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

Copyright © 2007 by John Wiley & Sons, Inc. All rights reserved

Chapter 7

The Time Value of MoneyThe Time Value of Money


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 ValueFuture Value

– Present ValuePresent Value

– Time Period and CompoundingTime Period and Compounding

– Loan AmortizationLoan Amortization


Time Value of Money Concept

• Time Value of Money (TVM)Time Value of Money (TVM)

– Based on face value and interest that can be Based on face value and interest that can be earnedearned

• Present Value (PV)Present Value (PV)

– Current value of an asset based on the Current value of an asset based on the amount and timing of projected cash flowsamount and timing of projected cash flows

• Future ValueFuture Value

– Value of an asset some time in the future Value of an asset some time in the future assuming a compounded rate of interestassuming a compounded rate of interest


Market Value Concept

• Present value of an asset based onPresent value of an asset based on

– Projected future cash flowsProjected future cash flows

– Factoring in theFactoring in the

• Timing of the cash flow

• Risk of the cash flow being generated

• Mix of capital used to finance the deal


Calculating TVM

• Calculations can be done utilizingCalculations can be done utilizing

– Complicated mathematical formulasComplicated mathematical formulas

– Shorter formulas using interest tablesShorter formulas using interest tables

– Business calculatorBusiness calculator

– Computer spreadsheetsComputer spreadsheets


Introduction to theBusiness Calculator

• Five basic function keysFive basic function keys

– N = number of yearsN = number of years

– I/Y = interest or discount rateI/Y = interest or discount rate

– PV = present valuePV = present value

– PMT = annuity paymentPMT = annuity payment

– FV = future valueFV = future value



• Set the calculator to four decimal places.Set the calculator to four decimal places.

– Steps to follow:Steps to follow:

• Press the “2nd” key and the “.” key

• The calculator will display DEC = 2.00

• Now enter “4” and press “ENTER”



• Set the calculator to annual Set the calculator to annual compounding.compounding.

– Steps to follow: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)


Single Sum

• Only a single sum of money is involved in the Only a single sum of money is involved in the calculationcalculation

Future Value of a Single SumFuture Value of a Single Sum

|----------|----------|----------|----------|----------||----------|----------|----------|----------|----------|

0 1 2 3 4 5 Years0 1 2 3 4 5 Years

$1,000 at 12% interest$1,000 at 12% interest FV =? FV =?


Single Sum

Present Value of a Single SumPresent Value of a Single Sum

|----------|----------|----------|----------|----------||----------|----------|----------|----------|----------|

0 1 2 3 4 5 Years0 1 2 3 4 5 Years

PV =? $1,762.34 at 12% PV =? $1,762.34 at 12% interestinterest


Single Sum

• The following items must be known in The following items must be known in order to calculate:order to calculate:

Future ValueFuture Value

PV

N

I/Y

CPT FV

Present ValuePresent Value

FV

N

I/Y

CPT PV


Annuity

• Amount of money received or paid during Amount of money received or paid during each compounding period for a set timeeach compounding period for a set time

– Regular AnnuityRegular Annuity

• Money is received or paid at the end of each compounding period

– Annuity DueAnnuity Due

• Money is received or paid at the beginning of each compounding period


Regular Annuity Calculations

|----------|----------|----------|----------|----------||----------|----------|----------|----------|----------|

0 1 2 3 4 5 Years0 1 2 3 4 5 Years

600 600 600 600 600 at 12% interest600 600 600 600 600 at 12% interest

PMT = $600PMT = $600

N = 5N = 5

I/Y = 12%I/Y = 12%

CPT FV = $3,811.71CPT FV = $3,811.71

CPT PV = $2,162.88CPT PV = $2,162.88


Annuity Due Calculations

|----------|----------|----------|----------|----------||----------|----------|----------|----------|----------|

0 1 2 3 4 5 Years0 1 2 3 4 5 Years

600 600 600 600 600600 600 600 600 600 at 12% interest at 12% interest

PMT = $600PMT = $600N = 5N = 5I/Y = 12%I/Y = 12%CPT FV = $4,269.11CPT FV = $4,269.11CPT PV = $2,422.41CPT PV = $2,422.41

Change calculator to Annuity Due modeChange calculator to Annuity Due modeSteps to follow:Steps to follow:• [2[2ndnd][PMT]][PMT]• If display shows the word END, enter:If display shows the word END, enter:• [2[2ndnd][ENTER]][ENTER]• [2[2ndnd][CPT]][CPT]


Perpetuity

• Special type of annuity that pays or Special type of annuity that pays or receives cash with no time limitreceives cash with no time limit

PV perpetuity = PMT / r, wherePV perpetuity = PMT / r, where

PMT = annuity paymentPMT = annuity payment

r = interest rater = interest rate


Uneven Stream of Cash Flow

• Where payments are not the same in all Where payments are not the same in all compounding periodscompounding periods


Uneven Stream of Cash Flow

|----------|----------|----------|----------|----------||----------|----------|----------|----------|----------|

0 1 2 3 4 5 Years0 1 2 3 4 5 Years

50 100 300 305 320 at 10% interest50 100 300 305 320 at 10% interest

Utilize [CF] button and enter:Utilize [CF] button and enter:CF0 = 0CF0 = 0CF1 = 50CF1 = 50CF2 = 100CF2 = 100CF3 = 300CF3 = 300CF4 = 305CF4 = 305CF5 = 320CF5 = 320

Now enter [CPT][NPV]Now enter [CPT][NPV]

I/Y = 10I/Y = 10

CPT NPV = $760.5075CPT NPV = $760.5075


Compounding Period

• Monthly compounding favors the lenderMonthly compounding favors the lender

• Interest expense is being accrued or paid Interest expense is being accrued or paid monthlymonthly

Annual CompoundingAnnual Compounding

FV = $1,762.34FV = $1,762.34N = 5N = 5I/Y = 12%I/Y = 12%CPT PV = $1,000.00CPT PV = $1,000.00

Monthly CompoundingMonthly Compounding

FV = $1,762.34FV = $1,762.34N = 5 X 12 = 60N = 5 X 12 = 60I/Y = 12% / 12 = 1%I/Y = 12% / 12 = 1%CPT PV = $970.08CPT PV = $970.08


Loan Amortization Schedule

YearYear Payment Payment Principal Principal Interest Interest Balance Balance

11 40,211.48 40,211.48 30,211.48 30,211.48 10,000.00 10,000.00 69,788.52 69,788.52

22 40,211.48 40,211.48 33,232.63 33,232.63 6,978.85 6,978.85 36,555.89 36,555.89

33 40,211.48 40,211.48 36,555.89 36,555.89 3,655.59 3,655.59 0.00 0.00

TotalTotal 120,634.44120,634.44 100,000.00100,000.00 20,634.44 20,634.44

Steps in developing a Loan Amortization ScheduleSteps in developing a Loan Amortization ScheduleStep 1 - Calculate debt serviceStep 1 - Calculate debt service

Step 2 - Calculate the interest amountStep 2 - Calculate the interest amount

Step 3 - Calculate principal paidStep 3 - Calculate principal paid

Step 4 - Calculate the balanceStep 4 - Calculate the balance

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

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