Chapter 5
Copyright © 2013 by The McGraw-Hill Companies, Inc. All rights reserved.
McGraw-Hill/Irwin

• Basic Definitions
• Future Value
• Financial Calculator
• Present Value
• Excel Spreadsheet Functions
1

• Def of time “value of money”:
• Future Value – later money on a time line
“Compounding of Single CFs”
• Present Value – earlier money on a time line
“Discounting of Single CFs”
.
• Interest rate:
– Discount rate
– Cost of capital
– Opportunity cost of capital
– Required return 2

• How much will I have at some point in the future if I have some amount today?
• For example, you invest $100 at a 20% interest. How much do you have in 1, 2, and 3 years?
3

• FV = PV(1 + r) t
– FV = future value
– PV = present value
– r = period interest rate
– t = number of periods
• (1 + r) t = future value interest factor
4

Financial Calculator:
Time Value of Money (TVM) Keys
• Texas Instruments BA-II Plus
– FV = future value
– PV = present value
– I/Y = period interest rate
– N = number of periods
– CPT and the variable you are looking for to “compute” the solution
5

6

• Remember to clear the registers
(CLR TVM) before each problem
• PV and FV have opposite signs
• I/Y = period interest rate

P/Y & C/Y must equal 1 so that the I/Y is an effective period rate

Interest is entered as a percent, not a decimal
• Set decimal places to 9
• Calculator should be in END mode
(exception: annuity due = BGN) 7

• You invest $5,000 today in an account that pays 12% per year. How much money will you have in 6 years?
• How much total interest, simple interest, and interest on interest did you earn?
8

• How much do I have to invest today to have some amount in the future?
FV = PV(1 + r) t
Rearrange the formula to solve for PV:
PV = FV / (1 + r) t
1 / (1 + r) t = present value interest factor
9

• You need to have $20,000 in three years to pay for your college tuition.
If you can earn 8% per year on your money, how much do you need to invest today?
10

• At what rate are you investing $100 if it becomes $150 in 6 periods?
11

• It will cost you $50,000 to send your child to school. You have $25,000 now and can earn 12% per year on your investment. How long will it take to get $50,000?
12

Excel Spreadsheet Functions
• Use the following formulas for TVM calculations
=FV(rate,nper,pmt,pv)
=PV(rate,nper,pmt,fv)
=RATE(nper,pmt,pv,fv)
=NPER(rate,pmt,pv,fv)
13