Page 259 - Plant design and economics for chemical engineers

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INTEREST AND INVESTMENT COSTS 229
value at the end of the useful life will be $2000. The depreciation will be charged
as a wst by making equal charges each year, the first payment being made at the
end of the first year. The depreciation fund will be accumulated at an annual
interest rate of 6 percent. At the end of the life period, enough money must have
been accumulated to account for the decrease in equipment value. Determine the
yearly cost due to depreciation under these conditions.
(NOTE: This method for determining depreciation k based on an ordinary annuity
and iv known as the sinking-fund method.)

Solution. This problem is a typical case of an ordinary annuity. Over a period of 10
years, equal payments must be made each year at an interest rate of 6 percent.
After 10 years, the amount of the annuity must be equal to the total amount of
depreciation.

Amount of annuity = S
Total amount of depreciation = $12,000 - $2000 = $10,000 = S
Equal payments per year = R = yearly cost due to depreciation
Number of payments = n = 10
Annual interest rate = i = 0.06.

From Eq. (21),
0.06
R = S (1 + iin _ 1 = $10,~ ~l.M~lo _ 1 = $759/year

Yearly cost due to depreciation = $759
Example 6 Application of annuities in determining amount of depreciation with
continuous cash flow and interest compounding. Repeat Example 5 with contin-
uous cash flow and nominal annual interest of 6 percent compounded wntin-
uously.

Solution. This problem is solved in exactly the same manner as Example 5, except
the appropriate Eq. (23) for the continuous-interest case is used in place of the
discrete-interest equation.

Amount of annuity = S
Total amount of depreciation = $12,000 - $2000 = S
Equal payments per year based on continuous cash flow and interest
compounding = E = yearly cost due to depreciation
Number of years = n = 10
Nominal interest rate with continuous compounding = r = 0.06

From Eq. (231,
0.06
K=s+ = %730/year
e = $10~meco.06xlo, = 1
Yearly cost due to depreciation = $730