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$$ Entrepreneurial Finance, 5th Edition Adelman and Marks 8-1 Pearson Higher Education ©2010 by Pearson Education, Inc. Upper Saddle River, NJ 07458 Chapter 8 Time Value of Money Part I: Future and Present Value of Lump Sums
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$$ 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.
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$$ Entrepreneurial Finance, 5th Edition Adelman and Marks 8-3 Pearson Higher Education ©2010 by Pearson Education, Inc. Upper Saddle River, NJ 07458 Learning Objectives (continued) Compare bank discount and simple interest. Calculate the internal rate of return with respect to the present value of a lump sum and future value of a lump sum. Integrate the present value of a lump sum and the future value of a lump sum to solve real-life financial problems.
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$$ 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)
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$$ Entrepreneurial Finance, 5th Edition Adelman and Marks 8-5 Pearson Higher Education ©2010 by Pearson Education, Inc. Upper Saddle River, NJ 07458 Simple Interest Simple interest is the amount of interest earned on the principal amount stated. Principal amount stated is the base amount that we borrow or save.
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$$ 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%:
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$$ Entrepreneurial Finance, 5th Edition Adelman and Marks 8-7 Pearson Higher Education ©2010 by Pearson Education, Inc. Upper Saddle River, NJ 07458 Total Due on Simple Interest Loans The total amount due (maturity amount) is equal to principal plus interest: Where
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$$ 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
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$$ Entrepreneurial Finance, 5th Edition Adelman and Marks 8-9 Pearson Higher Education ©2010 by Pearson Education, Inc. Upper Saddle River, NJ 07458 Fixed Principal Commercial Loans Fixed Principal Commercial Loans are made using a fixed principal payment that remains constant for the life of the loan. › Loan can be either fixed interest loan or variable interest loan. › Interest for loans tied to prime or some other federal rate as shown in table 8-1.
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$$ 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.
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$$ Entrepreneurial Finance, 5th Edition Adelman and Marks 8-11 Pearson Higher Education ©2010 by Pearson Education, Inc. Upper Saddle River, NJ 07458 Fixed principal variable interest loan Bank calculates daily interest which is adjusted every time prime interest rate changes. Provides borrower with an invoice every month. Using Table 8-1, prime rate changed on December 11. Therefore invoice for December would have 10 days of interest using prime of 7.5 percent and 21 days of interest using a prime rate of 7.25 percent.
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$$ 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.
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$$ Entrepreneurial Finance, 5th Edition Adelman and Marks 8-13 Pearson Higher Education ©2010 by Pearson Education, Inc. Upper Saddle River, NJ 07458 Bank Discount The bank discount is an amount of interest that is deducted from the amount you wish to borrow: Where
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$$ 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.
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$$ Entrepreneurial Finance, 5th Edition Adelman and Marks 8-15 Pearson Higher Education ©2010 by Pearson Education, Inc. Upper Saddle River, NJ 07458 Bank Discount (continued)
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$$ 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.
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$$ Entrepreneurial Finance, 5th Edition Adelman and Marks 8-17 Pearson Higher Education ©2010 by Pearson Education, Inc. Upper Saddle River, NJ 07458 Three-Month Treasury Bill
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$$ 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.
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$$ Entrepreneurial Finance, 5th Edition Adelman and Marks 8-19 Pearson Higher Education ©2010 by Pearson Education, Inc. Upper Saddle River, NJ 07458 Compound Interest (continued) We can bypass the multiple individual steps in computing compound interest by using the following compound interest formula to determine future value: Where
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$$ 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.
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$$ Entrepreneurial Finance, 5th Edition Adelman and Marks 8-21 Pearson Higher Education ©2010 by Pearson Education, Inc. Upper Saddle River, NJ 07458 Effective Rate (continued) Example: A bank quotes 8 percent annual rate. The bank wants monthly payments, so it compounds monthly.
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$$ 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
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$$ Entrepreneurial Finance, 5th Edition Adelman and Marks 8-23 Pearson Higher Education ©2010 by Pearson Education, Inc. Upper Saddle River, NJ 07458 Future Value of a Lump Sum (Examples) You save $10,000 at 5 percent interest for 10 years compounded annually. What is the future value of this investment after 10 years?
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$$ 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.
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$$ Entrepreneurial Finance, 5th Edition Adelman and Marks 8-25 Pearson Higher Education ©2010 by Pearson Education, Inc. Upper Saddle River, NJ 07458 Present Value of a Future Lump Sum What is the present value of a future lump sum amount for n periods at an i rate of return? Where
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$$ 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.
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$$ Entrepreneurial Finance, 5th Edition Adelman and Marks 8-27 Pearson Higher Education ©2010 by Pearson Education, Inc. Upper Saddle River, NJ 07458 Present Value of a Stream of Unequal Payments An athlete is offered a $20 million contract over 5 years with a $4 million signing bonus. The contract consists of $2 million for year 1, $3 million for year 2, $3 million for year 3, $3 million for year 4, and $5 million for year 5. What is the present value of the $20 million contract if money can earn 5 percent annual interest?
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$$ 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:
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$$ Entrepreneurial Finance, 5th Edition Adelman and Marks 8-29 Pearson Higher Education ©2010 by Pearson Education, Inc. Upper Saddle River, NJ 07458 Internal Rate of Return Internal Rate of Return (IRR) is the actual rate of return that equates a dollar invested now with a dollar received in the future.
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$$ 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)
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$$ Entrepreneurial Finance, 5th Edition Adelman and Marks 8-31 Pearson Higher Education ©2010 by Pearson Education, Inc. Upper Saddle River, NJ 07458 IRR Problem In January 2002, you bought 10,000 shares of a stock at $2 per share. In January 2006, you sold the 10,000 shares at $3 a share. What is the internal rate of return?
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$$ 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%?
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$$ 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)
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