Chapter 4 Introduction To Valuation: The Time Value Of Money

Chapter 4Introduction to Valuation:The Time Value of Money4-1

Where we are nowDoneIntroduction andFinancial StatementsTime Value ofMoney andDiscounted CashFlowsCapital InvestmentCriteriaChapters 1-3Chapters 4-5Chapters 8-9Bond and StockValuationRisk, Return andCost of CapitalChapters 6-7Chapters 10-12Midterm Exam #1 on 3/6 will cover Chapters 1-44-2

Chapter 4Chapter 5Introductionto ValuationDiscountedCash FlowValuation Understanding time valueof money Future value of multiplecash flows Future value of a singlelump-sum amount Present value of multiplecash flows Present value of a singlelump-sum future payment4-3

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528.8 million over 30 years- or 327.8 million today?4-5

Which do you choose if you won this jackpot - 528.8MM over30 years or 327.8MM today?A.Obviously 528.8MM over 30 years since it is a bigger number.B.Obviously 327.8MM today so I can immediately get a reallybig house plus a yacht plus a plane plus lots of other stuff.C.I’d choose the 528.8MM over 30 years so there was no riskthat I would spend it all too fast.D.I’d choose the 327.8MM today because I would invest it sowell that it would make me much more money than 528.8MMover 30 years.E.I’m really not sure, but can’t wait to learn the answer fromFINC 311!!!4-6

Mike’s ProjectEmily’s Project Invest 1MM in Year Invest 3MM in0 and Year 1 andYear 0Year 2 Receive 2MM inYear 3 and 2MM inYear 4Net Cash of 1MM Receive 5MM inYear 5Net Cash of 2MMRobert’s Project Invest 3MM in Year0 Receive 3.4MM inYear 1Net Cash of 0.4MM4-7

Which do you choose?A.Today 100B.- or -Year 1 1024-8

Both how much money and when youget it, or pay it4-9

How the factor of time impacts thevalue of money Money available today is worth morethan the same amount of money inthe future4-10

Because you can earn money on yourmoney InterestReturn on investment4-11

Interest is the price paid to borrowmoney Expressed as a percentage rate over aperiod of timeTwo ways to calculate Simple interest Compound interest4-12

Assume a 10% interest rate on 100Today 100 100Year 1 10 10 110 110Year 2 10 11 120SimpleInterest 121CompoundInterest 1 difference represents“interest on interest”(i.e., 10% of 10)4-13

Simple interest Interest earned only on the original principal Compound interest Interest earned on principal and on interestreceived“Interest on interest” – interest earned onreinvestment of previous interest paymentsCopyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.4-14

Decision makerWhen?How much?Assumed rateof return?Other termsInterest rateDiscount rateCost of capitalOpportunity cost of capitalRequired returnHurdle rateReturn on investment4-15

Today 100- or -Year 1 102If interest rate is 1%?If interest rate is 5%?Assume annual compounding4-16

Which do you choose – ifthe interest rate is 1%?A.Today 100B.- or -Year 1 1024-17

Which do you choose – ifthe interest rate is 5%?A.Today 100B.- or -Year 1 1024-18

Today 100- or -Year 1 102If interest rate is 1%?Choose 102 in 1 yearIf interest rate is 5%?Choose 100 today4-19

PresentValue (PV)TodayInterestRateYear 1 1001% 1015% 105 100InterestRate orDiscountRate(r)Time (t)FutureValue(FV)The future value (FV) of 100 in 1 year (t) at 1% interest (r) is 101.The present value (PV) of 105 in 1 year (t) at 5% interest (r) is 100.4-20

Future Value The amount an investment is worth afterone or more periods.“Later” money on a time line Present Value (FV)(PV)The current value of future cash flowsdiscounted at the appropriate discount rateValue at t 0 on a time lineCopyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.4-21

There are 5 options for solving timevalue of money problemsLong FormFormulaTablesExcelFinancialCalculatorCovered in class4-22

All else held constant, the future value of alump sum investment will decrease if the:A.Amount of the lump sum investmentincreases.B.Time period is increased.C.Interest is left in the investment.D.Interest rate increases.E.Interest is changed to simple interest fromcompound interest.4-23

Today 1000Year 1* (1 r) XYear 2* (1 r) YYear 3* (1 r) Z The long-form approach begins with drawing a time line ofthe problem. The future value of cash is manually calculated for each timeperiod. This approach is important to understand intuitively how tosolve time value of money problems However, it is not practical when numerous time periods areinvolved.4-24

FV PV * (1 r)tFV Future ValuePV Present Valuer Interest RateFuture Value Factort # of periodsNote: The yx function on many calculators is usefulwhen using the formula for solving problems.4-25

FV of 1 1 * (1 r)tFuture ValueFactorFV 1 * (1 .10)3 1 * 1.3310 1.33Future Value FactorsNote: When using tables, pay extra attention to following thecorrect row and column to get the correct factor amount.4-26

For a given interest rate: The longer the time period,The higher the future valueFV PV(1 r)tFor a given r, as t increases, FV increasesCopyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.4-27

For a given time period: The higher the interest rate,The larger the future valueFV PV(1 r)tFor a given t, as r increases, FV increasesCopyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.4-28

Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.4-29

Blue represents“interest on interest”Yellow representsprincipal plus simpleinterestCopyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.4-30

The “Rule of 72” is a quick approximationon doubling dollar amounts based on anycombination of rate and years equaling 72TodayRateYearsFutureValueRate *Years 1,0009%8 1,99372 1,00018%4 1,93972 1,0007%10 1,96770 1,0005%15 2,079754-31

Jane is a 20 year-old college student who invests 10,000 today and expects to earn 8% per year.Approximately how much money will Jane have fromthis investment when she retires at the age of 65?A. 50,000B. 90,000C. 160,000D. 320,000E. 450,0004-32

At 8% per year, your money will double in howmany years? 9 years Thus, how many “doublings” will take placeover 45 years? 5 doublings So, if you start with 10,000 and have 5doublings over 45 years, how much do youend up with? 10,000 20,000 (doubling #1) 40,000 (doubling #2) 80,000(doubling #3) 160,000 (doubling #4) 320,000 (doubling #5)Actual Answer is: FV PV*(1 r)t 10,000*(1.08)45 319,2044-33

Future Value The amount an investment is worth afterone or more periods.“Later” money on a time line Present Value (FV)(PV)The current value of future cash flowsdiscounted at the appropriate discount rateValue at t 0 on a time lineCopyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.4-34

Today 1,000PresentValueFuture Period“Compounding” tothe future“Discounting” totodayFutureValue 1,000Note: “Discounting” is the reverse of “compounding.”4-35

Today 100- or -Year 1 102Present value and future value math is all aboutgetting to an apples-to-apples comparison oran oranges-to-oranges comparison4-36

If you have 20 euros and 20, how much money doyou have? You need to convert the 20euros to the equivalent valuein dollars.Or you can convert the 20to the equivalent value ineuros.Conversion factor is FXexchange rate.4-37

If you have 100 cash and a Promissory Note for 102 in 1 year, how much money do you have?TodayPromissory Notevalue today1 Year“Discount”to today You need to convert the Promissory Note for 102in 1 year to the equivalent value today. Conversion factor is the present value factor.4-38

John and Sally want todeposit enough moneytoday to have 100,000in 18 years for theirchild’s college expenses.What is the presentvalue of 100,000 in18 years?Sam wants to depositenough money today tohave a 50,000 downpayment on a house in 5years.What is the presentvalue of 50,000 in 5years?4-39

FV PV * (1 r)tPV FV(1 r)t FV *Future Value FactorFV Future ValuePV Present Valuer Interest Rate1(1 r)tt # of periodsPresent Value Factor4-40

Which one of the following willincrease the present value of a lumpsum future amount to be received in15 years?A.An increase in the time period.B.An increase in the interest rate.C.A decrease in the future value.D.A decrease in the interest rate.E.Changing to compound interest fromsimple interest.4-41

Today XYear 1* 1/(1 r) YYear 2* 1/(1 r) ZYear 3* 1/(1 r) 1000 The long-form approach begins with drawing a time line ofthe problem. The present value of cash is manually calculated for eachtime period. This approach is important to understand intuitively how tosolve time value of money problems However, it is not practical when numerous time periods areinvolved.4-42

PV FV(1 r)t FV *FV Future ValuePV Present Value1(1 r)tr Interest Ratet # of periodsPresent Value FactorNote: The yx and 1/x functions on many calculators areuseful when using the formula for solving problems.4-43

PV of 1 1 * 1/(1 r)tPresent Value FactorPV 1 * 1/(1 .10)3 1 * .7513 0.75Present Value FactorsNote: When using tables, pay extra attention to following thecorrect row and column to get the correct factor amount.4-44

The current value of future cash flowsdiscounted at the appropriate discountrate Value at t 0 (or today) on a time line Answers the questions: How much do I have to invest today to havesome amount in the future?What is the current value of an amount to bereceived in the future?Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.4-45

For a given interest rate: The longer the time period,The lower the present valuePV FV(1 r)tFor a given r, as t increases, PV decreasesCopyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.4-46

What is the present value of 500 to bereceived in 5 years? 10 years? The discountrate is 10%0r 10% 310.46 PV?510 500 192.77 PV? 5005 yrs:PV 500/(1.10)5 310.4610 yrs: PV 500/(1.10)10 192.77Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.4-47

For a given time period: The higher the interest rate,The smaller the present valuePV FV(1 r)tFor a given t, as r increases, PV decreasesCopyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.4-48

What is the present value of 500 receivedin 5 years if the interest rate is 10%? 15%?Rate 10%Formula Solution:PV 500 / (1.1)5PV 310.46Rate 15%Formula Solution:PV 500 / (1.15)5PV 248.594-49

Copyright (c) 2017 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written consent ofMcGraw-Hill Education.4-50

You want to have 40,000 for a down payment on ahouse 4 years from now. If you can earn 5.6 percent,compounded annually on your savings, how much doyou need to deposit today to reach your goal?A. 32,166.54B. 34,420.73C. 27,880.69D. 28,211.17E. 30,886.404-51

ComputingReturn onInvestment4-52

You have been offered the following investmentopportunity from a reputable investmentmanagement company:Open an account today with a deposit of 5,000 and, in 12years, you will receive 10,000.Is this a good investment?A.Yes, this is a good investment.B.No, this is a bad investment.C.I don’t know, more information is needed.4-53