 1.469

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Julie Miller wants to know how large her deposit of Rs.10,000Rs.10,000 today will become at a compound annual interest rate of 10% for 5 years5 years.

Problem ExampleProblem Example

0 1 2 3 4 55

Rs.10,000Rs.10,000FVFV55

10%

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• Calculation based on Table: FVFV55

= Rs.10,000 (FVIFFVIF10%, 5)

Story Problem SolutionStory Problem Solution

Calculation based on general formula: FVFVnn = PV(1+i)n

FVFV55 =

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Present Value (PV)Present Value (PV)

• PV is the current value of a future amount of money, or a series of payments, evaluated at a given interest rate

• The process of finding future values is called DiscountingDiscounting

PV = FV (1 + i)⁻ⁿPV = FV (1 + i)⁻ⁿFV = Future ValueFV = Future ValuePV= Present ValuePV= Present Valuei= interest ratei= interest raten = No of yearsn = No of years

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Present Value (PV)Present Value (PV)

Assume that you need Rs. 1,000Rs. 1,000 in 2 years.2 years. Let’s examine the process to determine how much you need to deposit today at a discount rate of 7% compounded annually.

PV = FV (1 + i)⁻ⁿPV = FV (1 + i)⁻ⁿ

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0 1 22

Rs.1,000Rs.1,000

7%

PV1PVPV

Present Value Single Deposit (Graphic)Present Value Single Deposit (Graphic)

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PVPV = FVFV22 (1+i)⁻2 = Rs.1,000Rs.1,000 (1.07)⁻2

PV = FVFV22 (1+i)⁻2 = Rs.873.44Rs.873.44

Present Value Single Deposit (Formula)

Present Value Single Deposit (Formula)

0 1 22

Rs.1,000Rs.1,000

7%

PVPV

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PVPV = FVFV11 (1+i)⁻1

PVPV = FVFV22 (1+i)⁻2

General Present Value Present Value Formula:PVPV = FVFVnn (1+i)⁻n

or PVPV = FVFVnn (PVIFPVIFi,n)

General Present Value Formula

General Present Value Formula

etc.

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PVIFPVIFi,n

Valuation Using TableValuation Using Table

Period 6% 7% 8% 1 .943 .935 .926 2 .890 .873 .857 3 .840 .816 .794 4 .792 .763 .735 5 .747 .713 .681

.873

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Julie Miller wants to know how large of a deposit to make so that the money will grow to Rs.10,000Rs.10,000 in 5 years5 years at a discount rate of 10%.

Problem ExampleProblem Example

0 1 2 3 4 55

Rs.10,000Rs.10,000PVPV00

10%

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• Calculation based on general formula: PVPV = FVFV (1+i)⁻n

• Calculation based on Table:PVPV = Rs.10,000Rs.10,000 (PVIFPVIF10%, 5)

Problem SolutionProblem Solution

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Summary

• Time Value of Money• Simple Interest rate• Future Value• Graphical Representation• Why we use Compounding• Present Value• Graphical Representation