- Determine whether the existing machine should
be retired now
Since the cost of retaining the machine for 1 additional year ($4490) is less than the annu-
al cost of the new machine ($4800), the existing machine should not be retired at present.
Effects of InflationNotational SystemHere C 0 and C 1 are the costs of a commodity now and 1 year hence, respectively, and/=
annual rate of inflation during the coming year with respect to this commodity. Then/=
(C 1 - C 0 , or C 1 = C 0 (I +/). Also, Cn = cost of the commodity n years hence. If the annual
rate of inflation remains constant at/ then Cn = C 0 (I +/)" = C 0 (SPCA, / =/). In the sub-
sequent material, it is understood that the given inflation rate applies to the asset under
consideration.
DETERMINATION OF REPLACEMENT COST
WITH CONSTANT INFLATION RATE
A machine has just been purchased for $60,000. It is anticipated that the machine will be
held 5 years, that it will have a salvage value of $4000 as based on current prices, and that
the annual rate of inflation during the next 5 years will be 7 percent. The machine will be
replaced with a duplicate, and the firm will accumulate the necessary capital by making
equal end-of-year deposits in a reserve fund that earns 6 percent per annum. Determine
the amount of the annual deposit.
Calculation Procedure:- Compute the required replacement capital
Both the cost of a new machine and the salvage value of the existing machine increase at
the given rate. Thus, the amount of money the firm must accumulate to buy a new ma-
chine is ($60,000 - $4000)(1.07)^5 = $56,000(1.403) = $78,568. - Compute the annual deposit
Use this relation: Annual deposit R = 5(SFP). With i = 6 percent and n = 5, R =
$78,568(0.17740) = $13,938.
DETERMINATION OF REPLACEMENT COST
WITH VARIABLE INFLATION RATE
In the preceding calculation procedure, determine the amount of the annual deposit if the
annual rate of inflation is expected to be 7 percent for the next 3 years and 9 percent there-
after.