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300Lecture4-ch5-6

300Lecture4-ch5-6 - Fundamentals of Finance Chapters 5,6...

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Lecture 4, Spring 2008 1 Fundamentals of Finance Chapters 5,6 – Time Value of Money & Discounted Cash Flows and Valuation
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Lecture 4, Spring 2008 2 Time Value of Money If I can borrow $100 and pay back $100 in one year? What if I give you back $101, 102, 103? Money is more valuable now because you can invest it and earn more money!
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Lecture 4, Spring 2008 3 Time Value of Money Decision 1: Receive $100 in one yr OR $100 in 2 yrs Decision 2: Receive $100 in one yr OR $110 in 2 yrs What’s the difference in these 2 problems? 1. Same amount at different times 2. Different amounts at different times
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Lecture 4, Spring 2008 4 Mechanics Ex. What is the future value of $100 in 3 yrs if the interest rate is 9% OR what amount will $100 grow to at the end of three years if money earns 9% per year in interest? Approach 1 : The long way Step1 100.00 + 100.00(.09) = 109.00 Step 2 109.00 + 109.00(.09) = 118.81 Step 3 118.81 + 118.81(.09) = 129.50
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Lecture 4, Spring 2008 5 Mechanics Approach 2: Step 1: 100.00(1.09) = 109.00 Step 2: 100.00(1.09)(1.09) = 100.00(1.09) 2 = 118.81 Step 3: 100.00(1.09)(1.09)(1.09) = 100.00(1.09) 3 = 129.50
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Lecture 4, Spring 2008 6 Terminology 1. FV n = future value at time n; 2. PV = present value; the value of a cash flow right now (time zero) 3. i = the appropriate interest rate quoted in annual percentage terms 4. n = time period in question (remember this is the end of the n th period unless otherwise stated)
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Lecture 4, Spring 2008 7 Time Value of Money: FVIF i,n Future Value Interest Factor (FVIF) Using Table Terminology: FV = PV * (FVIF ) ====> and FVIF = (1+i) Go to the FVIF Table A-1. The values in the table are simply (1+i) n Previous example: i = 9%, n=3 ====> (1.09) 3 = 1.295029 FVIF 9%,3 = 1.295 (is what is listed in the table ... rounding?)
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Lecture 4, Spring 2008 8 Time Value of Money What if you received $100 today and invested it for 3 years at 9% compounded annually? FV 3 = $100(FVIF 9%,3 ) = 100*1.295 = $129.50 (same answer as before) The calculated values are set for the future value of one dollar which is invested today, so multiply by the dollar amount that you’re working with if your investment is for other than one dollar.
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Lecture 4, Spring 2008 9 Observations FVIF factors are always greater than 1 (why?) The larger the interest rate, the larger the FVIF (for a given time period) The longer the time period, the larger the FVIF (for a given interest rate)
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Lecture 4, Spring 2008 10 Simple and Compound Interest Simple = arithmetic calculation Compound = geometric calculation Ex. PV = 100, i=12%, n=2 yrs Simple interest: FV 2 = 100 + 12 + 12 = 124 Compound interest : FV 1 = 100(1.12) = 112 FV 2 = 100(1.12) 2 = 125.44
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Lecture 4, Spring 2008 11 Simple and Compound Interest 125.44 – 124 = 1.44 The difference is interest that is earned on previously earned interest (compound interest) (1+i)(1+i) = 1 + 2i + i 2 100 * (1+.12)(1+.12) = 100 * (1 + .24 + .0144 ) instead of 100 * (1+[2*.12]) = 100 * (1 + .24)
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Lecture 4, Spring 2008 12 Other than Annual Compounding
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