Chapter 8 Time Value of Money Part I

$$ $$ $$ $$ $$ Learning Objectives § Explain the relationship between the time

$$ $$ $$ $$ $$ Learning Objectives (continued) § Compare bank discount and simple

$$ $$ $$ $$ $$ Learning Objectives (continued) § Use financial tables to solve

$$ $$ $$ $$ $$ Simple Interest § Simple interest is the amount of

$$ $$ $$ $$ $$ Simple Interest (Examples) § Interest on $1, 000 borrowed

$$ $$ $$ $$ $$ Total Due on Simple Interest Loans § The total

$$ $$ $$ $$ $$ Manipulating Simple Interest § If we know any three

$$ $$ $$ $$ $$ Bank Discount § The bank discount is an amount

$$ $$ $$ $$ $$ Bank Discount (continued) § Proceeds are the amount the

$$ $$ $$ $$ $$ Bank Discount (continued) Entrepreneurial Finance, 4 th Edition By

$$ $$ $$ $$ $$ Federal Treasury Bills § There are situations in which

$$ $$ $$ $$ $$ Three-Month Treasury Bill Entrepreneurial Finance, 4 th Edition By

$$ $$ $$ $$ $$ Compound Interest § Compound interest is earned or charged

$$ $$ $$ $$ $$ Compound Interest (continued) § We can bypass the multiple

$$ $$ $$ $$ $$ Effective Rate § The stated or quoted rate is

$$ $$ $$ $$ $$ Effective Rate (continued) § Example: A bank quotes 8

$$ $$ $$ $$ $$ Future Value of a Lump Sum § What is

$$ $$ $$ $$ $$ Future Value of a Lump Sum (Examples) § You

$$ $$ $$ $$ $$ Future Value of a Lump Sum (Examples) § If

$$ $$ $$ $$ $$ Present Value of a Future Lump Sum § What

$$ $$ $$ $$ $$ Present Value of a Lump Sum (Examples) § How

$$ $$ $$ $$ $$ Present Value of a Stream of Unequal Payments §

$$ $$ $$ $$ $$ Present Value of a Stream of Unequal Payments (continued)

$$ $$ $$ $$ $$ Internal Rate of Return § Internal Rate of Return

$$ $$ $$ $$ $$ Internal Rate of Return (continued) § The IRR is

$$ $$ $$ $$ $$ IRR Problem § In January 2002, you bought 10,

$$ $$ $$ $$ $$ Rule of 72 § We can also find an

$$ $$ $$ $$ $$ Rule of 72 (continued) § We can also find

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$$ $$ $$ $$ $$ Chapter 8 Time Value of Money Part I: Future and Present Value of Lump Sums Entrepreneurial Finance, 4 th Edition By Adelman and Marks 8 - PRENTICE HALL © 2007 by Pearson Education, Inc. Upper Saddle River, NJ 07458

$$ $$ $$ $$ $$ Learning Objectives § Explain the relationship between the time value of money and inflation. § Distinguish between effective rate and stated rate. § Calculate the future value lump sum and present value lump sum factors that are used to solve time value of money problems. Entrepreneurial Finance, 4 th Edition By Adelman and Marks 8 -2 PRENTICE HALL © 2007 by Pearson Education, Inc. Upper Saddle River, NJ 07458

$$ $$ $$ $$ $$ Learning Objectives (continued) § Compare bank discount and simple interest. § Calculate the internal rate of return with respect to the present value of a lump sum and future value of a lump sum. § Integrate the present value of a lump sum and the future value of a lump sum to solve real-life financial problems. Entrepreneurial Finance, 4 th Edition By Adelman and Marks 8 -3 PRENTICE HALL © 2007 by Pearson Education, Inc. Upper Saddle River, NJ 07458

$$ $$ $$ $$ $$ Learning Objectives (continued) § Use financial tables to solve time value of money problems. § Use financial calculators to solve time value of money problems. Entrepreneurial Finance, 4 th Edition By Adelman and Marks 8 -4 PRENTICE HALL © 2007 by Pearson Education, Inc. Upper Saddle River, NJ 07458

$$ $$ $$ $$ $$ Simple Interest § Simple interest is the amount of interest earned on the principal amount stated. § Principal amount stated is the base amount that we borrow or save. Entrepreneurial Finance, 4 th Edition By Adelman and Marks 8 -5 PRENTICE HALL © 2007 by Pearson Education, Inc. Upper Saddle River, NJ 07458

$$ $$ $$ $$ $$ Simple Interest (Examples) § Interest on $1, 000 borrowed for one year at 8%: § Interest on $1, 000 borrowed for six months at 8%: Entrepreneurial Finance, 4 th Edition By Adelman and Marks 8 -6 PRENTICE HALL © 2007 by Pearson Education, Inc. Upper Saddle River, NJ 07458

$$ $$ $$ $$ $$ Total Due on Simple Interest Loans § The total amount due (maturity amount) is equal to principal plus interest: Where Entrepreneurial Finance, 4 th Edition By Adelman and Marks 8 -7 PRENTICE HALL © 2007 by Pearson Education, Inc. Upper Saddle River, NJ 07458

$$ $$ $$ $$ $$ Manipulating Simple Interest § If we know any three of the four variables: › Solving for principal › Solving for time Entrepreneurial Finance, 4 th Edition By Adelman and Marks 8 -8 PRENTICE HALL © 2007 by Pearson Education, Inc. Upper Saddle River, NJ 07458

$$ $$ $$ $$ $$ Bank Discount § The bank discount is an amount of interest that is deducted from the amount you wish to borrow: Where Entrepreneurial Finance, 4 th Edition By Adelman and Marks 8 -9 PRENTICE HALL © 2007 by Pearson Education, Inc. Upper Saddle River, NJ 07458

$$ $$ $$ $$ $$ Bank Discount (continued) § Proceeds are the amount the bank actually provides to the borrower after deducting the discount from the amount intended to be borrowed. Entrepreneurial Finance, 4 th Edition By Adelman and Marks 8 -10 PRENTICE HALL © 2007 by Pearson Education, Inc. Upper Saddle River, NJ 07458

$$ $$ $$ $$ $$ Federal Treasury Bills § There are situations in which the entrepreneur can actually perform the function of a bank. § What better source of investing than to lend the government of the United States money for a short period of time? § The government issues discounted treasury bills in denominations of $10, 000 for three months, six months, and one year. Entrepreneurial Finance, 4 th Edition By Adelman and Marks 8 -12 PRENTICE HALL © 2007 by Pearson Education, Inc. Upper Saddle River, NJ 07458

$$ $$ $$ $$ $$ Compound Interest § Compound interest is earned or charged on both the principal amount and on the accrued interest that has been previously earned or charged. Entrepreneurial Finance, 4 th Edition By Adelman and Marks 8 -14 PRENTICE HALL © 2007 by Pearson Education, Inc. Upper Saddle River, NJ 07458

$$ $$ $$ $$ $$ Compound Interest (continued) § We can bypass the multiple individual steps in computing compound interest by using the following compound interest formula to determine future value: where Entrepreneurial Finance, 4 th Edition By Adelman and Marks 8 -15 PRENTICE HALL © 2007 by Pearson Education, Inc. Upper Saddle River, NJ 07458

$$ $$ $$ $$ $$ Effective Rate § The stated or quoted rate is the rate of interest that is listed, normally on an annual basis, and it disregards compounding. § The effective annual rate is the actual rate that is paid by the borrower or earned by the investor after compounding is taken into consideration. Entrepreneurial Finance, 4 th Edition By Adelman and Marks 8 -16 PRENTICE HALL © 2007 by Pearson Education, Inc. Upper Saddle River, NJ 07458

$$ $$ $$ $$ $$ Effective Rate (continued) § Example: A bank quotes 8 percent annual rate. The bank wants monthly payments, so it compounds monthly. Entrepreneurial Finance, 4 th Edition By Adelman and Marks 8 -17 PRENTICE HALL © 2007 by Pearson Education, Inc. Upper Saddle River, NJ 07458

$$ $$ $$ $$ $$ Future Value of a Lump Sum § What is the future value of a lump sum amount for n periods and at i rate of return? Where Entrepreneurial Finance, 4 th Edition By Adelman and Marks 8 -18 PRENTICE HALL © 2007 by Pearson Education, Inc. Upper Saddle River, NJ 07458

$$ $$ $$ $$ $$ Future Value of a Lump Sum (Examples) § You save $10, 000 at 5 percent interest for 10 years compounded annually. What is the future value of this investment after 10 years? Entrepreneurial Finance, 4 th Edition By Adelman and Marks 8 -19 PRENTICE HALL © 2007 by Pearson Education, Inc. Upper Saddle River, NJ 07458

$$ $$ $$ $$ $$ Future Value of a Lump Sum (Examples) § If a wedding costs $20, 000 today, how much will the wedding cost 10 years from now if inflation averages 4% a year? § What is the future value of $100, 000 if money is compounded monthly at 6% for 18 years? Note: The answer below was obtained by using a calculator. If you use tables, the answer is $293, 680. Entrepreneurial Finance, 4 th Edition By Adelman and Marks 8 -20 PRENTICE HALL © 2007 by Pearson Education, Inc. Upper Saddle River, NJ 07458

$$ $$ $$ $$ $$ Present Value of a Future Lump Sum § What is the present value of a future lump sum amount for n periods at an i rate of return? Where Entrepreneurial Finance, 4 th Edition By Adelman and Marks 8 -21 PRENTICE HALL © 2007 by Pearson Education, Inc. Upper Saddle River, NJ 07458

$$ $$ $$ $$ $$ Present Value of a Lump Sum (Examples) § How much do you have to deposit in an account today that will have a value of $10, 000 in 7 years if annual interest is 6% compounded annually? Note: If tables are used rather than a calculator, the answer will be $6, 651, 000. Entrepreneurial Finance, 4 th Edition By Adelman and Marks 8 -22 PRENTICE HALL © 2007 by Pearson Education, Inc. Upper Saddle River, NJ 07458

$$ $$ $$ $$ $$ Present Value of a Stream of Unequal Payments § An athlete is offered a $20 million contract over 5 years with a $4 million signing bonus. The contract consists of $2 million for year 1, $3 million for year 2, $3 million for year 3, $3 million for year 4, and $5 million for year 5. What is the present value of the $20 million contract if money can earn 5 percent annual interest? Entrepreneurial Finance, 4 th Edition By Adelman and Marks 8 -23 PRENTICE HALL © 2007 by Pearson Education, Inc. Upper Saddle River, NJ 07458

$$ $$ $$ $$ $$ Present Value of a Stream of Unequal Payments (continued) § This requires us to build a table which is illustrated below: Entrepreneurial Finance, 4 th Edition By Adelman and Marks 8 -24 PRENTICE HALL © 2007 by Pearson Education, Inc. Upper Saddle River, NJ 07458

$$ $$ $$ $$ $$ Internal Rate of Return § Internal Rate of Return (IRR) is the actual rate of return that equates a dollar invested now with a dollar received in the future. Entrepreneurial Finance, 4 th Edition By Adelman and Marks 8 -25 PRENTICE HALL © 2007 by Pearson Education, Inc. Upper Saddle River, NJ 07458

$$ $$ $$ $$ $$ Internal Rate of Return (continued) § The IRR is found by using a calculator and the following formula: Entrepreneurial Finance, 4 th Edition By Adelman and Marks 8 -26 PRENTICE HALL © 2007 by Pearson Education, Inc. Upper Saddle River, NJ 07458

$$ $$ $$ $$ $$ IRR Problem § In January 2002, you bought 10, 000 shares of a stock at $2 per share. In January 2006, you sold the 10, 000 shares at $3 a share. What is the internal rate of return? Entrepreneurial Finance, 4 th Edition By Adelman and Marks 8 -27 PRENTICE HALL © 2007 by Pearson Education, Inc. Upper Saddle River, NJ 07458

$$ $$ $$ $$ $$ Rule of 72 § We can also find an approximation of the amount of time that it takes a present sum of money to double by dividing the number 72 by the interest rate earned on an investment. This procedure is known as the rule of 72. Example: How long will it take $1, 000 to double if it can be invested at 12%? Entrepreneurial Finance, 4 th Edition By Adelman and Marks 8 -28 PRENTICE HALL © 2007 by Pearson Education, Inc. Upper Saddle River, NJ 07458

$$ $$ $$ $$ $$ Rule of 72 (continued) § We can also find the interest required if we know how long it takes an investment to double. § Example: We want $1, 000 to double in eight years. What interest to we have to earn on our investment? Entrepreneurial Finance, 4 th Edition By Adelman and Marks 8 -29 PRENTICE HALL © 2007 by Pearson Education, Inc. Upper Saddle River, NJ 07458