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Time Value of Money Concepts
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Terms in this set (24)
Time Value of Money
Money Can be invested today to earn interest and grow to a larger dollar amount in the future
Interest
The amount of money paid or received in excess of the amount borrowed or lent
Simple Interest
Computed by multiplying an initial investment times both the applicable interest rate and period of time for which the money is used.
Compound Interest
Includes interest not only on the initial investment but also on the accumulated interest in previous periods
Effective rate
The actual rate in which the money grows per year
Future Value Equation
FV = I(1 + i)^n
Present Value
Today's equivalent to a particular amount in the future
Present Value Equation
PV = FV/(1 + i)^n
Monetary Assets
Include money and claims to receive money, the amount of which is fixed or determinable
Monetary Liabilities
Obligations to pay amounts of cash, the amount of which is fixed or determinable
Annuity
Series of cash flows
Ordinary annuity
Cash flows occur at the end of each period
Annuity Due ( annuity in advance)
Cash flows occur at the beginning of each period
Deferred Annuity
Exists when the first cash flow occurs more than one period after the date the agreement begins
A series of equal periodic payments that starts more than one period after the agreement is called
A deferred annuity
Present and future value tables of $1 at 3% are presented below:
N FV $1 PV $1 FVA $1 PVA $1 FVAD $1 PVAD $1
1 1.03000 0.97087 1.0000 0.97087 1.0300 1.00000
2 1.06090 0.94260 2.0300 1.91347 2.0909 1.97087
3 1.09273 0.91514 3.0909 2.82861 3.1836 2.91347
4 1.12551 0.88849 4.1836 3.71710 4.3091 3.82861
5 1.15927 0.86261 5.3091 4.57971 5.4684 4.71710
6 1.19405 0.83748 6.4684 5.41719 6.6625 5.57971
7 1.22987 0.81309 7.6625 6.23028 7.8923 6.41719
8 1.26677 0.78941 8.8923 7.01969 9.1591 7.23028
9 1.30477 0.76642 10.1591 7.78611 10.4639 8.01969
10 1.34392 0.74409 11.4639 8.53020 11.8078 8.78611
11 1.38423 0.72242 12.8078 9.25262 13.1920 9.53020
12 1.42576 0.70138 14.1920 9.95400 14.6178 10.25262
13 1.46853 0.68095 15.6178 10.63496 16.0863 10.95400
14 1.51259 0.66112 17.0863 11.29607 17.5989 11.63496
15 1.55797 0.64186 18.5989 11.93794 19.1569 12.29607
16 1.60471 0.62317 20.1569 12.56110 20.7616 12.93794
Today, Thomas deposited $160,000 in a 4-year, 12% CD that compounds quarterly. What is the maturity value of the CD?
$256,754
FV = $160,000 × 1.60471* = $256,754
*FV of $1: n = 16; i =3%
Present and future value tables of $1 at 3% are presented below:
N FV $1 PV $1 FVA $1 PVA $1 FVAD $1 PVAD $1
1 1.03000 0.97087 1.0000 0.97087 1.0300 1.00000
2 1.06090 0.94260 2.0300 1.91347 2.0909 1.97087
3 1.09273 0.91514 3.0909 2.82861 3.1836 2.91347
4 1.12551 0.88849 4.1836 3.71710 4.3091 3.82861
5 1.15927 0.86261 5.3091 4.57971 5.4684 4.71710
6 1.19405 0.83748 6.4684 5.41719 6.6625 5.57971
7 1.22987 0.81309 7.6625 6.23028 7.8923 6.41719
8 1.26677 0.78941 8.8923 7.01969 9.1591 7.23028
9 1.30477 0.76642 10.1591 7.78611 10.4639 8.01969
10 1.34392 0.74409 11.4639 8.53020 11.8078 8.78611
11 1.38423 0.72242 12.8078 9.25262 13.1920 9.53020
12 1.42576 0.70138 14.1920 9.95400 14.6178 10.25262
13 1.46853 0.68095 15.6178 10.63496 16.0863 10.95400
14 1.51259 0.66112 17.0863 11.29607 17.5989 11.63496
15 1.55797 0.64186 18.5989 11.93794 19.1569 12.29607
16 1.60471 0.62317 20.1569 12.56110 20.7616 12.93794
Shane wants to invest money in a 6% CD account that compounds semiannually. Shane would like the account to have a balance of $110,000 4-years from now. How much must Shane deposit to accomplish his goal?
$86,835
PV = $110,000 × 0.78941* = $86,835
*PV of $1: n=8; i=3%
Present and future value tables of $1 at 3% are presented below:
N FV $1 PV $1 FVA $1 PVA $1 FVAD $1 PVAD $1
1 1.03000 0.97087 1.0000 0.97087 1.0300 1.00000
2 1.06090 0.94260 2.0300 1.91347 2.0909 1.97087
3 1.09273 0.91514 3.0909 2.82861 3.1836 2.91347
4 1.12551 0.88849 4.1836 3.71710 4.3091 3.82861
5 1.15927 0.86261 5.3091 4.57971 5.4684 4.71710
6 1.19405 0.83748 6.4684 5.41719 6.6625 5.57971
7 1.22987 0.81309 7.6625 6.23028 7.8923 6.41719
8 1.26677 0.78941 8.8923 7.01969 9.1591 7.23028
9 1.30477 0.76642 10.1591 7.78611 10.4639 8.01969
10 1.34392 0.74409 11.4639 8.53020 11.8078 8.78611
11 1.38423 0.72242 12.8078 9.25262 13.1920 9.53020
12 1.42576 0.70138 14.1920 9.95400 14.6178 10.25262
13 1.46853 0.68095 15.6178 10.63496 16.0863 10.95400
14 1.51259 0.66112 17.0863 11.29607 17.5989 11.63496
15 1.55797 0.64186 18.5989 11.93794 19.1569 12.29607
16 1.60471 0.62317 20.1569 12.56110 20.7616 12.93794
At the end of each quarter, Patti deposits $2,300 into an account that pays 12% interest compounded quarterly. How much will Patti have in the account in 4 years?
$46,361
FVA = $2,300 × 20.1569* = $46,361
*FVA of $1: n=16; i=3%
Present and future value tables of $1 at 3% are presented below:
N FV $1 PV $1 FVA $1 PVA $1 FVAD $1 PVAD $1
1 1.03000 0.97087 1.0000 0.97087 1.0300 1.00000
2 1.06090 0.94260 2.0300 1.91347 2.0909 1.97087
3 1.09273 0.91514 3.0909 2.82861 3.1836 2.91347
4 1.12551 0.88849 4.1836 3.71710 4.3091 3.82861
5 1.15927 0.86261 5.3091 4.57971 5.4684 4.71710
6 1.19405 0.83748 6.4684 5.41719 6.6625 5.57971
7 1.22987 0.81309 7.6625 6.23028 7.8923 6.41719
8 1.26677 0.78941 8.8923 7.01969 9.1591 7.23028
9 1.30477 0.76642 10.1591 7.78611 10.4639 8.01969
10 1.34392 0.74409 11.4639 8.53020 11.8078 8.78611
11 1.38423 0.72242 12.8078 9.25262 13.1920 9.53020
12 1.42576 0.70138 14.1920 9.95400 14.6178 10.25262
13 1.46853 0.68095 15.6178 10.63496 16.0863 10.95400
14 1.51259 0.66112 17.0863 11.29607 17.5989 11.63496
15 1.55797 0.64186 18.5989 11.93794 19.1569 12.29607
16 1.60471 0.62317 20.1569 12.56110 20.7616 12.93794
Jimmy has $59,589 accumulated in a 401K plan. The fund is earning a low, but safe, 3% per year. The withdrawals will take place at the end of each year starting a year from now. How soon will the fund be exhausted if Jimmy withdraws $11,000 each year?
6 Years
$59,589 ÷ $11,000 = 5.41719
For PVA of $1 factor of 5.41719 and i of 3%, n = 6
Present and future value tables of 1 at 11% are presented below.
PV of $1 FV of $1 PVA of $1 FVA of $1
1 0.90090 1.11000 0.90090 1.0000
2 0.81162 1.23210 1.71252 2.1100
3 0.73119 1.36763 2.44371 3.3421
4 0.65873 1.51807 3.10245 4.7097
5 0.59345 1.68506 3.69590 6.2278
6 0.53464 1.87041 4.23054 7.9129
Polo Publishers purchased a multi-color offset press with terms of $35,000 down and a noninterest-bearing note requiring payment of $10,000 at the end of each year for six years. The interest rate implicit in the purchase contract is 11%. Polo would record the asset at:
$77,305
$35,000 + ($10,000 × 4.23054) = $77,305
*PVA of $1: n=6; i=11%
Mary Alice just won the lottery and is trying to decide between the annual cash flow payment option of $280,000 per year for 25 years beginning today and the lump-sum option. Mary Alice can earn 5% investing this money. At what lump-sum payment amount would she be indifferent between the two alternatives? (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1) (Round your "PVAD factors" to 5 decimal places and round final answer to nearest whole dollar amount.)
$4,143,619
$280,000 x 14.79864* = $4,143,619
*PVAD of $1: n = 25; i = 5%
Simpson Mining is obligated to restore leased land to its original condition after its excavation activities are over in three years. The cash flow possibilities and probabilities for the restoration costs in 3 years are as follows:
Cash overflow Probability
$102,000 40%
152,000 30%
202,000 30%
The company's credit-adjusted risk-free interest rate is 4%. The liability that Simpson must record at the beginning of the project for the restoration costs is (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1) (Round your "PV factors" to 5 decimal places and round your final answer to the nearest dollar amount):
rev: 10_09_2015_
$130683
Expected cash flow:
$102,000 × 40% = $ 40,800
$152,000 × 30% = 45,600
$202,000 × 30% = 60,600
$ 147,000 × 0.88900* = $130,683
*PV of $1: n = 3; i = 4%
Davenport Inc. offers a new employee a lump-sum signing bonus at the date of employment. Alternatively, the employee can take $38,000 at the date of employment and another $58,000, 3 years later. Assuming the employee's time value of money is 6% annually, what lump sum at employment date would make her indifferent between the two options? (FV of $1, PV of $1, FVA of $1, PVA of $1, FVAD of $1 and PVAD of $1) (Round your "PVAD factors" to 5 decimal places and round your final answer to the nearest dollar amount.)
$86,698
The lump-sum equivalent would be $38,000 + the present value of $58,000 where n = 3 and i = 6%. That is, $38,000 + ($58,000 x 0.83962 from Table 2) = $86,698.
An investor purchases a 20-year, $1,000 par value bond that pays semiannual interest of $40. If the semiannual market rate of interest is 5%, what is the current market value of the bond?
$828
$40 x 17.15909* = $686
$1,000 x 0.14205** = 142
$828
*PVA of $1: n = 40; i = 5%
**PV of $1: n = 40; i = 5%
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