10/18/99 Engineering Economics II 1
ENGINEERING ECONOMICS II
INVESTMENT ANALYSIS
t Companies (and individuals) invest money in order to
earn money
t Examples
eBuild a factory to make washing machines and dryers
eOpen a laundromat
eWrite a novel (what is being invested here?)
eGet a degree in chemical engineering
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PROJECT LIFE CYCLE
t Initial Investment
ePurchase of productive facilities
X Land and buildings
X Equipment
eStartup funds
eWorking capital
t Project Life
eStart up - come up to full potential
eOperate at full potential until end of project life
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Payout Time
Investment
Period
CASH
FLOW
TIME
Perfect
Startup
Real
Startup
Project Life
PROJECT CASH FLOW
DIAGRAM
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PROJECT ACCOUNTING I
t Gross Profit
(aka Profit Before Taxes or PBT)
PBT = Sales Revenue - Operating Expenses
t Operating Expenses
eRaw materials
eUtilities
eLabor
eMaintenance
eOverhead
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PROJECT ACCOUNTING II
t Net Profit
(aka Profit After Taxes or PAT)
PAT = (1 - Trate) (PBT - Depreciation)
where Trate = corporate income tax rate (~ 48%)
t Depreciation
Allowance for the depreciation of the fixed investment
(equipment wears out,etc.
Depreciation = [Fixed Investment]/Nd,Straight
line”
where Nd = depreciation period
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PROJECT ACCOUNTING III
t Cash Flow
What is left after expenses and taxes have been paid.
CF = PBT -Taxes
= (1 - Trate) PBT + Trate Deprec
t Example
Revenue = $1..0 MM /yr; Expenses = $0.5 MM/yr
Investment = $0.5 MM ; Nd = 5; Deprec = $0.1 MM
PBT = $1.0 MM - $0.5 MM = $0.5 MM; Trate = $0.48
CF = (1 - 0.48) 0.5 + (0.48) 0.1 = $0.308 MM
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PROJECT ACCOUNTING IV
t Accounts Receivable
Money owed to the businsess for goods shipped or
services provided
t Accounts Payable
Money owed by the business to suppiers and employees
(payroll) amd fpr taxes
t Working Capital (Wcap)
e Money set aside by the business to
X Provide a buffer between accounts payable and accounts
receivable
X Provide funds for emergency repairs,etc.
Rule of Thumb,Wcap = 15% of Total Investment
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PROFITABILITY EVALUATION I
t Return on Investment (ROI)
e Before Tax (ROIBT)
ROIBT = PBT/[Total Investment - Wcap]
(This can be compared with other before-tax investment
rates such as CD’s and Corporate Bonds)
e After Tax (ROIAT)
ROIAT = CF /[Total Investment - Wcap]
(This can be compared to other tax-exempt investments
such as municipal bonds.)
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PROFITABILTY EVALUATION II
t Payout Time (Tpay)
Time required to pay back initial investment (less
Wcap)
Tpay = [Fixed Capital + Start-Up] / CF
t ROI and Tpay
e Approximate estimates of profitability
e Easily evaluated
t Rigorous evaluation based on DCFROR (MBA’s
method)
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DISCOUNTED CASH FLOW I
Let CF(n) = the cash flow for the nth time period
Recall that the present value PV(n) of CF(n) is
PV(n) = CF(n)/(1 + i)n
For a series of N cash flows the net present value
(NPV) is
N
NPV = CF(n)/(1 + i)n
i=n
This is the discounted cash flow for a series of N cash flows
CF(n)
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DISCOUNTED CASH FLOW II
NPV > 0 represents a good investment at the interest rate i,
NPV < 0 does not.
Let N
NPV(r) = CF(n)/(1 + r)n
i=n
If we solve NPV(r ) = 0 for r,that value of r is known as the DCF
Rater of Return (DCFROR) or Internal Rate of Return (IRR),It
represents the interest rate corresponding to the cash flow series
such that the NPV = 0,This DCFROR can be compared with
external interest rates such as those paid by CD’s and Treasury
Bonds.