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matter what the investment.
The net present value rule does not control for the life of the project. Consequently,
â€¢
when comparing mutually exclusive projects with different lifetimes, the NPV rule is
biased towards accepting longer term projects.

Internal Rate of Return
The internal rate of return is based on discounted cash flows. Unlike the net
present value rule, however, it takes into account the projectâ€™s scale. It is the discounted
cash flow analog to the accounting rates of Internal Rate of Return (IRR): The IRR of

return. Again, in general terms, the internal rate a project measures the rate of return earned
by the project based upon cash flows,
of return is that discount rate that makes the net
allowing for the time value of money.

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present value of a project equal to zero. To illustrate, consider again the project described
at the beginning of the net present value discussion.

\$ 400 \$ 500 \$ 600
Cash Flow \$ 300

Investment <\$ 1000>

Internal Rate of Return = 24.89%

At the internal rate of return, the net present value of this project is zero. The linkage
between the net present value and the internal rate of return is most visible when the net
present value is graphed as a function of the discount rate in a net present value profile. A
net present value profile for the project described is illustrated in Figure 5.4.

Figure 5.4: NPV Profile

\$500.00

\$400.00

\$300.00

As the discount rate increases, the net present value decreases.
Net Present Value

\$200.00

\$100.00

\$0.00
0.1 11% 12% 13% 14% 15% 16% 17% 18% 19% 20% 21% 22% 23% 24% 25% 26% 27% 28% 29% 30%

(\$100.00)

(\$200.00)
Discount Rate

The net present value profile provides several insights on the projectâ€™s viability. First, the
internal rate of return is clear from the graph â€“ it is the point at which the profile crosses
the X axis. Second, it provides a measure of how sensitive the NPV â€“â€“ and, by extension,
the project decision â€“â€“ is to changes in the
NPV Profile: This measures the sensitivity of
the net present value to changes in the discount
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rate.
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discount rate. The slope of the NPV profile is a measure of the discount rate sensitivity of
the project. Third, when mutually exclusive projects are being analyzed, graphing both
NPV profiles together provides a measure of the break-even discount rate - the rate at
which the decision maker will be indifferent between the two projects.

5.13. â˜ž: Discount Rates and NPV
In the project described above, the NPV decreased as the discount rate was increased. Is
this always the case?
a. Yes.
b. No
If no, when might the NPV go up as the discount rate is increased?

Using the Internal Rate of Return
One advantage of the internal rate of return is that it can be used even in cases
where the discount rate is unknown. While this is true for the calculation of the IRR, it is
not true when the decision maker has to use the IRR to decide whether to take a project or
not. At that stage in the process, the internal rate of return has to be compared to the
discount rate - if the IRR is greater than the discount rate, the project is a good one;
alternatively, the project should be rejected.
Like the net present value, the internal rate of return can be computed in one of
two ways:
The IRR can be calculated based upon the free cash flows to the firm and the total
â€¢
investment in the project. In doing so, the IRR has to be compared to the cost of
capital.
The IRR can be calculated based upon the free cash flows to equity and the equity
â€¢
investment in the project. If it is estimated with these cash flows, it has to be
compared to the cost of equity, which should reflect the riskiness of the project.
Decision Rule for IRR for Independent Projects
A. IRR is computed on cash flows to the firm
If the IRR > Cost of Capital -> Accept the project
If the IRR < Cost of Capital -> Reject the project

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B. IRR is computed on cash flows to equity
If the IRR > Cost of Equity -> Accept the project
If the IRR < Cost of Equity -> Reject the project
When choosing between projects of equivalent risk, the project with the higher IRR is
viewed as the better project.

This spreadsheet allows you to estimate the IRR based upon cash flows to the firm
on a project

Illustration 5.16: Estimating the IRR based on FCFF - Disney Theme Park in Thailand
The cash flows to the firm from the proposed theme park in Thailand, are used to
arrive at a NPV profile for the project in Figure 5.5.

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The internal rate of return in dollar terms on this project is 11.97%, which is higher than
the cost of capital of 10.66%. These results are consistent with the findings from the NPV
rule, which also recommended investing in the theme parks. 11

Illustration 5.17: Estimating IRR Based Upon FCFE - Aracruz Cellulose
The net present value profile depicted in Figure 5.6 is based upon the equity
investment and the free cash flows to equity estimated for the paper plant for Aracruz.

Figure 5.6: NPV Profile on Equity Investment in Paper Plant: Aracruz

\$350,000.00

\$300,000.00

\$250,000.00

\$200,000.00
NPV

\$150,000.00

\$100,000.00

\$50,000.00

\$0.00
0%

0%

%

0%

0%

0%

%

0%

0%

%

0%
%

%

0%

0%

%

%

%

%

%

%

00

00

00
00

00

00

00

00

00

00

00

.0

.0

.0

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