Net Present Value (NPV)
The net present value (NPV) is the difference between an investment’s market value and its cost.
The investment should be accepted if the NPV is positive or rejected when the NPV is negative.
Advantages

It takes into account the time value of money

The method utilizes all the cash flows of the project

It is easy to understand and calculate
Disadvantages
Estimating the projects cash flows is difficult

Internal Rate of Return (IRR)
This is the discount rate that makes the NPV of an investment zero.
The investment is acceptable if the IRR exceeds the required return.
The required rate of return is the rate that is required to cover the cost of the investment.
Advantages

Closely related to NPV, often leading to identical decisions.

Easy to understand and communicate.
Disadvantages

May result in multiple answers or not ideal with nonconventional cash flows.

May lead to incorrect decisions in comparisons of mutually exclusive investments.

Profitability Index (PI)
This index is defined as the present value of the future cash flows divided by the initial investment.
The PI measures the benefit cost ratio.
The profitability index will be more than 1 if the NPV is positive, but it will be less than 1. An investment with PI more than 1 should be accepted but those with less than 1 should be rejected.
PI = Present value of cash inflows
Initial investment
Advantages

Closely related to NPV, generally leading to identical decisions.

Easy to understand and communicate.

May be useful when available investment funds are limited.
Disadvantages

May lead to incorrect decisions in comparisons of mutually exclusive investments.

Modified Internal Rate of Return (MIRR)
Addresses some of the problems that IRR had.
The basic idea of calculating MIRR is to modify the cash flows first and then calculate an IRR using the modified cash flows.
a. Discounting Approach. Discount all the negative cash flows and add to the initial cost. Then determine the IRR.
b. The Reinvestment Approach. All the cash flows are compounded (both positive and negative) cash flows except the first one to the last and then calculate the IRR. In other words we are reinvesting the cash flows.

The Combination Approach. This method combines the first two methods.
All the negative cash flows are discounted to the present and all the positive cash flows are compounded to the end of the project
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