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Special Saturday Session: Calculators/Mathematics of PV

Special Saturday Session: Calculators/Mathematics of PV. Corporate Finance (GSBA 548) J. K. Dietrich, March 3, 2007. Present Value Calculations. We concentrate on calculation of present value formulas now, not projecting cash flows or choosing a discount rate

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Special Saturday Session: Calculators/Mathematics of PV

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  1. Special Saturday Session:Calculators/Mathematics of PV Corporate Finance (GSBA 548) J. K. Dietrich, March 3, 2007

  2. Present Value Calculations • We concentrate on calculation of present value formulas now, not projecting cash flows or choosing a discount rate • There is often more than way to calculate a present value so you must be careful to understand the structure of present value problems and recognize that structure in different formats (paper, calculator, spreadsheet)

  3. Calculating Present Values • Present values can be calculated several ways • The oldest method is with present value tables like tables A1 to A6 in the text • Tables are limited to selected discount rates and numbers of periods • Spreadsheets also can be used to calculate present values and they are more flexible • We will emphasize calculators and use some examples of spreadsheets today

  4. Computing PVs with Calculators • Practice can make seemingly complex calculations easy (although your calculator must be able to exponentiate) • Many (HP12C or 17B) are preprogrammed but there is no substitute for understanding how formulas work • You should be able to compute present values yourself if you really understand the determinants of present values

  5. PV of Single Cash Flow • There are always several ways to approach problem with a calculator but all produce same answer • Calculate present value of $1 in five years at ten percent with HP 12C (RPN)Type “r”, enter, “1 +” Type “1 / x” and ” T” • With algebraic calculator, Type “(r +1)”,”1/x” , “yx” ,”T”, ” =“

  6. Calculator PV • Always check your results for plausibility • E.g. present value factors always less than one • Later period present value factors always smaller than near period present value factors • Calculators, unlike tables, allow you to use • Any discount rate • Any time period (I.e. T can be fraction of years or any other periods)

  7. Examples: PV Formula Sheet • Using calculator to calculate present value of a single cash flow • Using a calculator to calculate sequence of cash flows • Multiple periods must be calculated • Answers for each period must be added together • Knowledge of calculator mechanics useful

  8. Basic Present Value Set-Up • The general formula for calculating all present values is: • This is formula (2) on the formula sheet • All solutions are found by writing or calculating this formula, but many formats are possible

  9. Present Value Problem Structure Periods must be same length Discount factors decrease

  10. Alternative Structure (but Equal) Structure of problem is the same; answer is the same!

  11. Structure takes Different Forms • Spreadsheet • Horizontal or vertical period divisions • Can suppress certain steps, e.g. by using Excel functions • Calculator may be use to place different period cash flows into storage locations (1, 2, …, n) • Paper can be used to store interim answers (as in text examples) and can also be organized horizontally or vertically

  12. Saturday Class Example Discount Rate Can be Anything

  13. Annuity Formula Present Values • To solve problems you need a solution strategy - e.g. to compute PV of an annuity with reverse Polish on HP 12CType “r”, enter, “1 +” Type “1 / x” and ” T”, “yx”,, then “+/-” Type “1 +”, then “r -:-” • There is more than one way to solve each problem

  14. Calculating Present Values (cont’d) • To solve annuity value using algebraic mode calculator, you can“(r +1)”,”1/x” , “yx” ,”T”,”- 1” , ”-:-”, ”r =“, “+/-” • Again, there are many other and probably better ways to get the same result • Practice calculations and compare to answers in tables

  15. Problem Solving • Set up problem carefully • Look for simplifications • Patterns in cash flows • Sub-problems that can be solved using formulas • Calculate answer • Check answer for plausibility

  16. Learning Present Value Analysis • The only way to learn present value analysis is to practice it on your own • Solutions to text problems are available in the PM office • Teaching assistants are ready to help when you are really stuck but you should not contact them until you have really thought about the problem (no pain, no gain) • The TAs and I want you to feel comfortable with this

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