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Cost and Time Value of $$ Prof. Eric Suuberg ENGINEERING 90

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Cost and Time Value Lecture l 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. l What are our tools? »Material presented by Prof. Crawford »Discounting / Time Value of Money »Tax Savings through Depreciation

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So, what are we starting today? l Go through some of the “fun” math for Present Value Calculations l Do a teaching example of purchasing a machine for a manufacturing plant l Talk about costs – both the obvious kind as well as the non-obvious types l Time value of money calculations l Cost Comparisons l Depreciation l Put it all together – inc. continuous discounting and after-tax cost comparisons

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Have I Got a Deal for You l Would you be interested in investing in a company that has $1 million in annual sales?

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What More Would You Like to Know? l Annual operating expenses (salaries, raw materials, etc.) l Suppose these were $900,000/yr l Are you interested? (Come on - I’ve got to know now. There are a lot of people interested)

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Profit Profit = Sales (revenues) - expenses (costs) l Basis for taxation - What goes into the calculation is of great interest to Uncle Sam

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In Our Example l Profit = $1,000,000/yr - $900,000/yr = $100,000/yr l Is this a good business?

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What Would You be Willing to Pay Me for this Business? l $1 million? $2 million? l How do you decide? l This is one of the questions that we will answer in this part of the course.

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Present Value Calculations l Essential element of evaluating a business opportunity l Different variants »Simple discounting »Replacement and abandonment »Venture Worth, Present Value, Discounted Cash Flow Rate of Return

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What information do we need? l Investment (Capital assets, working capital) l Lifetime and Salvage Values l Operating Costs »Fixed »Variable l Interest Rate l Tax Rate l Depreciation Method l Revenues Information Required

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Capital Investment - Facility l Purchased Process Equipment l Field Constructed Equipment l Wiring, Piping, Instrumentation l Construction, Installation Costs l Site Preparation, Buildings l Storage Areas l Utilities l Services (Cafeterias, Parking lots, etc.) l Contingency

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Capital Investment- Manufacturing l Costs of process equipment may represent only 25% of actual investment! l Costs of process equipment scale according to the “six-tenths rule” »C 2 /C 1 = (Q 2 /Q 1 ) 0.6 l See, for example: »“Cost and Optimization Engineering” by F.C. Jelen and J.H. Black, McGraw-Hill, 1983.

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Other Items l Working Capital »Raw materials and supplies inventory »Finished goods in stock and Work in Progress »Accounts Receivable, Taxes payable l Operating Costs »Labor and Raw Materials »Utilities and Maintenance »Royalties l Fixed Costs »Insurance, rent, debt service, some taxes

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Time Value of Money l $1 today is more valuable than the promise of $1 tomorrow »Has nothing to do with inflation l “Discounting” is the term used to describe the process of correcting for the reduced value of future payments l Discount rate is the return that can be earned on capital invested today

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Future Worth of an Investment l P = Principal l i = Annual Interest Rate l S = Future value of investment Compound Interest Law S 1 = P (1+i) at the end of one year S 2 = S 1 (1+i) = P(1+i) 2 at end of year 2 S n = P (1+i) n at end of year n

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Present Value of a Future Amount P = S n / (1 + i) n = S n (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

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Simple Example l 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%? l PV = 10(1.20) -15 l = $.65 l Not enough to buy a soda these days

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Take Home Message l Not all dollars of profit are the same l Those that come earlier are “worth” more

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Start with Simple Example from Everyday Life l Do you buy the better made equipment with the higher price tag? or the low first cost equipment that has high maintenance?

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Cost Comparisons What are we doing here? l Comparing one project to another l Deciding to buy the expensive computer that has free maintenance versus the cheap one that makes you pay for service vs.

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Simple Cost Comparisons l 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 l Basic Rule: All comparisons must be performed on an equal time period basis

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Unequal Lifetime Cost Comparisons l Repeatability Assumption (to get to same time basis) l Annuity Comparison l Co-termination assumption

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First Some Useful Mathematical Machinery l Uniform periodic annual payments (annuities) l Projects frequently generate recurring income or cost streams on an annual basis 1 65 43 2 (m-1) m 0 x x xxx x xx x = annuity

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Discounting a Series of Payments

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Discounting a Series of Payments con’t

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Capital Recovery Factor

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Future Equivalents of Annuities Link to summary of useful formulae

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

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

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A Simple Replacement Problem l Process to be operated for 4 years and then junked l Do you buy a new low-maintenance machine now or not??? DATA (neglect tax effects) Options Stick w/old Buy new Purchase Price ($)04000 Operating Cost ($/yr) 2000500 Lifetime (yrs)44

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Cash Flow Time Lines 1 43 2 0 $2000 OLD 1 43 2 0 $500 NEW $4000

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The Key Role of Interest Rates l If management demands i = 10 %/yr P old =$6340, P new =$5585 new is better choice l If management demands i = 20 %/yr P old =$5180, P new =$5295 old is better choice

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Note l 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.

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Financial Comparisons with Unequal Lifetimes l Simple Example: Choose between 2 pieces of equipment, one of which is better built and has a longer lifetime l N is not the same for both l Not a fair comparison with N=2 unless process is to be shut down and both options have no residual value Well Built Poorly Built 20 year life 2 year life

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What to Do? l Option 1 - Repeatability Well Built20 year life Poorly Built2 year life (Buy 1) (Buy 10)

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Option 2 - Annualized Costs l Convert the investment and maintenance for both options into a single annual payment Alternative 1Alternative 2 Purchase Price ($) Annual Op. Cost ($/yr) Salvage Value ($) Service Life (yrs) 10,00020,000 15001000 500 1000 2 3 i = 0.15 / yr

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Annualized Cost of Alternative 1 = Now

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Annualized Cost of Alternative 2 0 1000 20,0001000 1 0 9472 1 3 2 = In this case, choose alternative 1 because yearly cost is lower. 2 3

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