We engineers exist, by definition, on the interface between the economic and sub-economic. It is often our job to try and define the boundary, and it is often defined by technological factors that have to be developed to a new point. Most colleges and universities give engineering students a course on engineering economics, but this does not translate to widespread use in practice. The following is a quick overview of engineering economics.

## Time Value of Money

Most engineers are familiar with the time value of money. A project earning $5 million in five years is earning less as one that earns $5 million right now. The compound interest rate formula is:

F = P(1+ i)^{N}

Where:

- F = Future value of a cash payment
- P = Today’s value
- i = interest rate
- N = number of compounding periods

* Nominal Interest* is the stated rate of interest for a given period.

*can be different as it takes into account the compounding within the period.*

**Effective interest**## Net Present Value

Net Present Value is the result when a series of cash flows (inflows and/or outflows) is converted into today’s value. It is particularly useful for projects where a large capital outlay is required upfront, like mines, software projects, or oil and gas facilities. The formula is the same as above, but each individual cash event is brought back to today and the result added up.

Net Present Value analysis should always use an interest rate called the * Minimum Attractive Rate of Return*, or MARR. This value is set by the organization financing the project and it takes into account the borrowing rate of the organization, the opportunity cost of the project, and the normal rate of return of other projects being funded.

## Internal Rate of Return

This metric measures the yield as a percentage of investment over time, and can be viewed side-by-side with the Net Present Value to determine project feasibility. It is also a good variable to compare to the funding organization’s MARR, given other projects and funding priorities.

Internal Rate of Return (IRR) is the break-even interest rate at which the present worth of the project’s cash outflows equals the present worth of the cash inflows. Each inflow and outflow must be converted to a present value to determine the IRR.

## Depreciation

Almost everything engineers build depreciates (I have to say ‘almost’ just in case, but I actually can’t think of anything). Most projects start with a * capital expenditure*, require an ongoing

*, and at any point in time have some sort of*

**operating expenditure***, even if you have to spend some money taking it apart to realize the value.*

**salvage value**How to determine the value of the asset from these three factors at any time in the life cycle is the subject of accounting textbooks, but the engineer should be familiar with the basics.

Depreciation methods include:

- Straight line
- Accelerated (declining balance, sum-of-years’ digits)
- units-of-production

## Methods of Financing

Project financing falls into two broad categories:

uses earnings or funds raised from the issuance of stock to finance a capital investment.**Equity financing**uses money raised through loans or by the issuance of bonds to finance a capital investment.**Debt financing**

* Leases* are financial instruments by which a firm obtains and uses capital equipment without purchasing and owning it outright. The mandatory elements of a lease contract include:

**Rental Payments:**The payments from the lessee to the lessor in exchange for the use of the equipment.**Expiration Dates:**The lease is negotiated for a finite period of time after which it may be renewed or renegotiated.**Return of Equipment:**Typically, at the expiration of the lease, the leased item returns to the lessor who may re-lease it or dispose of it.

## Benefit-Cost Analysis

This is a common method of analysis for public projects because benefits of a non-monetary nature can be factored into the analysis, like the value of a road. Public projects also have their difficulties, such as:

- Identification of all the diverse users of a project
- Quantification of the benefits
- Selection of an appropriate discount rate for present value

## Risk Analysis

There are three main ways to assess project risk:

**Sensitivity Analysis:**Identifying the project variables which have the greatest effect on project acceptability.**Breakeven Analysis:**Identifying the value of a particular variable that causes the project to break even.**Scenario Analysis:**Comparing a base case or expected project measurement to one or more additional scenarios such as best and worst case.