Review Quiz 2

1. Review Quiz 2 COMPARING ALTERNATIVES

2. RULE FOR CHOOSING AMONG ALTERNATIVES • The alternative that requires the minimum investment and produces satisfactory functional results will be chosen unless the incremental capital associated with an alternative having a larger investment can be justified with respect to its incremental savings (or benefits ). • The alternative requiring the least investment is the base alternative. • Rule ensures that as much capital as possible is invested at a rate of return equal to or greater than the MARR.

3. ENSURING COMPARABLE BASIS FOR SELECTING MUTUALLY-EXCLUSIVE ALTERNATIVES Include any economic impacts of alternative differences in estimated cash flows – Two Rules: Rule 1. When revenues and other economic benefits are present, select alternative that has greatest positive equivalent worth at i= MARR and satisfies project requirements. Rule 2. When revenues and economic benefits are not present, select alternative that minimizes cost.

4. INVESTMENT ALTERNATIVES Those alternatives with initial (i.e., front-end) capital investments(s) that produce positive cash flows from increased revenue, savings through reduced costs, or both.

5. COST ALTERNATIVES Those alternatives with negative cash flows except for a possible positive cash flow element from disposal of assets at the end of the project’s useful life.

6. USEFUL LIFE • Useful life of an asset is the time period during which it is kept in productive use in a trade or business.

7. REPEATABILITY ASSUMPTION • The study period over which the alternatives are being considered is either indefinitely long or equal to a common multiple of the lives of the alternatives. • The economic consequences that are estimated to happen in an alternative’s initial useful life span will also happen in all succeeding life spans (replacements) Actual situations in engineering practice seldom meet both conditions

8. COTERMINATED ASSUMPTION • A finite and identical study period is used for all alternatives • This planning horizon, combined with appropriate adjustments to the estimated cash flows, puts the alternatives on a common and comparable basis • Used when repeatability assumption is not applicable • Approach most frequently used in engineering practice

9. USING RATE OF RETURN METHODS TO EVALUATE MUTUALLY EXCLUSIVE ALTERNATIVES The best alternative produces satisfactory functional results and requires the minimum investment of capital, unless a larger investment can be justified with respect to the incremental costs and benefits it produces

10. SELECT THE EQUIVALENT WORTH ALTERNATIVE WITH THE GREATER WORTH • If : PWA (i) < PWB (i) then • PWA (i) ( A / P,i,N ) < PWB (i) ( A / P,i,N ) and • AWA (i) < AWB (i) similarly • PWA (i) ( F / P, i, N ) < PWB (i) ( F / P, i, N ) and • FWA (i) < FWB (i) Select alternative B

11. RATE OF RETURN METHOD RULES 1. Each increment of capital must justify itself by producing a sufficient rate of return on that increment. 2. Compare a higher investment alternative against a lower investment alternative only when the latter is acceptable. 3. Select the alternative that requires the largest investment of capital as long as the incremental investment is justified by benefits that earn at least the MARR. This maximizes equivalent worth on total investment at i = MARR.

12. INCREMENTAL INVESTMENT ANALYSIS PROCEDURE ( Helps avoid incorrect ranking problem ) 1. Order the feasible alternatives. 2. Establish a base alternative a. Cost alternatives -- The first alternative is the base b. Investment alternatives - If the first alternative is acceptable, select as base. If the first alternative is not acceptable, choose the next alternative 3. Use iteration to evaluate differences (incremental cash flows) between alternatives until no more alternatives exist a. If incremental cash flow between next alternative and current alternative is acceptable, choose the next b. Repeat, and select as the preferred alternative the last one for which the incremental cash flow was acceptable

13. IMPUTED MARKET VALUE TECHNIQUE • When current marketplace data is unavailable for an asset, it is sometimes necessary to estimate the market value of an asset • Referred to as an imputed or implied market value • Estimating is based on logical assumptions about the remaining life for the asset MVT = [ EW at the end of year T of remaining capital recovery amounts ] + [ EW at the end of year T of original market value at the end of useful life ] T < useful life EW is equivalent worth at i = MARR

14. CHAPTER 7 DEPRECIATION AND INCOME TAXES

15. DEPRECIATION • Decrease in value of physical properties with passage of time and use • Accounting concept establishing annual deduction against before-tax income - to reflect effect of time and use on asset’s value in firm’s financial statements - to match yearly fraction of value used by asset in production of income over asset’s economic life

16. DEPRECIATION METHODS Time Implemented Method Before 1981 (SL) Straight-Line (DB) Declining Balance (SYD) Sum-of-the-years-digits > 1980 > 1987 (ACRS) Accelerated Cost Recovery System Implemented by (ERTA) Economic RecoveryTax Act of 1981 >1986 (MACRS) Modified Accelerated Cost Recovery System Brought about by (TRA 86) TaxReform Act of 1986

17. STRAIGHT-LINE (SL) METHOD • Simplest depreciation method • Assumes constant amount is depreciated each year over depreciable (useful) life d k = ( B - SVN ) / N d k* = kdk for 1 < k < N BVk = B - d k* • This method requires an estimate of the final SV ( also the final book value at the end of year N )

18. DECLINING BALANCE (DB) METHOD • Sometimes called constant percentage method or Matheson formula • Assumed annual cost of depreciation is fixed percentage of BV at beginning of year • R is constant R = 2 / N when 200% declining balance used R = 1.5 / N when 150% declining balance used d 1 = B ( R ) d k = B ( 1 - R ) k - 1 ( R ) d k* = B [ 1 - (1 - R ) k ] BV k = B ( 1 - R ) k BV N = B ( 1 - R ) N • Because declining balance method never reaches BV = 0, it’s permissible to switch from this to straight-line method so asset’s SVN will be zero or other desired value

19. UNITS-OF-PRODUCTION METHOD • Not based on the idea that decrease in value of property is a function of time • Decrease in value is mostly a function of use • Method results in cost basis (minus final SV) being allocated equally over the estimated number of units produced during useful life of asset. Depreciation per unit of production = ( B - SVN ) / ( Estimated lifetime production in units )

20. CALCULATING DEPRECIATION DEDUCTIONS UNDER MACRS Depreciation Personal Approach Method Property Class GDS 3-, 5-, 7- 200% DB method 10-year with switch to SL when deduction greater GDS 15- & 20- 150% DB method year with switch to SL when deduction greater GDS residential SL over fixed GDS recovery & real rental periods ADS personal & SL method over fixed ADS real recovery periods

21. HALF-YEAR TIME CONVENTIONS FOR MACRS DEPRECIATION CALCULATIONS • All assets placed in service during the year are treated as if use began in the middle of the year -- 1/2- year depreciation is allowed • If asset is disposed of before the full recovery period is used, only half of the normal depreciation deduction can be taken for that year

22. MACRS DEPRECIATION GDS OR ADS ? GDS ADS Ascertain property class; Same as recovery period for personal Ascertain recovery period Compute depreciation amount; Asset’s cost basis SL = -------------------------- Recovery period Obtain recovery rates Compute depreciation deduction in year k (dk) by multiplying cost basis by recovery period. Compute depreciation deduction in year k (dk)

23. CALCULATING TAXABLE INCOME- NET INCOME BEFORE TAXES ( NIBT ) - • Calculate Gross Income Gross Profits ( revenues from sales - cost of goods sold ) + income from dividends, interest, rent, royalties, and gains (losses) from sale or exchange of capital assets • Deduct all ordinary and necessary operating expenses to conduct business Include interest but exclude capital investments • Deduct depreciation taxable income = gross income - all expenses - depreciation

24. EFFECTIVE (MARGINAL) CORPORATE INCOME TAX RATE • As personal income tax rates are based on income brackets, so, too, is corporate income tax • Depending on the bracket a firm’s income falls within, the marginal federal rate can vary from 15% to a maximum of 39% (for incomes between $100,000 and $335,000) • Incomes above $18,333,333 are taxed at a flat rate of 35% • TRA 86 responsible for lowering maximum rate from 46% to 35% • Also created alternative minimum tax (AMT)

25. CHAPTER 8 PRICE CHANGES AND EXCHANGE RATES

26. RELATING ACTUAL DOLLARS TO REAL DOLLARS • Use the following to convert actual dollars, as of time k, to real dollars of constant purchasing power (R$)K = (A$)K [1/ (1+f)]K-b = (A$)K(P / F, f %, k-b) • The equation changes as follows for a specific type cash flow (i.e. specific good or service “j ” ) (R$)K j = (A$)K j[1/ (1+f)]K-b = (A$)K j (P / F, f %, k-b) • In the base period, purchasing power of actual dollar and real dollar are the same

27. RELATING COMBINED AND REAL INTEREST RATES AND GENERAL INFLATION RATE i r = ( i c - f ) / ( 1 + f ) • Similarly, current-dollar internal rate of return is related to the real rate of return in the following way: IRR r = (IRR c - f ) / ( 1 + f )

28. MARKET INTEREST RATE RATE OF RETURN RELATIVE TO U.S. DOLLARS i f c = i US + f e + f e ( i US ) i US = ( i f c - f e ) / ( 1 + f e ) • i US = market (combined ) interest rate of return relative to US dollars • i f c = market (combined ) interest rate of return relative to foreign country currency • fe = Annual rate of change in exchange rate -- annual devaluation rate -- between foreign country currency and US dollar • fe +: foreign currency devalued relative to dollar • fe - : dollar devalued relative to foreign currency