Quiz 5: Present worth Analysis
Present worth analysis at different life alternatives
For this the PW of the alternatives must be compared over the same # of years and must end at the same time to satisfy the equal-service requirement. For either approach, calculate the PW at the MARR and use the same selection guideline as that for equal-life alternatives. Always use LCM method unless specified. Two ways to approach: 1. LCM: Compare the PW of alternatives over a period of time 'n' equal to the least common multiple of their estimated lives. Assumptions: - The service provided will be needed over the entire LCM yrs. or more. - The selected alternative can be repeated over each life cycle of the LCM in exactly the same manner. - Cash flow estimated are the same for each life cycle 2. Study period: Compare the PW of alternatives using a specified study period of 'n' years: - Once a study period is specified all cash flows after this time are ignored, so use the study period as the value of 'n' for each factor - Short study periods are often defined by management when business goals are short term. Study period are commonly used in equipment replacement analysis. Note: Salvage value is the estimated market value at the end of study period. Note: Overhaul is just another future value that must be added or subtracted, but it does have different periods so watch out for that. Note: If annual revenue is included in the cash flow then you must add the annual revenue with the cost per yr. Note: If salvage value is given in % then multiply that % with the initial cost to get the salvage value.
Present worth analysis of alternatives with equal life
Present worth P is renamed PW of the alternative. The present worth method is popular in industry because all future costs and revenues are transformed to equivalent monetary units NOW; that is all future cash lows and revenues are concerted to present amounts at a specific rate of return, which is the MARR. 1. You must calculate the PW value at the sated MARR for each alternative. For ME alternatives the following guidelines are applied to justify a single project or to select one from several alternatives: One alternative: If PW ≥ 0, the requested MARRR is met or exceeded and the alternative is justified. Two or more alternatives: Select the alternative with the PW that is numerically largest. When alternatives are mutually exclusive (ME) then only one alternative can be chosen so the alternatives are compared against each other in a pair and compete against each other, here the alternative which gives max benefit or has minimum cost effectively has to be opted. For independent projects, each PW is considered separately, that is, compared with the ND project, which always has PW = 0 One or more independent projects: Select all projects with PW ≥ 0 at the MARR When alternatives are independent then multiple alternatives can be chosen so the alternatives are competing against DN (do-nothing) option and are evaluated individually so all the alternatives can be chosen which have better outcome than DN alternative if no restrictions or conditions are given. Note: When your subcontracting, just find the present worth of the annual amounts then add the first cost which would be the same value that you used for the annual amounts. Note: When leasing to future value use (F/P,i,n) to find the future value of the 1st lease and then use (F/A, i, n-1)(P/F,i,1) to find the future worth of the annual amount
Future Worth Analysis
This is exactly like PW analysis, except we must calculate FW. Note: Everything is now backwards. The 1st cost you must use a (F/P) factor and now there's no need to use any factors on the salvage value if it's at the same period as the future 'n'.
Capitalized Cost Analysis (CC)
This is the present worth of a project that has a very long life, its equation: CC = P = A/i A = Interest on a perpetual investment Note: When you dealing with a infinite 'n' project add the initial investment and future values to the equation above (Obviously both must be negatives since its outflow. You may have some finite values that must be converted to A values, so pay attention to that (Somtimes your given a amount after 'n' yrs. that's actually a future value so use (A/F, i, n). Also if you see the word forever it means your using this method described to find the CC. Otherwise you will use the one below. You never consider salvage value. Note: For finite life alternatives, convert all cash flows into an 'A' value over one life cycle and apply the equation above. Note: To find CC for a given cash flow word problem do steps 1-2. To find how much money can be withdrawn for ever skip over to step 3. 1. Find PW for the cash flow 2. Find AW from PW to calculate CC 3. Find FW of PW now this is = to CC and i = what is given now solve for A. Note: Generally for cash flows it helps to think CC as a future value
Formulating Alternatives
Two types of economic proposals: 1. Mutually Exclusive Alternatives (ME): Only one can be selected; compete against each other. Each viable proposal is called an alternative. 2. Independent Projects: More than one proposal can be selected. It competes against the Do Nothing (DN), the DN alternative or project means that the current approach is maintained, nothing new is initiated. No new costs, revenues, or savings are generated. Each viable proposal is called a project. Two types of cash flow estimates: 1. Revenue: Alternatives include estimate of costs (cash outflows) and revenues (cash inflows) 2. Cost: Alternatives include only costs; revenues and savings assumed equal for all alternatives also called a service alternative.
