where UNDBASIS2, is equal to the acquisition price of the replacement property (p,2)
minus the taxable gain that was deferred at time t (DEFGAINt) by executing an exchange
strategy. DEFGAIN, = CG} +RECAP,', and DEP2 e is equal to
12 -LP2 DEFGAIN )
DEP2,e _(1 L D t (14)
RECPER
where L^ is the percentage of the replacement property's acquisition price that is non-
depreciable and RECPER is the allowable cost recovery period for the existing property.
Note that reducing the tax basis of the replacement property by the amount of the
deferred gain insures thatDEP2,s > DEP2 ". Total taxes due on the sale of the
replacement property in year t+n, conditional on an exchange strategy at time t, are
expected to be
TDS, = cgCG, +rRECAP2. (15)
The taxpayer should exchange into the replacement property if the net present value
of the exchange strategy [equation (11)] exceeds the net present value of the sale-
purchase strategy [equation (1)]. To determine the net present value of the sale-purchase
strategy, equations (7) and (8) are first substituted into equation (6). Equations (2), (3),
(4), and (6) are then substituted into equation (1). To determine the net present value of
the exchange strategy, equations (12), (13), and (14) are substituted into equation (11).
Finally, subtraction of equation (1) from equation (11) produces the following expression
for the incremental NPV of the exchange strategy