Introduction to Valuation: The Time Value

of Money

Chapter 5

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

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Chapter Outline

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

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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

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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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Future Value: 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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The Financial Calculator

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Issues with the Financial 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)

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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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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)