1. Copyright © 2007 by John Wiley & Sons, Inc. All rights reserved Chapter 7 The Time Value of Money

2. Copyright © 2007 by John Wiley & Sons, Inc. All rights reserved Chapter Overview Time Value of Money ConceptTime Value of Money Concept Market Value ConceptMarket Value Concept Time Value of Money CalculationsTime Value of Money Calculations –Future Value –Present Value –Time Period and Compounding –Loan Amortization

3. Copyright © 2007 by John Wiley & Sons, Inc. All rights reserved Time Value of Money Concept Time Value of Money (TVM)Time Value of Money (TVM) –Based on face value and interest that can be earned Present Value (PV)Present Value (PV) –Current value of an asset based on the amount and timing of projected cash flows Future ValueFuture Value –Value of an asset some time in the future assuming a compounded rate of interest

4. Copyright © 2007 by John Wiley & Sons, Inc. All rights reserved Market Value Concept Present value of an asset based onPresent value of an asset based on –Projected future cash flows –Factoring in the Timing of the cash flow Risk of the cash flow being generated Mix of capital used to finance the deal

5. Copyright © 2007 by John Wiley & Sons, Inc. All rights reserved Calculating TVM Calculations can be done utilizingCalculations can be done utilizing –Complicated mathematical formulas –Shorter formulas using interest tables –Business calculator –Computer spreadsheets

6. Copyright © 2007 by John Wiley & Sons, Inc. All rights reserved Introduction to the Business Calculator Five basic function keysFive basic function keys –N = number of years –I/Y = interest or discount rate –PV = present value –PMT = annuity payment –FV = future value

7. Copyright © 2007 by John Wiley & Sons, Inc. All rights reserved Introduction to the Business Calculator Set the calculator to four decimal places.Set the calculator to four decimal places. –Steps to follow: Press the “2nd” key and the “.” key The calculator will display DEC = 2.00 Now enter “4” and press “ENTER”

8. Copyright © 2007 by John Wiley & Sons, Inc. All rights reserved Introduction to the Business Calculator Set the calculator to annual compounding.Set the calculator to annual compounding. –Steps to follow: Press 2nd and I/Y. For new calculators, the factory setting will display P/Y = 12. Press the “1” key and the ENTER key which is on the top row of the calculator. The display will show P/Y = 1.00 To exit, press 2nd and CPT (QUIT)

9. Copyright © 2007 by John Wiley & Sons, Inc. All rights reserved Single Sum Only a single sum of money is involved in the calculationOnly a single sum of money is involved in the calculation Future Value of a Single Sum |----------|----------|----------|----------|----------| |----------|----------|----------|----------|----------| 0 1 2 3 4 5 Years 0 1 2 3 4 5 Years $1,000 at 12% interest FV =? $1,000 at 12% interest FV =?

10. Copyright © 2007 by John Wiley & Sons, Inc. All rights reserved Single Sum Present Value of a Single Sum |----------|----------|----------|----------|----------| |----------|----------|----------|----------|----------| 0 1 2 3 4 5 Years 0 1 2 3 4 5 Years PV =? $1,762.34 at 12% interest PV =? $1,762.34 at 12% interest

11. Copyright © 2007 by John Wiley & Sons, Inc. All rights reserved Single Sum The following items must be known in order to calculate:The following items must be known in order to calculate: Future Value PV N I/Y CPT FV Present Value FV N I/Y CPT PV

12. Copyright © 2007 by John Wiley & Sons, Inc. All rights reserved Annuity Amount of money received or paid during each compounding period for a set timeAmount of money received or paid during each compounding period for a set time –Regular Annuity Money is received or paid at the end of each compounding period –Annuity Due Money is received or paid at the beginning of each compounding period

13. Copyright © 2007 by John Wiley & Sons, Inc. All rights reserved Regular Annuity Calculations |----------|----------|----------|----------|----------| 0 1 2 3 4 5 Years 0 1 2 3 4 5 Years 600 600 600 600 600 at 12% interest 600 600 600 600 600 at 12% interest PMT = $600 N = 5 I/Y = 12% CPT FV = $3,811.71 CPT PV = $2,162.88

14. Copyright © 2007 by John Wiley & Sons, Inc. All rights reserved Annuity Due Calculations |----------|----------|----------|----------|----------| 0 1 2 3 4 5 Years 0 1 2 3 4 5 Years 600 600 600 600 600 at 12% interest 600 600 600 600 600 at 12% interest PMT = $600 N = 5 I/Y = 12% CPT FV = $4,269.11 CPT PV = $2,422.41 Change calculator to Annuity Due mode Steps to follow: [2 nd ][PMT] [2 nd ][PMT] If display shows the word END, enter: If display shows the word END, enter: [2 nd ][ENTER] [2 nd ][ENTER] [2 nd ][CPT] [2 nd ][CPT]

15. Copyright © 2007 by John Wiley & Sons, Inc. All rights reserved Perpetuity Special type of annuity that pays or receives cash with no time limitSpecial type of annuity that pays or receives cash with no time limit PV perpetuity = PMT / r, where PMT = annuity payment r = interest rate

16. Copyright © 2007 by John Wiley & Sons, Inc. All rights reserved Uneven Stream of Cash Flow Where payments are not the same in all compounding periodsWhere payments are not the same in all compounding periods

17. Copyright © 2007 by John Wiley & Sons, Inc. All rights reserved Uneven Stream of Cash Flow |----------|----------|----------|----------|----------| 0 1 2 3 4 5 Years 0 1 2 3 4 5 Years 50 100 300 305 320 at 10% interest 50 100 300 305 320 at 10% interest Utilize [CF] button and enter: CF0 = 0 CF1 = 50 CF2 = 100 CF3 = 300 CF4 = 305 CF5 = 320 Now enter [CPT][NPV] I/Y = 10 CPT NPV = $760.5075

18. Copyright © 2007 by John Wiley & Sons, Inc. All rights reserved Compounding Period Monthly compounding favors the lenderMonthly compounding favors the lender Interest expense is being accrued or paid monthlyInterest expense is being accrued or paid monthly Annual Compounding FV = $1,762.34 N = 5 I/Y = 12% CPT PV = $1,000.00 Monthly Compounding FV = $1,762.34 N = 5 X 12 = 60 I/Y = 12% / 12 = 1% CPT PV = $970.08

19. Copyright © 2007 by John Wiley & Sons, Inc. All rights reserved Loan Amortization Schedule Year Payment Principal Interest Balance 1 40,211.48 30,211.48 10,000.00 69,788.52 1 40,211.48 30,211.48 10,000.00 69,788.52 2 40,211.48 33,232.63 6,978.85 36,555.89 2 40,211.48 33,232.63 6,978.85 36,555.89 3 40,211.48 36,555.89 3,655.59 0.00 3 40,211.48 36,555.89 3,655.59 0.00 Total120,634.44100,000.00 20,634.44 Total120,634.44100,000.00 20,634.44 Steps in developing a Loan Amortization Schedule Step 1 - Calculate debt service Step 2 - Calculate the interest amount Step 3 - Calculate principal paid Step 4 - Calculate the balance