Artificial Intelligence (AI) for Investments
Lesson 3: Making investment decisions
Introduction
In this lesson we will cover the following topics:
• Review of NPV basics
• Alternatives to NPV rule – Payback period method
• Alternatives to NPV rule – Internal rate of return (IRR) method
• Pitfalls of IRR
• Capital investments with limited resources
• Summary and concluding remarks
Review of NPV basics
• Consider yourself in a position of a CFO where you are analyzing $1 million investment in a new
venture called project P
• That the current market value of your firm is $10 million, which includes $1 million cash that you plan
to invest min project P
• You find the NPV of this project by discounting the cash flows, adding them up to compute there PV,
and subtracting the initial investment of $1 million
• It is easy to understand if PV>9 this project has a positive NPV
Review of NPV basics
Review of NPV basics
• NPV rule recognizes that a dollar today is worth more than a dollar tomorrow
• Any decision rule that is affected by managers’ tastes, choice of accounting method, profitability of
existing business, or that of other projects will lead to an inefficient decision
• NPV(A+B) =NPV(A)+NPV(B)
• Book incomes are not necessarily the same as cash flows
• Profitability measures such as book rate of returns, heavily depend on the classification of various
items as capital investment and their rate of depreciation
Alternatives to NPV rule – Payback period
method
• A project’s payback period is simply found by estimating the years it takes for the project cash flows to
meet the initial investment
• A washing machine is costing $800. You spend $300 a year on washing your clothes. As a thumb
rule, if this machine is purchased, it will recover its expenses in 3 years
• The payback rule states that a project should be accepted if its payback period is less than some cut-
off period
• Consider a simple example here
Project C0 C1 C2 C3 Payback Period (years) NPV at 10%
A -2,000 500 500 5,000 3 +2,624
B -2,000 500 1,800 0 2 -58
C -2,000 1,800 500 0 2 +50
Alternatives to NPV rule – Discounted Payback
period method
• An improved version of payback period is to employ discounted cash flows
• This discounted payback rule examines that how many years it takes for the discounted cash flows to
recover the initial investment, i.e., become NPV positive
• Let us examine our previous example, with the help of discounted cash flows
Discounted Payback
Project C0 C1 C2 C3 Period NPV at 10%
(years)
500 500 5,000
A -2,000 = 455 = 413 = 3757 3 +2,624
1.1 1.12 1.13
500 1,800
B -2,000 = 455 = 1488 - - -58
1.1 1.12
1,800 500
C -2,000 = 1636 = 413 - 2 +50
1.1 1.12
Alternatives to NPV rule – Internal rate of return
(IRR) method
• IRR rule comes from the simple return measure
Profit Payoff Payoff
• Project return = = − 1; or −Investment + =0
Investment Investment 1+Project Return
• IRR is the return or discount rate at which NPV=0
C1 C2 CT
• NPV = C0 + + + ⋯+ =0
(1+IRR) 1+IRR 2 1+IRR T
𝑪𝟎 𝑪𝟏 𝑪𝟐
-4000 +2000 +4000
2000 4000
• 𝑁𝑃𝑉 = −4000 + + = 0 ; solving for this, we get IRR= 28.08%
1+𝐼𝑅𝑅 1+𝐼𝑅𝑅 2
Alternatives to NPV rule – Internal rate of return
(IRR) method
• If the opportunity cost of capital is less than the 28.08%
IRR, then the project has a positive NPV
• If opportunity cost of capital is greater than the IRR, the
project has a negative NPV
• Please note that IRR is a profitability measure and
depends solely on the timing of the project cash flows
• The opportunity cost of capital is the standard of
profitability to judge the worth (or NPV) of the project
Pitfalls of IRR
• Pitfall 1: Problem of Lending vs borrowing
• Consider the project cash flows from projects A and B as shown here
Projects 𝐂𝟎 𝐂𝟏 IRR NPV at 10%
A -1000 +1500 50% +364
B 1000 -1500 50% -364
• Both of these projects will give you the same IRR
• In project A, we are paying out $1000 initally, and getting $1500 later - Case of lending
• While in case of B, we are initially getting $1000 and paying back $1500 later- Case of borrowing
• When you lend money, you want a higher return and when you borrow money money you want a
lower return
Pitfalls of IRR
• Pitfall 2: Multiple rates of return
• Consider another project that involves an initial investment of $3 Billion and then produce a cash flow $1
Billion per year, for next nine years
• At the end of the project, the company will incur $6.5 billion of cleanup costs
𝑪𝟎 𝑪𝟏 𝑪𝟐 𝑪𝟑 𝑪𝟒
-3 1 1 1 1
𝑪𝟓 𝑪𝟔 𝑪𝟕 𝑪𝟖 𝑪𝟗
1 1 1 1 1
Pitfalls of IRR
• Pitfall 3: Mutually exclusive projects
• Firms often have to choose from mutually exclusive projects, since it may not be feasible to take all of
them
• In the project cash flows shown here, it seems IRR and NPV are contradicting each other
Projects 𝐂𝟎 𝐂𝟏 IRR (%) NPV at 10%
D -10000 +20000 100 8182
E 20000 +35000 75 11818
• In such cases, IRR can still be salvaged by examining incremental cash flows as shown here
Projects 𝑪𝟎 𝑪𝟏 IRR (%) NPV at 10%
E-D -10000 +15000 50 3636
IRR in Conclusion
• Many things can go wrong with IRR, but it is still a very useful benchmark
• To see its utility, have a look at the project cash flows, NPV, and IRR estimates for two projects X and Y
as shown here ($, thousands)
Projects 𝐂𝟎 𝐂𝟏 𝐂𝟐 𝐂𝟑 NPV at 8% IRR (%)
X -9.0 2.9 4.0 5.4 1.4 15.58
Y -9000 2560 3540 4530 1.4 8.01
• Both of these projects offer the same positive NPV of $1400
• As rational individuals you would select X over Y (Why?)
• The higher IRR associated with X (15.58%) reflects the low risk and efforts involved as compared with Y
Capital investments with limited resources
• Capital is a scarce resource, thus it is not possible to select all the positive NPV
projects
• Thus, firms would like to select those projects that offer highest NPV per dollar of
investment
NPV
• Profitability index (PI) =
Initial Investment
Cash Flows ($ Mn)
Project C0 C1 C2 NPV at 10% PI
A -10 +30 +5 21 2.1
B -5 +5 +20 16 3.2
C -5 +5 +15 12 2.4
Capital investments with limited resources
• Let us add another project D, which needs $40 Mn investment in second year
Project C0 C1 C2 NPV at 10% PI
A -10 +30 +5 21 2.1
B -5 +5 +20 16 3.2
C -5 +5 +15 12 2.4
D 0 -40 +60 13 0.4
• The firm can only raise $10 Mn in the second year: additional constraint of capital rationing
• The simple way of ranking projects as per PI may not work here
• This particular problem is rather simple, as A and D combined offer a higher NPV than B and C
combined
• However, more complex problems are solved with linear programming (LP) techniques
Summary and concluding remarks
• In addition to NPV, other rules are also employed to examine alternate investments
• These include book rate of return, payback period, and IRR method
• Book rate of return is simply computed as book income divided by book value of investment
• Payback method examines the project cash flows against a certain specific cut-off period
• Only those projects with payback period is less than cut-off period, are considered
• Lastly, IRR is the discount rate at which the firm NPV is zero
• As per the IRR rule, firms should accept those projects that have an IRR greater than opportunity cost of
capital
Thanks!
