# Cost and Time Value of \$\$ - PowerPoint PPT Presentation

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Cost and Time Value of \$\$. Prof. Eric Suuberg ENGINEERING 90. Cost and Time Value Lecture. What is our goal? To gain an understanding of what is and what is not a good project to undertake from a financial point of view. What are our tools? Material presented by Prof. Crawford

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Cost and Time Value of \$\$

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## Cost and Time Value of \$\$

Prof. Eric Suuberg

ENGINEERING 90

### Cost and Time Value Lecture

• What is our goal?

• To gain an understanding of what is and what is not a good project to undertake from a financial point of view.

• What are our tools?

• Material presented by Prof. Crawford

• Discounting / Time Value of Money

• Tax Savings through Depreciation

### So, what are we starting today?

• Go through some of the “fun” math for Present Value Calculations

• Do a teaching example of purchasing a machine for a manufacturing plant

• Talk about costs – both the obvious kind as well as the non-obvious types

• Time value of money calculations

• Cost Comparisons

• Depreciation

• Put it all together – inc. continuous discounting and after-tax cost comparisons

### Have I Got a Deal for You

• Would you be interested in investing in a company that has \$1 million in annual sales?

### What More Would You Like to Know?

• Annual operating expenses (salaries, raw materials, etc.)

• Suppose these were \$900,000/yr

• Are you interested? (Come on - I’ve got to know now. There are a lot of people interested)

### Profit

Profit = Sales (revenues) - expenses (costs)

• Basis for taxation - What goes into the calculation is of great interest to Uncle Sam

### In Our Example

• Profit = \$1,000,000/yr - \$900,000/yr= \$100,000/yr

• Is this a good business?

### What Would You be Willing to Pay Me for this Business?

• \$1 million?

\$2 million?

• How do you decide?

• This is one of the questions that we will answer in this part of the course.

### Present Value Calculations

• Essential element of evaluating a business opportunity

• Different variants

• Simple discounting

• Replacement and abandonment

• Venture Worth, Present Value, Discounted Cash Flow Rate of Return

Information Required

### What information do we need?

• Investment (Capital assets, working capital)

• Operating Costs

• Fixed

• Variable

• Interest Rate

• Tax Rate

• Depreciation Method

• Revenues

### Capital Investment - Facility

• Purchased Process Equipment

• Field Constructed Equipment

• Wiring, Piping, Instrumentation

• Construction, Installation Costs

• Site Preparation, Buildings

• Storage Areas

• Utilities

• Services (Cafeterias, Parking lots, etc.)

• Contingency

### Capital Investment- Manufacturing

• Costs of process equipment may represent only 25% of actual investment!

• Costs of process equipment scale according to the “six-tenths rule”

• C2/C1 = (Q2/Q1)0.6

• See, for example:

• “Cost and Optimization Engineering” by F.C. Jelen and J.H. Black, McGraw-Hill, 1983.

### Other Items

• Working Capital

• Raw materials and supplies inventory

• Finished goods in stock and Work in Progress

• Accounts Receivable, Taxes payable

• Operating Costs

• Labor and Raw Materials

• Utilities and Maintenance

• Royalties

• Fixed Costs

• Insurance, rent, debt service, some taxes

### Time Value of Money

• \$1 today is more valuable than the promise of \$1 tomorrow

• Has nothing to do with inflation

• “Discounting” is the term used to describe the process of correcting for the reduced value of future payments

• Discount rate is the return that can be earned on capital invested today

### Future Worth of an Investment

• P = Principal

• i = Annual Interest Rate

• S = Future value of investment

Compound Interest Law

S1 = P (1+i) at the end of one year

S2 = S1(1+i) = P(1+i)2 at end of year 2

Sn = P (1+i)n at end of year n

### Present Value of a Future Amount

P = Sn / (1 + i)n

= Sn (1 + i)-n

(1 + i)-n = Present Value Factor or

Discount Factor

The promise of \$1 million at a time 50 years in the future @ i = 15%/yr

P = \$1,000,000(1+0.15)-50 = \$923

### Simple Example

• What is the PV of \$10.00 today if I promise to give it to you in fifteen years, given a discount rate of 20%?

• PV = 10(1.20)-15

• = \$.65

• Not enough to buy a soda these days

### Take Home Message

• Not all dollars of profit are the same

• Those that come earlier are “worth” more

• Do you buy the better made equipment with the higher price tag? or the low first cost equipment that has high maintenance?

### Cost Comparisons

What are we doing here?

• Comparing one project to another

• Deciding to buy the expensive computer that has free maintenance versus the cheap one that makes you pay for service

vs.

### Simple Cost Comparisons

• Strategy

• Reduce costs (and/or revenues) to a common instant, usually the present time

• Work on full year periods

• approximate costs or revenues which occur over the year as single year-end amounts

• Basic Rule: All comparisons must be performed on an equal time period basis

• Repeatability Assumption (to get to same time basis)

• Annuity Comparison

• Co-termination assumption

x

x

x

x

x

x

x

x

1

(m-1)

2

m

3

4

5

6

0

x = annuity

### First Some Useful Mathematical Machinery

• Uniform periodic annual payments (annuities)

• Projects frequently generate recurring income or cost streams on an annual basis

### Future Equivalents of Annuities

Link to summary of useful formulae

### Examples

• What future payment N years from now shall I accept in return for an investment of \$P now, given I could instead invest my money elsewhere (e.g. a bank) and earn i %/yr?

• What set of annual revenues for N years will entice me to invest \$P, given the same alternative as above?

### Examples

• What price should I pay for an investment which returns \$X/yr for N years, if i %/yr is available to me in a bank?

• What annual interest rate (bank, etc.) would be required to make an investment returning \$S in N years on a present investment of \$P?

### A Simple Replacement Problem

• Process to be operated for 4 years and then junked

• Do you buy a new low-maintenance machine now or not???

DATA (neglect tax effects)

0

3

4

2

1

\$2000

\$2000

\$2000

\$2000

### Cash Flow Time Lines

OLD

NEW

0

3

4

2

1

\$4000

\$500

\$500

\$500

\$500

• If management demands i = 20 %/yrPold=\$5180, Pnew=\$5295 old is better choice

### The Key Role of Interest Rates

• If management demands i = 10 %/yrPold=\$6340, Pnew=\$5585 new is better choice

### Note

• In a replacement problem like this you could have added revenues to the analysis, but no need to do so if they are the same for both options.

### Financial Comparisons with Unequal Lifetimes

• Simple Example: Choose between 2 pieces of equipment, one of which is better built and has a longer lifetime

• N is not the same for both

• Not a fair comparison with N=2 unless process is to be shut down and both options have no residual value

20 year life

Well Built

Poorly Built

2 year life

Poorly Built

2 year life

### What to Do?

• Option 1 - Repeatability

Well Built

20 year life

Alternative 1

Alternative 2

Purchase Price (\$)

10,000

20,000

Annual Op. Cost (\$/yr)

1500

1000

1000

Salvage Value (\$)

500

3

Service Life (yrs)

2

### Option 2 - Annualized Costs

• Convert the investment and maintenance for both options into a single annual payment

i = 0.15 / yr

Now

=

### Annualized Cost of Alternative 2

1000

=

0

0

3

2

1

2

1

3

20,000

1000

1000

1000

9472

9472

9472

In this case, choose alternative 1 because yearly cost is lower.