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Intro to FP > Time Value of Money > Flashcards

Time Value of Money Flashcards

1
Q

n

A

Compounding period - not necessarily one year

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2
Q

i

A

interest rate per compounding period
If annual rate is 12%, semi-annual rate is 6%, quarterly is 3%, monthly is 1%

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3
Q

PV

A

Present value of a lump sum or annuity stream

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4
Q

PMT

A

Annuity

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5
Q

FV

A

Future value

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6
Q

Money going into an investment is?

A

Negative

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7
Q

Money coming out of an investment is?

A

Positive

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8
Q

Solve for a variable w/no periodic payments

A

May solve for any of the following 4 variables, given the other 3
n i PV FV

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9
Q

Solve for variable w/periodic pmts

A

solve any of the 5 variables given the other 4
n i PV PMT FV

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10
Q

Clearing your calculator

A

f REG f FIN

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11
Q

What lump sum today grows to 50k in 10 years at 7%

A

50000 FV 7 i 10 n PV = -25,417.46

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12
Q

Set calc to 2 decimals

A

f 2

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13
Q

Future value of lump sum
5.5 yrs, invest 12,300 at 4% compounded quarterly

A

12300 CHS PV 22 n 1 i FV

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14
Q

Discounting

A

-start with future amount and divide by 1 plus the interest rate
- this will give present value of some future amount

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15
Q

When discounting larger interest rates lead to

A

smaller present values

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16
Q

When discounting, smaller interest rates will lead to

A

larger present values

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17
Q

An annuity is

A

a series of equal payments
can be paid at the beginning or end of a period

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18
Q

Annuity due AD

A

pays at the beginning (before he gets injured)

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19
Q

Ordinary annuity

A

pays at the end of the period

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20
Q

most commercial loans, including mortgages, require payments when

A

at the end of the period

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21
Q

commercial annuity purchased from insurance company is

A

annuity due, will make payments at the beginning of the period

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22
Q

AD examples

A

college funding, life insurance needs for income replacement, retirement needs analysis

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23
Q

Time zero

A

today. 1 year from today is time 1

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24
Q

other terms for interest rate

A

opportunity cost, opportunity rate, required return, rate of return, internal rate of return, capitalization rate, cost of capital, discount rate

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25
Q

CHS

A

change sign key
cashflow into an investment is negative
cashflow out of an investment is positive

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26
Q

BEG

A

hit g key then function on the 7 key and BEGIN will be displayed - only used to denote an annuity whose payments are at BEGINNING

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27
Q

END

A

hit g key then blue funtion on the 8 key - only used to denote an annuity whose payments are at the END of a period

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28
Q

Calculating a present value will always involve

A

discounting

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29
Q

Calculating a future value will always involve

A

compounding

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30
Q

Present value of 500k that could be invested for 10% over 5 years

A

f REG f FIN
50000 FV 5 n 10 i PV

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31
Q

John annuitizing an annuity and expects to receive $422.25 per Q for 10 years. First payment starts today. John can grow the money by 4.6% a year.

A

f REG f FIN
g BEG 422.25 CHS PMT 40 n 1.15 i FV

BC is quarterly compounding the # of periods is 40 and the interest rate is 1.15

Also need to change calc back to end by hitting g END

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32
Q

Quality

A

investment with less risk preferable to one with more risk. “likelihood of payback” if both have equal rates of return the one with less risk is preferable

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33
Q

quantity

A

assume risks are equal, timing is identical, investment w/higher rate of return is preferable

at what rate is the investment earning or growing?

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34
Q

timing

A

when and/or how often must cash be put in and/or taken out of an investment

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35
Q

Drawback: Results of quantitative only as good as information provided

A

Garbage in garbage out

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36
Q

Net Present Value

A

Compares the outflow required at time zero, with the Present Value of future cash inflows discounted at the appropriate discount rate

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37
Q

Firm’s cost of capital

A

discount rate used to calculate the present value of future inflows

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38
Q

Investor’s opportunity rate

A

DISCOUNT RATE used to calculate the present value of the future cash inflows

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39
Q

How to know if NPV is positive?

A

if the PV of future cash inflows exceeds the outflow at time zero

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40
Q

What does it mean when NPV is positive?

A

the project or investment would increase the investor’s wealth if undertaken

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41
Q

What if the NPV is negative?

A

would reduce the investors wealth “destroy wealth”

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42
Q

Is NPV before tax or after tax?

A

After-tax cash flows
After-tax interest rate

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43
Q

Cash flows recorded annually when doing a TVM calc.

A

even if they occur monthly

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44
Q

When do we record cash flows as occurring?

A

At the end of the period

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45
Q

g CFo

A

Outflow at zero time

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46
Q

g CFi

A

records annual cash flows from year 1,2,3…

47
Q

g Nj

A

repeat prior cash flow

48
Q

f NPV

A

calc net present value after all entries are made

49
Q

First step in calculating NPV?

A

make a number line

50
Q

Internal Rate of Return

A

specific interest rate that that equates the present value of future cash flows to the out flow at time zero.
Forces NPV of an investment to zero

51
Q

NPV and IRR use the same what

A

cash flows

52
Q

What interest rate sets NPV to zero?

A

Internal Rate of Return

53
Q

Discounted Cash Flow Methods

A

Net Present Value
Internal Rate of Return

54
Q

How to enter repeat prior cash flow

A

g Nj

ex. 3 g Nj

55
Q

Other IRR calculations

A

Yield to Maturity, Yield to Call

56
Q

Another name for IRR

A

dollar weighted return

57
Q

First flaw in IRR

A

-possible to obtain MORE THAN ONE RESULT. (less severe flaw)
-happens when a project has a LARGE OUTFLOW during or toward the end of the project

58
Q

IRR Reinvestment assumption

A

Assumes you can reinvest future cashflows at rate equal to IRR
-major flaw

59
Q

When is IRR greater than Opportunity Rate

A

when NPV > 0

60
Q

When is IRR less than opportunity rate?

A

when NPV < 0

61
Q

When does IRR = NPV

A

when NPV = 0

62
Q

If NPV is positive, you expect IRR to be

A

greater than the investors opportunity rate

63
Q

When would you reject a project?

A

If the NPV is negative or the IRR less than opportunity rate

64
Q

When would you accept a project?

A

If the NPV is positive or the IRR is greater than the opportunity rate

65
Q

Can you solve for NPV and IRR at the same time?

A

Yes, you can use one session in your calculator since NPV and IRR are related

66
Q

When you have 2 projects and conflicting NPV and IRR, which do you go with?

A

NPV. IRR requires all future cash flows be REINVESTED AT IRR RATE. NPV assumes you can only reinvest at the DISCOUNT RATE. This is a more reasonable assumption

67
Q

Ordinary annuity has what vs annuity due?

A

Lapse of time

68
Q

In a practical situation the goal is not to calculate an exact answer but to do what?

A

Calculate if a goal can be met. For example retirement in 30 yrs using an i of 8% isn’t realistic bc you won’t get 8% every year

69
Q

How many decimal points should you use on your hp12c?

A

4 - you do that by pressing f and then 4

70
Q

How do you do 2 times 10 on the hp12c?

A

2 ENTER 10 X

71
Q

If you have 12.5% annual interest and you want to get the monthly rate how do you do that?

A

12.5 ENTER G 12DIVIDE

72
Q

Future Value defintion

A

the future amount to which $1 today will increase based on a defined interest rate and period of time

73
Q

In 1963 a Les Paul cost $323. Over the following 55 years it appreciated at 13.5% per year. What is the value today?

A

55N 13.55i 323 CHS PV FV ENTER
350,344.37

74
Q

When doing time value of money problems how do you start to enter them on the calculator?

A

left to right starting with N first

75
Q

In 1963 a Les Paul cost $323. Over the following 55 years it appreciated at 13.5% per year. What is the value today? COMPOUNDED MONTLY

A

55 G 12X 13.55 G 12DIVIDE 323 CHS PV FV ENTER
534,128.02

76
Q

Present Value defition

A

what a sum of money to be received in the future is worth in today’s dollars based on a specific discount rate

77
Q

If you fund your roth at the beginning of the month its what vs if you fund it at the end of the month

A

Annuity due vs. Regular Annuity

78
Q

When would you want to make a gift at the beginning or end of a period?

A

Beginning - you want to get it out of your estate

79
Q

BEG would be used for what cash inflows?

A

Social security, pensions, retirement planning, disability - you NEED this money up front in order to live

80
Q

Would insurance premium payments happen at the beginning or the end of a period?

A

Beginning - you have to pay for it so it doesn’t lapse during the period

81
Q

750k saved @ retirement. what is the monthly annuity payment received be assuming a 30 year period and 5.25% interest

A

G BEG
N = 360 (12 x 30 = 360))
i = .4375
PV = CHS 750000
PMT = 4,123.4875
FV = LEAVE BLANK

82
Q

If you have an I that’s monthly how do you enter that?

A

You just hit G i so it divides it by 12 that enters the i

83
Q

If you have an N that’s monthly how do you enter that?

A

enter the period, say 30 years, then hit G N

84
Q

Dales cc debt is 20k. His rate is 19.5%. Period is 4 years. What is his total interest payment?

A

N 48
PV 20000
i 1.625 (19.5/12)
PMT = 603.29

THEN you take that and multiply by 48 months and subtract the original payment

603.29*48 = 28,975.92 - 20000 = 8,975.92

85
Q

If a balance transfer question asks if there is a balance transfer fee, how do you do that?

A

You take the outstanding balance and multiply by whatever the fee is and then do the calculation so if 20k and the transfer fee is 3% the balance is 20,600 with the transfer fee

86
Q

For credit card questions the N is more than likely going to be what?

A

X12

87
Q

473,250 30 year mortgage with rate of 4.75%. Payment is 2,468 a month. Amortize to the 300 payment

A

PV = 473,250
n = 360 (30 gN)
i = 4.75 gI = .3958
PMT = 2468.70

To amortize to the 300 payment enter 60 f AMORT RCL PV = 433,015

88
Q

Say you’re contributing to a plan for 10 years and then you stop, but that money continues to grow, how do you do that?

A

The first calculation is going to have a PMT for 10 years, but then its a separate calculation of just future value without a payment

89
Q

Say a bond has a par value of 1000 and you receive coupon payments of $25? What is your I?

A

I=5 think 2 $25 semiannual payments is $50 which is 5% of 1000

90
Q

If a bond has a semiannual payment for 5 years what is you N?

A

N is 10 because you’re getting 2 payments a year

91
Q

If a bond has semiannual payments and the rate is 6% what is your I?

A

I is 3 because you divide by 2 since its semiannual

92
Q

You have a bond that matures in 5 years paying coupon of $25 and you can reinvest that at 6% how much should you pay for that bond?

A

N = 10 (2 payments a year for 5 years
I = 3 (6% semiannual)
PV =
FV = 1000

93
Q

MORTGAGES ARE ORDINARY ANNUITY OR ANNUITY DUE?

A

ORDINARY ANNUITY
YOU USE END

94
Q

After you find payment how do you amortize?

A

period F AMORT
THIS GIVES YOU THE INTEREST

95
Q

What does AMORT give you?

A

The interest

96
Q

What does cat eyes give you?

A

The principal

97
Q

How do you find the interest and principal?

A

You hit period F AMORT then
Cat Eyes
THEN ADD THOSE TOGETHER

98
Q

After you hit Cat Eyes how do you find the REMAINING Principal?

A

Hit RCL PV and that will show you how much there is left to pay

99
Q

Bond has a coupon of 4% but is yielding 3.8%

A

The yield is the I =3.8/2
PMT (coupon) = 20 (4/2 on 1000)

100
Q

What is the coupon payment on a bond?

A

The rate divided by 2

101
Q

BONDS ARE ALWAYS SEMI ANNUAL

A

Even if its a zero coupon bond

102
Q

When doing NPV problems always use what?

A

Timeline STARTING WITH TIME ZERO

103
Q

If NPV is zero do you undertake the investment?

A

Yes

104
Q

You have a $100 stock that pays $5 year 1, $6 year 2, $7 year 3 and you sell it year 3 for $100 what does the timeline look like

A

Year 0- ($100)
Year 1 - $5
Year 2 - $6
Year 3 - $117

105
Q

Doing NPV dont forget timeline AND

A

Year zero

106
Q

When you do NPV you need

A

-a timeline
-required rate of return is your I

107
Q

Bond has a market price of $910, Pays 11% coupon and matures in 6 years

A

N= 12
PV = 910
PMT = 1000 * .11 = $110/2 = 55
FV = 1000
FIND FOR I
I = 6.6097 * 2 = 13.22

108
Q

Current price of a bond that pays 10% coupon, matures in 8 years, comparable bonds are yielding 12.6%

A

N = 16
I = 6.3
FV = 1000
PMT = 50

PV = $871.29

109
Q

What is the IRR of a zero coupon bond w/$1000 face value, current price of $810 and will mature in 4 years?

A

PV = -810
n = 8 (4 * 2)
FV = 1000
PMT = 0
i = 2.6690 * 2 = 5.34

remember its a zero coupon

110
Q

On a bond the coupon is the what?

A

Payment

111
Q

You want to invest $10k a year into a fund that earns 4% a year. You want to make your first investment at the end of year 1, and the last investment at the end of year 3. What is the value at the end of year 4?

A

First find first 3 years of payments then grow that 1 more yr
N = 3 (your last investment is at end of yr 3)
I = 4
PV = 0
PMT = 10,000 CHS
FV = whatever it is
then FV * 1.04

112
Q

Find after tax savings, assuming 25% marginal tax rate, on a 250k 30 year mortgage at 4.75%

A

N = 360
I = .3958
PV = 250,000 CHS
PMT = $1304.12
Take PMT times 360 then subtract the original 250k
$469,482.6 - 250,000 = $219,482.6 * .25 = $54,870
THEN take the total minus the savings $469,482.6-$54,870 = $394,559 after tax cost of debt

113
Q

When your finding after tax cost savings, what do you do

A

Find the total cost of the mortgage, then subtract the original loan amount. That is the total interest, then multiply that by the tax rate. THEN subtract that from the total cost of the mortgage

114
Q

How would you compare interest and principal on a payment?

A

Find the payment then hit 1 f AMORT to get the interest on 1 payment then hit cat eyes to get the principal

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