# Financial Management

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Financial Management ­ MGT201
VU
Lesson 09
NET PRESENT VALUE (NPV) AND INTERNAL RATE OF RETURN (IRR)
Learning Objective:
In this lecture, we will discuss in detail the previous lecture topics that are
·  Net Present value (NPV)
·  Internal Rate of Return (IRR)
Net Present value (NPV):
The most important skill in this course is to understand the NPV equation and to calculate NPV
as reliably as possible. It is also the most important criteria in capital budgeting. It is very difficult to
calculate because different inputs used in Net present value equation are based upon a forecast, which
may or may not be accurate e.g. future cash flows and sales. Similarly, when we talk about the life of
the project, again we are estimating the duration of the project. We also have to choose subjectively the
discount rates to be used, including cost of capital, opportunity cost & required rate of return in the
calculation of Net present value. We will discuss how to choose the interest rate when we would talk
about risk. In NPV the idea is to bring back each cash flow to the present and then to add or subtract
them on present time. The project or investment, which is offering the highest NPV, gets the highest
rank.
Formula:
NPV = -Io + CFt / (1+i)t = -Io + CF1/(1+i) + CF2/(1+i) 2 + CF` /(1+i) 3 +..
Importance of NPV in terms of objectives of Financial Management:
The objective of FM is to maximize the shareholders wealth. Now, there is a direct link between
shareholder wealth maximization & NPV. It is mentioned earlier that the value of an asset is determined
by the future cash flows it generates. We used these future cash flows & discount them to present and
we call that the NPV. Hence, there is a direct link between NPV and future cash flows.
When the management of the company invest in the +ve NPV projects, they increase the economic
value added (E.V.A) and they also increase market value added (M.V.A). It should be clear by now that
when company invest in +ve NPV projects they brings in value to the company. Increase in the value of
the company implies increase in shareholders' wealth.
Example: Let us suppose that you invest Rs 100,000 in a Savings Certificate. After 1 Year you will
receive a coupon payment (or profit) of Rs 12,000 and you also reclaim your initial investment
(principal).
Solution:
Step 1: Identify the Variables: Io = Rs 100,000 CF1=Rs 12,000 Life = n=1year Required Rate
of Return = i =10% (assumed), Annual compounding. CF I1 = Rs 100,000
Here, we assume that i=10 because which is the opportunity cost as you can place that money in
a bank and can earn 10%. Do not forget that you get back your principal investment after 1 Year. This
is a positive cash flow and must be discounted back to the present just like any other future cash flow).
Step 2: Solve the NPV Equation
NPV =
-Io  +
CF1 / (1+ i)  +
CF I1 / (1+ i)
= -100,000 +  12,000/ (1+0.10) + 100,000/ (1+0.10)
= -100,000 +
10,909
+
90,909
= + Rs 1,818 NPV positive so investment acceptable
NOTE: PV = NPV + Io = 1,818 + 100,000 = Rs 101,818
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Financial Management ­ MGT201
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NPV Cash Flow Diagram
Savings Certificate Example
CFI1 = Rs
100,000
Rs 90,909
Rs 10,909
CF1= Rs
NPV =
12,000
i = 10%
Rs.1,818
Yr 0 (Today)
Yr 1
Io = Rs 100,000
In diagram initial downward sloping arrow shows the cash out flow and after one year two
upward pointing arrows (1. profit 2.return of initial investment) show the cash inflows.
Now let us talk about the Internal Rate of Return or IRR.
Internal Rate of Return or IRR:
IRR is a very commonly used criterion for capital budgeting. It is popular with the managers
because it gives a very simple answer in the form of annual percentage and you can compare it to the
inflation rate, cost of capital or financing or to the certain financial accounting ratios. The formula uses
trial & error method. We talk about the interpretation of IRR in the coming lectures.
The formula is similar to NPV
CFt / (1+IRR)t = -Io + CF1/(1+IRR) + CF2/(1+IRR) 2 + ..
NPV = 0 = -Io +
The value of i where NPV is zero is the value of IRR.
IRR represents the Break-even Return on Investment, but the important thing to remember is the
difference between IRR & NPV. When you are ranking different projects the ranking you get from NPV
may be different from the ranking you get from IRR, because, there is a major difference of
interpretation of i between NPV and IRR.
The difference is that in the case of NPV; we are externally specifying the discount rate based
on required rate of return. In NPV calculations, you have an idea of your opportunity cost for the capital
& you use it as `i'. As mentioned earlier that rate given by the banks on account is considered as
opportunity cost of your capital & you will invest in any project, which earns more than the rate offered
by a bank. However, in IRR i is derived from the cash flow pattern of the project. Remember that in
IRR project, we do not externally specify the interest rate but we calculated it from the cash flows.
Therefore, in the IRR it is what you called forecasted rate of return or an intrinsic rate of return. This is
an important difference to keep in mind between NPV & IRR.
Example:
Consider the Same Savings Certificate example for IRR calculation. The only difference is that
this time, we will not assume any value for "i" as we had done in the NPV calculation.
We set the NPV = 0 and solve the equation for "i" (or IRR).
NPV = 0 = -Io
+  [CF1 / (1+IRR)] + [CFI1 / (1+IRR)]
We add Rs 12,000 & Rs 10,000 as both appearing at the same time.
0 = -100,000 +
[(CF1 + CFI1) / (1+IRR)]
0 = -100,000 +
[(12,000+100,000) / (1+IRR)]
IRR= (112,000 / 100,000) - 1
(No need for trial & error because you have one variable & one unknown)
= 1.12 - 1.00 = 0.12 = 12 % per annum
Is that a good IRR, a high IRR or low IRR? These things we will discuss in this & in the next
lecture. Now, one very important thing, which you need to consider when you are evaluating an
investment proposal, is to look at NPV & to see how it changes as you change the discount rate .This is
known as NPV Profile (See Fig.). Logically, when you increase the discount rate, the denominator
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Financial Management ­ MGT201
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becomes larger & you net present value becomes smaller. What you find as a result is a downward
sloping line. The point where the NPV is zero would be the IRR for the project.
Graphical
IRR
Estimation
Using "NPV PROFILE"
8000
6000
NPV
4000
2000
IRR=12%
0
i=10%
i=15%
i=20%
-2000=5%
i
-4000
-6000
-8000
Using a low and a high value for "i", plot two points on the graph and extend the NPV line. Where the
line cuts the horizontal x-axis would be reflect the value of the IRR.
Use this Graphical Technique when:
1. The investment or project life is longer than 2 years.
2. Graphical technique very useful in IRR calculations as there are polynomial equations that are
time consuming to solve algebraically in terms of "i".
3. Comparing the NPV's of 2 or more investments, to study how sensitive the NPV's of the
different investments are to the discount rate "i"
The next issue is the ranking of different projects, which means given a choice of more than one
investment, which project is the best to invest in.
RANKING TWO DIFFERENT INVESTMENTS:
Which Investment is better?
Let us rank two Mutually Exclusive & Independent Investments using NPV and IRR criteria
Mutually Exclusive: means that you can invest in ONE of the investment choices and having chosen
one you cannot choose another.
Independent: implies that the cash flows of the two investments are not linked to each other
Example:
Let us consider two investment opportunities. One Investment is the Savings Certificate (which
we described earlier) and the second investment is a Bank Deposit of Rs 100,000 at 10% interest
compounded annually for two years.
NPV & IRR Numerical
Comparing the 2 Investments
Since we have calculated the NPV and IRR for the Savings Certificate, we would calculate the
NPV and IRR only for the Bank deposit rate.
Bank Deposit Example
FV = PV (1+i) n = 100,000 x (1.10)2 = 121,000
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Financial Management ­ MGT201
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NPV = -100,000 + 10,000/ (1.1) + 11,000/ (1.1)2 + 100,000/(1.1)2 = 100,000 + 9,090 + 91,736 = + Rs
826
IRR: NPV = 0 = -100,000 + 10,000/ (1+IRR) + 111,000/ (1+IRR)2 ... by trial & error IRR = 10.5%
Compare the Investment 1 (Savings Certificate) to Investment 2 (Bank Deposit):
Bank Deposit
Savings Certificate
NPV (i=10% pa)
+ Rs 1,818
+ Rs 826
IRR
12% pa
10.5% pa
Savings Certificate appears to be a better investment because it offers both a higher NPV and a higher
IRR.
Graphical
Comparison
of
2
Investments
"CROSS-OVER IRR"
15000
10000
Cross Over Point
5000
0
i=10%
i=15%
i=20%
-5000
i=5%
-10000
-15000
-20000
The above diagram shows NPV Profiles of investments intersect at the Cross Over Point. Slope
of Bank Deposit investment is steeper because larger cash flows (Rs 111,000) are taking place later
in time (2 years instead of 1 year for Saving Certificates). Size of the Discounting Factor grows
exponentially with time so NPV graph falls much faster. The IRR at this Point is 8.8%.
At this point, the NPV of both the investments is equal at about +Rs 2,950
When IRR is less than 8.8% (Cross-over IRR) then the NPV of Bank Deposit is higher!
Investment Criteria
IRR Interpretation - How high is high.
Macro Aspects
Inflation:
An IRR, which is considered low for a medium inflation country like Pakistan, may be
considered high for a low inflation country like USA, Japan, and Singapore where inflation is below
5%.
Risk Free Rate of Return:
Recall our discussion from earlier lecture on Interest Rates and Money Markets.
In Pakistan, we use the Government T-Bill rate, which varies from 7% to 12% per annum
depending on the Money Market. Considering the risk-free rate of return the IRR on investment is
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Financial Management ­ MGT201
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Investment Criteria
IRR Interpretation (Micro Aspects)
ROA & ROE:
If the Investor has an existing running business that generates cash flows, then any new project
that matches or exceeds the returns of the existing business is worth considering.
Problem: ROA & ROE are Financial Accounting Ratios based on Net Income (not cash) &
Historical Cost or Book Value (not market value) whereas IRR is based on Cash and Forecasted Market
Value. The financial ratios are calculated based on the profit reported in the income statement, whereas
the IRR takes into account the cash flows rather than the accounting profit in the calculations.
Weighted Average Cost of Capital (WACC) or Hurdle Rate:
If the Investors an existing operating business that runs on borrowed money (or financing)
then the Investor (the borrower) bears the cost of interest, say 18% pa in Pakistan. Obviously, the rate of
cash generation should exceed the rate of interest payment. The IRR of a new project should exceed the
WACC. We will discuss this in detail when we study Capital Structuring. When IRR is above the
WACC, the excess return represents surplus that increases shareholders' wealth. The details on WACC
would be further discussed in Capital Structure determination.
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