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Time Value of Money

Time Value of Money - MGMT 235 Dr Sharp 2004 Review...

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MGMT 235 Dr. Sharp Review Fundamentals of Valuation These class notes review this material and also provide some help for a financial calculator. It also has some self-test questions and problems. Class notes are necessarily brief. See any principles of finance book for a more extensive explanation. Eugene F. Brigham, Joel F. Houston Fundamentals of financial management HG 4026 B6693 1998 Ross, Stephen A, Westerfield, and Jordan Fundamentals of corporate finance HG 4026 .R677 1995 PART I : Single Sum. Time Value of Money: Know this terminology and notation FV Future Value (1+i) t Future Value Interest Factor [FVIF] PV Present Value 1/(1+i) t Present Value Interest Factor [PVIF] i Rate per period t # of time periods Question: Why are (1+i) and (1+i) t called interest factors? Answer: 1. Start with simple arithmetic problem on interest: How much will $10,000 placed in a bank account paying 5% per year be worth compounded annually? Answer: Principal + Interest $10,000 + $10,000 x .05 = $10,500 2. Factor out the $10,000. 10,000 x (1.05) = $10,500 3. This leaves (1.05) as the factor . 1. Find the value of $10,000 earning 5% interest per year after two years. Start with the amount after one year and multiply by the factor for each year. [ Amount after one year ] x (1.05) = [ $10,000 x (1.05) ] x (1.05) = $10,000 x (1.05) 2 = $11,025. . © 2004 So (1+i) t = (1+i)·(1+i)·(1+i)·(1+i)·(1+i)·(1+i)·(1+i)… ·(1+i) for “t” times
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Class Notes A. Future Value Find the value of $10,000 in 10 years. The investment earns 5% per year. FV = $10,000 · (1+i) · (1+i) · (1+i) · (1+i) · (1+i) · (1+i) · (1+i) · (1+i) · (1+i) · (1+i) FV = $10,000 · (1.05) · (1.05) · (1.05) · (1.05) · (1.05) · (1.05) · (1.05) · (1.05) · (1.05) · (1.05) FV = $10,000 x (1.05) 10 = $10,000 x 1.62889 = $16,289 Find the value of $10,000 in 10 years. The investment earns 8% for four years and then earns 4% for the remaining six years. FV = $10,000 · (1+i) · (1+i) · (1+i) · (1+i) · (1+i) · (1+i) · (1+i) · (1+i) · (1+i) · (1+i) FV = $10,000 · (1.08) · (1.08) · (1.08) · (1.08) · (1.04) · (1.04) · (1.04) · (1.04) · (1.04) · (1.04) FV = $10,000 x (1.08) 4 x (1.04) 6 FV = $17,214.53 B. Present Value : Same idea, but begin at the end. Rearrange the Future value equation to look like this: PV = FV÷ [(1+i) · (1+i) · (1+i) · (1+i) · (1+i) · (1+i) · (1+i) · (1+i) · (1+i) · (1+i)] P V = FV ÷ (1+i) t [2] Example: How much do I need to invest at 8% per year, in order to have $10,000 in__. a. One year: PV =10,000 ÷ (1.08) = $9,259.26 b. Two years: PV = $10,000 ÷ (1.08) ÷ (1.08) OR $10,000 ÷ (1.08) 2 = $8,573 c. Ten years PV = $10,000 ÷ (1.08) 10 = $10,000 ÷ 2.1589 = $4,632 C. Rate of Return START WITH SAME RELATIONHSIP: FV = PV x (1+i) t Solve for i. (1+i) t =FV/PV. 1+i = (FV/PV) 1/t i = (FV/PV) 1/t -1. Question: An investor deposits $10,000. Ten years later it is worth $17,910. What rate of return did the investor earn on the investment? Solution: $17,910 = $10,000 x (1+i) 10 (1+i) 10 = $17,910/10,000 = 1.7910 (1+i) = (1.7910) 1/10 = 1.060 i = .060 = 6.0% 2
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Class Notes D. Finding the Future Value Find the value of $10,000 today at the end of 10 periods at 5% per period. 1. Scientific Calculator: Use [y x ] y = (1+i) = 1.05 and x =t= 10. 1. Enter 1.05. 2. Press [y x ]. 3. Enter the exponent. 4. Enter [=]. 5. Multiply result by $10,000. 2. Spreadsheet: 3. Financial calculator. You may need to input something like this.
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