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chapter_14_Time_Value_No_Solutions_Sept_3_07

# chapter_14_Time_Value_No_Solutions_Sept_3_07 - CHAPTER 14...

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C HAPTER 14 T IME V ALUE OF M ONEY 14.1 I NTEREST , C OMPOUNDING , AND C ASH F LOW D IAGRAMS * S IMPLE I NTEREST & C OMPOUND I NTEREST The two most basic parameters affecting the real value of money is interest rate and time. You've heard the comment "…all it takes is time and money…" Well, they go together. The value of money is time dependent; value is always changing with time. The key is to determine the equivalent value of alternatives at a common point in time. Or, some present value is equal to some future sum of payments. This is called equivalenc e. Equivalence is the basis of the preceding examples where investors were deciding whether to invest in your company or to allow an improvement to increase productivity in an existing company, putting values to the same point in time as impacted by inflation, loan interest rates, or required rates of return. First, what is interest ? Interest is defined as the return on an investment or the fee charged by a lender by a borrower for the use of borrowed money, and which definition you use depends on whether you are in the position of the lender or the borrower. Most commonly the interest is expressed as a percentage of the borrowed money, and a compounding period is also specified. An example of this would be 8% interest compounded monthly. The interest if there are no compound periods is called simple interest and interest over multiple compound periods is called compound interest . The interest rate applicable in an economic transaction is affected by the perceived risk or probability of non-payment in the transaction. A bank may lend money to a low risk customer at 7.5%, but an entrepreneur may have to borrow money at much higher rates from potential investors, since high risk and bank loans are mutually exclusive. An interest rate has three components: 1. A risk-free component based on an economic concept called the marginal productivity of capital. Many economists believe this 1

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Chapter 14 - Time Value of Money rate is about 3 or 4 percent in a risk-free and inflation free environment. 2. A risk component to compensate for uncertainty or the possibility of nonpayment. 3. An inflation component applicable in periods of inflation. In periods of inflation, lenders demand higher rates of return to compensate for the decline in purchasing power between the time money is lent and the time it is paid. Simple Interest Simple interest is interest earned only on the original principal. The formula for calculating simple interest or earnings is n i P E = where, E = simple interest or earnings P = principal (amount borrowed or lent) i = interest rate per year n = number of years or fraction thereof Example 14.1 – simple interest If you borrow \$100 for one year at 10% per annum, the interest for the year is E = (\$100)(0.10)(1) = \$10 If you borrow \$100 for 3 months at 10%, the interest is (note the assumption is made of 10% per annum, so 3 months is 3/12 or 0.25).
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chapter_14_Time_Value_No_Solutions_Sept_3_07 - CHAPTER 14...

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