1. Chapter 5 The Time Value of Money
Foundations of Finance Arthur J. Keown John D. Martin J. William Petty David F. Scott, Jr.
Chapter 5
The Time Value of Money

2. Foundations of Finance
Learning Objectives
Explain the mechanics of compounding, which is how money grows over a time when it is invested.
Be able to move money through time using time value of money tables, financial calculators, and spreadsheets.
Discuss the relationship between compounding and bringing money back to present.
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3. Foundations of Finance
Learning Objectives
Define an ordinary annuity and calculate its compound or future value.
Differentiate between an ordinary annuity and an annuity due and determine the future and present value of an annuity due.
Determine the future or present value of a sum when there are nonannual compounding periods.
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4. Foundations of Finance
Learning Objectives
Determine the present value of an uneven stream of payments
Determine the present value of a perpetuity.
Explain how the international setting complicates the time value of money.
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5. Principles Used in this Chapter
Principle 2: The Time Value of Money – A Dollar Received Today Is Worth More Than a Dollar Received in The Future.
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6. Foundations of Finance
Simple Interest
Interest is earned on principal
$100 invested at 6% per year
1st year interest is $6.00
2nd year interest is $6.00
3rd year interest is $6.00
Total interest earned: $18.00
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7. Foundations of Finance
Compound Interest
When interest paid on an investment during the first period is added to the principal; then, during the second period, interest is earned on the new sum.
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8. Foundations of Finance
Compound Interest
Interest is earned on previously earned interest
$100 invested at 6% with annual compounding
1st year interest is $6.00 Principal is $106.00
2nd year interest is $6.36 Principal is $112.36
3rd year interest is $6.74 Principal is $119.11
Total interest earned: $19.11
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9. Foundations of Finance
Future Value
- The amount a sum will grow in a certain number of years when compounded at a specific rate.
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10. Foundations of Finance
Future Value
FV1 = PV (1 + i)
Where FV1 = the future of the investment at the end of one year
i= the annual interest (or discount) rate
PV = the present value, or original amount invested at the beginning of the first year
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11. Foundations of Finance
Future Value
What will an investment be worth in 2 years?
$100 invested at 6%
FV2= PV(1+i)2 = $100 (1+.06)2
$100 (1.06)2 = $112.36
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12. Foundations of Finance
Future Value
Future Value can be increased by:
Increasing number of years of compounding
Increasing the interest or discount rate
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13. Future Value Using Tables
FVn = PV (FVIFi,n)
Where FVn = the future of the investment at the end of n year
PV = the present value, or original amount invested at the beginning of the first year
FVIF = Future value interest factor or the compound sum of $1
i= the interest rate
n= number of compounding periods
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14. Foundations of Finance
Future Value
What is the future value of $500 invested at 8% for 7 years? (Assume annual compounding)
Using the tables, look at 8% column, 7 time periods. What is the factor?
FVn= PV (FVIF8%,7yr)
= $500 (1.714)
= $857
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15. Future Value Using Calculators
Using any four inputs you will find the 5th. Set to P/YR = 1 and END mode.
INPUTS
OUTPUT N 10
I/YR 6
-100 PV
PMT FV
179.10
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16. Future Value Using Spreadsheets
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17. Foundations of Finance
Present Value
The current value of a future payment
PV = FVn {1/(1+i)n}
Where FVn = the future of the investment at the end of n years
n= number of years until payment is received
i= the interest rate
PV = the present value of the future sum of money
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18. Foundations of Finance
Present Value
What will be the present value of $500 to be received 10 years from today if the discount rate is 6%?
PV = $500 {1/(1+.06)10}
= $500 (1/1.791)
= $500 (.558)
= $279
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19. Present Value Using Tables
PVn = FV (PVIFi,n)
Where PVn = the present value of a future sum of money
FV = the future value of an investment at the end of an investment period
PVIF = Present Value interest factor of $1
i= the interest rate
n= number of compounding periods
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20. Foundations of Finance
Present Value
What is the present value of $100 to be received in 10 years if the discount rate is 6%?
PVn = FV (PVIF6%,10yrs.)
= $100 (.558)
= $55.80
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21. Present Value Using Calculators
Using any four inputs you will find the 5th. Set to P/YR = 1 and END mode.
INPUTS
OUTPUT N 10 PV
-55.84
I/YR 6
PMT FV
100.00
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22. Foundations of Finance
Annuity
Series of equal dollar payments for a specified number of years.
Ordinary annuity payments occur at the end of each period
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23. Foundations of Finance
Compound Annuity
Depositing or investing an equal sum of money at the end of each year for a certain number of years and allowing it to grow.
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24. Foundations of Finance
Compound Annuity
FV5 = $500 (1+.06)4 + $500 (1+.06)3 +$500(1+.06)2 + $500 (1+.06) + $500
= $500 (1.262) + $500 (1.191) $500 (1.124) + $500 (1.090) $500
= $ $ $
$ $500
= $2,818.50
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25. Illustration of a 5yr $500 Annuity Compounded at 6%1 2 3 4 5 6%
500
500
500
500
500
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26. Future Value of an Annuity
FV = PMT {(FVIFi,n-1)/ i }
Where FV n= the future of an annuity at the end of the nth years
FVIFi,n= future-value interest factor or sum of annuity of $1 for n years
PMT= the annuity payment deposited or received at the end of each year
i= the annual interest (or discount) rate
n = the number of years for which the annuity will last
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27. Foundations of Finance
Compounding Annuity
What will $500 deposited in the bank every year for 5 years at 10% be worth?
FV = PMT {(FVIFi,n-1)/ i }
Simplified this equation is:
FV5 = PMT(FVIFAi,n)
= $500(5.637)
= $2,818.50
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28. Future Value of an Annuity Using Calculators
Using any four inputs you will find the 5th. Set to P/YR = 1 and END mode.
INPUTS
OUTPUT N 5 FV
-2,818.55 PV
I/YR 6
PMT
500
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29. Present Value of an Annuity
Pensions, insurance obligations, and interest received from bonds are all annuities. These items all have a present value.
Calculate the present value of an annuity using the present value of annuity table.
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30. Present Value of an Annuity
Calculate the present value of a $500 annuity received at the end of the year annually for five years when the discount rate is 6%.
PV = PMT(PVIFAi,n)
= $500(4.212)
= $2,106
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31. Foundations of Finance
Annuities Due
Ordinary annuities in which all payments have been shifted forward by one time period.
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32. Foundations of Finance
Amortized Loans
Loans paid off in equal installments over time
Typically Home Mortgages
Auto Loans
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33. Payments and Annuities
If you want to finance a new machinery with a purchase price of $6,000 at an interest rate of 15% over 4 years, what will your payments be?
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34. Future Value Using Calculators
Using any four inputs you will find the 5th. Set to P/YR = 1 and END mode.
INPUTS
OUTPUT N 4
PMT
-2,101.59 PV
6,000
I/YR 15 FV
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35. Foundations of Finance
Amortization of a Loan
Reducing the balance of a loan via annuity payments is called amortizing.
A typical amortization schedule looks at payment, interest, principal payment and balance.
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36. Amortization Schedule
Yr.
Annuity
Interest
Principal
Balance 1
$2,101.58
$900.00
$1,201.58
$4,798.42 2
719.76
1,381.82
3,416.60 3
512.49
1,589.09
1,827.51 4
274.07
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37. Compounding Interest with Non-annual periods
If using the tables, divide the percentage by the number of compounding periods in a year, and multiply the time periods by the number of compounding periods in a year.
Example:
8% a year, with semiannual compounding for 5 years.
8% / 2 = 4% column on the tables
N = 5 years, with semiannual compounding or 10
Use 10 for number of periods, 4% each
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38. Foundations of Finance
Perpetuity
An annuity that continues forever is called perpetuity
The present value of a perpetuity is
PV = PP/i
PV = present value of the perpetuity
PP = constant dollar amount provided by the of perpetuity
i = annuity interest (or discount rate)
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39. The Multinational Firm
Principle 1- The Risk Return Tradeoff – We Won’t Take on Additional Risk Unless We Expect to Be Compensated with Additional Return
The discount rate is reflected in the rate of inflation.
Inflation rate outside US difficult to predict
Inflation rate in Argentina in 1989 was 4,924%, in 1990 dropped to 1,344%, and in 1991 it was only 84%.
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