NCNPV SC EC (DEI -DEP2,e) dr (RECAP RECAP)2,e)
INCVP V, = [SCr ECt + TDSt ] 7 +
1 (1+k)' (1+k)"
S(CG,- _CG, )
+nn(16)
(l+k)"
The first term in equation (16), [SC1 EC, + TDS} ], captures the immediate net
benefit of tax deferral. Note that if the time t selling costs associated with the sale-
purchase strategy and exchange strategy are equal, the advantage of the exchange is equal
to TDS,, the deferred tax liability. To the extent exchanges are more expensive to
execute than sales, SC} EC, will be negative and this incremental outflow will be
netted against the positive deferral benefits.
As noted above, the tax basis of the replacement property is reduced by the amount
of the taxable gain deferred by the exchange, which insures that DEP2 > DEp2 ". The
second term in equation (16) captures the cumulative present value of the foregone
depreciation deductions over the n-year holding period. However, to the extent annual
depreciation deductions are reduced by an exchange, the amount of depreciation
recaptured when the replacement property is sold in year t+n is reduced by an exchange.
The present value of the reduced depreciation recapture taxes is reflected in the third term
in equation (16).
Finally, because the tax deferral associated with an exchange reduces the tax basis
in the replacement property, the taxable capital gain due on the sale of the replacement
property will be larger with an exchange. The negative effects of the increased capital
gain tax liability on the incremental NPV of an exchange are captured by the fourth term
in equation (16).