chapter 6
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Chapter 6. Accounting and the Time Value of Money. 1. Basics. Study of the relationship between time and money Money in the future is not worth the same as it is today because if had money today could invest it and earn interest not because of risk or inflation Based on compound interest - PowerPoint PPT PresentationTRANSCRIPT
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Chapter 6Accounting and the Time Value of Money
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1. BasicsStudy of the relationship between time
and moneyMoney in the future is not worth the same
as it is today◦because if had money today could invest it and
earn interest◦not because of risk or inflation
Based on compound interest◦not simple interest
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1. BasicsExamples of where TVM used in
accounting◦ Notes Receivable & Payable◦ Leases ◦ Pensions and Other Postretirement Benefits ◦ Long-Term Assets◦ Shared-Based Compensation◦ Business Combinations◦ Disclosures◦ Environmental Liabilities
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1I. Future Value of Single SumThe amount a sum of money will
grow to in the future assuming compound interest
Can be compute by◦formula: ◦tables: ◦calculator: TVM keys
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FV = PV ( 1 + i )n
FV = PV x FVIF(n,i) (Table 6-1)
FV = future value n = periodsPV = present value i = interest rateFVIF = future value interest factor
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1I. Future Value of Single SumExample
◦If you deposit $1,000 today at 5% interest compounded annually, what is the balance after 3 years?
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1I. Future Value of Single Sum Calculate by hand
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Event AmountDeposit 1-1-x1 $ 1,000.00Year 1 interest (1000 x .05) 50.00End of Year 1 Amount 1,050.00Year 2 interest (1050 x .05) 52.50End of Year 2 Amount 1102.50Year 3 interest (1102.50 x .05)
55.13
End of Year 3 Amount 1157.63
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1I. Future Value of Single SumCalculate by formula
FV = 1,000 (1 + . 05)3
= 1,000 x 1.15763
= 1,157.63
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1I. Future Value of Single SumCalculate by table
FV = 1,000 x Table factor for FVIF(3, .05)
= 1,000 x 1.15763
= 1,157.63ACCT-3030 8
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1I. Future Value of Single SumCalculate by calculator
Clear calculator: 2nd RESET; ENTER; CE|C and/or: 2nd CLR TVM3 N5 I/Y1,000 +/- PVCPT FV = 1,157.63
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1I. Future Value of Single SumAdditional example
◦If you deposit $2,500 at 12% interest compounded quarterly, what is the balance after 5 years? less than annual compounding so adjust n and i
n = 20 periods i = 3%
2,500 x 1.80611 = 4,515.2820N; 3 I/Y; -2500 PV; CPT FV = 4,515.28
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1II. Present Value of Single SumValue now of a given amount to be paid or
received in the future, assuming compound interest
Can be compute by◦formula: ◦tables: ◦calculator: TVM keys
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PV = FV · 1/( 1 + i )n
PV = FV x PVIF(n,i) (Table 6-2)
FV = future value n = periodsPV = present value i = interest ratePVIF = present value interest factor
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1II. Present Value of Single SumExample
◦If you will receive $5,000 in 12 years and the discount rate is 8% compounded annually, what is it worth today?
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1II. Present Value of Single SumCalculate by formula
PV = 5,000 · 1/(1 + . 08)12
= 5,000 x .39711
= 1,985.57
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1II. Present Value of Single SumCalculate by table
PV = 5,000 x Table factor for PVIF(12, .08)
= 5,000 x .39711
= 1,985.57ACCT-3030 14
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1II. Present Value of Single SumCalculate by calculator
Clear calculator12 N8 I/Y5,000 FVCPT PV = 1,985.57
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1II. Present Value of Single SumAdditional example
◦If you receive $1,157.63 in 3 years and the discount rate is 5%, what is it worth today? n = 3 periods i = 5%
1,157.63 x .863838 = 1,000.00
3 N; 5 I/Y; 1157.63 FV; CPT PV = -1,000.00
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1V. Unknown n or i Example 1
◦ If you believe receiving $2,000 today or $2,676 in 5 years are equal, what is the interest rate with annual compounding?
PV = FV x PVIF(n, i)
2,000 = 2,676 x PVIF(5, i)
PVIF(5, i) = 2,000/2,676 = .747384find above factor in Table 2: i ≈ 6%
5 N; -2,000 PV; 2,676 FV; CPT 1/Y = 6.00%ACCT-3030 17
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1V. Unknown n or i Example 2
◦ Same as last problem but assume 10% interest with annual compounding is the appropriate rate and calculate n.
PV = FV x PVIF(n, i)
2,000 = 2,676 x PVIF(n, 10%)
PVIF(n, 10%) = 2,000/2,676 = .747384find above factor in Table 2: n ≈ 3 years
10 I/Y; -2,000 PV; 2,676 FV; CPT N = 3.06 years
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V. AnnuitiesBasics
◦annuity a series of equal payments that occur at
equal intervals◦ordinary annuity
payments occur at the end of the period◦annuity due
payments occur at the beginning of the period
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V. AnnuitiesOrdinary annuity – payments at
endPresent Value
|_____|_____|_____|_____|_____|
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Year 1 Year 2 Year 3 Year 4 Year 5
Pmt 1 Pmt 2 Pmt 3 Pmt 4
EvaluatePV
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V. AnnuitiesAnnuity due – payments at
beginningPresent value
|_____|_____|_____|_____|_____|
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Year 1 Year 2 Year 3 Year 4 Year 5
Pmt 1 Pmt 2 Pmt 3 Pmt 4
EvaluatePV
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V. AnnuitiesFor Future Value of an annuity
◦more difficultDetermine whether the annuity is ordinary
or due based on the last period◦ if evaluate right after last pmt – ordinary◦ if evaluate one period after last pmt –
dueAn important part of annuity problems is
determining the type of annuity
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V. AnnuitiesOrdinary annuity – payments at
endFuture Value
|_____|_____|_____|_____|_____|
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Year 1 Year 2 Year 3 Year 4 Year 5
Pmt 1 Pmt 2 Pmt 3 Pmt 4
EvaluateFV
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V. AnnuitiesAnnuity due – payments at
beginningFuture Value (evaluate 1 period after last payment)
|_____|_____|_____|_____|_____|
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Year 1 Year 2 Year 3 Year 4 Year 5
Pmt 1 Pmt 2 Pmt 3 Pmt 4
EvaluateFV
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V. AnnuitiesTables available in book for
◦Future Value of Ordinary Annuity (Table 6-3)
◦Present Value of Ordinary Annuity (Table 6-4)
◦Present Value of Annuity Due (Table 6-5)
So no table for FV of annuity dueACCT-3030 25
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V. AnnuitiesAnnuity table factors conversion
◦ to calculate FV of annuity due look up factor for FV of ordinary annuity for 1 more period
and subtract 1.0000◦ to calculate PV of annuity due (can use table)
look up factor for PV of ordinary annuity for 1 less period and add 1.0000
Use calculator◦ change calculator to annuity due mode◦ 2nd BEG; 2nd SET; 2nd QUIT◦ to change back to ordinary annuity mode◦ 2nd BEG; 2nd CLR WORK; 2nd QUIT (or 2nd RESET)
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V1. Future Value of AnnuityCan be calculated by
◦formula:
◦table:
◦calculator: TVM keys
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FVA(ord) = Pmt -----------------(1 + i)n - 1
i
FVA(ord or due) = Pmt x FVIFA(ord or due) (n, i)
FV = future value n = periodsPV = present value i = interest rateFVIF = future value interest factor
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V1. Future Value of AnnuityCan be calculated by
◦formula:
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FVA(due) = Pmt --------------- x (1 + i)(1 + i)n - 1
i
FV = future value n = periodsPV = present value i = interest rateFVIF = future value interest factor
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V1. Future Value of AnnuityExample
◦Find the FV of a 4 payment, $10,000, ordinary annuity at 10% compounded annually.
(You could treat this as 4 FV of single sum problems and would get correct answer but that method is omitted.)
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V1. Future Value of AnnuityCalculate by formula
FVA-ord = 10,000 -----------
= 10,000 x 4.6410
= 46,410
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(1 + .1)4 - 1
.1
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V1. Future Value of AnnuityCalculate by table (Table 6-3)
FVA-ord = 10,000 x FVIFA-ord (4, .10)
= 10,000 x 4.64100
= 46,410
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V1. Future Value of AnnuityCalculate by calculator
4 N; 10 I/Y; -10000 PMT; CPT FV
46,410
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V1. Future Value of AnnuityAdditional examples
◦Find the FV of a $3,000, 15 payment ordinary annuity at 15%.FVA-ord = 3,000 x FVIFA-ord (15, .15)
= 3,000 x 47.58041 = 142,74115 N; 15 I/Y; -3000 PMT; CPT FV = 142,741
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V1. Future Value of AnnuityAdditional examples
◦Find the FV of a $3,000, 15 payment annuity due at 15%. (table – look up 1 more period -1.0000)
FVA-ord = 3,000 x FVIFA-due (15, .15) = 3,000 x 54.71747
= 164,152
2nd BGN; 2nd SET; 2nd QUIT15 N; 15 I/Y; -3000 PMT; CPT FV = 164,152
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VI1. Present Value of AnnuityCan be calculated by
◦formula:
◦table:
◦calculator: TVM keys
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PVA(ord) = Pmt ---------------------1 – (1/(1 + i)n)
i
PVA(ord or due) = Pmt x PVIFA(ord or due) (n, i)
FV = future value n = periodsPV = present value i = interest ratePVIF = present value interest factor
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VI1. Present Value of AnnuityCan be calculated by
◦formula:
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PVA(due) = Pmt --------------------- x (1 + i)1 – (1/(1 + i)n)
i
FV = future value n = periodsPV = present value i = interest ratePVIF = present value interest factor
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VI1. Present Value of AnnuityExample
◦What is the PV of a $3,000, 15 year, ordinary annuity discounted at 10% compounded annually?
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VI1. Present Value of AnnuityCalculate by formula
PVA-ord = 3,000 ----------------
= 3,000 x 7.60608
= 22,818
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1 – (1/(1 + .10)15
.10
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VI1. Present Value of AnnuityCalculate by table (Table 6-4)
PVA-ord = 3,000 x PVIFA-ord (15, 10)
= 3,000 x 7.60608
= 22,818
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VI1. Present Value of AnnuityCalculate by calculator
15 N; 10 I/Y; -3000 PMT; CPT PV
22,818
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VI1. Present Value of AnnuityAdditional examples
◦Find the PV of a $3,000, 15 payment annuity due discounted at 15%.
PVA-due = 3,000 x PVIFA-due (15, .15)
= 3,000 x 6.72488 = 20,175
2nd BGN; 2nd SET; 2nd QUIT15 N; 15 I/Y; -3000 PMT; CPT PV = 20,173
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VI1. Present Value of AnnuityAdditional examples
◦If you were to be paid $1,800 every 6 months (at the end of the period) for 5 years, what is it worth today discounted at 12%?
PVA-ord = 1,800 x PVIFA-ord (10, .06)
= 1,800 x 7.36009 = 13,248
10 N; 6 I/Y; -1800 PMT; CPT PV = 13,248ACCT-3030 42
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VI1. Present Value of AnnuityAdditional examples
◦If you consider receiving $12,300 today or $2,000 at the end of each year for 10 years equal, what is the interest rate?
12,300A-ord = 2,000 x PVIFA-ord (10, i)
PVIFA-ord (10, i) = 12,300/2,000 = 6.15000 i ≈ 10%
10 N; -2000 PMT; PV = 12300; CPT I/Y = 9.98%
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