Chapter 3 Time Value of Money Part 2

1
Chapter 3Time 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? Sometimesyes

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 (1r)