Engineering Economics III

Adjustments We learned how to compute the value of money at different times and under different scenarios. We also learned how to use this knowledge to choose between alternatives. The value of money needs to be adjusted for many reasons. The most important ones are taxes and inflation. Taxes depends on many variables and can be complicated to compute. One important factor to consider is depreciation.

Depreciation Depreciation involves the idea that in the process of producing a product or goods the capital value of equipment is consumed and must be replaced. Depreciation is the allocation of the cost (minus salvage value) of an asset over its useful or depreciable life for tax purposes. Why is it important? How about the time value of money? D total = P - S where: D total : total depreciation allowable over time; P : initial asset value; and S : Salvage value

Book value in year n (BVn): is the initial cost minus depreciation up to this point. It is the remaining value and always include the salvage value. BVn = P - D t where: BVn is the book value in year n, and D t is the depreciation taken at the END of year t or beginning of year n. Notice that: –BV is the value through year n, not at the end. –D t is the depreciation at the end of the previous year.

Computation of Depreciation We will cover some simple methods to distribute the total allowable depreciation among the useful years. Straight-line Depreciation (SLD): –Assuming that the value will drop annually in a linear fashion, then SLD t = 1/N (P - S) –where SLD t is depreciation taken at the end of year t Sum-of-the-years’-digit Depreciation (SOYDD): –total sum of the years’ digit = N/2 (N+1) –SOYDD t = (P - S) –Allows for larger deprecation amounts early in time.

Double declining balance depreciation (DDBD): DDBD t = 2/N (BV t ), where BV t : is the current book value = (P - total depreciation to date) Examples: 15-1, 2, and 3. DEPLETION: The investment in certain resources (such as timber and oil) is allowed to be deducted from income under certain rules. For example, how many units are sold and how many remain.

Example An asset is purchased for $10,000 and is to be depreciated over five years. Salvage value at the end of year 5 is $1,000. Using straight-line depreciation, what is the annual depreciation charge and schedule of book value?

Example Compute the SOYD depreciation for the data in example 15-1: P = $10,000, S = $1000, and N = 5.

Example Compute the DDB depreciation for the data of Example 15-1 and Example 15-2: P = $10,000, S = $1,000 and N = 5.

Taxes Corporate taxable income = gross income + capital gains net of capital loss - current expenses - depreciation - depletion allowances Individual –gross income –adjusted gross income (AGI) = gross income - adjustments ( such as qualifying payments to a retirement plan) –taxable income = AGI - exemptions - larger of standard deductions or itemized deductions.

Before and after tax rate of return: –taxes are levied on investment income. –taxes on investment must be subtracted from the cash flow to achieve a realistic rate of return. –If depreciation is applicable, it can be subtracted from the interest before the taxes are computed. –refer to the tables in example

Inflation Rise in price of a group or basket of commodities not offset by an increase in productivity. Results in a reduction of the real value of money. Measured by cost indices –CPI: consumer price index (Figure 15-3). It follows the cost of standard bundle of consumer goods over time. –CCI: construction cost index. Cost of labor and certain materials –BCI: building cost index. Skilled labors are considered –CWCCI: civil works construction cost index (after 1967). Basically for water resource development projects.

Inflation Rate (f) f is the compound rate of increase in price of a good or fixed package of goods expressed on an annual basis. F a = P a (1 + f) n where: F a : is the actual future price; P a : is the actual price in period zero; and f : is the inflation rate per period n: is the number of periods Cost indices at different times can be used as prices in the equation.

Inflation adjusted rate of return The return on investment is computed in FUTURE dollars, which are different than TODAY’s dollars. There is a different value for the dollar almost every year. To perform realistic analysis, all money must be in today’s dollars (same units). Nominal (total)rate(u): is the rate without accounting for inflation but accounting for taxes. Real rate (i*): is the rate taking the inflation into account. Will result in returns in today’s dollars. u= i* + f + i* f Example: a CD pays 6% if the inflation rate is 4%and assuming no taxes, the real rate is 1.96%

Risk Definition (in relation to engineering economics) A measure of uncertainty and its effect on future income and expenditures. Risk and risk assessment is a complex field of study in itself. In analyzing options in engineering economics we often assume the risks of different alternatives to be equal. “If you lend me money, what is the probability I will pay you back?”

Risk changes throughout a project Evolution of Project Knowledge through Project Development Graph from Project Risk Management Guidance for WSDOT Projects (July 2010)

17 WSDOT’s Cost Estimate and Validation Process (CEVP) Cost estimate involves uncertainty Group of experts quantifies it Cost estimate is a PDF