# Internal Rate of Return (IRR) Method in Capital Budgeting Decisions:

Learning Objectives:

1. Define and explain the internal rate of return (IRR) in Accounting.
2. Evaluate the acceptability of an investment project using the internal rate of return (IRR) method.
3. What are the advantages and disadvantages of internal rate of return?

## Definition and Explanation:

The internal rate of return (IRR) is the rate of return promised by an investment project over its useful life. It is some time referred to simply as yield on project. The internal rate of return is computed by finding the discount rate that equates the present value of a project’s cash out flow with the present value of its cash inflow In other words, the internal rate of return is that discount rate that will cause the net present value of a project to be equal to zero.

## Example:

A school is considering the purchase of a large tractor-pulled lawn mower. At present, the lawn is moved using a small hand pushed gas mower. The large tractor-pulled mower will cost \$ 16,950 and will have a useful life of 10 years. It will have only a negligible scrap value, which can be ignored. The tractor-pulled mower will do the job much more quickly than the old mower and would result in a labor savings of \$ 3,000 per year.

To compute the internal rate of return promised by the new mower, we must find the discount rate that will cause the new present value of the project to be zero. How do we do this?

The simplest and most direct approach when the net cash inflow is the same every year is to divide the investment in the project by the expected net annual cash inflow. This computation will yield a factor from which the internal rate of return can be determined.

The formula or equation is as follows:

[Factor of internal rate of return = Investment required / Net annual cash inflow]  (1)

The factor derived from formula (1) is then located in the present value tables to see what rate of return it represents. Using formula (1) and the data for school’s proposed project, we get:

Investment required / Net annual cash inflow

= \$16,950 / \$3,000

= 5.650

Thus, the discount factor that will equate a series of \$ 3,000 cash inflows with a present investment of \$16,950. Now we need to find this factor in the table to see what rate of return it represents. We would use the 10-period line in the table since the cash flows for the project continue for 10 years. If we scan along the 10-period line, we find that a factor of 5.650 represents a 12% rate of return. (See Future Value and Present Value Tables page – Table 4) We can verify this by computing the project’s net present value using a 12% discount rate. This computation is made as follows:

 Initial cost Life of the project (years) Annual cost savings Salvage value \$16,500 10 \$3,000 0 Item Years Amount of cash flow 12% factor Present value of cash flows Annual cost savings Initial investmentNet present value 1―10 Now \$3,000 (16,950) 5.650* 1,000 \$16,950 (16950) ——— 0 ====== *From Future Value and Present Value Tables page – Table 4

Notice that using a 12% discount rate equates the present value of the annual cash inflows with the present value of the investment required in the project, leaving a zero net present value. The 12% rate therefore represents the internal rate of return promised by the project.

## Salvage Value and Other Cash Flows:

The technique just demonstrated works very well if a project’s cash flow s are identical every year. But what if they are not? For example, what if a project will have some salvage value at the end of its life in addition to the annual cash inflows? Under these circumstances, a trial and error process may be used to find the rate of return that will equate the cash inflow with the cash outflows. The trial and error process can be carried out by hand; however, computer software programs such as spreadsheets can perform the necessary computations in seconds. In short, erratic or uneven cash flows should not prevent a manager from determining a project’s internal rate of return.

## Using the Internal Rate of Return:

Once the internal rate of return has been computed, what does the manager do with the information? The internal rate of return is compared to the company’s required rate of return. The required rate of return is the minimum rate of return that an investment project must yield to be acceptable. If the internal rate of return is equal to or greater than the required rate of return, than the project is acceptable. If it is less than the required rate of return, then the project is rejected. Quite often the company’s cost of capital is used as the required rate of return. The reasoning is that if a project cannot provide a rate of return at least as greater as the cost of the funds invested in it, then it is not profitable.

## The Cost of Capital as a Screening Tool:

The cost of capital often operates as a screening device, helping the manager screen out undesirable investment projects. This screening is accomplished in different ways, depending on whether the company is using the internal rate of return method or the net present value method in its capital budgeting analysis.

When the internal rate of return method is used, the cost of capital is used as the hurdle rate that a project must clear for acceptance. If the internal rate of return of a project is not great enough to clear the cost of capital hurdle, then the project is ordinarily rejected. We saw the application of this idea in the above example where the hurdle rate was set at 15%.

When the net present value method is used, the cost of capital is the discount rate used to compute the net present value of a proposed project. Any project yielding a negative net present value is rejected unless other factors are significant enough to require its acceptance.

The use of cost of capital as a screening tool is summarized below:

 The Cost of Capital as a Screening Tool The Net Present Value Method The Internal Rate of Return Method The cost of capital is used as the discount rate when computing the net present value of a project. Any project with a negative net present value is rejected unless other factors dictate its acceptance. The cost of capital is compared to the internal rate of return promised by a project. Any project whose internal rate of return is less than the cost of capital is rejected unless other factors dictate its acceptance.