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Engineering Economic Analysis - Coggle Diagram
Engineering Economic Analysis
Definition
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
Interest
Simple Interest
(Annual Basis)
Interest paid in any year = Pis
After n years total interest paid = Pisn
Total investment is worth = P + Pisn
Total investment after 1 year (n = 1) = P (1+is)
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
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)
ieff = effective annual interest rate
As m decreases ieff increases
Is there a limit as m goes to infinity
Yes – continuously compounded interest
Derivation – pp. 265-266
ieff (continuous) = e inom – 1
Cash Flow Diagram (CFD)
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
Discrete Cash Flow Diagram
Discrete refers to individual CFDs that are plotted
Cumulative CFD
Annuities
Uniform series of equally spaced, equal value cash flows
The first payment is at the beginning of year 1 not at t = 0
Future value (Fn)
Geometric progression
Discount Factors
Just a shorthand symbol for a formula in i and n
Table 9.1 has six
versions of these
Calculations with Cash Flow Diagrams
Annuity payments are all at the end of the year
Invest 5K, 1K, 2K at end of Years 0, 1, 3, and take 3K at end of Year 4
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
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
Salvage Value, S
Value of FCIL at end of project
Often = 0
Life of Equipment
n – set by IRS
Total Capital for Depreciation
FCIL - S
4 Basic Methods for Depreciation
Straight Line
Sum of Years Digits (SOYD)
Double Declining Balance (DDB)
Modified Accelerated Cost Recovery System (MACRS)
Current IRS-approved method
Based on combination of DDB and SL
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 (+ other cash flows)
Other cash flows might include working capital return, salvage value
Inflation
f = Average inflation rate between years j and n
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
