Project Feasibility Indicators
Discounted Measures of Project Worth
• The Project’s Cash Flow Profile
• Independent Projects and Mutually Exclusive
Alternatives
• The Net Present Value and Internal Rate of
Return Criteria
• Exercises in Discounted Cash Flow Analysis
Discounted Measures of Project Worth
• The Project’s Cash Flow Profile
– An investment project is a capital-forming activity that involves
the commitment of scarce resources now in view of generating
benefits in the future.
conventional
unconventional
(Conventional cash flow profiles change in sign only once.)
Net Present Value
• NPV is the sum of present and future net cash
flows of a project, discounted at one’s
opportunity cost of capital (OCC).
• If you are a net saver or lender, your OCC is
(roughly) the average interest rate that you
earn from your savings or lending.
• If you are a net borrower, your OCC is
(roughly) the average interest rate you pay on
your borrowings.
Net Present Value (NPV)
• To get the present value of a future flow F in
year t (where year 0 is 2013), we divide Ft by
(1 + r)t, where r is our discount rate. E.g., the
PV of P100 receivable in year 5 at 10%
discount rate = 100/(1.10)5 = 62.1.
– The value 1/(1 + r)t is called the discount factor or
the present worth factor (pwf).
• It is important always to report the discount
rate at which NPV is calculated.
Net Present Value (NPV)
• With constant cash flows over time, it is
convenient to use the sum of present worth
factors (spwf).
• The next slide gives a table of discount factors
where pwfs and spwfs are reported for
different time periods and discount rates.
• For example, the present value (PV) at 10% of
P100/year from years 1-10 is P100*(6.1446) =
P614.46. P100 receivable in year 40 is worth
only P0.02 at present if my OCC = 15%.
Discount Table
8%
prd
1
2
3
4
5
10
20
30
40
50
pwf
0.9259
0.8573
0.7938
0.7350
0.6806
0.4632
0.2145
0.0994
0.0460
0.0213
10%
spwf
0.9259
1.7833
2.5771
3.3121
3.9927
6.7101
9.8181
11.2578
11.9246
12.2335
15%
pwf
spwf
pwf
spwf
0.9091
0.8264
0.7513
0.6830
0.6209
0.3855
0.1486
0.0573
0.0221
0.0085
0.9091
1.7355
2.4869
3.1699
3.7908
6.1446
8.5136
9.4269
9.7791
9.9148
0.8696
0.7561
0.6575
0.5718
0.4972
0.2472
0.0611
0.0151
0.0037
0.0009
0.8696
1.6257
2.2832
2.8550
3.3522
5.0188
6.2593
6.5660
6.6418
6.6605
Net Future Value (NFV)
• For some, the concept of Net Future Value (NFV) is more intuitive
than NPV. Consider the cash flow:
0
-100
1
50
2
70
• If my OCC is 10%, my 100 shall have become 110 by year 1 if I do
not invest in the project. The project gives me back 50 in year 1; I
therefore have a deficit of -60, which shall have been 66 (=
60*1.1) in year 2, But then I get back 70 in year 2, which leaves
me with a surplus of +4 (= 70- 66).
• The project’s NFV at 10% is +4 . I.e., After taking into account the
return of my capital of 100 and the alternative return to my
capital of 19% per year, I still have +4 left over.
• The project is therefore financially viable for me.
Internal Rate of Return
• The IRR is the discount rate that equates the
NPV of the project’s net cash flows to zero.
• Manually (using a calculator), it is solved
through an iterative process (trial and error).
Spreadsheets (like MS Excel) have an IRR
function.
• For an unconventional cash flow profile, there
may be more than one positive IRR.
Benefit-Cost Ratio
• The Benefit-Cost Ratio (BCR) is the present
value of project benefits divided by the
present value of project costs, discounted at
our OCC.
• There are two types:
– BCR (1) has recurrent costs deducted from
benefits in the numerator.
– BCR (2) has recurrent costs included in the
denominator.
Measures of Project Worth
• Independent Projects
– A project is considered feasible if:
• NPV at opportunity cost of capital is not negative
• IRR is not less than opportunity cost of capital
• BCR is not less than unity
– The IRR is an interesting statistic, but not a good criterion
because:
• A project with unconventional cash flow profile may
have several IRRs
• If the discount rate varies over time, it is not clear
which discount rate we compare the IRR with.
Measures of Project Worth
• Mutually Exclusive Alternatives
– Choose the alternative with the highest (nonnegative) NPV at our opportunity cost of capital
– Do not choose the alternative with highest IRR
– Do not choose the alternative with highest BCR
– Dimensions of mutual exclusiveness:
•
•
•
•
Scale
Technique, design
Location
Timing
Cost-Effectiveness Analysis
• CEA is often used in the financial and
economic analysis of social projects.
• CEA applies when benefits can be measured
or quantified but cannot be given a monetary
value.
• Alternatives to be compared through CEA
have to be producing the same stream of
(physical) benefit flows.
Cost-Effectiveness Analysis
• Choose the alternative with the lowest
present value of cost (both capital and
recurring), discounted at our OCC.
• Choose the alternative with the higher initial
outlay if the marginal IRR on the additional
outlay (or the crossover or equalizing discount
rate) is higher than our OCC.
• Examples:
– Basic education: classrooms vs. distance learning
– Family planning: pills vs. IUD vs. injectables
Computational and Analytical Tools
• Learning electronic spreadsheet basics
– Review of MS Excel (or equivalent spreadsheet)
• Using financial functions
– NPV, IRR
• Doing sensitivity analysis
– Identifying key parameters for sensitivity analysis
and scenario setting
• Goal-seeking
– Breakeven analysis