Handbook of Civil Engineering Calculations

Calculation Procedure:

1. Compute the cash-flow rate
   Where money is invested daily, the cash flow may be considered to be continuous for all
   practical purposes. Assume that deposits are made every day of the year. The cash-flow
   rate R = $30(365) = $10,950 per year.


2. Compute the future-value factor
   Apply the equation CFFV - (ejn - I)Ij 9 where CFFV = future-value factor for a continu-
   ous cash flow of uniform rate. Thus, with n = 1.5 and j =14 percent, CFFV = (e^021 -
   1)70.14=1.669.


3. Compute the future value of the money invested
   SetS = R(CWV) = $10,950(1.669) = $18,280.

Depreciation and Depletion

Notational System

Here D 17 = depreciation charge for Uth year; D = annual depreciation; ^D 17 = cumulative
depreciation at end of Uth year = D 1 + D 2 + D 3 + • • • + DUy where the subscript numbers
refer to the year numbers; P 0 = original cost of asset; P 11 = book value of asset at end of
Uth year = P 0 - 2,D 17 ; IRS = Internal Revenue Service; L = salvage value; W = wearing
value, or total depreciation = P 0 - L\ N = longevity or life of asset, years.

STRAIGHT-LINE DEPRECIATION

The initial cost of a machine, including its installation, is $15,000. The IRS life of this

machine is 10 years. The estimated salvage value of the machine is $1000, and the cost of

dismantling the machine is estimated to be $200. Using straight-line depreciation, what is

the annual depreciation charge? What is the book value of the machine at the end of the

seventh year?

Calculation Procedure:

1. Compute the annual depreciation charge
   When straight-line depreciation is used, the annual depreciation charge is constant,
   D = WIN. Since P 0 = $15,000, L = $1000 - $200 = $800, W= $15,000 - $800 = $14,200,
   W= 10. ThenD = $14,200/10 = $1420.


2. Compute the book value of the machine at the end
   of the seventh year
   ^D 1 = 1D = 7($1420) = $9940. Then P 1 = $15,000 - $9940 = $5060.