Chapter 6

Chapter 6Accounting and the Time Value of Money

ACCT-3030 1

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

ACCT-3030 2

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

ACCT-3030 3

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

ACCT-3030 4

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

1I. Future Value of Single SumExample

◦If you deposit $1,000 today at 5% interest compounded annually, what is the balance after 3 years?

ACCT-3030 5

1I. Future Value of Single Sum Calculate by hand

ACCT-3030 6

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

1I. Future Value of Single SumCalculate by formula

FV = 1,000 (1 + . 05)3

= 1,000 x 1.15763

= 1,157.63

ACCT-3030 7

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

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

ACCT-3030 9

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

ACCT-3030 10

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

ACCT-3030 11

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

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?

ACCT-3030 12

1II. Present Value of Single SumCalculate by formula

PV = 5,000 · 1/(1 + . 08)12

= 5,000 x .39711

= 1,985.57

ACCT-3030 13

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

1II. Present Value of Single SumCalculate by calculator

Clear calculator12 N8 I/Y5,000 FVCPT PV = 1,985.57

ACCT-3030 15

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

ACCT-3030 16

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

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

ACCT-3030 18

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

ACCT-3030 19

V. AnnuitiesOrdinary annuity – payments at

endPresent Value

|_____|_____|_____|_____|_____|

ACCT-3030 20

Year 1 Year 2 Year 3 Year 4 Year 5

Pmt 1 Pmt 2 Pmt 3 Pmt 4

EvaluatePV

V. AnnuitiesAnnuity due – payments at

beginningPresent value

|_____|_____|_____|_____|_____|

ACCT-3030 21



EvaluatePV

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

ACCT-3030 22

V. AnnuitiesOrdinary annuity – payments at

endFuture Value

|_____|_____|_____|_____|_____|

ACCT-3030 23



EvaluateFV

V. AnnuitiesAnnuity due – payments at

beginningFuture Value (evaluate 1 period after last payment)

|_____|_____|_____|_____|_____|

ACCT-3030 24



EvaluateFV

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

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)

ACCT-3030 26

V1. Future Value of AnnuityCan be calculated by

◦formula:

◦table:

◦calculator: TVM keys

ACCT-3030 27

FVA(ord) = Pmt -----------------(1 + i)n - 1

i

FVA(ord or due) = Pmt x FVIFA(ord or due) (n, i)


V1. Future Value of AnnuityCan be calculated by

◦formula:

ACCT-3030 28

FVA(due) = Pmt --------------- x (1 + i)(1 + i)n - 1

i


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.)

ACCT-3030 29

V1. Future Value of AnnuityCalculate by formula

FVA-ord = 10,000 -----------

= 10,000 x 4.6410

= 46,410

ACCT-3030 30

(1 + .1)4 - 1

.1

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

ACCT-3030 31

V1. Future Value of AnnuityCalculate by calculator

4 N; 10 I/Y; -10000 PMT; CPT FV

46,410

ACCT-3030 32

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

ACCT-3030 33

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

ACCT-3030 34

VI1. Present Value of AnnuityCan be calculated by

◦formula:

◦table:

◦calculator: TVM keys

ACCT-3030 35

PVA(ord) = Pmt ---------------------1 – (1/(1 + i)n)

i

PVA(ord or due) = Pmt x PVIFA(ord or due) (n, i)


VI1. Present Value of AnnuityCan be calculated by

◦formula:

ACCT-3030 36

PVA(due) = Pmt --------------------- x (1 + i)1 – (1/(1 + i)n)

i


VI1. Present Value of AnnuityExample

◦What is the PV of a $3,000, 15 year, ordinary annuity discounted at 10% compounded annually?

ACCT-3030 37

VI1. Present Value of AnnuityCalculate by formula

PVA-ord = 3,000 ----------------

= 3,000 x 7.60608

= 22,818

ACCT-3030 38

1 – (1/(1 + .10)15

.10

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

ACCT-3030 39

VI1. Present Value of AnnuityCalculate by calculator

15 N; 10 I/Y; -3000 PMT; CPT PV

22,818

ACCT-3030 40

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

ACCT-3030 41


◦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


◦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%

ACCT-3030 43

Chapter 6

Documents

Transcript of Chapter 6