1. $$ Entrepreneurial Finance, 4th Edition By Adelman and Marks PRENTICE HALL ©2007 by Pearson Education, Inc. Upper Saddle River, NJ 07458 8-1 Chapter 8 Time Value of Money Part I: Future and Present Value of Lump Sums

2. $$ Entrepreneurial Finance, 4th Edition By Adelman and Marks PRENTICE HALL ©2007 by Pearson Education, Inc. Upper Saddle River, NJ 07458 8-2 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.

3. $$ Entrepreneurial Finance, 4th Edition By Adelman and Marks PRENTICE HALL ©2007 by Pearson Education, Inc. Upper Saddle River, NJ 07458 8-3 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.

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

5. $$ Entrepreneurial Finance, 4th Edition By Adelman and Marks PRENTICE HALL ©2007 by Pearson Education, Inc. Upper Saddle River, NJ 07458 8-5 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.

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

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

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

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

10. $$ Entrepreneurial Finance, 4th Edition By Adelman and Marks PRENTICE HALL ©2007 by Pearson Education, Inc. Upper Saddle River, NJ 07458 8-10 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.

11. $$ Entrepreneurial Finance, 4th Edition By Adelman and Marks PRENTICE HALL ©2007 by Pearson Education, Inc. Upper Saddle River, NJ 07458 8-11 Bank Discount (continued)

12. $$ Entrepreneurial Finance, 4th Edition By Adelman and Marks PRENTICE HALL ©2007 by Pearson Education, Inc. Upper Saddle River, NJ 07458 8-12 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.

13. $$ Entrepreneurial Finance, 4th Edition By Adelman and Marks PRENTICE HALL ©2007 by Pearson Education, Inc. Upper Saddle River, NJ 07458 8-13 Three-Month Treasury Bill

14. $$ Entrepreneurial Finance, 4th Edition By Adelman and Marks PRENTICE HALL ©2007 by Pearson Education, Inc. Upper Saddle River, NJ 07458 8-14 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.

15. $$ Entrepreneurial Finance, 4th Edition By Adelman and Marks PRENTICE HALL ©2007 by Pearson Education, Inc. Upper Saddle River, NJ 07458 8-15 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

16. $$ Entrepreneurial Finance, 4th Edition By Adelman and Marks PRENTICE HALL ©2007 by Pearson Education, Inc. Upper Saddle River, NJ 07458 8-16 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.

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

18. $$ Entrepreneurial Finance, 4th Edition By Adelman and Marks PRENTICE HALL ©2007 by Pearson Education, Inc. Upper Saddle River, NJ 07458 8-18 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

19. $$ Entrepreneurial Finance, 4th Edition By Adelman and Marks PRENTICE HALL ©2007 by Pearson Education, Inc. Upper Saddle River, NJ 07458 8-19 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?

20. $$ Entrepreneurial Finance, 4th Edition By Adelman and Marks PRENTICE HALL ©2007 by Pearson Education, Inc. Upper Saddle River, NJ 07458 8-20 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.

21. $$ Entrepreneurial Finance, 4th Edition By Adelman and Marks PRENTICE HALL ©2007 by Pearson Education, Inc. Upper Saddle River, NJ 07458 8-21 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

22. $$ Entrepreneurial Finance, 4th Edition By Adelman and Marks PRENTICE HALL ©2007 by Pearson Education, Inc. Upper Saddle River, NJ 07458 8-22 Present Value of a Lump Sum (Examples)  How much do you have to deposit in an account today that will have a value of $10,000,000 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.

23. $$ Entrepreneurial Finance, 4th Edition By Adelman and Marks PRENTICE HALL ©2007 by Pearson Education, Inc. Upper Saddle River, NJ 07458 8-23 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?

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

25. $$ Entrepreneurial Finance, 4th Edition By Adelman and Marks PRENTICE HALL ©2007 by Pearson Education, Inc. Upper Saddle River, NJ 07458 8-25 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.

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

27. $$ Entrepreneurial Finance, 4th Edition By Adelman and Marks PRENTICE HALL ©2007 by Pearson Education, Inc. Upper Saddle River, NJ 07458 8-27 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?

28. $$ Entrepreneurial Finance, 4th Edition By Adelman and Marks PRENTICE HALL ©2007 by Pearson Education, Inc. Upper Saddle River, NJ 07458 8-28 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%?

29. $$ Entrepreneurial Finance, 4th Edition By Adelman and Marks PRENTICE HALL ©2007 by Pearson Education, Inc. Upper Saddle River, NJ 07458 8-29  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? Rule of 72 (continued)