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NPV < 0IRR < Cost of CapitalReject the investment from the cash flow perspective. Other factors could be important. NPV = 0IRR = Cost of CapitalProvides the minimum return. Probably reject from the cash flow perspective. Others factors could be important. NPV > 0IRR > Cost of CapitalScreen in for further analysis. Other investments may provide better returns and capital should be rationed, i.e., go to the most profitable projects. Others factors could be important.
On the example, at first we calculated with NPV to see if the value is negative, the there is no need to accept the prokect. If the value is positive then you can accept it. When we decide to see the rules with IRR, then we can summarize the calculation with the formula: IRR > Cost of capital (should be accepted) IRR = Cost of capital (provides the minimum return) IRR < Cost of capital (shouldn’t be accepted)
IRR: 7,2% is where NPV A = NPV B Untill 7,2 the prject which should be chosen is B, whereas below 7,2 A is better. Therefore, there are some exceptions in IRR that in mutual project we always need to consider NPV and cost of capital to see where the balance changes. One way to understand the preference of NPV over IRR, more generally, is to recognize that NPV uses the “correct” rate, i.e., the cost of capital, to discount the cash flows, rather than an “arbitrary” rate, i.e., the IRR, that makes NPV =0. Another way to understand the superiority of the NPV rule is that the discounting process inherent in both the IRR and NPV techniques implicitly assumes the reinvestment of the cash flows at whatever discount rate is used, either IRR or the cost of capital. When the IRR is very high relative to the cost of capital it is unrealistic to assume reinvestment at that high rate. This is especially damaging when comparing two investments with very different timing of cash flows. We will revisit this reinvestment assumption later, under our discussion of yield to maturity on coupon bonds, where its meaning will become clearer.
From a comparison of NPV and IRR, it can be seen that NPV is actually a better measure than IRR, especially, in long term projects, not only because NPV considers different discount rates but also takes into account the cost of capital
Npv and IRR, a link to Project Management
Net Present Value Decision Rules
IRR (Internal Rate of Return)
in Project Management
The two most-used measures for evaluating projects are
the net present value and the internal rate of return!
Net Present Value
The difference between the present value of the future cash flows from
an investment and the amount of investment. Present value of the
expected cash flows is computed by discounting them at the required rate
N=total number of periods
T= the time of the cash flow
i= the discount rate (the rate of return that could be earned on an
Rt = the net cash flow i.e. cash inflow – cash outflow at time t (R0: it is
subtracted from the whole as any initial investments during first year is
not discounted for NPV purpose)
An Investment of $1,000 in year 1
The discount rate is 10%
In Year 2, we receive $110 in year 2
You expect to receive $1,200 in year 3
Therefore, NPV= ($ 1,000) + $ 100 + $ 991.74= $ 91.74
Hence, we can do this investment.
Internal Rate of Return
• The internal rate of return of a project is
known as the rate of return where the
particular project’s net present value
equals to zero.
– CF: Cash Flow
– r: Internal Rate of Return
Internal Rate of Return Rules
In IRR decisions, if we have only one project, most
of the time we need the basic rule «independent
IRR > Cost of capital (should be accepted)
IRR = Cost of capital (provides the minimum return)
IRR < Cost of capital (shouldn’t be accepted)
In addition, we need to take other situations into
account too. Especially, eventhough NPV and IRR
will generally give us the same decision, there are
•Nonconventional cash flows – cash flow signs
change more than once
•Mutually exclusive projects
Example: Independent Project
If we want to decide on to accept the project or not, we
should consider the comparison of IRR & cost of capital
for an individual project.
In this example;
•when the cost of capital is 15%, then the NPV is
-227,53 (don’t accept)
• Alternative: IRR < Cost of capital
•when the cost of capital is 10%, then the NPV is 34,27
• Alternative: IRR > Cost of capital
NPV versus IRR
• NPV Method is preferred over other methods since it calculates additional wealth and
the IRR Method does not
• The IRR Method is more used in evaluating short-term projects and NPV is more used
in evaluating long-term projects.
• one significant advantage of IRR -- managers tend to better understand the concept of
returns stated in percentages and find it easy to compare to the required cost of capital
• Applying NPV using different discount rates will result in different recommendations.
The IRR method always gives the same recommendation.
compare two mutually
NPV by i=8%
Link to Project Management
NPV and IRR in the decision taking process
Methods to evaluate a project
estimate the value of the project
choosing which project gets priority
NPV as time value of money (money figure)
IRR calculate the investments profitability as an interest rate
included in a business case prepared by the