Question

Nesa steel is evaluating two mutually exclusive projects that will allow the firm to increase its production capacity by 25\%. The first alternative requires an investment of $2,000,000 and is expected to generate net annual cash flows of $750,000 in each of the rext 5 years of its economic life. The required rate of return on this project is 15%, The second atternative requires an investment of $3,000,000 and is expected to generate net annual cash fiows of $700,000 in each of the next 10 years of its economic life. The second alternative is less risky than the first alternative, therefore, Mesa requires a 12% rate of return on the project. USE the equivalent annual annuity approach to determine which project should be adopted? Write out all steps to solve and explain.

Answer 1

To determine which project to adopt, we will use the equivalent annual annuity approach. The first project has an equivalent annual annuity of $514,525, while the second project has an equivalent annual annuity of $1,604,600. Therefore, the second project should be adopted.

To determine which project should be adopted, we will use the equivalent annual annuity approach. This approach allows us to compare the projects by converting their cash flows into an equivalent annual amount.

For the first project, we will calculate the equivalent annual annuity by dividing the net present value (NPV) of the project by the annuity factor. The annuity factor can be found using the formula:

Annuity Factor = (1 - (1 / (1 + r)^n)) / r

Where r is the required rate of return and n is the number of years. For the first project, the annuity factor is:

Annuity Factor = (1 - (1 / (1 + 0.15)^5)) / 0.15 = 3.3527

The net present value (NPV) of the first project can be calculated as:

NPV = Cash flows - Initial investment = ($750,000 * 3.3527) - $2,000,000 = $2,514,525 - $2,000,000 = $514,525

Therefore, the equivalent annual annuity for the first project is $514,525.

For the second project, we will use the same method to calculate the equivalent annual annuity. The annuity factor is:

Annuity Factor = (1 - (1 / (1 + 0.12)^10)) / 0.12 = 6.578

The NPV of the second project is:

NPV = Cash flows - Initial investment = ($700,000 * 6.578) - $3,000,000 = $4,604,600 - $3,000,000 = $1,604,600

Therefore, the equivalent annual annuity for the second project is $1,604,600.

Comparing the equivalent annual annuities, it can be seen that the second project has a higher equivalent annual annuity of $1,604,600 compared to the first project's equivalent annual annuity of $514,525. Therefore, the second project should be adopted.