1. Accounting and the Time Value of Money
Chapter 7
Accounting and the Time Value of Money
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2. 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 you had the money today you could invest it and earn interest
not because of risk or inflation
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3. 1. Basics
Based on compound interest
not simple interest
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4. 1. Basics Examples 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
Revenue Recognition
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5. 1I. Future Value of Single Sum
The amount a sum of money will grow to in the future assuming compound interest
Can be compute by
formula:
tables:
calculator: TVM keys
FV = PV ( i )n
FV = PV x FVIF(n,i) (Table 7A.1)
FV = future value n = periods
PV = present value i = interest rate
FVIF = future value interest factor
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6. 1I. Future Value of Single Sum
Example
If you deposit $1,000 today at 5% interest compounded annually, what is the balance after 3 years?
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7. 1I. Future Value of Single Sum
Calculate by hand
Event
Amount
Deposit 1-1-x1
$ 1,000.00
Year 1 interest (1000 x .05)
50.00
End of Year 1 Amount
1,050.00
Year 2 interest (1050 x .05)
52.50
End of Year 2 Amount
Year 3 interest ( x .05)
55.13
End of Year 3 Amount
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8. 1I. Future Value of Single Sum
Calculate by formula FV = 1,000 ( )3 = 1,000 x = 1,157.63
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9. 1I. Future Value of Single Sum
Calculate by table FV = 1,000 x Table factor for FVIF(3, .05) = 1,000 x
= 1,157.63
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10. 1I. Future Value of Single Sum
Calculate by calculator Clear calculator: 2nd RESET; ENTER; CE|C and/or: 2nd CLR TVM 3 N 5 I/Y 1,000 +/- PV CPT FV = 1,157.63
ACCT-3030

11. 1I. Future Value of Single Sum
Additional 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 = 4,515.28
20N; 3 I/Y; PV; CPT FV = 4,515.28
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12. 1II. Present Value of Single Sum
Value 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
PV = FV · 1/( i )n
PV = FV x PVIF(n,i) (Table 7A.2)
FV = future value n = periods
PV = present value i = interest rate
PVIF = present value interest factor
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13. 1II. Present Value of Single Sum
Example
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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14. 1II. Present Value of Single Sum
Calculate by formula PV = 5,000 · 1/( ) = 5,000 x = 1,985.57
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15. 1II. Present Value of Single Sum
Calculate by table PV = 5,000 x Table factor for PVIF(12, .08) = 5,000 x
= 1,985.57
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16. 1II. Present Value of Single Sum
Calculate by calculator Clear calculator 12 N 8 I/Y 5,000 FV CPT PV = 1,985.57
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17. 1II. Present Value of Single Sum
Additional example
If you receive $1, in 3 years and the discount rate is 5%, what is it worth today?
n = 3 periods
i = 5%
1, x = 1, N; 5 I/Y; FV; CPT PV = -1,000.00
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18. 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, = 2,676 x PVIF(5, i) PVIF(5, i) = 2,000/2,676 = find above factor in Table 2: i ≈ 6% 5 N; -2,000 PV; 2,676 FV; CPT 1/Y = 6.00%
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19. 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, = 2,676 x PVIF(n, 10%) PVIF(n, 10%) = 2,000/2,676 = find 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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20. V. Annuities Basics annuity ordinary annuity annuity due
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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21. V. Annuities Ordinary annuity – payments at end Present Value
|_____|_____|_____|_____|_____|
Year 1
Year 2
Year 3
Year 4
Year 5
Pmt 1
Pmt 2
Pmt 3
Pmt 4
Evaluate PV
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22. V. Annuities Annuity due – payments at beginning Present value
|_____|_____|_____|_____|_____|
Year 1
Year 2
Year 3
Year 4
Year 5
Pmt 1
Pmt 2
Pmt 3
Pmt 4
Evaluate PV
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23. V. Annuities For Future Value of an annuity
more difficult
Determine 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 – due
An important part of annuity problems is determining the type of annuity
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24. V. Annuities Ordinary annuity – payments at end Future Value
|_____|_____|_____|_____|_____|
Year 1
Year 2
Year 3
Year 4
Year 5
Pmt 1
Pmt 2
Pmt 3
Pmt 4
Evaluate FV
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25. V. Annuities
Annuity due – payments at beginning Future Value (evaluate 1 period after last payment)
|_____|_____|_____|_____|_____|
Year 1
Year 2
Year 3
Year 4
Year 5
Pmt 1
Pmt 2
Pmt 3
Pmt 4
Evaluate FV
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26. V. Annuities Tables available in book for
Future Value of Ordinary Annuity (Table 7A.3)
Future Value of Annuity Due (Table 7A.4)
Present Value of Ordinary Annuity (Table 7A.5)
Present Value of Annuity Due (Table 7A.6)
Sometimes not all tables are provided and you must use what is given and make the appropriate adjustment.
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27. V. Annuities Annuity table factors conversion Use calculator
to calculate FV of annuity due
look up factor for FV of ordinary annuity for 1 more period and subtract
to calculate PV of annuity due (can use table)
look up factor for PV of ordinary annuity for 1 less period and add
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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28. V1. Future Value of Annuity
Can be calculated by
formula:
table:
calculator: TVM keys
(1 + i)n - 1
FVA(ord) = Pmt i
FVA(ord or due) = Pmt x FVIFA(ord or due) (n, i)
FV = future value n = periods
PV = present value i = interest rate
FVIF = future value interest factor
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29. V1. Future Value of Annuity
Can be calculated by
formula:
(1 + i)n - 1
FVA(due) = Pmt x (1 + i) i
FV = future value n = periods
PV = present value i = interest rate
FVIF = future value interest factor
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30. V1. Future Value of Annuity
Example
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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31. V1. Future Value of Annuity
Calculate by formula FVA-ord = 10, = 10,000 x = 46,410
(1 + .1)4 - 1 .1
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32. V1. Future Value of Annuity
Calculate by table (Table 6-3) FVA-ord = 10,000 x FVIFA-ord (4, .10) = 10,000 x = 46,410
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33. V1. Future Value of Annuity
Calculate by calculator 4 N; 10 I/Y; PMT; CPT FV 46,410
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34. V1. Future Value of Annuity
Additional 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 = 142, N; 15 I/Y; PMT; CPT FV = 142,741
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35. V1. Future Value of Annuity
Additional examples
Find the FV of a $3,000, 15 payment annuity due at 15%. (table – look up 1 more period ) FVA-ord = 3,000 x FVIFA-due (15, .15) = 3,000 x = 164, nd BGN; 2nd SET; 2nd QUIT 15 N; 15 I/Y; PMT; CPT FV = 164,152
ACCT-3030

36. VI1. Present Value of Annuity
Can be calculated by
formula:
table:
calculator: TVM keys
1 – (1/(1 + i)n)
PVA(ord) = Pmt i
PVA(ord or due) = Pmt x PVIFA(ord or due) (n, i)
FV = future value n = periods
PV = present value i = interest rate
PVIF = present value interest factor
ACCT-3030

37. VI1. Present Value of Annuity
Can be calculated by
formula:
1 – (1/(1 + i)n)
PVA(due) = Pmt x (1 + i) i
FV = future value n = periods
PV = present value i = interest rate
PVIF = present value interest factor
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38. VI1. Present Value of Annuity
Example
What is the PV of a $3,000, 15 year, ordinary annuity discounted at 10% compounded annually?
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39. VI1. Present Value of Annuity
Calculate by formula PVA-ord = 3, = 3,000 x = 22,818
1 – (1/( )15
.10
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40. VI1. Present Value of Annuity
Calculate by table (Table 6-4) PVA-ord = 3,000 x PVIFA-ord (15, 10) = 3,000 x = 22,818
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41. VI1. Present Value of Annuity
Calculate by calculator N; 10 I/Y; PMT; CPT PV 22,818
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42. VI1. Present Value of Annuity
Additional 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 = 20, nd BGN; 2nd SET; 2nd QUIT N; 15 I/Y; PMT; CPT PV = 20,173
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43. VI1. Present Value of Annuity
Additional 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 = 13, N; 6 I/Y; PMT; CPT PV = 13,248
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44. VI1. Present Value of Annuity
Additional 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 = i ≈ 10% N; PMT; PV = 12300; CPT I/Y = 9.98%
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