## ! TVY, Time Value and Engineering Economy Calculations

TVY is a linked set of notes for decision, engineering economy, investment, and time value analysis. It originated as TVX a part of MYSYS which was coded in APL. Updated versions of TVX  are included in NUNET: The following are links to major topics:
[ Assumptions ] * [ Decision Variable ] * [ Taxes ] * [ Inflation ] * [ Compound Interest Models ] * [ Some Time Value Axioms ] * [ Personal Finance ]

#### NUNET also includes TOOLS and TECHNIQUES for analyzing a variety of situations. They assist evaluations of alternative courses of action. Sample problems provide examples.

TVY is useable with a browser. You can read the notes and do simple calculations using the built in functions.

For more serious work you should use:

a programable or special purpose Hand Calculator, or

the compound interest features available in most Spreadsheets, e.g. EXCEL or Lotus 123

Review TVY first to decide if its facilities are adequate for your purposes. If so then aonther facility is not required. The Time Value material was developed for student use on UNB's local area networks. TVY (and NUNET) may be available on the internet or loaded on a stand alone PC's.

Decision Variable:
Decisions about courses of action are usually judged by their relative merits. Merit is usually very useful if expressed quantitatively in terms of value or money . If the value flows are at several points in time then an accepted systematic method of comparision will be necessary. The usual decision (answer) variables are:

Receipts (inflows) are considered "+" and, Disbursements (outflows) "-".

• Present Value or Present Worth P is the value of a set of payments at time 0 . Present Value of a future Payment P/F ; Present Value of an Annuity Series of uniform payments) ; P/A ; Net Present Value of any series of payments NPV .
• Future Value F is Discounted Value at some time n . Future Value of a Present Value F/P ; Future Value of an Annuity F/A ; Net Future Value of any set of payments NFV .
• The equivalent uniform period amount A or annuity, which is easily related to period budgets.: Auuuity equivalent of a Present Value (Capital Recovery Amount) A/P ; Annuity equivalent of a Future Value (Sinking Fund Amount) A/F .
• i The internal Rate of Return or ROR ( unknown i ) is used for comparison with the yield from an alternative use of resources. TVY does not contain a routine for External Rate of Return used in the past because it was easier to calculate
• Some managers use the time, i.e. number of periods n ( NOP ) to repay a debt or break-even on an activity or investment as a decision criterion. .

The analyses of alternative value flows examines the estimated Receipts + (R) and Disbursements (D) -, the period net worth (C = R-D). Using accepted discounting practice you can determine the discounted (equivalent) P. or F , or i. To a list of the compound interest functions included in TVY.

The present is considered time 0 and the end of the analysis is at time n . The numbers of accounting periods will be n and the number of value flows (including 0 or no flow) is n+1.

Compound Interest Model
The functions use (unless otherwise noted) the end of period discrete compound interest model which assumes all payments (except at time 0 i.e. 'now') are applied as lump sums at the end of an accounting period. Continuous flow models are also discussed.

Assumptions:
The normal assumptions (
principles ) used in routine computation are unless otherwise noted:

• - central concept used for Time Value Calculations. Value amounts must be expressed in their equivalent values at a common point in time..
• CERTAINTY - results are expected to happen as predicted.
• SUPERPOSITION - the principle that the whole is the sum of the parts.
• CONSERVATION - the concept that for a closed system all the parts can be accounted for.
• Sunk Costs (prior decisions) - are not changeable and are irrevalent to current and future decisions.

Analyses similar to the traditional methods described in current and earlier texts, can be carried out using defined compound interest functions.

Uncertainty is modeled by using the Expected Value. The decision variable weights are the probabilities of each of the postulated futures, which must sum to 1.0. e.g. a set of four alternatives could have individual probabilities of 0.2, 0.4, 0.3, and 0.1, the sum of which equals 1.0.

The decision variable values are computed using CERTAINTY. The final Expected Value represents a weighted average of payoff probabilities and is not the forecast of a unique event.

Risk analyses applies probabilities of the estimated value of: receipts and/or disbursements of unusual events. E.g.. if the probability of damage during a period is 0.01 and the probable cost is \$1000. the period probable cost is 0.01 x 1000 or \$10.

There is no explicit function risk probability calculation, but amounts can be multiplied by probabilities using calculator facilities.

The risk costs and/or revenues assume a large number of potential events and as such may not accurately predict costs and/or revenues related to one or a few related events.

Taxes:
Taxes and Tariffs are value flows that should be included in estimates of costs and revenues. There are differences between the tax and tariff regeimes that apply to Public, Corporate, Private, and Personal operations. These regeimes vary locally in their application, so that it is difficult to generalize too deeply. Basically all analyses should consider the local taxes that are applicable at the time of the proposed decision. i.e. the results should be after tax Applicable Tarriff levies should also be included.

Inflation:
Inflation is the change in the value of money over a length of time. Typically inflation tends to decrease the amount of goods and services that can be purchased for a unit of currency. Deflation is the opposite effect as inflation.

Generally a time value analysis should include: an estimate of the effects of inflation and taxes. It is usually difficult to predict the inflation rates for different commodities and/or services the effects are ignored, or grouped as a single rate. Tax rates and effect are locally dependent and the latest data used as information to predict future situations.

^ [NUNET] * [Search Index * Files]

[ Decision analysis considering Time Value ] * [ Time Value and Engineering Economy Topics ]

[Decision, Time Value Analysis, some axioms ] * [Simple Interest Calculations. ]

[Accounting principles and terminology]  * [NOTAX - before or without income tax calculation. ]

[Discounted Cash Flow Analysis]  * [Introduction to Decision Tree Analysis. ]

End to date: 080128, ams