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Chapter 3 Time Value of Money Part 2

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Chapter 3 Time Value of Money Part 2

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    1. Chapter 3 Time Value of Money Part 2 Valuing a series of cash flow Future Value of payment stream Annuity Stream Present Value of Annuity Stream Waiting Time Ordinary Annuity vs. Annuity Due Perpetuities Amortization Schedule

    2. Perpetuities Never Ending Annuity Stream How can you handle an infinite number of payments? Formula reduces to:

    3. Amortization Schedule Typical consumer loans make equal payments every period What is the balance (principal) at the end of any month if some of the payment is for interest and some for principal reduction? Amortization Schedule shows each payments application to interest expense and principal reduction

    4. Amortization Schedule How to build an amortization schedule Step One – Determine the payment for each period given number of periods (n), interest rate (r), and the present value (PV). Step Two – Determine each periods required interest payment Outstanding Balance x Interest rate = Interest expense Step Three – Determine principal reduction Payment – Interest expense = Principal Reduction Step Four – Determine remaining principal Beginning of Period Principal – Principal reduction = End of Period Principal Step Five – Repeat Steps Two through Four, n-1 times

    5. Problems Problem 10 – Perpetuities Problem 15 – Future Value Problem 17 – Present Value Problem 19 – Payments Problem 21 – Number of Payments Problem 25 – Amortization Schedule

    6. Valuing a Series of Cash Flow Chapter 2 dealt with a single payment or lump sum, but what if there are multiple payments? Just apply chapter 2 tools to each individual payment or cash flow and then add them up Must be at same point in time Can be very tedious Is there a short-cut? Sometimes…yes

    7. Future Value of Multiple Cash Flow Different Amounts of Cash Flow No shortcut Take all cash flow to same point in time and add up the pieces Same Amount each time and same time interval between each cash flow Shortcut – Annuity Stream Evaluation Visualize with time line

    8. Future Value of Multiple Cash Flow Formula with PMT as the annual payment amount

    9. Future Value of Multiple Cash Flow Four methods again for finding FV Table Method where we find FVIFA Equation Method Calculator Method Spreadsheet Method Example 3.1 Scholarship for Lisa $500 annual payment into scholarship fund Earns 7% interest over 18 years FV is approximately $17,000

    10. Present Value of Annuity Stream A similar shortcut for present value Four methods but same equation

    11. Waiting Time Same shortcut for Waiting Time, find n with an annuity stream

    12. Ordinary Annuity versus Annuity Due Need to visualize the difference between an annuity at the start of the period versus and annuity at the end of a period Start of Period – Annuity Due Example rent payment End of Period – Ordinary Annuity Example car payment Original Formulas for Ordinary Annuity Adjustment for Annuity Due – multiply by (1+r)

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