# Chapter_05

Chapter 5

### Introduction to Valuation: The Time Value of Money

McGraw-Hill/Irwin

### Chapter Outline

• Basic Definitions

• Future Value

• Financial Calculator

• Present Value

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### Basic Definitions

• 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

### Future Value

• 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?

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### General Formula

• 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

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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

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### Calculator

• 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

### Example

• 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?

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### Present Value

• 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

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### Example

• 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?

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### Example

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

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### Example

• 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?

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• 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)

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