1. CITY UNIVERSITY OF HONG KONG
DEPARTMENT OF ACCOUNTANCY
AC6531 Financial Management
Topic B – Time value of Money
1. The concept of time value of money - a dollar paid to you tomorrow is NOT worth a
dollar today. How much does it worth? In order to be able to make correct financial
management decisions to maximize stockholder wealth, we need methods that will
allow us to compare sums existing at different points in time.
2. Future value (FVn) is defined as the value to which a beginning lump sums or present
value (PV) will grow in a certain number of periods, n, at a specified rate of interest i.
FVn = PV(1+i)n
3. Present value (PVn) - the present value of a sum due n years in the future is the amount
which, if it were on hand today and invested at the specified interest i, would grow to
equal the future sum.
PV = FVn/(1+i)n
4. Annuity - a series of payments of fixed amount for a specified number of periods.
Payments occur at the end of each period is called ordinary (deferred) annuity.
Payments occur at the beginning of each period is called annuity due.
Future value of an annuity (FVAn) is the total amount one would have at the end of the
annuity period if payment were invested at a given periodic interest rate and held to the
end of the annuity period.
FVAn = PMT∑(1+i)n-t
5. Present value of an annuity (PVAn) is the lump sum required to invest today at interest
rate i in order to provide an annuity for n periods.
PVAn = PMT∑1/(1+i)t
We call ∑1/(1+i)t the present value interest factor annuity (PVIFAi,n).
The present value of an uneven stream of future cash flow is the sum of the PVs of the
individual cash flow components.
6. Nominal interest and effective interest - interest may be quoted as inom but compounded
m times a year. The future value for 1 year is then
FV = PV(1+inom/m)m
The effective annual rate (EAR) is defined as the rate under annual compounding that
would produce the same result if we used m compounding periods, i.e.
FV = PV(1+inom/m)m = PV(1+EAR)
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2. EAR = (1+inom/m)m - 1
7. Amortization – An amortized loan is one that paid off in equal payments over a
specified period. An amortization schedule shows how much of each payment
constitutes interest, how much is used to reduce the principal, and the unpaid balance
at each point in time.
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