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# FIN 3080 Prof Xin Li Week 3 Notes FIN 3080C

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This 3 page Class Notes was uploaded by Brady Zuver on Thursday September 8, 2016. The Class Notes belongs to FIN 3080C at University of Cincinnati taught by Xin Li in Fall 2016. Since its upload, it has received 10 views. For similar materials see Business Finance in Finance at University of Cincinnati.

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Date Created: 09/08/16

Finance 3080 Prof Xin Li Week 3 Notes Chapter 5: Introduction of Valuation: The Time Value of Money 1. Future Value and Compounding a. Future Value (FV): Cash value of an investment at some time in the future i. $1 today is not the same as $1 in the future b. Investing for a single period i. For $100 invested for 1 year at 10% 1. Future value after 1 year would be $110 a. $100 original principal + $10 interest 2. In general to invest for one period at a rate of r a. Investment equals 1+r per dollar invested b. In this case $100 x (1.1)= $110 c. Investing more than one period i. Same example as above, but adding a second year at 10% 1. $110 x .10= $11 interest in the second year a. $110+$11=$121 i. This $121 has 4 parts 1. $100 original principal 2. $10 interest of first year ($110) 3. Another $10 interest for the second year ($120) 4. The final $1 is interest earned in the second year on the first year’s interest ($10*.1=$1) ($121) d. Types of interest i. Simple Interest 1. The interest is not reinvested, the interest earned is only on the initial principal ii. Compound Interest 1. The process of leaving money and any accumulated interest in an investment for more than one period a. Essentially you are “reinvesting” the interest b. The interest from the first year gets compounded and interest is earned on that also e. Using Financial Calculator for Future Value i. Enter initial principal (with negative): -100 and press PV button ii. Enter Interest rate as a whole number (10% as 10) press I/Y button iii. Enter N (number of periods) and press N button iv. Press CPT button then Press FV button 2. Present Value and Discounting a. Present Value is the current value of future cash flows discounted at the appropriate discount rate. i. Single period case 1. How much do we invest today at 10% to get $1 in a year? 2. Present Value x 1.1=$1 a. $1/1.1= $.909 3. PV=$1/(1+r) ii. Multiple periods 1. PV=$1/(1+r) t a. r is the rate b. t is the number of cycles 2. Finding PV on calc a. Enter Future Value and press FV key b. Enter Rate and press I/Y Key c. Enter Number of compounding periods and press N Key d. Press CPT then the PV Keys 3. More about Present and Future Values a. There are only 4 parts to find Present/Future Values i. Present Value (PV) ii. Future Value (FV) iii. Discount rate (interest rate) (r) iv. Number of periods (life of investment) (t) b. If you know 3 of these, you can always get the 4 th i. Input all the given information on financial calculator 1. Compute for missing value 4. Future and Present Values of Multiple Cash Flows (In EXAM) a. Future Value i. Pay $100 today at 8%, add $100 next year. How much in the second year? 1. $100 at 8% interest = 108$ after first compound in year 1 a. Add $100 at the end of year 1 = $208 b. $208 at 8% interest = 224.64 after 2 years ii. Another way to do this 2 (total compounding) 1. $100 (original principal) x 1.08 (rate) = 116.64 2. PLUS: $100 (added after year 1) x 1.08= 108 3. Add: 116.64+108= 224.64 iii. Two ways to find future for multiple cash flows 1. Compound accumulated balance forward one year at a time (part a above) 2. Find FV of each cash flow individually and add them up (part b above) b. Present Value i. PV calculated by each CF discounted separately 1. $1000 FV every year for 5 years, interest 6% a. To find the present value for first year i. $1000/1.06 b. For any year after Nhe first year i. $1000/1.06 ii. N=number of compounding 1. 2nd year N=2, 3 N=3 and so on 2. After finding PV for each cash flow, ADD them all up to find the total Present Value ii. PV calculated by discounting 1 year at a time 1. Start in final year (5 ) with $1000 a. Discount ($1000/1.06) = 943.4 b. Add $1000 for the FV of the second year for total of $1943.4 i. Discount (1943.4/1.06) = 1833.4 rd c. Add $1000 for 3 year for total of 2833.4 i. Discount (2833.4/1.06)= 2673.01 d. Add $1000 for second year =3673.01 i. Discount (3673.01/1.06)= 3465.11 e. Add $1000 for first year of investment = 4465.11 i. Discount for final PV (4465.11/1.06) =4212.37 ii. You need to invest 4212.37 today at 6% to be able to withdraw $1000 each year for 5 years

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