1. Introduction to Valuation: The Time Value of Money Chapter 5 Copyright © 2013 by The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill/Irwin

2. 1 Chapter Outline Basic Definitions Future Value Financial Calculator Present Value Excel Spreadsheet Functions

3. 2 Basic Definitions Def of time “value of money”:. Future Value – later money on a time line “Compounding of Single CFs” Present Value – earlier money on a time line “Discounting of Single CFs” Interest rate: –Discount rate –Cost of capital –Opportunity cost of capital –Required return

4. 3 Future Value How much will I have at some point in the future if I have some amount today? For example, you invest $100 at a 20% interest. How much do you have in 1, 2, and 3 years?

5. 4 Future Value: General Formula FV = PV(1 + r) t –FV = future value –PV = present value –r = period interest rate –t = number of periods (1 + r) t = future value interest factor

6. 5 Financial Calculator: Time Value of Money (TVM) Keys Texas Instruments BA-II Plus –FV = future value –PV = present value –I/Y = period interest rate –N = number of periods –CPT and the variable you are looking for to “compute” the solution

7. 6 The Financial Calculator

8. 7 Issues with the Financial Calculator Remember to clear the registers (CLR TVM) before each problem PV and FV have opposite signs I/Y = period interest rate  P/Y & C/Y must equal 1 so that the I/Y is an effective period rate  Interest is entered as a percent, not a decimal Set decimal places to 9 Calculator should be in END mode (exception: annuity due = BGN)

9. 8 Example You invest $5,000 today in an account that pays 12% per year. How much money will you have in 6 years? How much total interest, simple interest, and interest on interest did you earn?

10. 9 Present Value How much do I have to invest today to have some amount in the future? FV = PV(1 + r) t Rearrange the formula to solve for PV: PV = FV / (1 + r) t 1 / (1 + r) t = present value interest factor

11. 10 Example You need to have $20,000 in three years to pay for your college tuition. If you can earn 8% per year on your money, how much do you need to invest today?

12. 11 Example At what rate are you investing $100 if it becomes $150 in 6 periods?

13. 12 Example It will cost you $50,000 to send your child to school. You have $25,000 now and can earn 12% per year on your investment. How long will it take to get $50,000?

14. 13 Excel Spreadsheet Functions Use the following formulas for TVM calculations =FV(rate,nper,pmt,pv) =PV(rate,nper,pmt,fv) =RATE(nper,pmt,pv,fv) =NPER(rate,pmt,pv,fv)