Mutually exclusive projects are a set of projects from which at most one will be accepted, for example, a set of projects which accomplish the same task.

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Thus when choosing between mutually exclusive projects, more than one of the projects may satisfy the capital budgeting criterion, but only one project can be accepted. It is a widely used measure of investment efficiency. To maximize return, sort projects in order of IRR. Many projects have a simple cash flow structure, with a negative cash flow at the start, and subsequent cash flows are positive.

## Capital Budgeting's Importance in Business

In such a case, if the IRR is greater than the cost of capital, the NPV is positive, so for non-mutually exclusive projects in an unconstrained environment, applying this criterion will result in the same decision as the NPV method. An example of a project with cash flows which do not conform to this pattern is a loan, consisting of a positive cash flow at the beginning, followed by negative cash flows later.

The greater the IRR of the loan, the higher the rate the borrower must pay, so clearly, a lower IRR is preferable in this case. Excluding such cases, for investment projects, where the pattern of cash flows is such that the higher the IRR, the higher the NPV, for mutually exclusive projects, the decision rule of taking the project with the highest IRR will maximize the return, but it may select a project with a lower NPV.

The IRR exists and is unique if one or more years of net investment negative cash flow are followed by years of net revenues. But if the signs of the cash flows change more than once, there may be several IRRs. The IRR equation generally cannot be solved analytically but only via iterations.

IRR is the return on capital invested, over the sub-period it is invested. It may be impossible to reinvest intermediate cash flows at the same rate as the IRR. Accordingly, a measure called Modified Internal Rate of Return MIRR is designed to overcome this issue, by simulating reinvestment of cash flows at a second rate of return.

Despite a strong academic preference for maximizing the value of the firm according to NPV, surveys indicate that executives prefer to maximize returns [ citation needed ]. The equivalent annuity method expresses the NPV as an annualized cash flow by dividing it by the present value of the annuity factor. It is often used when assessing only the costs of specific projects that have the same cash inflows.

In this form it is known as the equivalent annual cost EAC method and is the cost per year of owning and operating an asset over its entire lifespan. It is often used when comparing investment projects of unequal lifespans. For example, if project A has an expected lifetime of 7 years, and project B has an expected lifetime of 11 years it would be improper to simply compare the net present values NPVs of the two projects, unless the projects could not be repeated.

Alternatively the chain method can be used with the NPV method under the assumption that the projects will be replaced with the same cash flows each time. To compare projects of unequal length, say 3 years and 4 years, the projects are chained together , i. The chain method and the EAC method give mathematically equivalent answers.

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The assumption of the same cash flows for each link in the chain is essentially an assumption of zero inflation , so a real interest rate rather than a nominal interest rate is commonly used in the calculations. Real options analysis has become important since the s as option pricing models have gotten more sophisticated.

The discounted cash flow methods essentially value projects as if they were risky bonds, with the promised cash flows known. But managers will have many choices of how to increase future cash inflows, or to decrease future cash outflows.

In other words, managers get to manage the projects - not simply accept or reject them. Real options analysis tries to value the choices - the option value - that the managers will have in the future and adds these values to the NPV. Under this method, the entire company is considered as a single profit-generating system. Throughput is measured as an amount of material passing through that system.

The analysis assumes that nearly all costs are operating expenses , that a company needs to maximize the throughput of the entire system to pay for expenses, and that the way to maximize profits is to maximize the throughput passing through a bottleneck operation. A bottleneck is the resource in the system that requires the longest time in operations. This means that managers should always place a higher priority on capital budgeting projects that will increase throughput passing through the bottleneck.

### What About the Time Value of Money?

Discounted cash flow DCF analysis looks at the initial cash outflow needed to fund a project, the mix of cash inflows in the form of revenue, and other future outflows in the form of maintenance and other costs. These costs, except for the initial outflow, are discounted back to the present date. Projects with the highest NPV should rank over others unless one or more are mutually exclusive.

Payback analysis is the simplest form of capital budgeting analysis but it's also the least accurate. It's still widely used because it's quick and can give managers a "back of the envelope" understanding of the real value of a proposed project. This analysis calculates how long it will take to recoup the costs of an investment. The payback period is identified by dividing the initial investment in the project by the average yearly cash inflow that the project will generate.

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## 1.1 Introduction to Capital Budgeting

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### CAPITAL BUDGETING TECHNIQUES / METHODS

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