There are 2 ways to calculate FVs for multiple cash flows:
1. compound the accumulated balance forward one year at a time or
2. calculate the FV of each CF first and then add these up
PV for multiple cash flows:
1. Discount back one perios at a timeor
2. Calculate the PV individually and add them up
*the amount that you would need today in order to exactly duplicate those future cash flows (for a given discount rate)
annuity
a level stream of cash flows for a fixed period of time
PV of an annuity of C dollars per t period
Annuity PV = C*(1-PVF/r)
= C*{1-[1/(1+r)^t]/r}
annuity due
an annuity for which the cash flows occur at the beggining of the month/period
ex: Leases
any amount that needs to be prepaid the same amount each period
annuity due value= ordinary annuity value * (1+r)
two steps:
1. calc the PV or FV as though it were an ordinary annuity and 2. multiply your answer by (1+r)
Perpetuity
level of stream of cash flows continues forever
cash flows are perpetual
also called consols (in Canada and UK)
PV for a perpetuity = C/r
preferred stock (preference stock) is an example of a
perpetuity
stated interest rate (quoted interest rate)
the interest rate expressed in terms of the interest payment made each period
effective annual rate (EAR)
the interest rate expressed as if it were compunded once per year
(1+ Quoted rate/m)^{m }- 1
(1+ APR/12)^{12} - 1
Annual Percentage Rate (APR)
the interest charged per period multiplied by the number of periods per year
also called nominal rate
Payday loan example
FV = PV * (1+r)^{1}
120 = 100 * (1+r)^{1}
1.20 = (1+r)
r = .20 or 20%
APR = .20* 365/18
APR = 4.0556 or 405.56%
EAR = (1+quoted rate/m)^{m}-1
EAR = (1+.20)^{365/18}-1
EAR = 39.3292 or 3,932.92%
3 basic types of loans
pure discount
interest only
amortized
Pure Discount Loans
simplest form of loan
borrower received money today and repays a single sum at some time in the future.
very common when the term is short (one year or less)
Interest Only Loans
the borrower pays interest each period and to repay the entire principal (the original loan amount) at some point in the future
(if there is just one period it is the same as a pure discount loan)
amortized loans
lender may require the borrower to repay parts of the loan amount over time. The process of paying off a loan by making regular principal reductions is called amortizing the loan
pay interest plus some fixed amount
common with medium term business loans
most common (cars and homes)- borrower makes a single fixed payment every period
Ex: 5 yr 9% $5,000 loan
5,000 = C * (1-1/1.09^{5})/.09
= C * (1-.6499)/.09
C= 5,000/3.8897
= 1,285.46
There are two ways to calculate PV and FV when there are multiple cash flows.
True
A series of constant cash flows that arrive or are paid at the end of each period is called an
ordinary annuity
Interest rates can be quoted in a variety of ways. For Financial decisions, it is important that any rates being compared be first converted to effective rates. The relationship between a quoted rate, such as an APR and EAR is given by
EAR = (1+quoted rate/m)^{m}-1
m= the # of times per year the money is compounded (or the # of payments per year)