Question

Your factory has been offered a contract to produce a part for a new printer. The contract would last for 3 ​years, and your cash flows from the contract would be $ 5.03 million per year. Your​ up-front setup costs to be ready to produce the part would be $ 8.01 million. Your discount rate for this contract is 7.7 %.

a. What is the IRR​?

b. The NPV is $ 5.02 ​million, which is positive so the NPV rule says to accept the project. Does the IRR rule agree with the NPV​ rule?

Answer 1

a)

The internal rate of return is defined as the interest rate that makes the net present value of the future cash flows of an investment equal to its initial cash outlay.

The IRR is the interest rate r which makes the net present value of the future cash flows of an investment equal to its initial cash outlay of $ 8.01 million.

The value of r can be found by trial and error

let r = 40%

NPV = - $ 17,725.95

Let r = 39%

NPV = $85,028.74

IRR = 39.83 %

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b)

The IRR rule states that wherever the internal rate of return is greater than the project's discount rate, the project should be accepted. In this example, the IRR is greater than the project discount rate of 7.7%, hence the project should be accepted. The underlying reason is that when IRR exceeds the discount rate, a surplus will remain after paying for the cost of capital thereby resulting in  increase of shareholder's wealth.

In this example the IRR rule agrees with the NPV rule because the NPV is positive and the IRR exceeds the project discount rate. Hence using both NPV and IRR rule we can accept the project.