Ch 6- Discounted CF Valuation Flashcards
How to solve for future value with multiple cash flows?
- draw a timeline, today is time 0
- every new period is a jump you make
IF THE CASH FLOWS AT EVERY YEAR IS CONSTANT
(Present Value)x(1+Discount)^n
IF THE CASH FLOWS AT EVERY YEAR CHANGES:
PV Y1 x 1.0# + PMT Y1= FV Y1
FV Y1 x 1.0# + PMT Y2= FV Y2
FV Y2 x 1.-0# + PMT Y3= FV Y3 …
How to solve for the present value with multiple cash flows?
Discount back one period at a time
- draw a time line (now is time 0)
- Year 1: FV/1.0#
- Year 2: FV/1.0#^2
- Year 3: FV/1.0#^3 etc
-Sum these up!
Using a timeline, when moving forward you
multiply then ADD
Using a timeline when moving backwards
you divide then add
When do we assume cash flows occur unless we are told otherwise
AT THE END OF THE PERIOD!
Ordinary Annuity vs Perperutity
Ordinary Annuity: series of constant or level cf at the end of each period for a fixed # of periods
Perpetuity
How to calculate PV for Annuity CF?
(present value of multiple future cash flows)
- Small # of cashflows? use the timeline method
-PV= (PMT1/1.0#^1)+(PMT2/1.0#^2)+(PMT3/1.0#^3)…
BUT IF IT IS TOO MANY CASH FLOWS?
Annuity PV= C x (1- 1/(1+r)^n /r)
What is the PVIFA
the term inside the brackets of the Present Value formula!!!
1/(1+r)^t
How to check if you did a calcualting present value of multiple future cash flows question properly?
GO THROUGH THE PROCESS AS IF YOU’RE MOVING ON THE TIMELINE
- find the pv you calculated
- multiply it by 1.0#
- take out whatever amt of money you would get back in y1 (subtract it!)
- the difference is the amount of money that will continue to be compounded
- multiply this amount by 1.0# and this should equal exactly the amount you’re recieving in year 2
(different if this is with more than 2 years of cash flows but repeat 3,4 if needed)
how to solve for the discount rate for an annuity?
- use your calculator
- use trial and error to guess amounts (remember PV and discount rates move in opposite directions!!! use this to adjust)q
How to do questions where they compare two different deals, a lump sum and multiple cash inflows?
- lump sum= straight up take this money
- this is a calculating rate question, so identify n, fv, pmt (fv/n)
- once you solve for the rate, compare it with other rates given! take it if you like
4.
How to calculate the future value of annuities?
EX: you are putting 2k in rrsp paying 8%, in 30 years how much will you have?
- Calculate the present value of this annuity first as a lump sum (use the annuity pv formula)
Annuity PV= C * (1- 1/r^t)/r
- Then calculate the future vlaue of this lump sum (using future value method)
FV= PV * 1+r^t
What is the annuity futurue value factor
((1+r)^t -1)/r
ordinary annuity vs annuity due
ordinary: pmt due at the end if the degree
annuity due: pmt due at the beginning of the period
how to convert ordinary annuity to annuity due
1) switch to beginning in your calculator
2) annuity due value= ordinary annuity value * (1+r)
Perpetuities
when a level stream of cash flows continue forever!!! perpetuity has infinite number of cash flows
PV of a perpetuity that is constant
Cash flow/r
PV of a perpetuity that is growing + 3 conditions
PV= C/r-g
givem, C is CF at period 1 not period 0
r>g
and timing is constant
What is a growing annuity
an annuity (Fixed amount of payments) that increases in cash flow value over time
Fomrula for PV of a growing annuity
PV= C/r-g [1- ( (1+g)/(1+r))^t]
Is 10% annually and 10% compounded semiannually the smaE?
no! 10% annually is 10% yearly
10% semiannually= 5% every 6 mos, then the 5% you got is also compounded so = 10.025%
What is the effecitve annual ratee
the actual rate that you will earn
stated interst rate or quoted interest rate
the rate that is decribed
interest rate charged per period x number of periods per year
Converting quoted interst rate to effective annual rate
1) divide quoted rate by # of times that the interest rate is compounded
2) add one to your answer and raise it to the power of the # of times interest is compounded
3) subtract the 1
EAR= [1+(Quoted rate/m)]^m -1
why do we care about the quoted rate?
this is what we use to determine how much our paymetns are
how to figure out your mortgage payment
1) calculate your effective annual rate= [1+ quoted rate/m]^m - 1
2) find the quoted monthly rate to calculate the payments
a) Quoted rate/m = (EAR+1)^1/m - 1
b) use annuity pv formula to isolate for C!
pv= c*(1-1/1+r^t)/r
C= payment
What is an APR
the rate all banks are required to display!!!!
is APR the same as EAR
only if it is compounding annnually!!!! if anything esle than no!!!!!
APR= interest rate per period x # of periods in a year
(formula for APR ignores compounding!!)
is there a limit to the compounding we can do?
no ! we can compound forever and ever!!! but aftre a point we hit the upper limit (compounding every minute)
the formula for the upper limit is
EAR= e^q -1
q= the %
pure discount loan
simplest type of loan, borrorer recieves money today and repays on esingle lump sum in the future
how to caclcualte a pure discount loan
PV= loan value/ 1 + r ^t
interest only loans
borrorer must pay interest each period and to repay the entire principal
if there is only one period then — and — are the same thing
interst only loan and pure discount loan
amortized loans
borrower repays parts of the principal over time
(interest only and pure disc the principal paid all at once)
in this method, the total payment will decline each year bc the total amount loaning decreases therefore the interest charged on top of the loan is gonna get smaller
amortized loan schedule
year beginbal totalpay intpaid princpaid endbal
2 4000 1360 360 1000 3000
3 3000 1270 270 1000 2000
4 2000 1180 180 1000 1000
5 1000 1090 90 1000
int paid= begin bal x interest rate
end bal last year= begin bal this year
pmt= pv of ordinary annuity
If you are calculating the future value of multiple cash flows, with money going in and out, how do you solve it?
callcualte it slowly, jump forward until the next payment or withdrawal
IF PAYMENT, add it in then continue jumping and mulitplying (pv * 1.+r^t)
IF WITHDRAWAL, subtract it from the current amount, and continue compounding it
if asked to calculate the present value of the package, do you include the year 0 cash payment you get?
self test 6.1
no!!!!!! only include the year 1 and on DO NOT INCLUDUE THE FIRST YEAR PAYMENT
