Ch 5 Flashcards
Present value of multiple cash flows?
Discount each FV of each cash flow
1/(1+r)^t + 1/(1 + r)^(t +n)
Future value of multiple cash flows
Multiple payments earning interest over the years
Ex. Receive $100 over 4 years, in account earning 8% int. 100. Yr. 4 \+ 100 X 1.08. Yr. 3 \+ 100 X 1.08^2. Yr. 2 \+ 100 X 1.08^3. Yr. 1
Receive $100 over 4 years, in account earning 8% int. How to calculate?
100. Yr. 4 \+ 100 X 1.08. Yr. 3 \+ 100 X 1.08^2. Yr. 2 \+ 100 X 1.08^3. Yr. 1
What is the amount of cash you need to invest at a 9% rate of return to get $1000 in 1 year and $2000 in 2 years?
1/(1.09) x 1000
+
1/(1.09)^2 X 2000
= $2,600.79
Annuity
Level stream of cash flows from fixed period of time
Annuity present value equation?, abbreviation?
Annuity present value = C x ((1-present value factor)/r)
= C x {1 - [1/(1 + r)^t]/r}
Where C = annuity payment
r = rate of return
t = # of periods
PVIFA(r,t)
Annuity present value factor equation?
Ex. Where interest rate is 10% and period is 3 years?
What’s the present value of a $500 annuity?
Annuity present value factor = (1-present value factor)/r
= (1 - (1/1.1^3))/.10 = 2.48685
Annuity present value = 500 X 2.48685 = $1,243.43
Annuity future value factor equation?
Annuity FV factor = (Future value factor - 1)/r
= [(1 + r)^t - 1]/r
What is the future value of a 30-yr. $2,000 annuity paying 8 percent interest?
Annuity value factor = (1.08^30 -1)/.08 = 113.2832
Annuity future value = $2,000 X 113.2832 = $226,566.42
Annuity due, ex.?
Annuity for which the cash flows occur at the
beginning of the period, prepaying
Ex. A lease, where rent is prepaid
Annuity due value equation?
Annuity due value = Ordinary annuity value X (1 + r)
Perpetuity AKA Consol?
An annuity where cashflows continue forever
PV for perpetuity equation?
PV for a perpetuity = C/r
Stated interest rate AKA Quoted interest rate?
Interest rate expressed in terms of interest payment
Made each period
Effective annual rate (EAR)?
Interest rate expressed as if it were compounded once
Per year
What is the effective annual rate (EAR) of 15.5% compounded quarterly and 15 % compounded daily? Calculate
.155/4 = 0.03875 , $1 X 1.03875^4 = $1.1642
.15/365= .000411, $1 X 1.000411^365 = $1.1618
Equation for Effective annual rate (EAR)?
What is EAR for 12% monthly?
EAR = [(1 + Quoted rate/m)^m] - 1
EAR = (1 + .12/12)^12 - 1= 12.6825%
Annual percentage rate (APR)
Interest rate charged per period multiplied by number of
Periods per year
EAR on an interest rate of 18 percent APR with monthly payments? Calculate
EAR = (1 + .18/12)^12 - 1
= 1.015^12 - 1 = 19.56%
3 major types of loans?
Pure discount loans,
interest-only loans
Amortized loans
Pure discount loans
Borrow receives present value of money and
Pays lump sum in the future
Interest only bonds
Loan has repayment plan where borrower pays interest
Each period and eventually repays entire principal
Form of most corporate bonds
Amortizing loan
Process of paying off loan by making regular principal
Reductions called amortizing
