Introduction to Time Value of Money

FINANCIAL MANAGEMENTFINANCIAL MANAGEMENT

Title: Financial Management

Objective

In today’s dynamic world engineers along with taking technical decisions also have to take financial decisions. So they need to understand, analyze and interpret financial data and financial issues. This course will help them in understanding the concepts and principles of accounting and finance with the support of software packages so that they can make quick informed financial decisions.

Learning Outcomes

At the end of the course the students will be able to understand:

basic accounting principles.

how to measure the performance of a business.

how to make and evaluate the impact of business decisions at all levels.

Methodology

The course will be taught with the aid of lectures, case studies, and use of computer spreadsheet programs. The students will self-learn the usage of accounting packages available in the industry.

Text Book Financial Management by M.Y. Khan, and P.K. Jain, Tata McGraw

Hill.

Financial Management by Prasanna Chandra, Tata McGraw Hill.

Books for Reference Principles of corporate finance by Brealey, Richard A. and Myers,

Stewart C. Tata McGraw-Hill Publishing Delhi.

Fundamentals of financial management by Brigham, Eugene F,Houston, Joel F. Thomson Asia Pte Ltd.

Financial management by I.M. Pandey, Vikas Publishing House Pvt Ltd.

Course ContentsCourse ContentsTopic-

IntroductionBasic Financial ConceptsLong Term Sources of FinanceCapital Budgeting: Principle TechniquesConcept and measurement of cost of capitalCash Flows for Capital BudgetingFinancial statements & analysisLeverages and Capital structure decisionWorking capital managementDividend Policy

Evaluation (Lecture Course)Evaluation (Lecture Course)Exam % of Marks Duration of

Examination Coverage / Scope

(i) TEST-1 (T-1)

20 1 Hour Syllabus covered upto test 1

(ii) TEST -2 (T-2)

25 1 Hour 15 Minutes

Mainly syllabus covered after Test-1, plus some questions from portions covered upto test 1

(iii)TEST-3 (T-3)

30 1 Hour 30 Minutes

Mainly syllabus covered after Test-2, and upto Test-3 Plus some questions from portions covered Test-1 and Test-2.

(iv) Assignments, Quizzes, home work & Regularity in attendance.

25 Quizzes: 5

Attendance: 5Assignment: 5Project work:

10

Entire Semester

As decided and announced by the teacher concerned in the class at the beginning of the course

AN OVERVIEW

DEFINITIONDEFINITION

Financial Management is broadly concerned with the acquisition (investment), financing and management of assets by a business firm

GOALS OF THE FIRMGOALS OF THE FIRM

Maximizing owners/shareholders’ wealth

Maximizing the price per share

Market price of a share serves as a barometer for

business performance

It indicates how well management is doing on behalf

of its’ shareholders

OBJECTIVES OF FINANCIAL OBJECTIVES OF FINANCIAL MANAGEMENTMANAGEMENT

Maximize owners' wealth

Market value of equity

SCOPE OF FINANCIAL MANAGEMENTSCOPE OF FINANCIAL MANAGEMENT

What should be the composition of the firms’ assets?

What should be the mix of the firms’ financing?

How should the firm analyse, plan and control its financial affairs?

Financial Analysis, Planning and Control

Balance Sheet

Long Term Financing

Short Term Financing

Fixed Assets

CurrentAssets

Managementof the Firm’s Asset Structure

Managementof the Firm’sFinancial Structure

KEY ACTIVITIES OF FINANCIAL MANAGEMENT

Capital Budgeting Decisions

Capital Structure Decisions

Dividend Decisions

Working Capital Decisions

Return

Risk

Market Value ofthe Firm

RISK RETURN TRADE OFF

FINANCE AND ECONOMICSFINANCE AND ECONOMICS

Macro Economics

Necessary for understanding the environment in which the firm operates

• Growth rate of economy, tax environment, availability of funds, rate of inflation, terms on which the firm can raise finances

Micro Economics

Helpful in sharpening the tools of decision making

• Principle of marginal analysis is applicable to decision making

FINANCE AND ACCOUNTINGFINANCE AND ACCOUNTING

Value Maximising vs. Score Keeping

Cash Flow Method vs. Accrual Method

Uncertainty vs. Certainty

Time Value of Money

Time Value of Money

Obviously, Rs10,000 todayRs10,000 today.

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

The Interest RateThe Interest RateThe Interest RateThe Interest Rate

Which would you prefer – Rs10,000 Rs10,000 today today or Rs10,000 in 5 yearsRs10,000 in 5 years?

TIMETIME allows you the opportunity to postpone consumption and earn INTERESTINTEREST

A rupee today represents a greater real purchasing powerpurchasing power than a rupee a year hence

Receiving a rupee a year hence is uncertain so riskrisk is involved

Why TIME?Why TIME?Why TIME?Why TIME?

Why is TIMETIME such an important element in your decision?

Time Value AdjustmentTime Value Adjustment

Two most common methods of adjusting cash flows for time value of money: Compounding—the process of

calculating future values of cash flows and

Discounting—the process of calculating present values of cash flows.

Types of InterestTypes of InterestTypes of InterestTypes of Interest

Compound InterestCompound Interest

Interest 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).

Simple Interest FormulaSimple Interest FormulaSimple Interest FormulaSimple Interest Formula

FormulaFormula SI = P0(i)(n)

SI: Simple Interest

P0: Deposit today (t=0)

i: Interest Rate per Period

n: Number of Time Periods

SI = P0(i)(n)= Rs1,000(.07)(2)= Rs140Rs140

Simple Interest ExampleSimple Interest ExampleSimple Interest ExampleSimple Interest Example

Assume that you deposit Rs1,000 in an account earning 7% simple interest for 2 years. What is the accumulated interest at the end of the 2nd year?

FVFV = P0 + SI = Rs1,000 + Rs140= Rs 1,140Rs 1,140

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

Simple Interest (FV)Simple Interest (FV)Simple Interest (FV)Simple Interest (FV)

What is the Future Value Future Value (FVFV) of the deposit?

The Present Value is simply the Rs 1,000 you originally deposited. That is the value today!

Present ValuePresent Value is the current value of a future amount of money, or a series of payments, evaluated at a given interest rate.

Simple Interest (PV)Simple Interest (PV)Simple Interest (PV)Simple Interest (PV)

What is the Present Value Present Value (PVPV) of the previous problem?

Assume that you deposit Rs 1,000Rs 1,000 at a compound interest rate of 7%

for 2 years2 years.

Future ValueFuture ValueSingle Deposit (Graphic)Single Deposit (Graphic)Future ValueFuture ValueSingle Deposit (Graphic)Single Deposit (Graphic)

0 1 22

Rs 1,000Rs 1,000

FVFV22

7%

FVFV11 = PP00 (1+i)1 = Rs 1,000Rs 1,000 (1.07) = Rs 1,070Rs 1,070

FVFV22 = FV1 (1+i)1 = PP0 0 (1+i)(1+i) = Rs1,000Rs1,000(1.07)(1.07)= PP00 (1+i)2 = Rs1,000Rs1,000(1.07)2

= Rs1,144.90Rs1,144.90

You 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)

FVFV11 = P0(1+i)1

FVFV22 = P0(1+i)2

General Future Value Future Value Formula:

FVFVnn = P0 (1+i)n

or FVFVnn = P0 (FVIFFVIFi,n)

General Future General Future Value FormulaValue FormulaGeneral Future General Future Value FormulaValue Formula

etc.

Reena 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 Problem Problem Problem

0 1 2 3 4 55

Rs10,000Rs10,000

FVFV55

10%

SolutionSolutionSolutionSolution

Calculation based on general formula:

FVFVnn = P0 (1+i)n

FVFV55 = Rs10,000 (1+ 0.10)5

= Rs 16,105.10Rs 16,105.10

We will use the ““Rule-of-72Rule-of-72””..

Double Your Money!!!Double Your Money!!!Double Your Money!!!Double Your Money!!!

Quick! How long does it take to double Rs 5,000 at a compound rate of 12%

per year (approx.)?

Doubling Period = 72 / Interest Rate

6 years

For accuracy use the ““Rule-of-69Rule-of-69””..

Doubling Period

=0.35 +(69 / Interest Rate)

6.1 years

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.

0 1 22

Rs 1,000Rs 1,000

7%

PV1PVPV00

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

PVPV00 = FVFV22 / (1+i)2 = Rs 1,000Rs 1,000 / (1.07)2 = FVFV22 / (1+i)2 = Rs 873.44Rs 873.44

Present Value Present Value Single Deposit (Formula)Single Deposit (Formula)Present Value Present Value Single Deposit (Formula)Single Deposit (Formula)

0 1 22

Rs 1,000Rs 1,000

7%

PVPV00

PVPV00 = FVFV11 / (1+i)1

PVPV00 = FVFV22 / (1+i)2

General Present Value Present Value Formula:

PVPV00 = FVFVnn / (1+i)n

or PVPV00 = FVFVnn (PVIFPVIFi,n)

General Present General Present Value FormulaValue FormulaGeneral Present General Present Value FormulaValue Formula

etc.

Reena 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%.

ProblemProblem ProblemProblem

0 1 2 3 4 55

Rs 10,000Rs 10,000PVPV00

10%

Calculation based on general formula: PVPV00 = FVFVnn / (1+i)n

PVPV00 = Rs 10,000Rs 10,000 / (1+ 0.10)5

= Rs 6,209.21Rs 6,209.21

Problem SolutionProblem SolutionProblem SolutionProblem Solution

Types of AnnuitiesTypes of AnnuitiesTypes of AnnuitiesTypes of Annuities

Ordinary AnnuityOrdinary Annuity: Payments or receipts occur at the end of each period.

Annuity DueAnnuity Due: Payments or receipts occur at the beginning of each period.

An AnnuityAn Annuity represents a series of equal payments (or receipts) occurring over a specified number of equidistant periods.

Examples of AnnuitiesExamples of Annuities

Student Loan Payments

Car Loan Payments

Insurance Premiums

Retirement Savings

Parts of an AnnuityParts of an AnnuityParts of an AnnuityParts of an Annuity

0 1 2 3

Rs 100 Rs 100 Rs 100

(Ordinary Annuity)EndEnd of

Period 1EndEnd of

Period 2

Today EqualEqual Cash Flows Each 1 Period Apart

EndEnd ofPeriod 3

Parts of an AnnuityParts of an AnnuityParts of an AnnuityParts of an Annuity

0 1 2 3

Rs 100 Rs 100 Rs 100

(Annuity Due)BeginningBeginning of

Period 1BeginningBeginning of

Period 2

Today EqualEqual Cash Flows Each 1 Period Apart

BeginningBeginning ofPeriod 3

FVAFVAnn = A(1+i)n-1 + A(1+i)n-2 + ... + A(1+i)1 + A(1+i)0

Ordinary Annuity -- FVAOrdinary Annuity -- FVAOrdinary Annuity -- FVAOrdinary Annuity -- FVA

A A A

0 1 2 n n n+1

FVAFVAnn

A = Periodic Cash Flow

Cash flows occur at the end of the period

i% . . .

Example of anExample of anOrdinary Annuity -- FVAOrdinary Annuity -- FVAExample of anExample of anOrdinary Annuity -- FVAOrdinary Annuity -- FVA

Rs1,000 Rs1,000 Rs1,000

0 1 2 3 3 47%


FVAFVA33 = 1,000(1.07)2 + 1,000(1.07)1 + 1,000(1.07)0

= 1,145 + 1,070 + 1,000 = Rs 3,215Rs 3,215

Example of anExample of anOrdinary Annuity -- FVAOrdinary Annuity -- FVAExample of anExample of anOrdinary Annuity -- FVAOrdinary Annuity -- FVA

Rs1,000 Rs1,000 Rs1,000

0 1 2 3 3 4

Rs3,215 = Rs3,215 = FVAFVA33

7%

Rs1,070

Rs1,145


General Formula for Calculating General Formula for Calculating Future Value of an Ordinary Future Value of an Ordinary

AnnuityAnnuity

AiAiAFVAn nn ...)1()1( 21

i

iA

n 1)1(

FVADFVADnn = R(1+i)n + R(1+i)n-1 + ... + R(1+i)2 +

R(1+i)1 = FVAFVAn n (1+i)

Annuity Due -- FVADAnnuity Due -- FVADAnnuity Due -- FVADAnnuity Due -- FVAD

R R R R R

0 1 2 3 n-1n-1 n

FVADFVADnn

i% . . .

Cash flows occur at the beginning of the period

FVADFVAD33 = 1,000(1.07)3 + 1,000(1.07)2 + 1,000(1.07)1

= 1,225 + 1,145 + 1,070 = Rs 3,440Rs 3,440

Example of anExample of anAnnuity Due -- FVADAnnuity Due -- FVADExample of anExample of anAnnuity Due -- FVADAnnuity Due -- FVAD

1,000 1,000 1,000 1,070

0 1 2 3 3 4

Rs 3,440 = Rs 3,440 = FVADFVAD33

7%

Rs1,225

Rs1,145


PVAPVAnn = R/(1+i)1 + R/(1+i)2

+ ... + R/(1+i)n

Ordinary Annuity -- PVAOrdinary Annuity -- PVAOrdinary Annuity -- PVAOrdinary Annuity -- PVA

R R R

0 1 2 n n n+1

PVAPVAnn

R = Periodic Cash Flow

i% . . .


Example of anExample of anOrdinary Annuity -- PVAOrdinary Annuity -- PVAExample of anExample of anOrdinary Annuity -- PVAOrdinary Annuity -- PVA

Rs1,000 Rs1,000 Rs1,000

0 1 2 3 3 47%


PVAPVA33 = 1,000/(1.07)1 + 1,000/(1.07)2 +

1,000/(1.07)3

= 934.58 + 873.44 + 816.30 = 2,624.322,624.32

Example of anExample of anOrdinary Annuity -- PVAOrdinary Annuity -- PVAExample of anExample of anOrdinary Annuity -- PVAOrdinary Annuity -- PVA

Rs1,000 Rs1,000 Rs1,000

0 1 2 3 3 4

Rs 2,624.32 = PVARs 2,624.32 = PVA33

7%

934.58873.44 816.30


nn i

A

i

A

i

APVA

)1(...

)1()1( 2

n

n

ii

iA

)1(

1)1(

General Formula for Calculating General Formula for Calculating Present Value of an Ordinary Present Value of an Ordinary

AnnuityAnnuity

PVADPVADnn = R/(1+i)0 + R/(1+i)1 + ... + R/(1+i)n-1

= PVAPVAn n (1+i)

Annuity Due -- PVADAnnuity Due -- PVADAnnuity Due -- PVADAnnuity Due -- PVAD

R R R R

0 1 2 n-1n-1 n

PVADPVADnn

R: Periodic Cash Flow

i% . . .


PVADPVADnn = 1,000/(1.07)0 + 1,000/(1.07)1 + 1,000/(1.07)2 = Rs 2,808.02Rs 2,808.02

Example of anExample of anAnnuity Due -- PVADAnnuity Due -- PVADExample of anExample of anAnnuity Due -- PVADAnnuity Due -- PVAD

1,000.00 1,000 1,000

0 1 2 33 4

2,808.02 2,808.02 = PVADPVADnn

7%

934.58873.44


Reena will receive the set of cash flows below. What is the Present Present Value Value at a discount rate of 10%10%?

Mixed Flows ExampleMixed Flows ExampleMixed Flows ExampleMixed Flows Example

0 1 2 3 4 55

600 600 400 400 100600 600 400 400 100

PVPV00

10%10%

SolutionSolutionSolutionSolution

0 1 2 3 4 55

600 600 400 400 100600 600 400 400 10010%

545.45545.45495.87495.87300.53300.53273.21273.2162.0962.09

Rs 1677.15 Rs 1677.15 = = PVPV00 of the Mixed Flowof the Mixed Flow

General Formula:

FVn = PVPV00(1 + [i/m])mn

Or

== PV PV00 * PVIF i/m,m*n

n: Number of Yearsm: Compounding Periods per Year i: Annual Interest Rate FVn,m: FV at the end of Year n

PVPV00: PV of the Cash Flow today

Shorter Discounting PeriodsShorter Discounting PeriodsShorter Discounting PeriodsShorter Discounting Periods

Reena has Rs1,000Rs1,000 to invest for 1 year at an annual interest rate of 12%.

ExampleExample

Annual FV = 1,0001,000(1+ [.12/1])(1)(1) = 1,1201,120

Semi FV = 1,0001,000(1+ [.12/2])(2)(1)

= 1,123.61,123.6

Effective vs. Nominal Rate of Effective vs. Nominal Rate of InterestInterest

Rs. 1000 Rs.1123.6

So,

Rs. 1000 grows @ 12.36% annually

Effective Rate of Interest

r = 1 + i/m m

- 1

Basket Wonders (BW) has a Rs1,000 CD at the bank. The interest rate is 6%

compounded quarterly for 1 year. What is the Effective Annual Interest Rate (EAREAR)?

ProblemProblemProblemProblem

EAREAR = ( 1 + 6% / 4 )4 - 1 = 1.0614 - 1 = .0614 or

6.14%!6.14%!

PerpetuityPerpetuity

A perpetuity is an annuity with an infinite number of cash flows.

The present value of cash flows occurring in the distant future is very close to zero.

At 10% interest, the PV of Rs 100 cash flow occurring 50 years from today is Rs 0.85!

Present Value of a Present Value of a PerpetuityPerpetuity

nn i

A

i

A

i

APVA

)1(...

)1()1( 2

When n=

PVperpetuity = [A/(1+i)]

[1-1/(1+i)]

= A(1/i) = A/i

Present Value of a Present Value of a PerpetuityPerpetuity

What is the present value of a perpetuity of Rs270 per year if the interest rate is 12% per year?

PVPV AAii

perpetuityperpetuity Rs270Rs270

0.120.12Rs 2250Rs 2250

1. Calculate the payment per period.

2. Determine the interest in Period t. Loan balance at (t-1) x (i%)

3. Compute principal payment principal payment in Period t.(Payment - interest from Step 2)

4. Determine ending balance in Period t.(Balance - principal payment principal payment from Step

3)

5. Start again at Step 2 and repeat.

Steps to Amortizing a LoanSteps to Amortizing a LoanSteps to Amortizing a LoanSteps to Amortizing a Loan

Reena is borrowing Rs10,000 Rs10,000 at a compound annual interest rate of 12%. Amortize the loan

if annual payments are made for 5 years.

Amortizing a Loan ExampleAmortizing a Loan ExampleAmortizing a Loan ExampleAmortizing a Loan Example

Step 1: Payment

PVPV00 = A(PVIFA i%,n)

Rs10,000 Rs10,000 = A(PVIFA 12%,5)

Rs10,000Rs10,000 = A(3.605)

A A = Rs10,000Rs10,000 / 3.605 = Rs2,774Rs2,774


End of Year

Payment Interest Principal Ending Balance

0

1

2

3

4

5


End of Year


0 --- --- --- Rs10,000

1 Rs2,774 Rs1,200 Rs1,574 8,426

2

3

4

5

[Last Payment Slightly Higher Due to Rounding]


End of Year


0 --- --- --- Rs10,000

1 Rs2,774 Rs1,200 Rs1,574 8,426

2 2,774 1,011 1,763 6,663

3 2,774 800 1,974 4,689

4 2,774 563 2,211 2,478

5 2,775 297 2,478 0

Rs13,871 Rs3,871 Rs10,000

[Last Payment Slightly Higher Due to Rounding]

Usefulness of AmortizationUsefulness of Amortization

2.2. Calculate Debt Outstanding Calculate Debt Outstanding -- The quantity of outstanding debt

may be used in financing the day-to-day activities of the firm.

1.1. Determine Interest Expense Determine Interest Expense -- Interest expenses may reduce taxable income of the firm.

EXERCISEEXERCISE

Ashish recently obtained a Rs.50,000 loan. The loan carries an 8% annual interest. Amortize the loan if annual payments are made for 5 years.

SOLUTIONSOLUTION50000 5 0.08

12523

TIME PAYMENT INTERESTPRINCIPAL AMOUNTOUTSTANDING

0 500001 12523 4000 8523 414772 12523 3318 9205 322723 12523 2582 9941 223314 12523 1786 10737 115945 12522 928 11594 0

EXERCISEEXERCISE

Compute the present value of the following future cash inflows, assuming a required rate of 10%: Rs. 100 a year for years 1 through 3, and Rs. 200 a year from years 6 through 15.

ANS: 1011.75

SolutionSolution

100 100 100 200 200 200

0 1 2 3 6 7 15

248.70

i% . . .


. . .

1228.9

763.05

1011.75

Till 5th

year

Introduction to Time Value of Money

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