Time Value of Money Flashcards
n
Compounding period - not necessarily one year
i
interest rate per compounding period
If annual rate is 12%, semi-annual rate is 6%, quarterly is 3%, monthly is 1%
PV
Present value of a lump sum or annuity stream
PMT
Annuity
FV
Future value
Money going into an investment is?
Negative
Money coming out of an investment is?
Positive
Solve for a variable w/no periodic payments
May solve for any of the following 4 variables, given the other 3
n i PV FV
Solve for variable w/periodic pmts
solve any of the 5 variables given the other 4
n i PV PMT FV
Clearing your calculator
f REG f FIN
What lump sum today grows to 50k in 10 years at 7%
50000 FV 7 i 10 n PV = -25,417.46
Set calc to 2 decimals
f 2
Future value of lump sum
5.5 yrs, invest 12,300 at 4% compounded quarterly
12300 CHS PV 22 n 1 i FV
Discounting
-start with future amount and divide by 1 plus the interest rate
- this will give present value of some future amount
When discounting larger interest rates lead to
smaller present values
When discounting, smaller interest rates will lead to
larger present values
An annuity is
a series of equal payments
can be paid at the beginning or end of a period
Annuity due AD
pays at the beginning (before he gets injured)
Ordinary annuity
pays at the end of the period
most commercial loans, including mortgages, require payments when
at the end of the period
commercial annuity purchased from insurance company is
annuity due, will make payments at the beginning of the period
AD examples
college funding, life insurance needs for income replacement, retirement needs analysis
Time zero
today. 1 year from today is time 1
other terms for interest rate
opportunity cost, opportunity rate, required return, rate of return, internal rate of return, capitalization rate, cost of capital, discount rate
CHS
change sign key
cashflow into an investment is negative
cashflow out of an investment is positive
BEG
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
END
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
Calculating a present value will always involve
discounting
Calculating a future value will always involve
compounding
Present value of 500k that could be invested for 10% over 5 years
f REG f FIN
50000 FV 5 n 10 i PV
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.
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
Quality
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
quantity
assume risks are equal, timing is identical, investment w/higher rate of return is preferable
at what rate is the investment earning or growing?
timing
when and/or how often must cash be put in and/or taken out of an investment
Drawback: Results of quantitative only as good as information provided
Garbage in garbage out
Net Present Value
Compares the outflow required at time zero, with the Present Value of future cash inflows discounted at the appropriate discount rate
Firm’s cost of capital
discount rate used to calculate the present value of future inflows
Investor’s opportunity rate
DISCOUNT RATE used to calculate the present value of the future cash inflows
How to know if NPV is positive?
if the PV of future cash inflows exceeds the outflow at time zero
What does it mean when NPV is positive?
the project or investment would increase the investor’s wealth if undertaken
What if the NPV is negative?
would reduce the investors wealth “destroy wealth”
Is NPV before tax or after tax?
After-tax cash flows
After-tax interest rate
Cash flows recorded annually when doing a TVM calc.
even if they occur monthly
When do we record cash flows as occurring?
At the end of the period
g CFo
Outflow at zero time
g CFi
records annual cash flows from year 1,2,3…
g Nj
repeat prior cash flow
f NPV
calc net present value after all entries are made
First step in calculating NPV?
make a number line
Internal Rate of Return
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
NPV and IRR use the same what
cash flows
What interest rate sets NPV to zero?
Internal Rate of Return
Discounted Cash Flow Methods
Net Present Value
Internal Rate of Return
How to enter repeat prior cash flow
g Nj
ex. 3 g Nj
Other IRR calculations
Yield to Maturity, Yield to Call
Another name for IRR
dollar weighted return
First flaw in IRR
-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
IRR Reinvestment assumption
Assumes you can reinvest future cashflows at rate equal to IRR
-major flaw
When is IRR greater than Opportunity Rate
when NPV > 0
When is IRR less than opportunity rate?
when NPV < 0
When does IRR = NPV
when NPV = 0
If NPV is positive, you expect IRR to be
greater than the investors opportunity rate
When would you reject a project?
If the NPV is negative or the IRR less than opportunity rate
When would you accept a project?
If the NPV is positive or the IRR is greater than the opportunity rate
Can you solve for NPV and IRR at the same time?
Yes, you can use one session in your calculator since NPV and IRR are related
When you have 2 projects and conflicting NPV and IRR, which do you go with?
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
Ordinary annuity has what vs annuity due?
Lapse of time
In a practical situation the goal is not to calculate an exact answer but to do what?
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
How many decimal points should you use on your hp12c?
4 - you do that by pressing f and then 4
How do you do 2 times 10 on the hp12c?
2 ENTER 10 X
If you have 12.5% annual interest and you want to get the monthly rate how do you do that?
12.5 ENTER G 12DIVIDE
Future Value defintion
the future amount to which $1 today will increase based on a defined interest rate and period of time
In 1963 a Les Paul cost $323. Over the following 55 years it appreciated at 13.5% per year. What is the value today?
55N 13.55i 323 CHS PV FV ENTER
350,344.37
When doing time value of money problems how do you start to enter them on the calculator?
left to right starting with N first
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
55 G 12X 13.55 G 12DIVIDE 323 CHS PV FV ENTER
534,128.02
Present Value defition
what a sum of money to be received in the future is worth in today’s dollars based on a specific discount rate
If you fund your roth at the beginning of the month its what vs if you fund it at the end of the month
Annuity due vs. Regular Annuity
When would you want to make a gift at the beginning or end of a period?
Beginning - you want to get it out of your estate
BEG would be used for what cash inflows?
Social security, pensions, retirement planning, disability - you NEED this money up front in order to live
Would insurance premium payments happen at the beginning or the end of a period?
Beginning - you have to pay for it so it doesn’t lapse during the period
750k saved @ retirement. what is the monthly annuity payment received be assuming a 30 year period and 5.25% interest
G BEG
N = 360 (12 x 30 = 360))
i = .4375
PV = CHS 750000
PMT = 4,123.4875
FV = LEAVE BLANK
If you have an I that’s monthly how do you enter that?
You just hit G i so it divides it by 12 that enters the i
If you have an N that’s monthly how do you enter that?
enter the period, say 30 years, then hit G N
Dales cc debt is 20k. His rate is 19.5%. Period is 4 years. What is his total interest payment?
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
If a balance transfer question asks if there is a balance transfer fee, how do you do that?
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
For credit card questions the N is more than likely going to be what?
X12
473,250 30 year mortgage with rate of 4.75%. Payment is 2,468 a month. Amortize to the 300 payment
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
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?
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
Say a bond has a par value of 1000 and you receive coupon payments of $25? What is your I?
I=5 think 2 $25 semiannual payments is $50 which is 5% of 1000
If a bond has a semiannual payment for 5 years what is you N?
N is 10 because you’re getting 2 payments a year
If a bond has semiannual payments and the rate is 6% what is your I?
I is 3 because you divide by 2 since its semiannual
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?
N = 10 (2 payments a year for 5 years
I = 3 (6% semiannual)
PV =
FV = 1000
MORTGAGES ARE ORDINARY ANNUITY OR ANNUITY DUE?
ORDINARY ANNUITY
YOU USE END
After you find payment how do you amortize?
period F AMORT
THIS GIVES YOU THE INTEREST
What does AMORT give you?
The interest
What does cat eyes give you?
The principal
How do you find the interest and principal?
You hit period F AMORT then
Cat Eyes
THEN ADD THOSE TOGETHER
After you hit Cat Eyes how do you find the REMAINING Principal?
Hit RCL PV and that will show you how much there is left to pay
Bond has a coupon of 4% but is yielding 3.8%
The yield is the I =3.8/2
PMT (coupon) = 20 (4/2 on 1000)
What is the coupon payment on a bond?
The rate divided by 2
BONDS ARE ALWAYS SEMI ANNUAL
Even if its a zero coupon bond
When doing NPV problems always use what?
Timeline STARTING WITH TIME ZERO
If NPV is zero do you undertake the investment?
Yes
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
Year 0- ($100)
Year 1 - $5
Year 2 - $6
Year 3 - $117
Doing NPV dont forget timeline AND
Year zero
When you do NPV you need
-a timeline
-required rate of return is your I
Bond has a market price of $910, Pays 11% coupon and matures in 6 years
N= 12
PV = 910
PMT = 1000 * .11 = $110/2 = 55
FV = 1000
FIND FOR I
I = 6.6097 * 2 = 13.22
Current price of a bond that pays 10% coupon, matures in 8 years, comparable bonds are yielding 12.6%
N = 16
I = 6.3
FV = 1000
PMT = 50
PV = $871.29
What is the IRR of a zero coupon bond w/$1000 face value, current price of $810 and will mature in 4 years?
PV = -810
n = 8 (4 * 2)
FV = 1000
PMT = 0
i = 2.6690 * 2 = 5.34
remember its a zero coupon
On a bond the coupon is the what?
Payment
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?
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
Find after tax savings, assuming 25% marginal tax rate, on a 250k 30 year mortgage at 4.75%
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
When your finding after tax cost savings, what do you do
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
How would you compare interest and principal on a payment?
Find the payment then hit 1 f AMORT to get the interest on 1 payment then hit cat eyes to get the principal
