Lecture 3: Annual Worth, and the Temporal Horizon
Future Worth
In the last lecture, we discussed the comparison of alternatives by reducing the
payouts and receipts associated with each strategy to their equivalent present worth.
We can equally well compare them by selecting some future date and calculating their
equivalent worth at that date. This will lead to the same conclusions as the present-worth
comparison. The only reason that we have the two separate methods is that it sometimes
seems more natural to look at a future date; for example, different strategies of
investment for retirement income could be evaluated in terms of the capital they make
available at your retirement date.
Annual Worth
Many of the expenses a company must meet -- rent, wages, taxes -- occur on a regular periodic
basis. It is therefore attractive to present investment options in terms of their
equivalent uniform annual cost. The calculations for this approach are simple --
we convert present worth to equivalent annual worth by multiplying by the appropriate conversion
factor -- but some care is needed in deciding what period of time to consider.
For example, suppose we have a machine that we purchase for a given cost P, and which we expect
to sell after N years for a salvage cost S. What is the equivalent annual cost of the machine?
(This number is useful if we want to compare buying the machine outright with renting it
for a period.)
The equivalent cost is conventionally referred to as capital recovery, and can be
calculated from
CR=P(A/P,i,N) - S(A/F,i,N)
where the first term on the right-hand side is known as the capital recovery factor.
We encounter a possible difficulty if we want to compare two alternatives which have different
life expectancies. There are two ways of dealing with this: firstly, if we expect the two alternatives
to be available into the indefinite future, we can choose a time period which is a common multiple
of their life expectancies. Secondly, if we expect the situation to change before the common
multiple is reached, we can choose a shorter study period and estimate the salvage values of the
equipment at the end of that period.
John Jones
Thu Jul 8 10:38:23 PDT 2008