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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

Cost and Time Value of $$

Prof. Eric Suuberg

ENGINEERING 90


Cost and time value lecture

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

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

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

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

Profit = Sales (revenues) - expenses (costs)

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


In our example

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

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

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


What information do we need

Information Required

What information do we need?

  • Investment (Capital assets, working capital)

  • Lifetime and Salvage Values

  • Operating Costs

    • Fixed

    • Variable

  • Interest Rate

  • Tax Rate

  • Depreciation Method

  • Revenues


Capital investment facility

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

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

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

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

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

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

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

Take Home Message

  • Not all dollars of profit are the same

  • Those that come earlier are “worth” more


Start with simple example from everyday life

Start with Simple Example from Everyday Life

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


Cost comparisons

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

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


Unequal lifetime cost comparisons

Unequal Lifetime Cost Comparisons

  • Repeatability Assumption (to get to same time basis)

  • Annuity Comparison

  • Co-termination assumption


First some useful mathematical machinery

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


Discounting a series of payments

Discounting a Series of Payments


Discounting a series of payments con t

Discounting a Series of Payments con’t


Capital recovery factor

Capital Recovery Factor


Future equivalents of annuities

Future Equivalents of Annuities

Link to summary of useful formulae


Examples

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?


Examples1

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

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 ($)04000Operating Cost ($/yr) 2000500Lifetime (yrs)44


Cash flow time lines

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


The key role of interest rates

  • 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


Cost and time value of

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

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


What to do

Poorly Built

2 year life

What to Do?

  • Option 1 - Repeatability

Well Built

20 year life

(Buy 1)

(Buy 10)


Option 2 annualized costs

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 1

Annualized Cost of Alternative 1

Now

=


Annualized cost of alternative 2

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.


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