14 Fresh Chapter

Chapter 2

Engineering Economic Analysis Fundamentals

Introduction to the Chapter

This chapter is perhaps one of the most important to provide the fundamental concepts and terminology used in engineering economic analysis. This chapter discusses the concept of time value of money and economic equivalence, the variables of analysis, setting up the problem and the input variables, the different ways to utlilize interest rates, and the basic economic equivalence functions to be used throughout the book. 

Learning Objectives

1. To understand the fundamental concepts of time value of money and economic equivalence
2. To describe the variables of engineering economic analysis
3. To be able to setup the input variables for engineering economic analysis problems within a cash flow diagram
4. To be able to calculate simple and compound interest and understand the impact of inflation upon interest rate

See Skill-builder 2.1

1.0 Concepts of Engineering Economic Analysis – Time Value of Money and Others

Time Value of Money (TVM)

The principal concept that envelops engineering economic analysis is the concept of being able to invest in projects that will provide financial benefits, versus investing that money in other projects or financial portfolios that will make a satisfying return, called the Minimum Acceptable Rate of Return (MARR). The return on the investment is realized because of the concept of the time value of money. Time Value of Money (TVM) is the concept that money can be invested at a certain interest rate and increase in value, over time through receiving the interest from the investment. A simple illustration is putting $100 in a savings bank account that earns high interest, say 5%, at the present time, t, where t represents a point in time. 

Economic Equivalence

The concept of economic equivalence conveys that $100 today is not equivalent to $100 in the future. Because you could be earning interest on the $100, if you were receiving 5% interest, the $100 today is worth $105 one year in the future. So if someone asked you to take $100 today, or $105 in the future, you should be indifferent to the time difference at an interest rate of 5%, because they are economically equivalent. This assumes that you don’t need the money for something else right now! The problems in this book are based on converting cash flows that are received and/or paid at different times during the project, to a single point in time, such as, time 0, or the present time, the future time, at time t, which could be five years in the future, or an equal amount each period of the project life. 

This is a blockquote!

End of Period Convention

Another concept that is a typical standard used in engineering economic analysis studies is that interest is accrued across the time period, but received at the end of the period. In Excel, when we use the financial functions that we’ll discuss later in this chapter, the default is to use the end of period convention. If our $100 will remain in the savings bank account for 1 year, and you receive 5% interest, or of interest, it is received at the end of the year. So, you would then have $105 or have dollars in your account at the end of the year. Note that the asterisk, or , stands for multiplication. This end of period convention greatly simplifies calculations for the economic decisions.

2.0 Variables of Analysis

There are several variables that are used in the engineering economic analyses. Following are the variables and their definitions.

= Interest rate = the rate that is charged on a loan, or earned on an investment

t = time period = the specified time period that a cash flow is received or paid out

n = nper = number of interest periods of the project life

P = PV = NPV = Present Value or Net Present Value, the value of a cash flow series at the present time

F = FV = Future Value, the value of a cash flow series at a date in the future, usually at least one year or interest period in the future, but typically at the end of the project life

A = PMT = Equal series of cash flows for the life of the project

See Skill-builder 2.2

3.0 Cash Flow Diagrams – Setup of Variables

Cash flow diagrams are a useful tool to setup the known and unknown variables in the project. They represent the costs and benefits of an investment project. The cash flow diagram is a timeline, beginning at time 0, the present time when the project starts, and going through the life of the project. The interest compounding period is typically a year in engineering projects, so the timeline is divided into the number of interest periods equally spaced on the timeline. Arrows that represent cash inflows, or money being received by the company making the investment point vertically up on the timeline, shown as $3,000, in years 1 through 5 on the diagram, in Figure 1. The money being received can be interest on a financial investment, revenues from sales, savings in expense, etc. Arrows that represent cash outflows, or money going out of or paid by the company in initial investment costs ($5,000 at time 0 on the diagram), or other operating or maintenance costs ($1,000 in years 3, 4, and 5) are shown as arrows that point vertically down the page from the timeline. The unknown variable, in this example, the future value of the cash flows is shown as a thick green arrow, pointing up on the cash flow diagram. Before we do the calculations, we do not know if the unknown value is positive (cash inflow) or negative (cash outflow), but because we desire a positive value, we have it point vertically up as if it is a cash inflow. The problem statement may also specify whether the unknown variable is positive or negative. We can add the known interest rate, , as a percentage, above the cash flow diagram, where there is room. 

Cash flows for Cash Flow Diagram Sample

·       $3,000 cash inflows in years 1 through 5

·       $5,000 cash outflow at time 0

·       $1,000 cash outflows in years 3, 4 and 5

·       Unknown future value of the cash flows, at the end of year 5.

Only initial known and unknown variables are represented on the cash flow diagram, no calculations of interest are shown on the diagram. This is to represent ONLY the input variables of the initial problem to be solved. 

Figure 2.1: Cash Flow Diagram Sample

The net cash flow table is shown in Table 2.1. The table shows cash inflows, cash outflows, and net cash flows (cash inflows minus cash outflows). 

Table 2.1 Net Cash Flow Table for Sample

Example 1: Cash Flow Diagram

The Industrial Engineer is investigating purchasing a new palletizer for placing the products when they are assembled and then shrink wrapped. The initial cost of the palletizer including installation costs are $175,000, at time 0. The project will save the salary expense of 2 operators, which can be moved to other positions in the company, at a savings of $100,000, starting at the end of year 1, going through the project life of year 5. There is a salvage value of being able to re-sell parts of the palletizer at the end of the project life for $15,000. There is an annual operating and maintenance cost of the palletizer of $20,000 per year, starting at the end of year 1 and going through year 5. We want to calculate the unknown Present Value (PV) of the net cash flows. The cash flow diagram is shown in Figure 2.2. 

Figure 2.2 shows all of the cash flows described. 

·       The cash inflows are the $100,000 per year, from year 1 through 5, and the $15,000 salvage value at the end of year 5.

·       The cash outflows are the $175,000 cost of the palletizer at time 0, and the $20,000 per year annual operating and maintenance costs.

Figure 2.2 Example 1 Cash Flow Diagram with Individual Cash Flows Shown

A cash flow table can also be constructed in Excel, which will be used to apply the financial functions to perform the engineering economic analysis of the cash flows. Table 2 illustrates the cash flow table for Example 1.

Table 2.2 Cash Flow Table for Example 1

The cash flow diagram can also show the net cash flows, where the cash outflows are subtracted from the cash inflows during each period, as shown in Figure 3.

Figure 2.3 Example 1 Cash Flow Diagram with Net Cash Flows Shown

Note: In Excel, the currency formatting for negative currency is typically shown as a number in red font, within parentheses. Another common currency formatting for negative currency is showing the number in black font within parentheses. We will use the red font in parentheses to denote negative currency.

Skill-builder 2.3: Creating a Cash Flow Diagram and Cash Flow Table 

For the following cash flows described, create a cash flow diagram and cash flow table. Show all cash inflows and outflows, do not show the net cash flows for each period. The solution can be found at the end of the chapter.

The initial investment for a Customer Relationship Management (CRM) software is $250,000 purchased at the beginning of the project, in year 0.

·       The project life is 6 years.

·       The interest rate is 8%.

·       The license fee per year, starting in year 1 and going through year 6 is $25,000

·       There is an upgrade cost of $15,000 in year 3.

·       You anticipate increased revenues of $80,000 per year due to better customer relationships and sales.

·       You are trying to find the present value of the cash flows.

4.0 Interest Rates

There are two basic types of interest, simple and compound interest. We first present simple interest, to understand the concept of interest, and then describe compound interest which will be used as the interest mechanism throughout the remaining chapters of the book.

4.1 Simple Interest

4.1.1 Simple Interest for a Savings Account or Investment

When someone places money in a savings account, or another type of financial investment, the goal is to earn a return on this investment, with the simplest mechanism, receiving interest from the financial institution. 

If a person places $100, the principal amount (beginning amount) in a savings account, that makes 5% interest for a year, at the end of the year, they will receive interest of This $100 is also called the present value at time 0. If they then take the principle and the interest out of the bank, they will have $105.00 as the future value (1 year in the future from the present value at the beginning of the investment period). 

If they place the $100 in the savings account at time 0, and leave it for 2 interest periods, or years, then they will have or $110.00 

The formula for the simple interest calculation is:  

Where: 

Total simple interest earned

P = principle or Present Value

= interest rate in percentage or decimal

n = number of interest periods

This is called simple interest because the saver does not receive interest on the interest, it is simply interest on the principal amount for the number of periods that the principal amount remains in the 

investment or savings account. 

The Future Value or total amount of the principle plus the interest using simple interest is not calculated as:

4.1.2 Simple Interest for a Loan

Let’s look at simple interest from the perspective of a loan, such as a car loan or a home mortgage loan. The same concept applies but you are paying interest, not receiving it. You have a principal amount at the beginning of the loan at time 0. You are charged an interest rate, and you pay back the principle plus the interest at the end of the interest periods. 

You borrow a certain amount of money to purchase a car or loan, which is the principal amount and the present value at time 0, at the beginning of the loan. If simple interest is used (which it rarely is), then the borrower would pay the total amount of the interest calculating in the same way as above in the discussion of the savings account. If the total amount of the car loan was $25,000, the interest rate is 5%, and the number of interest periods is 5 years, then the total amount of interest is 

P = $25,000

= 5%

n = 5 

The future value of principle plus interest = 

Or

See Skill-builder 2.4

4.2 Compound Interest

4.2.1 Compound Interest for a Savings Account or Investment

We illustrated simple interest mainly to introduce the concept of interest earned or paid. However, in reality, interest is almost always compounded, on the interest, as long as you keep the interest in the investment, or you don’t pay back the loan until the end of the loan repayment period. This better aligns to the concept of making engineering economic investments, where you are using the equipment to produce parts for the life of the project, you receive “interest” or “earnings” on your investment, and this interest is compounded each compounding period.

The total interest earned or paid; is calculated as:

Where:

I_t = Total Interest at end of time period t

P = Principle or Present Value

= Interest rate

For example, the Interest earned for the savings account with compound interest for two years, is calculated as follows:

P = $100

= 5%

t = 2

For our same example, if you wanted to know how much interest is earned after 1 year, the same formula is used, with t = 1, and the is $5. Notice that there is an additional $.25 due to the compounding effect of the compound interest mechanism. 

For the end of each year the Interest is calculated as:

The Future Value for each year adds the Principle plus total interest earned through the end of the period:

4.2.2 Compound Interest for a Loan

For our car loan example now with compounding interest, the Interest at the end of each year is calculated as follows.

P = $25,000

= 5%

n = 5 

Principle = P = PV	$25,000
= interest rate	5%
Number of periods	5
Period	Total Interest per period
1	$ 1,250.00
2	$ 2,562.50
3	$ 3,940.63
4	$ 5,387.66
5	$ 6,907.04	Total Compounded interest through year 5
FV	$ 31,907.04
	$ 6,250.00	Total Simple interest through year 5
	$ 657.04		Difference in interest

Notice the difference in interest paid between the simple and compounded interest for the car loan is $657.04.

See Skill-builder 2.5

4.3 Minimum Acceptable Rate of Return

The interest rate, , selected for engineering economic analysis can be referred to as a Minimum Acceptable Rate of Return (MARR), which is typically set by the finance or treasury department in the organization. The department calculates this rate based on the return on their investments, if they were to invest in financial investments versus investing in engineering and operational improvement investments. The MARR can also be considered as the interest rate at which the organization could acquire funds to invest in engineering and other capital projects. Capital projects are strategic projects that improve the financial viability of a company, through improving the operations, products, customer service, etc., that a customer will pay for. 

Capital can be obtained in two main ways: (Blank and Tarquin, 2016)

Equity financing: The organization uses their own funds from cash on hand, stock sales or retained earnings. 

Debt financing: The organization borrows funds, and pays the principle plus interest back to the organization that lends them the funds. Typical investment types that provide capital through debt financing are bonds, loans, mortgages, venture capital, and credit cards. 

4.4 Interest Rate Before and After Taxes

The interest rate, , that is typically used is an after tax rate. If the analysis is performed with an after tax rate, and the Present Worth (discussed in Chapter 5) is close to zero, a before tax rate can be calculated using an effective tax rate (Blank and Tarquin, 2016)

The Before-tax MARR is calculated as:

After tax interest rate or MARR =

Effective tax rate =

Before-tax MARR =

For example, if the after tax interest rate or MARR = = 14%, and the effective tax rate is 40%, then

Before-tax MARR =

The interest rate used is then 23.3% in the engineering economic analysis instead of 14%, if the estimates are before tax estimates.

See Skill-builder 2.6

4.5 Interest Rate Impacted by Inflation

Inflation is a rise in prices of commodities over time, which reduces the purchasing power over time, so a dollar today, doesn’t buy as much product as a dollar tomorrow, next week or next year. We discuss inflation in Chapter 14.

4.6 Interest Rate for Compounding Periods other than Years

Generally, the lives of engineering investment projects are multiple years. A new robot purchased to automate a manufacturing process should last for several years. Therefore, interest compounding periods are typically a year, and the compounding goes on for the life of the project. 

However, there are times when the compounding period is less than a year, such as months, semi-annually (twice a year), quarterly (four times a year), etc. Examples are interest compounded monthly in a savings account, bond interest compounded semi-annually, car loans or credit cards interest compounded monthly. 

It is straightforward to calculate the engineering economic equivalents that we’ll see in the following chapters as long as the engineer aligns the number of interest compounding periods appropriately. For instance, if compounding is monthly, and the annual or nominal interest rate is 12%, then the monthly compounding interest rate is . 

Then the number of compounding interest periods should be multiplied by the project life, or life of the loan, such as,

One aspect of interest compounding more frequently than a year is that the nominal or annual interest rate does not equate to the effective rate, or the actual impact of the interest compounding. 

The effective rate is calculated as:

Where:

4.6.1 Example of Interest Compounding More Frequently than Annually

An example of the impact of interest compounding more frequently than annually, and the impact on the effective interest rate follows:

= 12%

=

The EFFECT function in Excel calculates the effective interest rate:

= EFFECT (nominal_rate, npery) = EFFECT (12%, 12) = 12.68%

Skill-builder 2.7: Effective Interest Rate

If interest for a savings account is compounded quarterly, and the nominal rate, is 8%, what is the effective interest rate, ?

The solution can be found at the end of the chapter.

5.0 Conclusions

In this chapter we covered the basic terms needed for understanding engineering economic analysis techniques. We discussed the concept of time value of money and economic equivalence, the variables of analysis, setting up the problem and the input variables, the different ways to use interest rates, and the basic economic equivalence functions to be used throughout the book. 

6.0 Reference

Blank, L. and Tarquin, A. (2018), Engineering Economy, Eight Edition, McGraw-Hill, New York, NY.

Skill-builder Solutions

Skill-builder 2.3: Creating a Cash Flow Diagram and Discounted Cash Flow Table

Solution Cash Flow Diagram

Solution: Cash Flow Table

Year (Period)	Cash Inflows	Cash Outflows	Net Cash Flows
0		$250,000	($250,000)
1	$80,000	$25,000	$55,000
2	$80,000	$25,000	$55,000
3	$80,000	$40,000	$40,000
4	$80,000	$25,000	$55,000
5	$80,000	$25,000	$55,000
6	$80,000	$25,000	$55,000

Skill-builder 2.7: Effective Interest Rate

r = 8.24%

= 8%

=

The EFFECT function in Excel calculates the effective interest rate:

= EFFECT (nominal_rate, npery) = EFFECT (8%, 4) = 8.24%