Lecture Notes on Time Value of Money

Lecture Notes on Time Value of Money - MGMT 235 Dr. Sharp...

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© 2004 So (1+i) t = (1+i)·(1+i)·(1+i)·(1+i)·(1+i)·(1+i)·(1+i)… ·(1+i) for “t” times KEY RELATIONHSIP: FV = PV x (1+i) t KEY RELATIONHSIP: PV = FV ÷ (1+i) t KEY RELATIONHSIP: (1+i) t =FV÷PV (1+i) = (FV÷PV) 1/t FV = PV x (1+i 1 ) x (1+i 2 ) x (1+i 3 ) x … x (1+i t ). Long way. Short Way The interest factor on that payment is 1. The first payment earns interest for t-1 periods, not t periods. Use Short Cut Formula 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. .
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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)] PV = 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.
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Lecture Notes on Time Value of Money - MGMT 235 Dr. Sharp...

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