#!/usr/bin/env python
# coding: utf-8

# # Financial Planning and Management
# 
# ## Economics - The Dismal Science in Support of Decision Making
# 
# ### Defining Alternatives
# - Application of economics principles to assign **value** to an alternative
# - Decision principles used to select the best alternative based on **value**

# ### Physical consequences
# 
# - Economic value – a basis for comparisons
# - Definitions/Concepts
# - Economic Analysis
#   - Principles of engineering economics
#   - Cash flows
#   - Discounting methods

# ### Cash Flow Diagrams
# 
# Graphic representation of cash outflow (costs) and inflow (revenue).  
# 
# ![](cashflow.png)
# 
# 
# - Convention is revenue (benefit) is plotted upward, and expenses (costs) is plotted downward.
# - All cash flows during a year are usually lumped into sums occurring at the end of the year 
# 
# #### Discounting Factors
# 
# - Discounting factor is a tool to convert a value at one date to an economically equivalent value at another date
# - All discounting problems can be expressed as combinations of two fundamental factors
#   - Single-payment Compound-amount Factor
#   - Single-payment Present-worth Factor
#   
# #### Present Value to Future Value
# 
# The factor computes the number of monetary units (FV) that will accumulate in N years for every initial unit (PV) invested at a rate of return of *i-percent*.
# 
# $$FV=PV(1 + i)^N$$
# 
# #### Future Value to Present Value
# 
# The factor computes the number of current monetary units (PV) that a future value (FV) is worth if the monetary units are invested at a rate of return of *i-percent*.
# 
# $$PV=FV(1 + i)^{-N}$$
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# #### Other Factors
# 
# Notice the cash flow diagram looks the same – it is a tool to move values along the time axis. All other diagrams can be determined by combinations of these two concepts.
# 
# >Can either apply algebra to make the combinations, or just use simple computer programming (e.g. R)

# ### Example
# 
# Determine the present worth (PV) of a stream of annual payments, each payment is \$100 for a period of 10 years. The discount rate is 3-percent per year.
# 
# - Sketch a cash flow diagram

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# ### Discounting Techniques
# 
# Refers to systematic application of discounting factors to compare alternatives
# 
# The 4 accepted techniques are:
# - Present worth method
# - Rate-of-return method
# - Benefit-cost ratio method 
# - Annual-cost method
# 
# Each method produces the same evaluation of relative value

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# ## References
# 
# 1.
# 
# 2. [Cleveland, T. G. (2017) *ECONOMIC ANALYSIS MATHEMATICS Notes to Accompany CE 5366 at TTU*](http://54.243.252.9/ce-5333-systems-webroot/1-Lectures/Lecture03/powerpoint/CE5366-Lesson-07.pdf)

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