Cost and Time Value of \$\$

1 / 38

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

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

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about ' Cost and Time Value of \$\$' - jamar

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

### 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)

Options Stick w/old Buy newPurchase Price (\$) 0 4000Operating Cost (\$/yr) 2000 500Lifetime (yrs) 4 4

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.
• 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

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.