1. Financial Management
Assignment 1
Relationship between
IRR & NPV
IRR & Modified IRR
By
Zeeshan Valliani (12543)
MBA Executive
July 14th, 2012

2. Relationship between IRR & NPV
IRR – Internal Rate of Return
NPV - Net Present Value
NPV and IRR, are measures that are used to evaluate a potential capital project or investment.
With both IRR and NPV, we evaluate a stream of expected cash inflows and outflows to help
determine if we should make a specific investment or not. The IRR indicates the potential growth
percentage of the investment. The NPV, on the other hand, indicates the value of a project's
income potential today.
Calculations
IRR gives insight into the potential profitability of an investment when the NPV still equals zero.
The IRR is also commonly known as the discount rate. When we compare potential investments, a
higher IRR usually indicates a better investment choice.
Formula
Initial Cash Outlay = CF1/(1 + IRR)^1 + CF2/(1 + IRR)^2 + ... + CFn/(1 + IRR)^n.
In this formulation, CF stands for cash flow. Each expected future cash flow must be divided by (1
+ IRR) raised to the nth power, where n equals the number of years after the initial cash outlay
when the cash inflow is expected to occur. For fractional years, you must raise the value in
parentheses to the fractional power. If you will have three cash flows expected in one, two and four
and a half years after the initial cash outlay respectively, the denominators will be (1 + IRR), (1 +
IRR)^2 and (1 + IRR)^4.5, respectively.
Amounts of Return
Consider the minimum rate of return you find acceptable. For an investor, the IRR must at least
equal the minimum amount of return expected for a particular investment. If the IRR does not meet
this minimum, look for another investment. The NPV, on the other hand, shows the investment's
value in today's dollars. The NPV will equal zero if the investment's future discounted income,
minus the initial cash outflow of the project, does not carry any present-day value.
Break-Even Point
When measuring an investment's profitability through the IRR, always consider the break-even
point of that investment. The IRR assumes that your investment will generate neither a loss nor a
cash profit and that future income from the investment will occur only at specific milestones and
monetary values during the lifetime of the investment.
Predetermined Return Rate
When calculating the NPV, compare what you invested today with the present value of the cash
receipts expected in the future. Use the NPV calculation to discount all the future income streams
based on the expected rate of return. For example, if you want to earn a minimum return of 4
percent on your investment, discount each of the future income payments using this percentage to

3. determine the present-day value of the investment. Subsequently, to obtain the NPV calculation,
add all the discounted future income payments and subtract this sum from the project's initial cash
outflow.
Relationship between IRR & Modified IRR
IRR – Internal Rate of Return
Modified IRR– Modified Internal Rate of Return
The modified internal rate of return is the same concept as the internal rate of return. The
difference between the two indicates that the formula has been slightly modified to get a more
realistic idea of how lucrative a deal you are considering.
The internal rate of return normally considers only the initial investment. A modified calculation
adds another variable to the equation by considering the rate of return on money that is re-invested.
So, if there is an investment with a high yield, but the money will be invested with a regular return,
the modified internal rate of return will reflect the true value of the venture.
It is the rate of return that a project generates to cover its costs -- taking into account the time value
of money. IRR, as a methodology, has limitations that modified IRR attempts to address. The
acceptance rule is the same for basic and modified: Accept the project if IRR is greater than the
required return on the project. A modified IRR of 25 percent or greater is often acceptable.
Calculations
MIRR is calculated as follows:
where n is the number of equal periods at the end of which the cash flows occur (not the number of
cash flows), PV is present value (at the beginning of the first period), FV is future value (at the end
of the last period).
The formula adds up the negative cash flows after discounting them to time zero using the external
cost of capital, adds up the positive cash flows including the proceeds of reinvestment at the
external reinvestment rate to the final period, and then works out what rate of return would cause
the magnitude of the discounted negative cash flows at time zero to be equivalent to the future
value of the positive cash flows at the final time period.
Relation to Capital Budgeting and NPV
Modified IRR is a common investment criterion in capital budgeting decisions (e.g., which fixed
assets to buy, products to launch or markets to enter). The most effective investment criterion,

4. however, is the net present value approach, or NPV. In essence, NPV is the difference between a
project's market value and its cost; thus, acceptable projects are those with positive NPV. A
project's market value is the sum of its discounted future cash flows. IRR relates to NPV in that it is
the rate of return at which a project's NPV is zero.
IRR Problem No. 1: Negative Cash Flows
When a project has negative future cash flows, solving for the rate at which NPV is zero yields
multiple IRRs; this is also known as the multiple rates of return problem. You cannot tell which
rate is the correct IRR -- perhaps both or neither. To address this, compute the present value of
negative future cash flows at first and add it to the cost of the project. Next, set NPV to zero and
solve for the "modified" IRR.
IRR Problem No. 2: Comparing Mutually Exclusive Projects
Modified IRR and the NPV approach produce conflicting recommendations when comparing
mutually exclusive projects. This often occurs for projects with low required rates of return. The
reason is timing of cash flows: At low discount rates, deferred cash flows are more valuable. A
project with significant cash flows around the end of its life yields a lower modified IRR compared
to a similar project with significant cash flows around the beginning of its life. Ultimately, the
project with the highest NPV is always the value-maximizing choice.
Qualitative Considerations
Do not forget to consider the strategic implications of undertaking a project. A seemingly
profitable project can destroy value over the long run as a company loses its competitive advantage
in the market. This calls for a wider assessment of a project, taking into account potential changes
in the business environment, strategic position relative to the competition, and real options (i.e.
options embedded in the project). Examples of real options include the option to delay, expand or
abandon a project.