1 / 29

480 likes | 1.12k Views

Chapter 8. Time Value of Money Part I: Future and Present Value of Lump Sums. Learning Objectives. Explain the relationship between the time value of money and inflation. Distinguish between effective rate and stated rate.

Download Presentation
## Chapter 8

**An Image/Link below is provided (as is) to download presentation**
Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.
Content is provided to you AS IS for your information and personal use only.
Download presentation by click this link.
While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.
During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

**Chapter 8**Time Value of Money Part I: Future and Present Value of Lump Sums**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.**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.**Learning Objectives (continued)**• Use financial tables to solve time value of money problems. • Use financial calculators to solve time value of money problems.**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.**Simple Interest (Examples)**• Interest on $1,000 borrowed for one year at 8%: • Interest on $1,000 borrowed for six months at 8%:**Total Due on Simple Interest Loans**• The total amount due (maturity amount) is equal to principal plus interest: Where**Manipulating Simple Interest**• If we know any three of the four variables: • Solving for principal • Solving for time**Bank Discount**• The bank discount is an amount of interest that is deducted from the amount you wish to borrow: Where**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.**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.**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.**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**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.**Effective Rate (continued)**• Example: A bank quotes 8 percent annual rate. The bank wants monthly payments, so it compounds monthly.**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**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?**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.**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**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.**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?**Present Value of a Stream of Unequal Payments (continued)**• This requires us to build a table which is illustrated below:**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.**Internal Rate of Return (continued)**• The IRR is found by using a calculator and the following formula:**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?**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%?**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?

More Related