Handbook of Civil Engineering Calculations

Cost Comparisons with Taxation and Technological Advances

In the preceding material, the costs of alternative proposals were compared by disregard-

ing taxation and assuming that financial and technological conditions remain static. The

cost analysis is now made more realistic by including the effects of taxation and techno-

logical advances. Later the effects of inflation also are included.

CALCULATION OFANNUAL COST

ON AFTER-TAX BASIS

An asset has the following cost data: First cost, $80,000; life, 10 years; salvage value,
$5000; annual operating cost, $3600. The firm that owns the asset is subject to a tax rate
of 47 percent, and its investment rate is 8 percent after payment of taxes. Compute the
after-tax annual cost of this asset if depreciation is allocated by (a) the straight-line
method and (b) the sum-of-digits method.

Calculation Procedure:

1. Compute the annual depreciation charge
   under the straight-line method
   The charge is D = ($80,000 - $5000)710 = $7500.


2. Compute the annual cost under straight-line depreciation
   Most income earned by a corporation is subject to the payment of corporate income tax.
   The effective (or after-tax) income is the difference between the original income and the
   tax payment pertaining to that income. The before-tax investment rate ib = rate of return
   on an investment as calculated on the basis of original income; the after-tax investment
   rate ia = rate of return as calculated on the basis of effective income. Every cost incurred
   in operating an asset serves to reduce taxable income and thus the tax payment. The effec-
   tive cost is the difference between the actual expenditure and the tax savings that results
   from the expenditure. The cost of an asset is said to be computed on an after-tax basis if
   all calculations are based on effective costs and the after-tax investment rate.
   Let t = tax rate and D = annual depreciation charge. Where annual operating costs and
   depreciation charges are uniform, the annual cost A = (P — Z)(CR, n = N 9 i = ia) + Li 0 +
   c(l-0~ Dt. The last term represents the tax savings that accrues from the depreciation
   charge. With n = 10, ia = 8 percent, and t = 47 percent, A = ($80,000 - $5000)(0.14903) +
   $5000(0.08) + $3600(0.53) - $7500(0.47) = $9960.


3. Compute the annual depreciation charges
   under the sum-of-digits method
   As given in an earlier calculation procedure, DU — W(N- U+ 1)/0.5[W(W+ I)], where Dv
   = depreciation charge for t/th year and W= total depreciation. With W= $75,000 and W=
   10, Z) 1 = $13,636, and every depreciation charge thereafter is $1363.64 less than the pre-
   ceding charge.


4. Convert the depreciation charges under the sum-of-digits
   method to an equivalent uniform depreciation charge,
   using an 8 percent interest rate
   Refer to an earlier calculation procedure for converting a uniform-gradient series
   to an equivalent uniform series. The equivalent uniform depreciation charge D = D 1 +