FIN335 CH04-05 Time Value

8/3/2019 FIN335 CH04-05 Time Value

1/29

All Rights ReservedAll Rights Reserved Chapter 2Chapter 2 11

Time Value of MoneyTime Value of Money

Chapters 4 & 5Chapters 4 & 5

Future and Present ValuesFuture and Present Values

Loan Amortization, AnnuitiesLoan Amortization, Annuities

Financial CalculatorFinancial Calculator


2/29


Time Value of MoneyTime Value of Money

I.I. Four Critical FormulasFour Critical Formulas

A.A. Future Value: value tomorrow of $1 invested today.Future Value: value tomorrow of $1 invested today.

B.B. Present Value: value today of $1 to be receivedPresent Value: value today of $1 to be received

tomorrow.tomorrow.

C.C. Future Value of an Annuity: value several periods fromFuture Value of an Annuity: value several periods from

now of anow of astreamstream of $1 investments.of $1 investments.

D.D. Present Value of an Annuity: value today of aPresent Value of an Annuity: value today of astreamstream ofof

$1 payments to be received for a set number of future$1 payments to be received for a set number of futureperiods.periods.


3/29


4/29


Important TVM ConceptsImportant TVM Concepts

B.B. Present Value;Present Value;

1.1. The value today of $1 to be received tomorrow.The value today of $1 to be received tomorrow.

2.2. Solving the Future Value Equation for PV;Solving the Future Value Equation for PV;a.a. PV = FVPV = FV zz (1+i) single period discounting.(1+i) single period discounting.

b.b. PV = FVPV = FV zz (1+i)(1+i)nn multimulti--period discounting.period discounting.

c.c. PV = FVPV = FV vv (1+i)(1+i)--nn common form.common form.

d.d. (1+i)(1+i)--nn = Present Value Interest Factor.= Present Value Interest Factor.e. PVIF = 1 / FVIF (and vicee. PVIF = 1 / FVIF (and vice--versa for same i, n)versa for same i, n)


5/29



C.C. Future Value of an Annuity (FVA)Future Value of an Annuity (FVA)

e.g. Retirement Funds: IRA, 401(k), Keoughe.g. Retirement Funds: IRA, 401(k), Keough

1.1. A series of equal deposits (contributions) overA series of equal deposits (contributions) over

some length of time.some length of time.2.2. Contributions are invested in financial securities;Contributions are invested in financial securities;

stocks, bonds, or mutual funds.stocks, bonds, or mutual funds.

3.3. TheThe ffutureuture vvalue of accumulationalue of accumulation is a function ofis a function of

the number and magnitude of contributions,the number and magnitude of contributions,reinvested interest, dividends, andreinvested interest, dividends, and undistributedundistributedcapital gains. FVA = PMT * FVIFAcapital gains. FVA = PMT * FVIFA


6/29



D.D. Present Value of an Annuity (PVA)Present Value of an Annuity (PVA)1.1. Insurance AnnuitiesInsurance Annuities

a.a. Provide recipient with a regular income (PMT) for aProvide recipient with a regular income (PMT) for a

set period of time.set period of time.b.b. TheThepresent value (PV)present value (PV) of the payments to be receivedof the payments to be received

is theis thepriceprice of the insurance annuity.of the insurance annuity.

c.c. PVA = PMT * PVIFAPVA = PMT * PVIFA

2.2. Types of AnnuitiesTypes of Annuities::a.a. OrdinaryOrdinary AnnuityAnnuity: payments received at end: payments received at end--ofof--period.period.b.b. AnnuityAnnuity Due: payments received at beginningDue: payments received at beginning--ofof--

periodperiod


7/29



3.3. Annuitize Investment AccumulationsAnnuitize Investment Accumulations

a.a. We have accumulated a sum of money and now desireWe have accumulated a sum of money and now desire

to begin a series of [N] regular payouts: e.g. monthlyto begin a series of [N] regular payouts: e.g. monthly

checkschecksb.b. We assume accumulated funds will continue to earnWe assume accumulated funds will continue to earn

some rate of return (I/YR)some rate of return (I/YR)

c.c. The accumulation is treated as the present value (PV).The accumulation is treated as the present value (PV).

d.d. How muchHow much incomeincome (PMT) will a certain accumulated(PMT) will a certain accumulatedamount produce?amount produce?


8/29


Computing FVAComputing FVA

A.A. FVA formula:FVA formula:

1. FVA = P1. FVA = P vv ([(1+i)([(1+i)nn -- 1]1] zz i) = Pi) = P vv FVIFAFVIFA

[(1+i)[(1+i)nn -- 1]1] zz i = future value interest factor for ani = future value interest factor for an

annuity or FVIFAannuity or FVIFAi,ni,n..

1.1. Assumption; steady return rate over time andAssumption; steady return rate over time and

equal dollar amount contributions.equal dollar amount contributions.


9/29


Computing PVAComputing PVA

A.A. PVA formula:PVA formula:

1. PVA = P1. PVA = P vv ([1([1 -- (1+i)(1+i)--nn]] zz i) = Pi) = P vv PVIFAPVIFA

[1[1 -- (1+i)(1+i)--nn ]] zz i = present value interest factor for ani = present value interest factor for an

annuity or PVIFAannuity or PVIFAi,ni,n..

1.1. Assumption; constant return rate over time andAssumption; constant return rate over time and

equal dollar amount distributions.equal dollar amount distributions.


10/29


Current LawCurrent Law

A. Traditional and Roth IRAsA. Traditional and Roth IRAsContribution limits for Traditional and Roth IRAsContribution limits for Traditional and Roth IRAswill rise from $2000 to $5,000 between 2002 andwill rise from $2000 to $5,000 between 2002 and

2008. After 2008, the limit may be adjusted2008. After 2008, the limit may be adjustedannually for inflation.annually for inflation.

Tax YearTax Year LimitLimit

20022002--20042004 $3,000$3,000

20052005--20062006 $4,000$4,00020082008 $5,000$5,000

20092009--20102010 Indexed to InflationIndexed to Inflation


11/29


Current LawCurrent Law

B. 401(k), 403(b), and 457 PlansB. 401(k), 403(b), and 457 PlansThese limits are on pretax contributions to certain employerThese limits are on pretax contributions to certain employer--sponsored retirement plans. Remember that employers havesponsored retirement plans. Remember that employers havethe option of imposing lower limits than the governmentthe option of imposing lower limits than the governmentmaximums, which will rise to $15,000 by 2006.maximums, which will rise to $15,000 by 2006.

Tax YearTax Year LimitLimit

20022002 $11,000$11,000

20032003 $12,000$12,000

20042004 $13,000$13,000

20052005 $14,000$14,00020062006 $15,000$15,000

20072007--20102010 Indexed to InflationIndexed to Inflation


12/29


Sample IRA ProblemSample IRA Problem

A.A. Suppose you want to know how much an IRASuppose you want to know how much an IRA

(individual retirement account) plan will grow to if(individual retirement account) plan will grow to if

you deposit $5,000 per year (the maximum underyou deposit $5,000 per year (the maximum under

current law) orcurrent law) or $416.67 per month$416.67 per month every monthevery month forforthe nextthe next 20 years20 years oror 240 monthly deposits240 monthly deposits. Well. Well

assume monthly compounded interest andassume monthly compounded interest and annualannual

rate of 7 percentrate of 7 percent (7%(7% per annumper annum).).

B.B. What is the Future Value of the AccumulationWhat is the Future Value of the Accumulation

(FVA)?(FVA)?


13/29


Future Value of an AccumulationFuture Value of an Accumulation

1.1. ClearClear thethe TVMTVM registers;registers;

BAII+:BAII+:press [press [2nd2nd], then [], then [FVFV] (] (CLR TVMCLR TVM))

HP10B:HP10B:presspress [YK] [INPUT] ([YK] [INPUT] (CLEAR ALLCLEAR ALL))

2. Set the Periods per year register2. Set the Periods per year register

BAII+:BAII+:

Press [Press [2nd2nd] [] [I/YI/Y] for the] for the P/YP/Y function;function;

enterenter1212, then press [, then press [ENTERENTER]]

[[22ndnd]] [[CPTCPT] to] to QUITQUIT this subroutine.this subroutine.

HP10B:HP10B:

enter 12, press [YK] [PMT] (enter 12, press [YK] [PMT] (P/YRP/YR))


14/29



3.3. EnterEnter240240, press [, press [NN].].

4.4. EnterEnter77, press [, press [I/YI/Y]; interest rate per annum.]; interest rate per annum.

5.5. EnterEnter416.67416.67, then [, then [+/+/--] and then [] and then [PMTPMT].].

6. BAII+:6. BAII+: Press [Press [CPTCPT] then [] then [FVFV];]; 217,154.51217,154.51 (display)(display)

HP10B: PressHP10B: Press [FV][FV]:: 217,054.51217,054.51 display (display)display (display)

Don't clear the values yet. We're going to use themDon't clear the values yet. We're going to use them

in the next problemin the next problem..


15/29



A.A. What effect does an extra 10 years of $416.67What effect does an extra 10 years of $416.67

deposited per month have on the FVA?deposited per month have on the FVA?

The FVA after 30 years of monthly savingsThe FVA after 30 years of monthly savings......

a.a. BAII+:BAII+: EnterEnter360360, press [, press [NN]]

PressPress [CPT] [FV][CPT] [FV];; $508,325.31$508,325.31 (display)(display)

HP10B: enterHP10B: enter360360, press [, press [NN]]

PressPress [FV][FV]:: $508,32

5.31$508,32

5.31 (display)(display)b. =c.b. =c. The total deposits are 416.67 * 360 = $150,001.20.The total deposits are 416.67 * 360 = $150,001.20.

The other $358,324.11 is the accumulated interest.The other $358,324.11 is the accumulated interest.


16/29



1.1. What effect does the rate of return have on theWhat effect does the rate of return have on the

size of the accumulation? Suppose the interestsize of the accumulation? Suppose the interest

rate was 12%, what is the FVA?rate was 12%, what is the FVA?

a.a. EnterEnter1212, press [I/Y]., press [I/Y].

b. BAII+:b. BAII+: Press [CPT] [FV];Press [CPT] [FV]; $1,456,246.71$1,456,246.71

HP10B: Press [FV]:HP10B: Press [FV]: $ 1,456,246.71$ 1,456,246.71

2.2. The FVA if we assume 30 years of monthlyThe FVA if we assume 30 years of monthly

deposits of 416.67 accumulating at 12% perdeposits of 416.67 accumulating at 12% per

annum compounded monthly.annum compounded monthly.


17/29


TaxTax--Deferred RetirementDeferred Retirement

SavingsSavingsB.B. Other Types of Retirement Savings Plans;Other Types of Retirement Savings Plans;

1.1. 401(k) plans; company and individual401(k) plans; company and individual

contributions.contributions.

2.2. 403(b) plans; used by non403(b) plans; used by non--profit organizations.profit organizations.

3.3. Simple plans; plans fore the selfSimple plans; plans fore the self--employed.employed.

4.4. Keough Plans; for professionals such as doctorsKeough Plans; for professionals such as doctors

and lawyers.and lawyers.


18/29


ANNUITIZING ACCUMULATIONSANNUITIZING ACCUMULATIONS

A.A. Annuitizing Pension Fund Accumulations;Annuitizing Pension Fund Accumulations;1.1. In the last problem, we accumulated $1,456,246.71In the last problem, we accumulated $1,456,246.71

over a 30over a 30--year period with monthly contributions toyear period with monthly contributions toan IRA. We assumed a monthly compounded rate ofan IRA. We assumed a monthly compounded rate of

return of 12% per annum. Current tax law permitsreturn of 12% per annum. Current tax law permitsthe annuitization of IRAs and other similar plans atthe annuitization of IRAs and other similar plans atage 59 years and 6 months.age 59 years and 6 months.

2.2. Annuitization of plans must commence when aAnnuitization of plans must commence when aperson reaches 70 years and 6 months. For RMD;person reaches 70 years and 6 months. For RMD;

http://www.ira.com/faq/faqhttp://www.ira.com/faq/faq--54.htm54.htm3.3. AnnuitizingAnnuitizingan accumulation is the reverse process.an accumulation is the reverse process.

Now instead of paying into the retirement plan, theNow instead of paying into the retirement plan, theplan will make payments to you.plan will make payments to you.


19/29



B.B. Suppose we use theSuppose we use the $1,456,246.71$1,456,246.71 to buy ato buy a

"single payment""single payment" ordinary annuityordinary annuity whichwhich

will guarantee a 7% rate of return P.A. forwill guarantee a 7% rate of return P.A. for

2525--years. How much will the monthlyyears. How much will the monthly

payment be?payment be?

1.1. (Well ignore the fee(Well ignore the fee--premium for the annuity for thepremium for the annuity for the

time being.)time being.)


20/29



A.A. Calculating Monthly PayoutCalculating Monthly Payout1. C1. Clear TVM registers:lear TVM registers:

BAII+:BAII+: [2[2ndnd] [FV] (CLR TVM)] [FV] (CLR TVM)HP10B;HP10B; [YK] [INPUT] (CLEAR ALL)[YK] [INPUT] (CLEAR ALL)

2.2. EnterEnter300300 and press [and press [NN] key.] key.3.3. EnterEnter77 and press [and press [I/YI/Y] key.] key.4.4. EnterEnter1456246.711456246.71. Press [. Press [+/+/--], then [], then [PVPV].].5. BAII+:5. BAII+: Press [Press [CPTCPT] key then [] key then [PMTPMT]]

HP10B: Press [HP10B: Press [PMTPMT]] 10,292.4510,292.45 (display)(display)7. T7. Total payout over 25 years = $10,292.45 * 300otal payout over 25 years = $10,292.45 * 300

== $3,087,734.63$3,087,734.63. (all this from a $150,000. (all this from a $150,000investment)investment)


21/29


ORDINARY ANNUITIESORDINARY ANNUITIES

A.A. Calculating the Price of an Insurance AnnuityCalculating the Price of an Insurance Annuity

[Policy] using the BA II Plus[Policy] using the BA II Plus

1.1. Suppose we desire to collect $5,000 per monthSuppose we desire to collect $5,000 per month

for 20 years (240 payments) and the rate offor 20 years (240 payments) and the rate of

return is 9% compounded monthly.return is 9% compounded monthly.

2.2. How much must we pay for an annuity contractHow much must we pay for an annuity contract

that will pay 5,000 per month for 20 years?that will pay 5,000 per month for 20 years?


22/29


ORDINARY ANNUITIESORDINARY ANNUITIES

B.B. Calculating the Price an Insurance AnnuityCalculating the Price an Insurance Annuity[Policy] using Financial Calculator;[Policy] using Financial Calculator;

1.1. Clear the TVM registers.Clear the TVM registers.

2.2. EnterEnter2

402

40 and press [and press [NN

].].3.3. EnterEnter99 and press [and press [I/YI/Y].].4.4. EnterEnter50005000 and press [and press [PMTPMT].].5.5. Press [Press [CPTCPT] and [] and [PVPV] or [PV]] or [PV]6. D6. Display should show;isplay should show; --555,724.77555,724.77$555,724.77 is$555,724.77 is the pricethe price of annuity.of annuity. The negative signThe negative sign

reminds us that this is a price (negative cash flow).reminds us that this is a price (negative cash flow).


23/29


Total ReturnsTotal Returns


24/29


geom. mean arith.mean std high ret. low ret.

S&P total return 10.30 12.45 22.28 42.56 -29.73

U.S. Small Stock TR 12.28 17.28 35.94 73.46 -36.74

U.S. LT Govt TR 4.91 5.21 8.00 15.23 -8.41

U.S. LT Corp. TR 5.49 5.73 7.16 13.76 -8.90

U.S. 30 day T-Bills 3.70 3.70 0.96 1.35 -0.06

Summary Statistics of U.S. Investments from 1926 through March, 1995.

Source:Ibbotson Associates Investment

INVESTMENT RETURNS


25/29


LOAN REPAYMENTSLOAN REPAYMENTS

A.A. How much will the monthly payments for aHow much will the monthly payments for a$23,000 car loan be if the per annum rate is$23,000 car loan be if the per annum rate is4.75% for 60 months. (SECU payroll4.75% for 60 months. (SECU payroll--deduct ordeduct or5.25% direct pay)? We'll solve this problem5.25% direct pay)? We'll solve this problemusing the BAII+.using the BAII+.

1.1. Clear the TVM registers.Clear the TVM registers.2.2. Check the values set for P/Y (=12).Check the values set for P/Y (=12).3.3. EnterEnter6060, press [, press [NN].].

4.4. EnterEnter4.754.75, press [, press [I/Y

RI/Y

R].].5.5. EnterEnter2300023000, press [, press [PVPV].].6. BAII+:6. BAII+: Press [Press [CPTCPT] [] [PMTPMT]; PMT =]; PMT = --431.41431.41 (display)(display)

$436.68$436.68 (if direct pay at 5.25%)(if direct pay at 5.25%)


26/29


MORTGAGE LOANSMORTGAGE LOANS

A.A. How much will the monthly payments for aHow much will the monthly payments for a $160,000$160,000 loanloanbe if the per annum rate isbe if the per annum rate is 4.75%4.75% and the term is 30 yearsand the term is 30 years((360360 months)?months)?

1.1. Clear the TVM registers.Clear the TVM registers.

2.2. Check the values set for P/Y (=12).Check the values set for P/Y (=12).3.3. EnterEnter360360, press [, press [NN].].4.4. EnterEnter44..7575, press [, press [I/YRI/YR].].5.5. EnterEnter160,000160,000, press [, press [PVPV]; $160,000 mortgage loan.]; $160,000 mortgage loan.6. BAII+:6. BAII+: Press [Press [CPTCPT] [] [PMTPMT];]; PMT =PMT = --834.64834.64 (display)(display)

Leave these values in the calculator. Welluse them toLeave these values in the calculator. Welluse them tocompute the amortization schedule.compute the amortization schedule.


27/29


MORTAGE AMORTIZATIONMORTAGE AMORTIZATION

A.A. All loans are amortized over their life. EachAll loans are amortized over their life. Each

payment includes an interest portion and apayment includes an interest portion and a

principle portion. The BAII+ computesprinciple portion. The BAII+ computes

amortization schedules using theamortization schedules using the AMORTAMORT

function.function.

BAII+: [2BAII+: [2NDND] [PV]] [PV]


28/29


MORTAGE AMORTIZATIONMORTAGE AMORTIZATION

A.A. BAII+ (12 month totals)BAII+ (12 month totals)

1.1. Press [2nd] [PV]: P1 = 1.00 (display)Press [2nd] [PV]: P1 = 1.00 (display)

2.2. Press [Press [qq

]: P2 = 1 or 12.00 (display)]: P2 = 1 or 12.00 (display)a.a. If P2 = 1.00 then enter 12, [ENTER]: P2 = 12.00If P2 = 1.00 then enter 12, [ENTER]: P2 = 12.00

3.3. Press [Press [qq]:]: BAL = 157,531.03BAL = 157,531.03

4.4. Press [Press [qq]:]: PRN =PRN = --2,468.972,468.97

5.5. Press [Press [qq]:]: INT =INT = --7,546.717,546.71

6.6. Press [Press [qq]: then press [CPT]: P1 = 13.00]: then press [CPT]: P1 = 13.00

7.7. Press [Press [qq]: P2 = 24.00 (continue]: P2 = 24.00 (continue [[qq] for values)] for values)


29/29


Homework AssignmentsHomework Assignments

Chapter 4Chapter 4

A.A. Critical Thinking & Concepts: 4.1, 4.2, 4.3Critical Thinking & Concepts: 4.1, 4.2, 4.3

B.B. Questions & Problems: 2, 3, 4, 5, 7, 8, 13Questions & Problems: 2, 3, 4, 5, 7, 8, 13C.C. Whats on the Web? 4.1, 4.2Whats on the Web? 4.1, 4.2

Chapter 5Chapter 5

A.A. Critical Thinking & Concepts: 5.1, 5.2, 5.3, 5.4Critical Thinking & Concepts: 5.1, 5.2, 5.3, 5.4

B.B. Questions and Problems: 1, 4, 5, 6, 12, 30, 35Questions and Problems: 1, 4, 5, 6, 12, 30, 35

FIN335 CH04-05 Time Value

Documents

Transcript of FIN335 CH04-05 Time Value