1. Chapter 9 – Engineering Economic Analysis

2. Outline Interest Rates Cash Flow Diagrams
Annuities and Discount Factors
Depreciation
Taxation, Cash Flow, and Profit
Inflation

3. Definitions P – Principal or Present Value (of an investment)
Fn – Future Value (of an investment)
n – Years (or other time unit) between P and F
i – Interest Rate (based on time interval of n) per anum
Basis premise: Money when invested earns money
$1 today is worth more than $1 in the Future

4. Interest Simple Interest – Annual Basis
Interest paid in any year = Pis
Pis – Fraction of investment paid as interest per year
After n years total interest paid = Pisn
Total investment is worth = P + Pisn
What is the drawback of simple interest?
We can earn interest on earned interest

5. Interest Compound Interest At time 0 we have P
At the end of Year 1, we have F1 = P (1 + i)
At the end of Year 2, we have F2 = P (1 + i)2
At the end of Year n, we have Fn = P (1 + i)n
or P = Fn / (1 + i)n

6. Example
How much would i need to invest at 8 % p.a. to yield $5000 in 10 years

7. What if Interest Rate Changes with Time?
Eq. (9.7)

8. Different Time Basis for Interest Calculations
Relates to statement “ Your loan is 6 % p.a. compounded monthly”
Define actual interest rate per compounding period as r
inom = Nominal annual interest rate
m = Number of compounding periods per year (12)

9. Different Time Basis for Interest Calculations cont.
ieff = Effective annual interest rate
Look at condition after 1 year

10. Example
Invest $1000 at 10 % p.a. compounded monthly. How much do I have in 1 year, 10 years?

11. Example cont. As m increases ieff increases
Is there a limit as m goes to infinity
Yes – continuously compounded interest
Derivation – in Chapter 9
ieff (continuous) = e inom – 1

12. Cash Flow Diagrams
Represent timings and approximate magnitude of investment on a cfd
x-axis is time and y-axis is magnitude
both positive and negative investments are possible.
In order to determine direction (sign) of cash flows, we must define what system is being considered.

13. Consider a Discrete Cash Flow Diagram
Discrete refers to individual cfds that are plotted

14. Example
I borrow $20k for a car and repay as a $400 monthly payment for 5 years.
For Bank
For Me
$20,000
$400 1 2 3 60 1 2 3 60
$400
$20,000

15. Cumulative CFD
Cumulative CFD

16. Annuities n
Uniform series of equally spaced – equal value cash flows
Note: The first payment is at the end of year 1 not at t = 0

17. Annuities
What is future value Fn = ?
Geometric progression

18. Calculations with Cash Flow Diagrams
Invest $5k, $1k, $2k at End of Years 0, 1, 3, and take $3k at End of Year 4
$3,000
$2,000
$1,000
$5,000 3 7 4 1

19. Example 1 How much in account at end of Year 7 if i = 8% p.a.
What would investment be at Year 0 to get this amount at Year 7

20. Example 2
What should my annual monthly car payment be if interest rate is 8% p.a. compounded monthly? A
$20,000

21. Example 2 cont’d Compare at n = 60 Interest paid = $4,331.80

22. Discount Factors Just a shorthand symbol for a formula in i and n
See Table 9.1

23. More Examples on Cash Flow Calculations
You decide to start saving for a child’s college education as soon as your child is born. You estimate that it will cost a total of $18,000 per year for 4 years! How much should you put away into an account that bears an average interest rate of 7% pa in order to cover the costs of education?
Assume that your child will start college at age 18, your first investment occurs at year 1, and that payments are made at the end of years 18, 19, 20, and 21. Also assume that you continue to invest until he/she graduates.

24. More Examples on Cash Flow Calculations
$ 18,000

25. More Examples on Cash Flow Calculations
How much would you need to invest in a lump sum at the time of the birth of your child to pay for the education?
What are the balances in the investment account in years 18, 19, 20, and 21 just before the $18,000 withdrawals have been made?

26. More Examples on Cash Flow Calculations
$ 18,000

27. More Examples on Cash Flow Calculations
$ 18,000

28. Depreciation
Total Capital Investment = Fixed Capital + Working Capital
Fixed Capital – All costs associated with new construction, but Land cannot be depreciated
Working Capital – Float of material to start operations cannot depreciate

29. Definitions Salvage Value, S Life of Equipment
Value of FCIL at end of project
Often = 0
Life of Equipment
n – Set by IRS
Not related to actual equipment life
Total Capital for Depreciation
FCIL - S

30. 3 Basic Methods for Depreciation
Straight Line
Sum of Years Digits (SOYD)
Double Declining Balance (DDB)
Modified Accelerated Cost Recovery System (MACRS)

31. n = # of years over which depreciation is taken
Straight Line
n = # of years over which depreciation is taken

32. Sum of Years Digits (SOYD)

33. Double Declining Balance (DDB)
Adjust final year so that total depreciation is FCIL - S
Book value

34. Example 9.21
Same for Years 1-7

35. Example 9.21 (cont’d)
Sum of Year’s Digits

36. Example 7.21 (cont’d)
Double Declining Balance

37. MACRS ½ year convention
Double declining balance method over 5, 7, 9 years (depends on equipment use – most chemical processes are 5 yrs) with a ½ year convention and switching to SL over remaining years when depreciation for SL method is greater than DDB.
Example for 5 year life – using a basis of 100
k dkDDB dkSL
1 2/5(100 – 0)(0.5) = 20
2 2/5(100 – 20) = 32 (100-20)/4.5 = 17.78
2/5(100 – 52) = (100 – 52)/3.5 = 13.71
4 2/5(100 – 71.2) = (100 – 71.2)/2.5 = 11.52
2/5(100 – 82.72) = (100 – 82.72)/1.5 = 11.52
6 (0.5)(100 – 94.24)/0.5 = 5.76
½ year convention

38. MACRS Year, i diMACRS 1 20.00 % 2 32.00 % 3 19.20 % 4 11.52 %% % % % % %

39. Taxation, Cash Flow, and Profit
Tables 9.3 – 9.4
Expenses = COMd + dk
Income Tax = (R – COMd - dk)t
After Tax (net)Profit =
(R – COMd –dk)(1 – t)
After Tax Cash Flow =
(R – COMd – dk)(1 – t) + dk (+ Investment)

40. Inflation $ Now Net Worth vs. $ Next Year
f = Average inflation rate between Years j and n

41. Inflation
Example

42. Inflation Effect of Inflation on Interest Rate
f affects the purchasing power of the $
Look at the purchasing power of future worth, then
If this future worth was obtained by investing at a rate i, then the inflation adjusted interest rate, i ’ is given by

43. Summary Investment involves principal, interest rate, and time
The timing of transactions is conveniently shown on a Cash Flow Diagram
Depreciation of equipment value impacts the amount of tax that one pays
Inflation reduces the power of investment and decreases the buying power of future investments.