1. $$ Entrepreneurial Finance, 5th Edition Adelman and Marks 8-1 Pearson Higher Education ©2010 by Pearson Education, Inc. Upper Saddle River, NJ 07458 Chapter 8 Time Value of Money Part I: Future and Present Value of Lump Sums

2. $$ Entrepreneurial Finance, 5th Edition Adelman and Marks 8-2 Pearson Higher Education ©2010 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.

3. $$ Entrepreneurial Finance, 5th Edition Adelman and Marks 8-3 Pearson Higher Education ©2010 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.

4. $$ Entrepreneurial Finance, 5th Edition Adelman and Marks 8-4 Pearson Higher Education ©2010 by Pearson Education, Inc. Upper Saddle River, NJ 07458  Present a spreadsheet of the mathematics of finance.  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, 5th Edition Adelman and Marks 8-5 Pearson Higher Education ©2010 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.

6. $$ Entrepreneurial Finance, 5th Edition Adelman and Marks 8-6 Pearson Higher Education ©2010 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%:

7. $$ Entrepreneurial Finance, 5th Edition Adelman and Marks 8-7 Pearson Higher Education ©2010 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

8. $$ Entrepreneurial Finance, 5th Edition Adelman and Marks 8-8 Pearson Higher Education ©2010 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

9. $$ Entrepreneurial Finance, 5th Edition Adelman and Marks 8-9 Pearson Higher Education ©2010 by Pearson Education, Inc. Upper Saddle River, NJ 07458 Fixed Principal Commercial Loans  Fixed Principal Commercial Loans are made using a fixed principal payment that remains constant for the life of the loan. › Loan can be either fixed interest loan or variable interest loan. › Interest for loans tied to prime or some other federal rate as shown in table 8-1.

10. $$ Entrepreneurial Finance, 5th Edition Adelman and Marks 8-10 Pearson Higher Education ©2010 by Pearson Education, Inc. Upper Saddle River, NJ 07458 Example Fixed Interest Commercial Loan, fixed interest. Loan for $120,000. Five years at 9.5 percent interest. Bank provides borrower with amortization table and payment book.

11. $$ Entrepreneurial Finance, 5th Edition Adelman and Marks 8-11 Pearson Higher Education ©2010 by Pearson Education, Inc. Upper Saddle River, NJ 07458 Fixed principal variable interest loan  Bank calculates daily interest which is adjusted every time prime interest rate changes.  Provides borrower with an invoice every month.  Using Table 8-1, prime rate changed on December 11. Therefore invoice for December would have 10 days of interest using prime of 7.5 percent and 21 days of interest using a prime rate of 7.25 percent.

12. $$ Entrepreneurial Finance, 5th Edition Adelman and Marks 8-12 Pearson Higher Education ©2010 by Pearson Education, Inc. Upper Saddle River, NJ 07458 Bridge Loans  Bridge loans are simple interest loans provided to borrowers who need a temporary loan to provide funds between the sale of one piece of property and the purchase of another piece of property.  Borrower actually owns two properties while awaiting the release of funds from the first piece of property.  Owner must have sufficient funds to make simultaneous payments on two properties.  When first property sells, and funds are released the borrower has sufficient funds to pay back bridge loan which is based on the days the loan is in effect.

13. $$ Entrepreneurial Finance, 5th Edition Adelman and Marks 8-13 Pearson Higher Education ©2010 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

14. $$ Entrepreneurial Finance, 5th Edition Adelman and Marks 8-14 Pearson Higher Education ©2010 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.

15. $$ Entrepreneurial Finance, 5th Edition Adelman and Marks 8-15 Pearson Higher Education ©2010 by Pearson Education, Inc. Upper Saddle River, NJ 07458 Bank Discount (continued)

16. $$ Entrepreneurial Finance, 5th Edition Adelman and Marks 8-16 Pearson Higher Education ©2010 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.

17. $$ Entrepreneurial Finance, 5th Edition Adelman and Marks 8-17 Pearson Higher Education ©2010 by Pearson Education, Inc. Upper Saddle River, NJ 07458 Three-Month Treasury Bill

18. $$ Entrepreneurial Finance, 5th Edition Adelman and Marks 8-18 Pearson Higher Education ©2010 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.

19. $$ Entrepreneurial Finance, 5th Edition Adelman and Marks 8-19 Pearson Higher Education ©2010 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

20. $$ Entrepreneurial Finance, 5th Edition Adelman and Marks 8-20 Pearson Higher Education ©2010 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.

21. $$ Entrepreneurial Finance, 5th Edition Adelman and Marks 8-21 Pearson Higher Education ©2010 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.

22. $$ Entrepreneurial Finance, 5th Edition Adelman and Marks 8-22 Pearson Higher Education ©2010 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

23. $$ Entrepreneurial Finance, 5th Edition Adelman and Marks 8-23 Pearson Higher Education ©2010 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?

24. $$ Entrepreneurial Finance, 5th Edition Adelman and Marks 8-24 Pearson Higher Education ©2010 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.

25. $$ Entrepreneurial Finance, 5th Edition Adelman and Marks 8-25 Pearson Higher Education ©2010 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

26. $$ Entrepreneurial Finance, 5th Edition Adelman and Marks 8-26 Pearson Higher Education ©2010 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 $10,000,000 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.

27. $$ Entrepreneurial Finance, 5th Edition Adelman and Marks 8-27 Pearson Higher Education ©2010 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?

28. $$ Entrepreneurial Finance, 5th Edition Adelman and Marks 8-28 Pearson Higher Education ©2010 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:

29. $$ Entrepreneurial Finance, 5th Edition Adelman and Marks 8-29 Pearson Higher Education ©2010 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.

30. $$ Entrepreneurial Finance, 5th Edition Adelman and Marks 8-30 Pearson Higher Education ©2010 by Pearson Education, Inc. Upper Saddle River, NJ 07458  The IRR is found by using a calculator and the following formula: Internal Rate of Return (continued)

31. $$ Entrepreneurial Finance, 5th Edition Adelman and Marks 8-31 Pearson Higher Education ©2010 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?

32. $$ Entrepreneurial Finance, 5th Edition Adelman and Marks 8-32 Pearson Higher Education ©2010 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%?

33. $$ Entrepreneurial Finance, 5th Edition Adelman and Marks 8-33 Pearson Higher Education ©2010 by Pearson Education, Inc. Upper Saddle River, NJ 07458  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)