FINANCIAL MANAGEMENT

Title: Financial Management

ObjectiveIn 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 OutcomesAt 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.MethodologyThe 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 ContentsTopic-Introduction to Accounting and financial managementBasic 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 management

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)

20 1 Hour Syllabus covered after Test-1 upto T-2.

(iii)TEST-3 (T-3)

35 2 Hours Whole syllabus

(iv) Teacher’s Assessment

25Attendance: 10Class Discipline:5Project /Quizzes: 10

Entire Semester

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

Time Value of Money

The Interest Rate

Obviously, Rs10,000 todayRs10,000 today.

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

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

Why TIME?

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 is TIMETIME such an important element in your decision?

Time 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 Interest

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

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

Simple InterestSimple InterestInterest paid (earned) on only the original

amount, or principal borrowed (lent).

Simple Interest Formula

FormulaFormula SI = P0(i)(n)SI: Simple InterestP0: Deposit today (t=0)

i: Interest Rate per Periodn: Number of Time Periods

Simple Interest Example

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

• 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?

Simple Interest (FV)

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.

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

Simple Interest (PV)

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.

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

Future ValueSingle Deposit (Graphic)

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

0 1 22

Rs 1,000Rs 1,000FVFV22

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)

General Future Value 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)

Problem

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.

0 1 2 3 4 55

Rs10,000Rs10,000

FVFV55

10%

Solution

Calculation based on general formula:FVFVnn = P0 (1+i)n

FVFV55 = Rs10,000 (1+ 0.10)5

= Rs 16,105.10Rs 16,105.10

Double Your Money!!!

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

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

Present Value Single Deposit (Graphic)

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 1,0007%

PV1PVPV00

Present Value Single Deposit (Formula)

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

0 1 22

Rs 1,000Rs 1,0007%

PVPV00

General Present Value Formula

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)

etc.

ProblemReena 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%.

0 1 2 3 4 55

Rs 10,000Rs 10,000PVPV00

10%

Problem Solution

• 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

Types 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 Annuities

• Student Loan Payments• Car Loan Payments• Insurance Premiums• Retirement Savings

Parts 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 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

Ordinary Annuity -- FVA

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

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 anOrdinary Annuity -- FVA

Rs1,000 Rs1,000 Rs1,000

0 1 2 3 3 47%

Cash flows occur at the end of the period

Example of anOrdinary Annuity -- FVA

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

Rs1,000 Rs1,000 Rs1,000

0 1 2 3 3 4

Rs3,215 = Rs3,215 = FVAFVA33

7%

Rs1,070Rs1,145

Cash flows occur at the end of the period

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

AnnuityAnnuity

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

iiAn 1)1(

Annuity Due -- FVAD

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

= FVAFVAn n (1+i)

R R R R R

0 1 2 3 n-1n-1 n

FVADFVADnn

i% . . .

Cash flows occur at the beginning of the period

Example of anAnnuity Due -- FVAD

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

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

0 1 2 3 3 4

Rs 3,440 = Rs 3,440 = FVADFVAD33

7%

Rs1,225Rs1,145

Cash flows occur at the beginning of the period

Ordinary Annuity -- PVA

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

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

R R R

0 1 2 n n n+1

PVAPVAnn

R = Periodic Cash Flow

i% . . .

Cash flows occur at the end of the period

Example of anOrdinary Annuity -- PVA

Rs1,000 Rs1,000 Rs1,000

0 1 2 3 3 47%

Cash flows occur at the end of the period

Example of anOrdinary Annuity -- PVA

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

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

Cash flows occur at the end of the period

nn iA

iA

iAPVA

)1(...

)1()1( 2

n

n

iiiA

)1(1)1(

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

AnnuityAnnuity

Annuity Due -- PVAD

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

R R R R

0 1 2 n-1n-1 n

PVADPVADnn

R: Periodic Cash Flow

i% . . .

Cash flows occur at the beginning of the period

Example of anAnnuity Due -- PVAD

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

1,000.00 1,000 1,000

0 1 2 33 4

2,808.02 2,808.02 = PVADPVADnn

7%

934.58873.44

Cash flows occur at the beginning of the period

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

0 1 2 3 4 55

600 600 400 400 100600 600 400 400 100PVPV00

10%10%

Solution

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

Shorter Discounting PeriodsGeneral Formula:

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

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

n: Number of Years m: Compounding Periods per Yeari: Annual Interest Rate FVn,m: FV at the end of Year nPVPV00: PV of the Cash Flow today

Example

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

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 InterestRs. 1000 Rs.1123.6So, Rs. 1000 grows @ 12.36% annually Effective Rate of Interest

r = 1 + i/m m

- 1

Problem

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)?

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

6.14%!6.14%!

Perpetuity

• 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 Perpetuity

nn iA

iA

iAPVA

)1(...

)1()1( 2

When n=

PVperpetuity = [A/(1+i)]

[1-1/(1+i)]

= A(1/i) = A/i

Present Value of a Perpetuity

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

PVPV AAiiperpetuityperpetuity Rs270Rs270

0.120.12Rs 2250Rs 2250

Steps to Amortizing a Loan

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.

Amortizing a Loan Example

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.

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

Amortizing a Loan Example

End of Year

Payment Interest Principal Ending Balance

0 1 2 3 4 5

Amortizing a Loan Example

End of Year

Payment Interest Principal Ending Balance

0 --- --- --- Rs10,000 1 Rs2,774 Rs1,200 Rs1,574 8,426 2 3 4 5

[Last Payment Slightly Higher Due to Rounding]

Amortizing a Loan Example

End of Year

Payment Interest Principal Ending Balance

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 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.

EXERCISE

• 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.

SOLUTION50000 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

EXERCISE

• 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

Solution

100 100 100 200 200 200

0 1 2 3 6 7 15

248.70

i% . . .

Cash flows occur at the end of the period

. . .

1228.9

763.051011.75

Till 5th

year