Introduction to Time Value of Money
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Transcript of Introduction to Time Value of Money
![Page 1: Introduction to Time Value of Money](https://reader033.fdocuments.in/reader033/viewer/2022061105/543cd320afaf9fbe618b484d/html5/thumbnails/1.jpg)
FINANCIAL MANAGEMENTFINANCIAL MANAGEMENT
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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.
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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.
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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
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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
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AN OVERVIEW
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DEFINITIONDEFINITION
Financial Management is broadly concerned with the acquisition (investment), financing and management of assets by a business firm
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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
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OBJECTIVES OF FINANCIAL OBJECTIVES OF FINANCIAL MANAGEMENTMANAGEMENT
Maximize owners' wealth
Market value of equity
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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?
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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
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Capital Budgeting Decisions
Capital Structure Decisions
Dividend Decisions
Working Capital Decisions
Return
Risk
Market Value ofthe Firm
RISK RETURN TRADE OFF
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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
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FINANCE AND ACCOUNTINGFINANCE AND ACCOUNTING
Value Maximising vs. Score Keeping
Cash Flow Method vs. Accrual Method
Uncertainty vs. Certainty
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Time Value of Money
Time Value of Money
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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?
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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?
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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.
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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).
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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
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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?
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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?
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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?
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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 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%
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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)
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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.
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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%
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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
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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.)?
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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
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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)
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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
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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.
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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%
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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
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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.
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Examples of AnnuitiesExamples of Annuities
Student Loan Payments
Car Loan Payments
Insurance Premiums
Retirement Savings
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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
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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
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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% . . .
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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%
Cash flows occur at the end of the period
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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
Cash flows occur at the end of the period
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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(
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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
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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
Cash flows occur at the beginning of the period
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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% . . .
Cash flows occur at the end of the period
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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%
Cash flows occur at the end of the period
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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
Cash flows occur at the end of the period
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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
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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% . . .
Cash flows occur at the beginning of the period
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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
Cash flows occur at the beginning of the period
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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%
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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
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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
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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
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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
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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%!
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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!
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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
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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
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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
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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
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Amortizing a Loan ExampleAmortizing a Loan ExampleAmortizing a Loan ExampleAmortizing a Loan Example
End of Year
Payment Interest Principal Ending Balance
0
1
2
3
4
5
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Amortizing a Loan ExampleAmortizing a Loan ExampleAmortizing a Loan ExampleAmortizing 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]
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Amortizing a Loan ExampleAmortizing a Loan ExampleAmortizing a Loan ExampleAmortizing 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]
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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.
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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.
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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
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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
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SolutionSolution
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
763.05
1011.75
Till 5th
year