By Muhammad Shahid Iqbal

Slides:



Advertisements
Similar presentations
Copyright © 2008 Pearson Education Canada 7-1 Chapter 7 Interest.
Advertisements

FA2 Module 5. Interest concepts of future and present value 1.Time value of money 2.Basic interest concepts 3.Present and future values a.Single payment.
D- 1 TIME VALUE OF MONEY Financial Accounting, Sixth Edition D.
(c) 2002 Contemporary Engineering Economics
(c) 2002 Contemporary Engineering Economics
Topic 9 Time Value of Money.
MTH108 Business Math I Lecture 25.
Chapter 4: The Time Value of Money
Grade 12 Mathematics of Finance Prepared by: Mr. C. Hull VOCABULARY  Interest – the cost of borrowing money o Nominal interest rate – the quoted rate.
All Rights Reserved Ch. 8: 1 Financial Management © Oxford Fajar Sdn. Bhd. ( T) 2010.
© 2010 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible Web site, in whole or in part.
Warm Up What is wealth and why is it desirable?. Definition of Wealth.
D- 1 Interest  Payment for the use of money.  Excess cash received or repaid over the amount borrowed (principal). Variables involved in financing transaction:
© 2005 The McGraw-Hill Companies, Inc., All Rights Reserved McGraw-Hill/Irwin Slide 1 CHAPTER THREE THE INTEREST RATE FACTOR IN FINANCING.
Exercise Write 5% as a decimal Write 6.5% as a decimal Exercise.
Managing your Personal Finances Simple vs. Compound Interest Mr
Basic Finance The Time Value of Money
Chapter 5 Learning Objectives
Chapter 5 The time value of money.
Time Value of MoNey - business applications
Time Value of Money Annuity.
Understanding the Time Value of Money
Chapter 4: The Time Value of Money
Understanding and Appreciating the Time Value of Money
Copyright © 2005 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved.
Lecture 5: Time Value of Money
Copyright © 2006 Brooks/Cole, a division of Thomson Learning, Inc.
Sullivan Algebra and Trigonometry: Section 6.6
Section 6.7 Financial Models.
Chapter 11 Introduction to Finance and Review of Financial Mathematics
CHAPTER 2 VALUE: THE CENTRAL IDEA
CHAPTER 4 THE TIME VALUE OF MONEY.
Time Value of Money.
CHAPTER 3 COMPOUND INTEREST
QMT 3301 BUSINESS MATHEMATICS
Corporate Finance Lecture 2
Time Value of Money $$$ n $ % MBAmaterials.
Learning Goals LG1 Discuss the role of time value in finance, the use of computational tools, and the basic patterns of cash flow. LG2 Understand the.
PowerPoint® presentation by
Practical uses of time value of money factors
Chapter 2 Time Value of Money
Chapter 3 Mathematics of Finance
CHAPTER 6 Time Value of Money
Compound Interest, Future Value, and Present Value
Chapter 9 Time Value of Money
Learning Goals LG1 Discuss the role of time value in finance, the use of computational tools, and the basic patterns of cash flow. LG2 Understand the.
Interest Principal (p) - Amount borrowed or invested.
Session 3 TIME VALUE OF MONEY
Longwood University 201 High Street Farmville, VA 23901
FM5 Annuities & Loan Repayments
Chapter 4 Time Value of Money.
Chapter 4: The Time Value of Money
Effective Personal Financial Planning
Financial Applications -Annuities (Present Value)
Translating Today’s Benefits to the Future
Grade 12 Mathematics of Finance
Financial Management: Principles & Applications
MoneyCounts: A Financial Literacy Series
Chapter 4: The Time Value of Money
Contemporary Engineering Economics
Sub- Business Mathematics and Statistics
HOW TO MAKE MONEY WITHOUT DOING ANY WORK
FIN 360: Corporate Finance
Example 1: Because of general price inflation in the economy, the purchasing power of the Turkish Lira shrinks with the passage of time. If the general.
Time Value of Money Concepts
Problem 1 You deposit $5000 in a savings account that earns 10% simple interest per year and withdraw all your money at the end of the fifth year. But.
Chapter 4: The Time Value of Money
Copyright © 2006 Brooks/Cole, a division of Thomson Learning, Inc.
Discounted Cash Flow Valuation
Presentation transcript:

By Muhammad Shahid Iqbal Engineering Economics Module No. 06 Time Value of Money By Muhammad Shahid Iqbal

The Time Value of Money A fundamental idea in finance that money that one has now is worth more than money one will receive in the future. Because money can earn interest or be invested, it is worth more to an economic actor if it is available immediately. The time value of money is money's potential to grow in value over time. Because of this potential, money that's available in the present is considered more valuable than the same amount in the future. For example, 100 dollars of today's money invested for one year and earning 5 percent interest will be worth 105 dollars after one year. Therefore, 100 dollars paid now or 105 dollars paid exactly one year from now both have the same value to the recipient who assumes 5 percent interest.

The Concepts Interest Interest is a charge for borrowing money, usually stated as a percentage of the amount borrowed over a specific period of time. Simple Interest Rate: The total interest earned or charged is linearly proportional to the initial amount of the loan (principal), the interest rate and the number of interest periods for which the principal is committed. I = ( P ) ( i ) ( N ) where P = principal amount lent or borrowed N = number of interest periods ( e.g., years ) i = interest rate per interest period

The Concepts Interest Compound Interest Rate: Whenever the interest charge for any interest period is based on the remaining principal amount plus any accumulated interest charges up to the beginning of that period. Compound interest is always assumed in TVM problems. Period Amount Owed Beginning of the period Interest Amount per period @ 10% Amount Owed at end of period 1 1000 100 1100 2 110 1210 3 121 1331

The Time Value of Money If a investor invests a sum of RS. 1000 in a fixed deposit with interest rate 15% compounded annually. The accumulated amount at the end of the year is Year end interest Compounded amount 100.00 1 15.00 115.00 2 17.25 132.25 3 19.84 152.09 4 22.81 174.90 5 26.24 201.14

The Time Value of Money Year end Present worth Compounded amount 100 1 Alternatively If we want RS. 100 at the end of 5 years what is the amount that we deposit now at a given interest rate say 15% Year end Present worth Compounded amount 100 1 86.96 2 75.61 3 65.75 4 57.18 5 49.72

Present Value Present Value is an amount today that is equivalent to a future payment, or series of payments, that has been discounted by an appropriate interest rate.  The future amount can be a single sum that will be received at the end of the last period, as a series of equally-spaced payments (an annuity), or both.  Since money has time value, the present value of a promised future amount is worth less the longer you have to wait to receive it. The time value of money principle says that future dollars are not worth as much as dollars today.

Present Value PV = FV/(1 + r)t FV = Future Value PV = Present Value r = the interest rate per period t= the number of compounding periods What is the present value of $8,000 to be paid at the end of three years if the correct (risk adjusted interest rate) is 11%? PV = 8,000/(1.11)3 = 8,000/1.36 = 5,849 I will give you $1000 in 5 years. How much money should you give me now to make it fair to me. You think a good interest rate would be 6% FV= PV ( 1 + i )N 1000 = PV ( 1 + .06)5 1000 = PV (1.338) 1000 / 1.338 = PV 747.38 = PV

Future Value Future Value is the amount of money that an investment with a fixed, compounded interest rate will grow to by some future date. The investment can be a single sum deposited at the beginning of the first period, a series of equally-spaced payments (an annuity), or both.  Since money has time value, we naturally expect the future value to be greater than the present value. The difference between the two depends on the number of compounding periods involved and the going interest rate.

Future Value What is the future value of $34 in 5 years if the interest rate is 5%? (i=.05) FV= PV ( 1 + r )t FV= 34 ( 1+ .05 ) 5 FV= 34 (1.2762815) FV= 43.39. Determine Future Value Compounded Monthly What is the future value of $34 in 5 years if the interest rate is 5%? (i equals .05 divided by 12, because there are 12 months per year. So 0.05/12=.004166, so i=.004166) FV= PV ( 1 + i )N FV= 34 ( 1+ .004166 )60 FV= 34 (1.283307) FV= 43.63.

Equal Payment series compounded amount If we want to find the future worth of n equal payments which are made at the end of year of the nth period at an interest rate of i compounded annually. FV= A (1 +i)n – 1 i A person who is now 35 years old is planning for his retired life. He plans to invest an equal sum of Rs. 10,000 at the end of every next 25 years. The bank gives 20% interest rate compounded annually. Find the maturity value of his account when he is 60 years old.

Equal Payment series Sinking Fund If we want to find the equivalent amount A that should be deposited at the end of year of the nth period to realize a future sum F at an interest rate of i compounded annually. A = FA i (1 +i)n – 1 A company has to replace the present facility after 15 years of Rs. 500,000. it plans to deposit an equal amount at the end of every year for 15 years at an interest rate of 18% compounded annually. Find the equivalent amount that must be deposited at the end of every year for the next 15 years.

Equal Payment Series Present Worth Amount If we want to find the present worth of an equal payment made at the end of year of the nth period at an interest rate of i compounded annually. P = A (1 +i)n – 1 i (1 + i)n A company wants to set up a reserve to an annual equivalent amount of Rs. 10,00,000 for next 20 years. The reserve is assumed to grow at the rate of 15% annually. Find the single payment that must be paid now as the reserve amount.

Equal Payment Series Capital Recovery Amount If we want to find the annual equivalent amount A which is to be recovered at the end of year of the nth period for a loan P which is sanctioned now at an interest rate of i compounded annually. A = P i(1 + i)n (1 +i)n – 1 A Bank give a loan to a company worth Rs. 10,00,000 at an interest rate of 18% compounded annually. This amount should be repaid in 15 yearly equal installments. Find the installment amount that company has to pay to the bank.

Effective interest Rate Let i be the nominal interest rate compounded annually. But in practice compounding may occur less than a year like monthly, quarterly or semi-annually. The formula to compute effective interest rate is Effective interest rate, R = (1 + i/C)C -1 A person invests Rs. 5,000 in a bank at a nominal interest rate of 12% for 10 years. The compounding is quarterly. Find the maturity amount of the deposit after 10 years. Effective interest rate, R = (1 + i/C)C -1 F = P(1 + R)n