Time Value Analysis

# Time Value Analysis

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## Time Value Analysis

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1. Time Value Analysis Corporate Finance Dr. A. DeMaskey

2. Learning Objectives • Questions to be answered: • What is time value of money? • What is compounding? Discounting? • How are the principles of time value analysis applied to the various types of cash flows? • What different types of interest rates are used in finance?

3. Basic Concepts • Why time value of money? • Evaluating financial transactions • Expected cash flows • Risk

4. Time Lines 0 1 2 3 i% CF0 CF1 CF2 CF3 Tick marksat ends of periods, so Time 0 is today; Time 1 is the end of Period 1; or the beginning of Period 2.

5. Single Cash Flow 0 1 2 Year i% 100 Time line for a \$100 lump sum due at the end of Year 2.

6. Even Cash Flows: Annuity 0 1 2 3 i% 100 100 100 Time line for an ordinary annuity of \$100 for 3 years.

7. Uneven Cash Flows 0 1 2 3 i% -50 100 75 50

8. Compounding 0 1 2 3 10% 100 FV = ? Finding FVs (moving to the right on a time line) is called compounding.

9. Discounting Finding PVs is discounting, and it’s the reverse of compounding. 0 1 2 3 10% 100 PV = ?

10. Three Ways to Solve TVM Problems • Solve the equation with a regular calculator. • Use a financial calculator. • Use a spreadsheet.

11. Time Value of A Lump Sum • Future Value • Present Value

12. Time Value of a Series of Even Cash Flows • Types of Annuities • Ordinary annuity • Annuity due • Perpetual annuity • Future Value • Present Value

13. Future Value of an Ordinary Annuity 0 1 2 3 10% 100 100 100 110 121 FV = 331

14. Present Value of an Ordinary Annuity 0 1 2 3 10% 100 100 100 90.91 82.64 75.13 248.69 = PV

15. Difference Between an OrdinaryAnnuity and an AnnuityDue Ordinary Annuity 0 1 2 3 i% PMT PMT PMT Annuity Due 0 1 2 3 i% PMT PMT PMT PV FV

16. Time Value of Uneven Cash Flows • Present Value • Sum of PVs of individual cash flow components • Future Value • Sum of FVs of individual cash flow components

17. Compounding Periods • Periodic Rate • iPer = iNom/m • Annual Percentage Rate (APR) • iNom = iPerx m • Effective Annual Rate (EAR) • EFF% = (1 + iNom/m)m – 1.0