Evaluating Business and
Engineering Assets – Part II
Part II
Professor C. S. Park
Copyright © 2005
Payback Period
Lecture No.14
Professor C. S. Park
Fundamentals of Engineering Economics
Copyright © 2005
1
Chapter 5
Present-Worth Analysis
„
„
„
„
Loan versus Project
Cash Flows
Initial Project Screening
Methods
Present-Worth Analysis
Methods to Compare
Mutually Exclusive
Alternatives
Chapter Opening Story – Federal Express
Nature of Project:
„ Equip 40,000 couriers
with PowerPads
„ Save 10 seconds per
pickup stop
„ Investment cost: $150
million
„ Expected savings: $20
million per year
Federal Express
2
Ultimate Questions
„
„
„
Is it worth investing $150 million to save $20
million per year, say over 10 years?
How long does it take to recover the initial
investment?
What kind of interest rate should be used in
evaluating business investment
opportunities?
Mr. Bracewell’s Investment Problem
• Built a hydroelectric plant using his personal savings of $800,000
• Power generating capacity of 6 million kwhs
• Estimated annual power sales after taxes - $120,000
• Expected service life of 50 years
Was Bracewell's $800,000 investment a wise one?
How long does he have to wait to recover his initial investment,
and will he ever make a profit?
3
Mr. Brcewell’s Hydro Project
Bank Loan vs. Investment Project
Bank Loan
Loan
Customer
Bank
Repayment
Investment Project
Investment
Project
Company
Return
4
Describing Project Cash Flows
Year
(n)
Cash Inflows
(Benefits)
0
0
1
Cash
Outflows
(Costs)
Net
Cash Flows
$650,000
-$650,000
215,500
53,000
162,500
2
215,500
53,000
162,500
…
…
…
…
8
215,500
53,000
162,500
Payback Period
‰ Principle:
How fast can I recover my initial investment?
‰ Method:
Based on cumulative cash flow (or accounting
profit)
‰ Screening Guideline:
If the payback period is less than or equal to
some specified payback period, the project
would be considered for further analysis.
‰ Weakness:
Does not consider the time value of money
5
Example 5.1 Payback Period
N
Cash Flow
0
1
2
3
4
5
6
Cum. Flow
-$85,000
-$50,000
-$5,000
$45,000
$95,000
$140,000
$175,000
-$105,000+$20,000
$35,000
$45,000
$50,000
$50,000
$45,000
$35,000
Payback period should occurs somewhere
between N = 2 and N = 3.
$45,000
$45,000
Annual cash flow
$35,000
$35,000
$25,000
$15,000
0
1
2
Years
3
4
5
4
5
6
Cumulative cash flow ($)
$85,000
150,000
3.2 years
Payback period
100,000
50,000
0
-50,000
-100,000
0
1
2
3
6
Years (n)
6
Practice Problem
„
How long does it take to recover the initial
investment for Federal Express?
„
How long does it take to recover the
investments made by Mr. Bracewell from his
hydroelectric project?
Discounted Payback Period
‰ Principle:
How fast can I recover my initial investment
plus interest?
‰ Method:
Based on cumulative discounted cash flow
‰ Screening Guideline:
If the discounted payback period (DPP) is less
than or equal to some specified payback period,
the project would be considered for further
analysis.
‰ Weakness:
Cash flows occurring after DPP are ignored
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Example 5.2 Discounted Payback Period Calculation
Period
Cash Flow
0
-$85,000
1
Cost of Funds
(15%)*
Cumulative
Cash Flow
0
-$85,000
15,000
-$85,000(0.15) = -$12,750
-82,750
2
25,000
-$82,750(0.15) = -12,413
-70,163
3
35,000
-$70,163(0.15) = -10,524
-45,687
4
45,000
-$45,687(0.15) =-6,853
-7,540
5
45,000
-$7,540(0.15) = -1,131
36,329
6
35,000
$36,329(0.15) = 5,449
76,778
* Cost of funds = (Unrecovered beginning balance) X (interest rate)
Summary
Payback periods can be used as a screening
tool for liquidity, but we need a measure of
investment worth for profitability.
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