# 金融代写|公司金融学代写Corporate Finance代考|THE INTERNAL RATE OF RETURN

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## 金融代写|公司金融学代写Corporate Finance代考|THE INTERNAL RATE OF RETURN

Now we come to the most important alternative to the NPV approach, the internal rate of return, universally known as the IRR. The IRR is about as close as you can get to the NPV without actually being the NPV. The basic rationale behind the IRR is that it tries to find a single number that summarizes the merits of a project. That number does not depend on the interest rate that prevails in the capital market. That is why it is called the internal rate of return; the number is internal or intrinsic to the project and does not depend on anything except the cash flows of the project.

For example, consider the simple project $(-\$ 100, \$110)$ in Figure 6.2. For a given rate, the net present value of this project can be described as
$$\mathrm{NPV}=-\ 100+\frac{\ 110}{1+r}$$

where $r$ is the discount rate.
What must the discount rate be to make the NPV of the project equal to zero? We begin by using an arbitrary discount rate of 0.08 , which yields
$$\ 1.85=-\ 100+\frac{\ 110}{1.08}$$
Since the NPV in equation (6.3) is positive, we now try a higher discount rate, say, 0.12. This yields
$$-\ 1.79=-\ 100+\frac{\ 110}{1.12}$$
Since the NPV in equation (6.4) is negative, we lower the discount rate to, say, 0.10 . This yields
$$0=-\ 100+\frac{\ 110}{1.10}$$

## 金融代写|公司金融学代写Corporate Finance代考|PROBLEMS WITH THE IRR APPROACH

Definition of Independent and Mutually Exclusive Projects
An independent project is one whose acceptance or rejection is independent of the acceptance or rejection of other projects. For example, imagine that McDonald’s is considering putting a hamburger outlet on a remote island. Acceptance or rejection of this unit is likely to be unrelated to the acceptance or rejection of any other restaurant in their system. The remoteness of the outlet in question insures that it will not pull sales away from other outlets.

Now consider the other extreme, mutually exclusive investments. What does it mean for two projects, $A$ and $B$, to be mutually exclusive? You can accept $A$ or you can accept $B$ or you can reject both of them, but you cannot accept both of them. For example, $A$ might be a decision to build an apartment house on a corner lot that you own, and $B$ might be a decision to build a movie theater on the same lot.

We now present two general problems with the IRR approach that affect both independent and mutually exclusive projects. Next, we deal with two problems affecting mutually exclusive projects only.
Two General Problems Affecting Both Independent and Mutually Exclusive Projects
We begin our discussion with project $A$, which has the following cash flows:
$$(-\ 100, \ 130)$$
The IRR for project $A$ is 30 percent. Table 6.3 provides other relevant information on the project. The relationship between NPV and the discount rate is shown for this project in Figure 6.5. As you can see, the NPV declines as the discount rate rises.
Problem 1: Investing or Financing? Now consider project $B$, with cash flows of
$$(\ 100,-\ 130)$$

## 金融代写|公司金融学代写CORPORATE FINANCE代考|THE INTERNAL RATE OF RETURN

$$\mathrm{NPV}=-\ 100+\frac{\ 110}{1+r}$$

$$\ 1.85=-\ 100+\frac{\ 110}{1.08}$$

$$-\ 1.79=-\ 100+\frac{\ 110}{1.12}$$

$$0=-\ 100+\frac{\ 110}{1.10}$$

## 金融代写|公司金融学代写CORPORATE FINANCE代考|PROBLEMS WITH THE IRR APPROACH

$$(-\ 100, \ 130)$$

$$(\ 100,-\ 130)$$

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