Why do engineers care about finance?

Projects often require an investment of money up front.

Often receive money back in later years after project completion.

Need to determine if project will be profitable.

Must compare monies spent today to monies received in the future.

$$ Time Value of Money $$

Why is "time value of money" important? Money grows through compound interest.

A savings account with 5% interest paid annually. Put $100 in account now, how much do you have in a year? The money grows every year by 5%.

• One year 100 (1+ 0.05) = $105• 2 years: $100 (1+ 0.05) (1+ 0.05) = 100 ( 1+ 0.05)2 = $110.25• 10 years: $100 ( 1+ 0.05)10 = $162.90

Basic Formula: FV=Future Value, PV=Present Value for a fixed interest rate in

decimals (i) for n periods

What if I compounded more than annually (once a year)?

So we can compare, we’ll use the same numbers:

A savings account starting with $100 with 5% interest PAID MONTHLY. Now how much do you have in a year?

New formula:

A=Future Value and P=Present Value

This time we get $105.12, instead of just $105.00 . . . .

What if I compounded “continuously”?

We’ll use the same numbers: A savings account starting with $100 with 5% interest

compounded continuously. Now how much do you have in a year?

New formula using Euler’s constant,

e ≈ 2.7128:

Future Value (FV)=Present Value (PV)*ert

This time we get $105.13, instead of just $105.12 (compounded monthly) or $105.00 (annual interest rate).

This is from only $100.00 initial investment. A ten million dollar investment yields a $13,000 difference between continuous compound interest and annual interest.

Handy formula for future value.

where: N = annual amount received

r = interest rate

n = total no. of payment periods. Important: This formula is applicable when cash amount N is

the same every payment.

r

rN

n 11 valueFuture

You borrow $500 from your dad and have to pay it back in 1 year.

How much would you pay per month if the saving account interest is 0.4% monthly?

r

rN

n 11 valueFuture

76.40$

004.0

1004.01 $500

12

N

N

If you won the $100M lottery, would you take 50% now OR even monthly payments worth the $100M for 25 years?

If the full payment is based on an annual 5% return over 25 years, what would you get each month?

That’s $52.5M at the end, $2.5M more than the $50M you’d get if you took the 50% offer now.

month.per $175K or year per $2.095MN

05.0

105.01 $100M

25

N

Would you rather have $100 today or $162.89 in 10 years?

Compound interest says they are the same !! Assumes future cash flows have no risk - Is that always true?

$162.89 in 10 years is equal to $100 today Assumes 5% interest rate for every year - Is that going to be true?

We say $162.89 in 10 years has a “present value” of $100

We also say $100 has a “future value” of $162.89 in 10 years.

Savings accounts are a way of making sure your money maintains its “present value”.

Annual Compound interest in Reverse. . .

$100 you get next year is worth $95.24 today.

The $162.50 received in 10 years has a value today of:

This is called “discounted cash flow”. It gives a way to compare future money with present

money.

05.01

100$24.95$

1005.01

90.162$100$

Would you rather have $20 a year for 5 years OR receive what $25 is worth at 6% interest each year for 5 years?

Cash by 5 annual payments of $20 = $100 Cash back must be discounted, assume an annual interest

rate of 6%. $25 in 1 year: $25/(1.06) = $23.58 $25 in 2 years: $25/(1.06)2 = $22.25$25 in 3 years: $25/(1.06)3 = $20.99$25 in 4 years: $25/(1.06)4 = $19.80$25 in 5 years: $25/(1.06)5 = $18.68Present Value of cash received= $105.30

This will generate $105.30 - $100.00 = $5.30 in today’s dollars. Multiply by a million for an engineering project.

Discount everything to the present time.

where N = annual amount received, r = interest rate, n = total no. of years

This formula is applicable when the cash amount N is the same every year.

For our example: N=$25, r=.06 n= 5:

r

rN

n11 luePresent va

30.105$

06.0

06.01125$ PV

5

Engineering Economics

Answers the question: Will this project be profitable? • How long will it take to get to get my money back?• How much money do I have at risk?

Requires assumptions about future costs and revenue. Considers the “time value of money”. Allows alternative implementation scenarios.

• Can I reduce risk by implementing the project slower (or faster)?

Allows a comparison of alternative projects to determine which is most profitable.

Tonight’s Homework (from ‘07 Final)Problem 1:

Your company assigns you the task of evaluating the costs of obtaining and running a $19K company car for 10 years. Three options are possible: 1) Placing $500/month in a savings account at 5% annual interest,

compounded monthly until you’ve accumulated $19K, then buying the car for cash

2) Buying the car with no money down and $500/month payments3) Leasing a car, 39 months at a time, for $200/month plus a down

payment of $4K. What are the total costs for each option? Why can’t these costs can’t all be legitimately compared?

Problem 2:It’s never too early to begin planning for retirement, so you begin socking away $200/month in an account that pays 6% annually, compounded monthly. After some number of months you’ll have enough money in the account so that you can stop making payments and start drawing out $200/month—forever. How many months will it take?

Request for Proposal (RFP)

Teams of 3 Respond to the City Councils of two separate towns who are

looking for a cost effective and dependable engineering solution to individual problems facing their communities.

Each team will deliver a 12-minute formal PowerPoint presentation to City Council Members which will include: Detailed Graphic representing solution Specific timeline of development, testing and

implementation Present and Future Cost Analysis including: 1) upfront

monies required, 2) production costs (manpower, materials, etc.), 3) reoccurring costs 4) short and long term maintenance costs

Safety considerations

RFP Teams 2010

Team 1

Colin

Jessica

Jesus

Team 2

Flaviu

Eduardo

Nick

Team 3

Jim

Jose

Sam

Team 4

Sami

Joseph

Kelly

Team 5

Arjun

Michelle

Craig

Team 6

Mike

Ivan

Ryan

Team 7

Alejandra

Niko

Chris

What data do you need?

One time costs (or capital investments)• Buildings, equipment, research etc.

Recurring costs (non-revenue producing)• Salaries, Rent, utilities, insurance etc.

Production costs• Materials, packaging, shipping etc.

Revenue projections• How much can I sell it for?• When will I get paid?