Ch 6- Discounted CF Valuation

Question 1

How to solve for future value with multiple cash flows?

Answer 1

1. draw a timeline, today is time 0
2. 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 …

Question 2

How to solve for the present value with multiple cash flows?

Answer 2

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!

Question 3

Using a timeline, when moving forward you

Answer 3

multiply then ADD

Question 4

Using a timeline when moving backwards

Answer 4

you divide then add

Question 5

When do we assume cash flows occur unless we are told otherwise

Answer 5

AT THE END OF THE PERIOD!

Question 6

Ordinary Annuity vs Perperutity

Answer 6

Ordinary Annuity: series of constant or level cf at the end of each period for a fixed # of periods

Perpetuity

Question 7

How to calculate PV for Annuity CF?

(present value of multiple future cash flows)

Answer 7

• 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)

Question 8

What is the PVIFA

Answer 8

the term inside the brackets of the Present Value formula!!!

1/(1+r)^t

Question 9

How to check if you did a calcualting present value of multiple future cash flows question properly?

Answer 9

GO THROUGH THE PROCESS AS IF YOU’RE MOVING ON THE TIMELINE

1. find the pv you calculated
2. multiply it by 1.0#
3. take out whatever amt of money you would get back in y1 (subtract it!)
4. the difference is the amount of money that will continue to be compounded
5. 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)

Question 10

how to solve for the discount rate for an annuity?

Answer 10

• use your calculator
• use trial and error to guess amounts (remember PV and discount rates move in opposite directions!!! use this to adjust)q

Question 11

How to do questions where they compare two different deals, a lump sum and multiple cash inflows?

Answer 11

1. lump sum= straight up take this money
2. this is a calculating rate question, so identify n, fv, pmt (fv/n)
3. once you solve for the rate, compare it with other rates given! take it if you like

4.

Question 12

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?

Answer 12

1. 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

2. Then calculate the future vlaue of this lump sum (using future value method)

FV= PV * 1+r^t

Question 13

What is the annuity futurue value factor

Answer 13

((1+r)^t -1)/r

Question 14

ordinary annuity vs annuity due

Answer 14

ordinary: pmt due at the end if the degree

annuity due: pmt due at the beginning of the period

Question 15

how to convert ordinary annuity to annuity due

Answer 15

1) switch to beginning in your calculator

2) annuity due value= ordinary annuity value * (1+r)

Question 16

Perpetuities

Answer 16

when a level stream of cash flows continue forever!!! perpetuity has infinite number of cash flows

Question 17

PV of a perpetuity that is constant

Answer 17

Cash flow/r

Question 18

PV of a perpetuity that is growing + 3 conditions

Answer 18

PV= C/r-g

givem, C is CF at period 1 not period 0
r>g
and timing is constant

Question 19

What is a growing annuity

Answer 19

an annuity (Fixed amount of payments) that increases in cash flow value over time

Question 20

Fomrula for PV of a growing annuity

Answer 20

PV= C/r-g [1- ( (1+g)/(1+r))^t]

Question 21

Is 10% annually and 10% compounded semiannually the smaE?

Answer 21

no! 10% annually is 10% yearly

10% semiannually= 5% every 6 mos, then the 5% you got is also compounded so = 10.025%

Question 22

What is the effecitve annual ratee

Answer 22

the actual rate that you will earn

Question 23

stated interst rate or quoted interest rate

Answer 23

the rate that is decribed

interest rate charged per period x number of periods per year

Question 24

Converting quoted interst rate to effective annual rate

Answer 24

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

Question 25

why do we care about the quoted rate?

Answer 25

this is what we use to determine how much our paymetns are

Question 26

how to figure out your mortgage payment

Answer 26

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

Question 27

What is an APR

Answer 27

the rate all banks are required to display!!!!

Question 28

is APR the same as EAR

Answer 28

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!!)

Question 29

is there a limit to the compounding we can do?

Answer 29

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 %

Question 30

pure discount loan

Answer 30

simplest type of loan, borrorer recieves money today and repays on esingle lump sum in the future

Question 31

how to caclcualte a pure discount loan

Answer 31

PV= loan value/ 1 + r ^t

Question 32

interest only loans

Answer 32

borrorer must pay interest each period and to repay the entire principal

Question 33

if there is only one period then — and — are the same thing

Answer 33

interst only loan and pure discount loan

Question 34

amortized loans

Answer 34

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

Question 35

amortized loan schedule

Answer 35

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

Question 36

If you are calculating the future value of multiple cash flows, with money going in and out, how do you solve it?

Answer 36

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

Question 37

if asked to calculate the present value of the package, do you include the year 0 cash payment you get?

self test 6.1

Answer 37

no!!!!!! only include the year 1 and on DO NOT INCLUDUE THE FIRST YEAR PAYMENT