Growing Annuities
Cash flow (CF) for N periods that grows at a constant rate of g% a
year.
Problem: Cannot use financial calculator
PV(Growing Annuity) =
Growing Annuities
FV(Growing Annuity) =
Assumption: i > g
Remember: In formula, cash flow is as of ti
Finding the Payment
Suppose you want to borrow $20,000 for a new car. You can borrow
at 8% per year, compounded monthly (8/12 = .667% per month). If you take
a 4 year loan, what is your monthly payment?
To change decimal places press
last row)
To Compute
Effective Annual Rates Financial Calculator
If APR = 10%, what is EAR if interest is compounded semi-annually?
m=?
NOM =
C/Y =
EFF =
Effective Annual Rates - Solve
If APR = 10%, what is EAR if m = 1, 4, 12, 365?
EARANNUAL
EARQUARTERLY
EARMONTHLY
EARDAILY
Time Line
Annual Percentage Rate - APR
Given interest rate per period (i/m) we can find APR by multiplying by
m.
APR = (i/m)*m
Annual Percentage Rate - APR
Interest rate every 6 months is 5%. What is the APR (i)?
APR = (i/m)*m
Effective Annual Rates - EAR
Buying a House
If I plan to buy a house for $350,000 and put 20% down. If the lender
charges me 6% APR but payments have to be made monthly for the next
30 years. What is the constant payment that I have to make each month?
Amount Borrowed: 0.8*350,000
=
1.
For a project with an initial investment of $3,000 and cash inflows of
$2,000 each year for 1 years, calculate NPV given a required return
of 13%.
A) $341
B) $213
C) $
0
D) $144
E) $552
Answer: C
1
Response: NPV = -$3,000 + 2,000 [(1 - 1/1.13 ) / .13]
Should know:
to calculate PV and FV of an Annuity and Annuity Due
To solve using financial calculator, table, formula, and EXCEL
Give 4 of the 5 variables, to solve for the 5th
Cash Flow
Annuity (Due) Constant Cash Flow, Fixed Period, Third row,
Financial
Annuities on the Spreadsheet - Example
If annuity due, add 1 after FV (or PV in case of FV(Annuity Due) in
the formulas.
Example
Compounding more than once a year
What happens to our formulas if interest is compounded more than
once per year.
m>1
Replace
Bill plans to open a do-it-yourself dog bathing center in a storefront. The
bathing equipment will cost $50,000. Bill expects the after-tax cash inflows
to be $15,000 annually for 3 years, after which he plans to scrap the
equipment and retire to the beac
Perpetuity
A constant stream of cash flows received at the end of each year that
continues forever.
Perpetuity Basic Formula
No FV(Perpetuity) because there is no end date continues forever.
Perpetuity - Example
You will receive $100 a year forever. How m