Question

Dwight Donovan, the president of Munoz Enterprises, is considering two investment opportunities. Because of limited resources, he will be able to invest in only one of them. Project A is to purchase a machine that will enable factory automation; the machine is expected to have a useful life of four years and no salvage value. Project B supports a training program that will improve the skills of employees operating the current equipment. Initial cash expenditures for Project A are $106,000 and for Project B are $47,000. The annual expected cash inflows are $40,947 for Project A and $16,131 for Project B. Both investments are expected to provide cash flow benefits for the next four years. Munoz Enterprises’ desired rate of return is 6 percent. (PV of $1 and PVA of $1) (Use appropriate factor(s) from the tables provided.) Required Compute the net present value of each project. Which project should be adopted based on the net present value approach? Compute the approximate internal rate of return of each project. Which one should be adopted based on the internal rate of return approach?

Answer 1

The net present value of a project is the sum of the present values of all the expected cash inflows and outflows for the project, discounted at the desired rate of return. The net present value is used to evaluate the profitability of a project by taking into account the time value of money, which is the idea that a dollar received today is worth more than a dollar received in the future.

To calculate the net present value of Project A, we need to find the present value of each expected cash inflow and outflow, and then sum them together. The initial cash expenditure for Project A is $106,000, and the annual expected cash inflows are $40,947. Using the present value of $1 table, we can find the present value of each cash inflow and outflow by multiplying the amount by the present value factor corresponding to the desired rate of return (6 percent) and the number of years until the cash flow occurs:

Initial expenditure: $106,000 * 0.943 = $99,858

Annual inflows: $40,947 * 0.943 * 0.943 * 0.943 * 0.943 = $136,046

The net present value of Project A is the sum of the present values of all the cash inflows and outflows, which is $136,046 - $99,858 = $36,188.

To calculate the net present value of Project B, we can use the same approach. The initial cash expenditure for Project B is $47,000, and the annual expected cash inflows are $16,131. Using the present value of $1 table, we can find the present value of each cash inflow and outflow by multiplying the amount by the present value factor corresponding to the desired rate of return (6 percent) and the number of years until the cash flow occurs:

Initial expenditure: $47,000 * 0.943 = $44,441

Annual inflows: $16,131 * 0.943 * 0.943 * 0.943 * 0.943 = $52,210

The net present value of Project B is the sum of the present values of all the cash inflows and outflows, which is $52,210 - $44,441 = $7,769.

Based on the net present value approach, the best project to invest in is the one with the highest net present value. In this case, Project A has a higher net present value than Project B, so it would be the better choice.

The internal rate of return of a project is the discount rate that makes the net present value of the project equal to 0. In other words, it is the rate of return that an investor would expect to earn from the project if all the expected cash flows were realized.

To calculate the internal rate of return of Project A, we can use the present value of an annuity of $1 table. The initial cash expenditure for Project A is $106,000, and the annual expected cash inflows are $40,947. We can use the present value of an annuity of $1 table to find the present value of the cash inflows by multiplying the annual cash inflow by the present value factor corresponding to the desired rate of return (6 percent) and the number of years until the cash flow occurs:

Annual inflows: $40,947 * 4.597 = $187,340

We can then use the present value annuity formula to find the internal rate of return of Project A, which is the rate that makes the net present value of the project equal to 0:

0 = $106,000 + $187,340 / (1 + r)^4

Solving for r, we find that the internal rate of return of Project A is approximately 10.35 percent.

To calculate the internal rate of return of Project B, we can use the same approach. The initial cash expenditure for Project B is $47,000, and the annual expected cash inflows are $16,131. We can use the present value of an annuity of $1 table to find the present value of the cash inflows by multiplying the annual cash inflow by the present value factor corresponding to the desired rate of return (6 percent) and the number of years until the cash flow occurs:

Annual inflows: $16,131 * 4.597 = $73,711

We can then use the present value annuity formula to find the internal rate of return of Project B, which is the rate that makes the net present value of the project equal to 0:

0 = $47,000 + $73,711 / (1 + r)^4

Solving for r, we find that the internal rate of return of Project B is approximately 10.09 percent.

Based on the internal rate of return approach, the best project to invest in is the one with the highest internal rate of return. In this case, Project A has a higher internal rate of return than Project B, so it would be the better choice.

Overall, both the net present value approach and the internal rate of return approach suggest that Project A is the better investment option for Munoz Enterprises. Project A has a higher net present value and a higher internal rate of return than Project B, indicating that it is likely to be more profitable and provide a higher rate of return on the investment.