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Discounted cash flow - Coggle Diagram
Discounted cash flow
Valuing Annuities
and Perpetuities
ordinary annuity
a series of constant or level cash flows that occur at the end of each period for
some fixed number of periods
Annuity present value=C x (1- present value factor)/r
refer pg 178
present value interest factor
for annuities (PVIFA)
Annuity table pg 179
future value factor
Annuity!FV!factor = (Future!value!factor − 1 ) / r
((1+r)^t - 1) /r pg 184
Annuity Due
An
annuity due is an annuity for which the cash flows occur at the beginning of each period.
Annuity due!value = Ordinary annuity!value × (1 + r )
Perpetuities
An important special case of an annuity arises when the level stream of cash flows continues
forever.
One type of
perpetuity is called a consol.
Fixed-rate preferred stock is an important example of a perpetuity
Growing Perpetuities
perpetuities we have discussed so far are annuities with constant payments.
PV = C/(r-g)
interest rate r must be greater than the growth rate
Summary of annuity and perpetuity calculations IN PG 186
Growing Annuity
Formula in pg 189
two ways to calculate future values for multiple cash flows
compound the accumulated balance forward one year at a time
calculate the future value of
each cash flow first and then add them up
Cash flow assumed to occur at the end of each period
Comparing Rates: The Effect
of Compounding
Effective Annual Rates and Compounding
Stated interest rate or quoted interest rate
It is simply the
interest rate charged per period multiplied by the number of periods per year
Actual rate that you will earn, is called the effective annual rate (EAR).
Formula in pg 191
Mortgages
Mortgages are a very common example of an annuity with monthly payments
financial institutions require that mortgage rates be quoted with semiannual compounding
EARs and APRs
Annual percentage rate
Cost of borrowing disclosure
regulations (part of the Bank Act)
the APR is simply equal to the interest rate per period multiplied by the
number of periods in a year.6 This method ignores the compounding of interest
If we let q
stand for the quoted raterate, then, as the number of times the interest is compounded gets extremely large, the EAR approaches pg195
Loan Types and Loan
Amortization
Pure discount loan
repays a single lump sum at some time in the future
Interest only loans
A second type of loan repayment plan calls for the borrower to pay interest each period and to
repay the entire principal (the original loan amount) at some point in the future.
Amortized loans
lender may require the borrower to repay parts of the principal over
time.
principal reduction