Handbook of Civil Engineering Calculations

APPARENT RATES OF RETURN

ONA CONTINUING INVESTMENT

A firm leasing construction equipment purchased an asset for $24,000, charging depreci-
ation on a straight-line basis. The life used was 4 years; salvage value, zero. The asset was
used for 6 years and scrapped for $800. Net revenues obtained from this asset are listed in
Table 11. The firm's normal income was taxed at 50 percent, but the proceeds from the
salvage sale were taxed at 25 percent. What were the apparent rates of return on this asset
investment, after taxes, computed during the life of the asset?

Calculation Procedure:

1. Compute the annual depreciation charge
   Using the straight-line method and a 4-year life, we get the annual depreciation =
   $24,000/4 = $6000, assuming zero salvage. Record the depreciation charge in the third
   column of Table 11.


2. Compute the net profit before taxes
   Deduct from the annual net revenue the annual depreciation charge, Table 11, and enter
   the result in column 4. Thus, for the first year with a revenue of $10,000, the net income
   before taxes = $10,000 - $6000 = $4000.


3. Compute the after-tax profit
   With a tax of 50 percent of the profit before taxes, multiply the value in Table 11, column


4. by 0.50 to determine the after-tax profit. Thus, for year 1, the after-tax profit =
   $4000(0.50) = $2000.


5. Record the asset book value at the beginning of the year
   In this type of calculation, the book value = the unrecovered capital investment for that
   year. Or, for year 1, the book value = $24,000. For year 2, the book value = $24,000 -
   $6000 - $18,000. In this relation, $6000 is the depreciation during year 1.


6. Compute the apparent rate of return
   Divide the after-tax profit for any year by the book value of the asset at the beginning of
   the year to determine the apparent rate of return. Or, for year 2, apparent rate of return =
   $1800/$ 18,000 = 0.10, or 10.0 percent.

TABLE 11. Determination of Apparent Rates of Return

Book value Apparent
Depreciation Net profit Net profit beginning rate of
Year Net revenue, $ charge, $ before tax, $ aftertax, $ of year, $ return, %

1 10,000 6,000 4,000 2,000 24,000 8.3

2 9,600 6,000 3,600 1,800 18,000 10.0

3 8,000 6,000 2,000 1,000 12,000 8.3

4 6,400 6,000 400 200 6,000 3.3

5 4,400 ... 4,400 2,200 ... Infinite

6 2,400 ... 2,400 1,200 ... Infinite

800* ... 800 600

*Income from sale of asset.